Joint spectral radius

In mathematics, the joint spectral radius is a generalization of the classical notion of spectral radius of a matrix, to sets of matrices. In recent years this notion has found applications in a large number of engineering fields and is still a topic of active research.
General description.
The joint spectral radius of a set of matrices is the maximal asymptotic growth rate of products of matrices taken in that set. For a finite (or more generally compact) set of matrices formula_1 the joint spectral radius is defined as follows:
It can be proved that the limit exists and that the quantity actually does not depend on the chosen matrix norm (this is true for any norm but particularly easy to see if the norm is sub-multiplicative). The joint spectral radius was introduced in 1960 by Gian-Carlo Rota and Gilbert Strang, two mathematicians from MIT, but started attracting attention with the work of Ingrid Daubechies and Jeffrey Lagarias. They showed that the joint spectral radius can be used to describe smoothness properties of certain wavelet functions. A wide number of applications have been proposed since then. It is known that the joint spectral radius quantity is NP-hard to compute or to approximate, even when the set formula_3 consists of only two matrices with all nonzero entries of the two
matrices which are constrained to be equal. Moreover, the question "formula_4" is an undecidable problem. Nevertheless, in recent years much progress has been done on its understanding, and it appears that in practice the joint spectral radius can often be computed to satisfactory precision, and that it moreover can bring interesting insight in engineering and mathematical problems.
Computation.
Approximation algorithms.
In spite of the negative theoretical results on the joint spectral radius computability, methods have been proposed that perform well in practice. Algorithms are even known, which can reach an arbitrary accuracy in an a priori computable amount of time. These algorithms can be seen as trying to approximate the unit ball of a particular vector norm, called the extremal norm. One generally distinguishes between two families of such algorithms: the first family, called polytope norm methods, construct the extremal norm by computing long trajectories of points. An advantage of these methods is that in the favorable cases it can find the exact value of the joint spectral radius and provide a certificate that this is the exact value.
The second family of methods approximate the extremal norm with modern optimization techniques, such as ellipsoid norm approximation, semidefinite programming, Sum Of Squares, and conic programming. The advantage of these methods is that they are easy to implement, and in practice, they provide in general the best bounds on the joint spectral radius.
The finiteness conjecture.
Related to the computability of the joint spectral radius is the following conjecture:
"For any finite set of matrices formula_5 there is a product formula_6 of matrices in this set such that
In the above equation "formula_8" refers to the classical spectral radius of the matrix formula_9
This conjecture, proposed in 1995, was proven to be false in 2003. The counterexample provided in that reference uses advanced measure-theoretical ideas. Subsequently, many other counterexamples have been provided, including an elementary counterexample that uses simple combinatorial properties matrices and a counterexample based on dynamical systems properties. Recently an explicit counterexample has been proposed in. Many questions related to this conjecture are still open, as for instance the question of knowing whether it holds for pairs of binary matrices.
Applications.
The joint spectral radius was introduced for its interpretation as a stability condition for discrete-time switching dynamical systems. Indeed, the system defined by the equations
is stable if and only if formula_11
The joint spectral radius became popular when Ingrid Daubechies and Jeffrey Lagarias showed that it rules the continuity of certain wavelet functions. Since then, it has found many applications, ranging from number theory to information theory, autonomous agents consensus, combinatorics on words...
Related notions.
The joint spectral radius is the generalization of the spectral radius of a matrix for a set of several matrices. However, much more quantities can be defined when considering a set of matrices: The joint spectral subradius characterizes the minimal rate of growth of products in the semigroup generated by formula_3.
The p-radius characterizes the rate of growth of the formula_13 average of the norms of the products in the semigroup.
The Lyapunov exponent of the set of matrices characterizes the rate of growth of the geometric average.


The Raytheon AN/MSQ-18 Battalion Missile Operations System (AN/TSQ-38 for the helicopter-transportable variant) was a Project Nike command, control, and coordination system for "each associated missile battery" to control a Nike missile as directed from a Raytheon AN/MSQ-28 at the Army Air Defense Command Post. Raytheon Company constructed the AN/MSQ-18 as 2 separate subsystems:


Anticausal system

In systems theory, an anticausal system is a hypothetical system with outputs and internal states that depend "solely" on future input values. Some textbooks and published research literature might define an anticausal system to be one that does not depend on past input values, allowing also for the dependence on present input values.
An acausal system is a system that is not a causal system, that is one that depends on some future input values and possibly on some input values from the past or present. This is in contrast to a causal system which depends only on current and/or past input values. This is often a topic of control theory and digital signal processing (DSP).
Anticausal systems are also acausal, but the converse is not always true. An acausal system that has any dependence on past input values is not anticausal.
An example of acausal signal processing is the production of an output signal that is processed from an input signal that was recorded by looking at input values both forward and backward in time (from a predefined time arbitrarily denoted as the "present" time). In reality, that "present" time input, as well as the "future" time input values, have been recorded at some time in the past, but conceptually it can be called the "present" or "future" input values in this acausal process. This type of processing cannot be done in real time as future input values are not yet known, but is done after the input signal has been recorded and is post-processed.
Digital room correction in some sound reproduction systems rely on acausal filters.


Implication table

An implication table is a tool used to facilitate the minimization of states in a state machine. The concept is to start assuming that every state may be able to combine with every other state, then eliminate combinations that are not possible. When all the impossible combinations have been eliminated, the remaining state combinations are valid, and thus can be combined.
The procedure is as follows:


Spectral submanifold

In dynamical systems, a spectral submanifold (SSM) is the unique smoothest invariant manifold serving as the nonlinear extension of a spectral subspace of a linear dynamical system under the addition of nonlinearities. SSM theory provides conditions for when invariant properties of eigenspaces of a linear dynamical system can be extended to a nonlinear system, and therefore motivates the use of SSMs in nonlinear dimensionality reduction.
Definition.
Consider a nonlinear ordinary differential equation of the form
with constant matrix formula_2 and the nonlinearities contained in the smooth function formula_3.
Assume that formula_4 for all eigenvalues formula_5 of formula_6, that is, the origin is an asymptotically stable fixed point. Now select a span formula_7 of formula_8 eigenvectors formula_9 of formula_6. Then, the eigenspace formula_11 is an invariant subspace of the linearized system
Under addition of the nonlinearity formula_13 to the linear system, formula_11 generally perturbs into infinitely many invariant manifolds. Among these invariant manifolds, the unique smoothest one is referred to as the spectral submanifold.
An equivalent result for unstable SSMs holds for formula_15.
Existence.
The spectral submanifold tangent to formula_11 at the origin is guaranteed to exist provided that certain non-resonance conditions are satisfied by the eigenvalues formula_17 in the spectrum of formula_11. In particular, there can be no linear combination of formula_17 equal to one of the eigenvalues of formula_6 outside of the spectral subspace. If there is such an outer resonance, one can include the resonant mode into formula_11 and extend the analysis to a higher-dimensional SSM pertaining to the extended spectral subspace.
Non-autonomous extension.
The theory on spectral submanifolds extends to nonlinear non-autonomous systems of the form
with formula_23 a quasiperiodic forcing term.
Significance.
Spectral submanifolds are useful for rigorous nonlinear dimensionality reduction in dynamical systems. The reduction of a high-dimensional phase space to a lower-dimensional manifold can lead to major simplifications by allowing for an accurate description of the system's main asymptotic behaviour. For a known dynamical system, SSMs can be computed analytically by solving the invariance equations, and reduced models on SSMs may be employed for prediction of the response to forcing.
Furthermore these manifolds may also be extracted directly from trajectory data of a dynamical system with the use of machine learning algorithms.


HyperNEAT

Hypercube-based NEAT, or HyperNEAT, is a generative encoding that evolves artificial neural networks (ANNs) with the principles of the widely used NeuroEvolution of Augmented Topologies (NEAT) algorithm developed by Kenneth Stanley. It is a novel technique for evolving large-scale neural networks using the geometric regularities of the task domain. It uses Compositional Pattern Producing Networks (CPPNs), which are used to generate the images for Picbreeder.org and shapes for EndlessForms.com . HyperNEAT has recently been extended to also evolve plastic ANNs and to evolve the location of every neuron in the network.


Neighbourhood components analysis

Neighbourhood components analysis is a supervised learning method for classifying multivariate data into distinct classes according to a given distance metric over the data. Functionally, it serves the same purposes as the K-nearest neighbors algorithm and makes direct use of a related concept termed "stochastic nearest neighbours".
Definition.
Neighbourhood components analysis aims at "learning" a distance metric by finding a linear transformation of input data such that the average leave-one-out (LOO) classification performance is maximized in the transformed space. The key insight to the algorithm is that a matrix formula_1 corresponding to the transformation can be found by defining a differentiable objective function for formula_1, followed by the use of an iterative solver such as conjugate gradient descent. One of the benefits of this algorithm is that the number of classes formula_3 can be determined as a function of formula_1, up to a scalar constant. This use of the algorithm, therefore, addresses the issue of model selection.
Explanation.
In order to define formula_1, we define an objective function describing classification accuracy in the transformed space and try to determine formula_6 such that this objective function is maximized.
formula_7
Leave-one-out (LOO) classification.
Consider predicting the class label of a single data point by consensus of its formula_3-nearest neighbours with a given distance metric. This is known as "leave-one-out" classification. However, the set of nearest-neighbours formula_9 can be quite different after passing all the points through a linear transformation. Specifically, the set of neighbours for a point can undergo discrete changes in response to smooth changes in the elements of formula_1, implying that any objective function formula_11 based on the neighbours of a point will be "piecewise-constant", and hence "not differentiable".
Solution.
We can resolve this difficulty by using an approach inspired by stochastic gradient descent. Rather than considering the formula_3-nearest neighbours at each transformed point in LOO-classification, we'll consider the entire transformed data set as "stochastic nearest neighbours". We define these using a softmax function of the squared Euclidean distance between a given LOO-classification point and each other point in the transformed space:
formula_13
The probability of correctly classifying data point formula_14 is the probability of classifying the points of each of its neighbours with the same class formula_9:
formula_16 where formula_17 is the probability of classifying neighbour formula_18 of point formula_14.
Define the objective function using LOO classification, this time using the entire data set as stochastic nearest neighbours:
formula_20
Note that under stochastic nearest neighbours, the consensus class for a single point formula_14 is the expected value of a point's class in the limit of an infinite number of samples drawn from the distribution over its neighbours formula_22 i.e.: formula_23. Thus the predicted class is an affine combination of the classes of every other point, weighted by the softmax function for each formula_24 where formula_25 is now the entire transformed data set.
This choice of objective function is preferable as it is differentiable with respect to formula_1 (denote formula_27):
formula_28
formula_29
Obtaining a gradient for formula_1 means that it can be found with an iterative solver such as conjugate gradient descent. Note that in practice, most of the innermost terms of the gradient evaluate to insignificant contributions due to the rapidly diminishing contribution of distant points from the point of interest. This means that the inner sum of the gradient can be truncated, resulting in reasonable computation times even for large data sets.
Alternative formulation.
"Maximizing formula_11 is equivalent to minimizing the formula_32-distance between the predicted class distribution and the true class distribution (ie: where the formula_33 induced by formula_1 are all equal to 1). A natural alternative is the KL-divergence, which induces the following objective function and gradient:" (Goldberger 2005)
formula_35
formula_36
In practice, optimization of formula_1 using this function tends to give similar performance results as with the original.
History and background.
Neighbourhood components analysis was developed by Jacob Goldberger, Sam Roweis, Ruslan Salakhudinov, and Geoff Hinton at the University of Toronto's department of computer science in 2004.


Outline of machine learning

The following outline is provided as an overview of and topical guide to machine learning. Machine learning is a subfield of soft computing within computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. In 1959, Arthur Samuel defined machine learning as a "field of study that gives computers the ability to learn without being explicitly programmed". Machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from an example training set of input observations in order to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions.
Machine learning methods.
Dimensionality reduction.
Dimensionality reduction
Ensemble learning.
Ensemble learning
Meta-learning.
Meta-learning
Reinforcement learning.
Reinforcement learning
Supervised learning.
Supervised learning
Bayesian.
Bayesian statistics
Decision tree algorithms.
Decision tree algorithm
Linear classifier.
Linear classifier
Unsupervised learning.
Unsupervised learning
Artificial neural networks.
Artificial neural network
Association rule learning.
Association rule learning
Hierarchical clustering.
Hierarchical clustering
Cluster analysis.
Cluster analysis
Anomaly detection.
Anomaly detection
Semi-supervised learning.
Semi-supervised learning
Deep learning.
Deep learning
History of machine learning.
History of machine learning
Machine learning projects.
Machine learning projects
Machine learning organizations.
Machine learning organizations


Distributed parameter system

In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are systems described by partial differential equations or by delay differential equations.
Linear time-invariant distributed-parameter systems.
Abstract evolution equations.
Discrete-time.
With "U", "X" and "Y" Hilbert spaces and "formula_1" ∈ "L"("X"), "formula_2" ∈ "L"("U", "X"), "formula_3" ∈ "L"("X", "Y") and "formula_4" ∈ "L"("U", "Y") the following difference equations determine a discrete-time linear time-invariant system:
with "formula_7" (the state) a sequence with values in "X", "formula_8" (the input or control) a sequence with values in "U" and "formula_9" (the output) a sequence with values in "Y".
Continuous-time.
The continuous-time case is similar to the discrete-time case but now one considers differential equations instead of difference equations:
An added complication now however is that to include interesting physical examples such as partial differential equations and delay differential equations into this abstract framework, one is forced to consider unbounded operators. Usually "A" is assumed to generate a strongly continuous semigroup on the state space "X". Assuming "B", "C" and "D" to be bounded operators then already allows for the inclusion of many interesting physical examples, but the inclusion of many other interesting physical examples forces unboundedness of "B" and "C" as well.
Example: a partial differential equation.
The partial differential equation with formula_12 and formula_13 given by
fits into the abstract evolution equation framework described above as follows. The input space "U" and the output space "Y" are both chosen to be the set of complex numbers. The state space "X" is chosen to be "L"2(0, 1). The operator "A" is defined as
It can be shown that "A" generates a strongly continuous semigroup on "X". The bounded operators "B", "C" and "D" are defined as
Example: a delay differential equation.
The delay differential equation
fits into the abstract evolution equation framework described above as follows. The input space "U" and the output space "Y" are both chosen to be the set of complex numbers. The state space "X" is chosen to be the product of the complex numbers with "L"2(−"τ", 0). The operator "A" is defined as
It can be shown that "A" generates a strongly continuous semigroup on X. The bounded operators "B", "C" and "D" are defined as
Transfer functions.
As in the finite-dimensional case the transfer function is defined through the Laplace transform (continuous-time) or Z-transform (discrete-time). Whereas in the finite-dimensional case the transfer function is a proper rational function, the infinite-dimensionality of the state space leads to irrational functions (which are however still holomorphic).
Discrete-time.
In discrete-time the transfer function is given in terms of the state-space parameters by formula_24 and it is holomorphic in a disc centered at the origin. In case 1/"z" belongs to the resolvent set of "A" (which is the case on a possibly smaller disc centered at the origin) the transfer function equals formula_25. An interesting fact is that any function that is holomorphic in zero is the transfer function of some discrete-time system.
Continuous-time.
If "A" generates a strongly continuous semigroup and "B", "C" and "D" are bounded operators, then the transfer function is given in terms of the state space parameters by formula_26 for "s" with real part larger than the exponential growth bound of the semigroup generated by "A". In more general situations this formula as it stands may not even make sense, but an appropriate generalization of this formula still holds.
To obtain an easy expression for the transfer function it is often better to take the Laplace transform in the given differential equation than to use the state space formulas as illustrated below on the examples given above.
Transfer function for the partial differential equation example.
Setting the initial condition formula_27 equal to zero and denoting Laplace transforms with respect to "t" by capital letters we obtain from the partial differential equation given above
This is an inhomogeneous linear differential equation with formula_31 as the variable, "s" as a parameter and initial condition zero. The solution is formula_32. Substituting this in the equation for "Y" and integrating gives formula_33 so that the transfer function is formula_34.
Transfer function for the delay differential equation example.
Proceeding similarly as for the partial differential equation example, the transfer function for the delay equation example is formula_35.
Controllability.
In the infinite-dimensional case there are several non-equivalent definitions of controllability which for the finite-dimensional case collapse to the one usual notion of controllability. The three most important controllability concepts are:
Controllability in discrete-time.
An important role is played by the maps formula_36 which map the set of all "U" valued sequences into X and are given by formula_37. The interpretation is that formula_38 is the state that is reached by applying the input sequence "u" when the initial condition is zero. The system is called
Controllability in continuous-time.
In controllability of continuous-time systems the map formula_42 given by formula_43 plays the role that formula_36 plays in discrete-time. However, the space of control functions on which this operator acts now influences the definition. The usual choice is "L"2(0, ∞;"U"), the space of (equivalence classes of) "U"-valued square integrable functions on the interval (0, ∞), but other choices such as "L"1(0, ∞;"U") are possible. The different controllability notions can be defined once the domain of formula_42 is chosen. The system is called
Observability.
As in the finite-dimensional case, observability is the dual notion of controllability. In the infinite-dimensional case there are several different notions of observability which in the finite-dimensional case coincide. The three most important ones are:
Observability in discrete-time.
An important role is played by the maps formula_50 which map "X" into the space of all "Y" valued sequences and are given by formula_51 if "k" ≤ "n" and zero if "k" > "n". The interpretation is that formula_52 is the truncated output with initial condition "x" and control zero. The system is called
Observability in continuous-time.
In observability of continuous-time systems the map formula_56 given by formula_57 for "s∈[0,t]" and zero for "s>t" plays the role that formula_50 plays in discrete-time. However, the space of functions to which this operator maps now influences the definition. The usual choice is "L"2(0, ∞, "Y"), the space of (equivalence classes of) "Y"-valued square integrable functions on the interval "(0,∞)", but other choices such as "L"1(0, ∞, "Y") are possible. The different observability notions can be defined once the co-domain of formula_56 is chosen. The system is called
Duality between controllability and observability.
As in the finite-dimensional case, controllability and observability are dual concepts (at least when for the domain of formula_63 and the co-domain of formula_64 the usual "L"2 choice is made). The correspondence under duality of the different concepts is:


Design for assembly

Design for assembly (DFA) is a process by which products are designed with ease of assembly in mind. If a product contains fewer parts it will take less time to assemble, thereby reducing assembly costs. In addition, if the parts are provided with features which make it easier to grasp, move, orient and insert them, this will also reduce assembly time and assembly costs. The reduction of the number of parts in an assembly has the added benefit of generally reducing the total cost of parts in the assembly. This is usually where the major cost benefits of the application of design for assembly occur. Critics of DFA from within industry argue that DFA/DFM is simply a new term for something that has existed as long as manufacturing itself, and is otherwise known as engineering design.
Approaches.
Design for assembly can take different forms. In the 1960s and 1970s various rules and recommendations were proposed in order to help designers consider assembly problems during the design process. Many of these rules and recommendations were presented together with practical examples showing how assembly difficulty could be improved. However, it was not until the 1970s that numerical evaluation methods were developed to allow design for assembly studies to be carried out on existing and proposed designs.
The first evaluation method was developed at Hitachi and was called the Assembly Evaluation Method (AEM). This method is based on the principle of "one motion for one part." For more complicated motions, a point-loss standard is used and the ease of assembly of the whole product is evaluated by subtracting points lost. The method was originally developed in order to rate assemblies for ease of automatic assembly.
Starting in 1977, Geoff Boothroyd, supported by an NSF grant at the University of Massachusetts Amherst, developed the Design for Assembly method (DFA), which could be used to estimate the time for manual assembly of a product and the cost of assembling the product on an automatic assembly machine. Recognizing that the most important factor in reducing assembly costs was the minimization of the number of separate parts in a product, he introduced three simple criteria which could be used to determine theoretically whether any of the parts in the product could be eliminated or combined with other parts. These criteria, together with tables relating assembly time to various design factors influencing part grasping, orientation and insertion, could be used to estimate total assembly time and to rate the quality of a product design from an assembly viewpoint. For automatic assembly, tables of factors could be used to estimate the cost of automatic feeding and orienting and automatic insertion of the parts on an assembly machine.
In the 1980s and 1990s, variations of the AEM and DFA methods have been proposed, namely: the GE Hitachi method which is based on the AEM and DFA; the Lucas method, the Westinghouse method and several others which were based on the original DFA method. All methods are now referred to as "design for assembly" methods.
Implementation.
Most products are assembled manually and the original DFA method for manual assembly is the most widely used method and has had the greatest industrial impact throughout the world.
The DFA method, like the AEM method, was originally made available in the form of a handbook where the user would enter data on worksheets to obtain a rating for the ease of assembly of a product. Starting in 1981, Geoffrey Boothroyd and Peter Dewhurst developed a computerized version of the DFA method which allowed its implementation in a broad range of companies. For this work they were presented with many awards including the National Medal of Technology. There are many published examples of significant savings obtained through the application of DFA. For example, in 1981, Sidney Liebson, manager of manufacturing engineering for Xerox, estimated that his company would save hundreds of millions of dollars through the application of DFA. In 1988, Ford Motor Company credited the software with overall savings approaching $1 billion. In many companies DFA is a corporate requirement and DFA software is continually being adopted by companies attempting to obtain greater control over their manufacturing costs. There are many key principles in design for assembly.
Notable examples.
Two notable examples of good design for assembly are the Sony Walkman and the Swatch watch. Both were designed for fully automated assembly. The Walkman line was designed for "vertical assembly", in which parts are inserted in straight-down moves only. The Sony SMART assembly system, used to assemble Walkman-type products, is a robotic system for assembling small devices designed for vertical assembly.
The IBM Proprinter used design for automated assembly (DFAA) rules. These DFAA rules help design a product that can be assembled automatically by robots, but they are useful even with products assembled by manual assembly.
Further information.
For more information on Design for Assembly and the subject of Design for Manufacture and Assembly see:


Harley Davidson Motor Company Factory No. 7 is a factory building of the Harley-Davidson company in Milwaukee listed on the Wisconsin State Register of Historic Places. It was at this plant where the company invented and refined the automated system for casting and milling engine parts and wheel hubs for their motorcycles, which helped to secure the company's position as a leader in motorcycle manufacturing. This factory building was added to the state register on August 14, 2020.


Hybrid intelligent system

Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as:
From the cognitive science perspective, every natural intelligent system is hybrid because it performs mental operations on both the symbolic and subsymbolic levels. For the past few years, there has been an increasing discussion of the importance of A.I. Systems Integration. Based on notions that there have already been created simple and specific AI systems (such as systems for computer vision, speech synthesis, etc., or software that employs some of the models mentioned above) and now is the time for integration to create broad AI systems. Proponents of this approach are researchers such as Marvin Minsky, Ron Sun, Aaron Sloman, and Michael A. Arbib.
An example hybrid is a hierarchical control system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning.
Intelligent systems usually rely on hybrid reasoning processes, which include induction, deduction, abduction and reasoning by analogy.


Gated recurrent unit

Gated recurrent units (GRUs) are a gating mechanism in recurrent neural networks, introduced in 2014 by Kyunghyun Cho et al. The GRU is like a long short-term memory (LSTM) with a forget gate, but has fewer parameters than LSTM, as it lacks an output gate.
GRU's performance on certain tasks of polyphonic music modeling, speech signal modeling and natural language processing was found to be similar to that of LSTM. GRUs showed that gating is indeed helpful in general, and Bengio's team came to no concrete conclusion on which of the two gating units was better.
Architecture.
There are several variations on the full gated unit, with gating done using the previous hidden state and the bias in various combinations, and a simplified form called minimal gated unit.
The operator formula_1 denotes the Hadamard product in the following.
Fully gated unit.
Initially, for formula_2, the output vector is formula_3.
Variables
Activation functions
Alternative activation functions are possible, provided that formula_15.
Alternate forms can be created by changing formula_8 and formula_9
Minimal gated unit.
The minimal gated unit (MGU) is similar to the fully gated unit, except the update and reset gate vector is merged into a forget gate. This also implies that the equation for the output vector must be changed:
Variables
Light gated recurrent unit.
The light gated recurrent unit (LiGRU) removes the reset gate altogether, replaces tanh with the ReLU activation, and applies batch normalization (BN):
LiGRU has been studied from a Bayesian perspective. This analysis yielded a variant called light Bayesian recurrent unit (LiBRU), which showed slight improvements over the LiGRU on speech recognition tasks.


List of Unified Modeling Language tools

This article compares UML tools. UML tools are software applications which support some functions of the Unified Modeling Language.


Sherline

Sherline is a machine tool builder founded in Australia and currently headquartered in Vista, California, USA. It builds miniature machine tools (microlathes and micromills) and a wide range of tooling to be used on them. Within the miniature segment of the machine tool industry, Sherline is one of the most widely known brands. According to Sherline, their line of OEM accessories (chucks, vises, rotary tables, and so on) is more comprehensive than that of any other builder of machine tools, regardless of machine size.
Sherline tools are often used by hobbyists for making nearly any kind of part that can be machined, as long as it fits within a miniature machine tool's limits of slide travel. Sherline's products are also used by industry. They provide an inexpensive way to build custom tooling using modular components (XY tables, machine slides, etc.).
Sherline's sales are global. Its product line helps to put machine tools in places where traditionally they would be unlikely to go by lowering the threshold for market entry. Its turnkey CNC systems are some of the least expensive CNC machine tools on the market, making it possible for individual hobbyists to enter a market that in past decades was almost entirely industrial.


Electrohydraulic servo valve

An electrohydraulic servo valve (EHSV) is an electrically-operated valve that controls how hydraulic fluid is sent to an actuator. Servo valves are often used to control powerful hydraulic cylinders with a very small electrical signal. Servo valves can provide precise control of position, velocity, pressure, and force with good post-movement damping characteristics.
History of electrohydraulic servo valves.
The electrohydraulic servo valve first appeared in World War II. The EHSVs in use during the 1940s was characterized by poor accuracy and slow response times due to the inability to rapidly convert electrical signals into hydraulic flows. The first two-stage servo valve used a solenoid to actuate a first stage spool which in turn drove a rotating main stage. The servo valves of the World War II-era were similar to this — using a solenoid to drive a spool valve.
Advancement of EHSVs took off in the 1950s, largely due to the adoption of permanent magnet torque motors as the first stage (as opposed to solenoids). This resulted in greatly improved response times and a reduction in power used to control the valves.
Description.
Types.
Electrohydraulic servo valves may consist of one or more stages. A single-stage servo valve uses a torque motor to directly position a spool valve. Single-stage servo valves suffer from limitations in flow capability and stability due to torque motor power requirements. Two-stage servo valves may use flapper, jet pipe, or deflector jet valves as hydraulic amplifier first stages to position a second-stage spool valve. This design results in significant increases in servo valve flow capability, stability, and force output. Similarly, three-stage servo valves may use an intermediate stage spool valve to position a larger third stage spool valve. Three-stage servo valves are limited to very high power applications, where significant flows are required.
Furthermore, two-stage servo valves may be classified by the type of feedback used for the second stage; which may be spool position, load pressure, or load flow feedback. Most commonly, two-stage servo valves use position feedback; which may further be classified by direct feedback, force feedback, or spring centering.
Control.
A servo valve receives pressurized hydraulic fluid from a source, typically a hydraulic pump. It then transfers the fluid to a hydraulic cylinder in a closely controlled manner. Typically, the valve will move the spool proportionnaly to an electrical signal that it receives, indirectly controlling flow rate. Simple hydraulic control valves are binary, they are either on or off. Servo valves are different in that they can continuously vary the flow they supply from zero up to their rated maximum flow, or until the output pressure reaches the supplied pressure. More complex servo valves can control other parameters. For instance, some have internal feedback so that the input signal effectively control flow or output pressure, rather than spool position.
Servo valves are often used in a feedback control where the position or force on a hydraulic cylinder is measured, and fed back into a controller that varies the signal sent to the servo valve. This allows very precise control of the cylinder.
Examples of usage.
Manufacturing.
One example of servo valve use is in blow molding where the servo valve controls the wall thickness of extruded plastic making up the bottle or container by use of a deformable die. The mechanical feedback has been replaced by an electric feedback with a position transducer. Integrated electronics close the position loop for the spool. These valves are suitable for electrohydraulic position, velocity, pressure or force control systems with extremely high dynamic response requirements.
Aircraft.
Servo valves are used to regulate the flow of fuel into a turbofan engine governed by FADEC. In fly-by-wire aircraft the control surfaces are often moved by servo valves connected to hydraulic cylinders. The signals to the servo valves are controlled by a flight control computer that receives commands from the pilot and monitors the flight of the aircraft.


Automated guided vehicle

An automated guided vehicle (AGV), different from an autonomous mobile robot (AMR), is a portable robot that follows along marked long lines or wires on the floor, or uses radio waves, vision cameras, magnets, or lasers for navigation. They are most often used in industrial applications to transport heavy materials around a large industrial building, such as a factory or warehouse. Application of the automatic guided vehicle broadened during the late 20th century.
Introduction.
The AGV can tow objects behind them in trailers to which they can autonomously attach. The trailers can be used to move raw materials or finished products. The AGV can also store objects on a bed. The objects can be placed on a set of motorized rollers (conveyor) and then pushed off by reversing them. AGVs are employed in nearly every industry, including pulp, paper, metals, newspaper, and general manufacturing. Transporting materials such as food, linen or medicine in hospitals is also done.
An AGV can also be called a laser guided vehicle (LGV). In Germany the technology is also called "Fahrerloses Transportsystem" (FTS) and in Sweden "förarlösa truckar". Lower cost versions of AGVs are often called Automated Guided Carts (AGCs) and are usually guided by magnetic tape. The term AMR is sometimes used to differentiate the mobile robots that do not rely in their navigation on extra infrastructure in the environment (like magnetic strips or visual markers) from those that do; the latter are then called AGVs.
AGVs are available in a variety of models and can be used to move products on an assembly line, transport goods throughout a plant or warehouse, and deliver loads.
The first AGV was brought to market in the 1950s, by Barrett Electronics of Northbrook, Illinois, and at the time it was simply a tow truck that followed a wire in the floor instead of a rail. Out of this technology came a new type of AGV, which follows invisible UV markers on the floor instead of being towed by a chain. The first such system was deployed at the Willis Tower (formerly Sears Tower) in Chicago, Illinois to deliver mail throughout its offices.
Over the years the technology has become more sophisticated and today automated vehicles are mainly Laser navigated e.g. LGV (Laser Guided Vehicle). In an automated process, LGVs are programmed to communicate with other robots to ensure product is moved smoothly through the warehouse, whether it is being stored for future use or sent directly to shipping areas. Today, the AGV plays an important role in the design of new factories and warehouses, safely moving goods to their rightful destination.
Navigation.
Wired.
A slot is cut in to the floor and a wire is placed approximately 1 inch below the surface. This slot is cut along the path the AGV is to follow. This wire is used to transmit a radio signal. A sensor is installed on the bottom of the AGV close to the ground. The sensor detects the relative position of the radio signal being transmitted from the wire. This information is used to regulate the steering circuit, making the AGV follow the wire.
Guide tape.
AGVs (some known as automated guided carts or AGCs) use tape for the guide path. The tapes can be one of two styles: magnetic or colored.
The AGV is fitted with the appropriate guide sensor to follow the path of the tape.
One major advantage of tape over wired guidance is that it can be easily removed and relocated if the course needs to change. Colored tape is initially less expensive, but lacks the advantage of being embedded in high traffic areas where the tape may become damaged or dirty. A flexible magnetic bar can also be embedded in the floor like wire but works under the same provision as magnetic tape and so remains unpowered or passive. Another advantage of magnetic guide tape is the dual polarity. Small pieces of magnetic tape may be placed to change states of the AGC based on polarity and sequence of the tags.
Laser target navigation.
The navigation is done by mounting reflective tape on walls, poles or fixed machines. The AGV carries a laser transmitter and receiver on a rotating turret. The laser is transmitted and received by the same sensor. The angle and (sometimes) distance to any reflectors that in line of sight and in range are automatically calculated. This information is compared to the map of the reflector layout stored in the AGV's memory. This allows the navigation system to triangulate the current position of the AGV. The current position is compared to the path programmed in to the reflector layout map. The steering is adjusted accordingly to keep the AGV on track. It can then navigate to a desired target using the constantly updating position.
Inertial (Gyroscopic) navigation.
Another form of an AGV guidance is inertial navigation. With inertial guidance, a computer control system directs and assigns tasks to the vehicles. Transponders are embedded in the floor of the work place. The AGV uses these transponders to verify that the vehicle is on course. A gyroscope is able to detect the slightest change in the direction of the vehicle and corrects it in order to keep the AGV on its path. The margin of error for the inertial method is ±1 inch.
Inertial can operate in nearly any environment including tight aisles or extreme temperatures. Inertial navigation can include use of magnets embedded in the floor of the facility that the vehicle can read and follow.
Natural feature (Natural Targeting) navigation.
Navigation without retrofitting of the workspace is called Natural Features or Natural Targeting Navigation. One method uses one or more range-finding sensors, such as a laser range-finder, as well as gyroscopes or inertial measurement units with Monte-Carlo/Markov localization techniques to understand where it is as it dynamically plans the shortest permitted path to its goal. The advantage of such systems is that they are highly flexible for on-demand delivery to any location. They can handle failure without bringing down the entire manufacturing operation, since AGVs can plan paths around the failed device. They also are quick to install, with less down-time for the factory.
Vision guidance.
Vision-Guided AGVs can be installed with no modifications to the environment or infrastructure. They operate by using cameras to record features along the route, allowing the AGV to replay the route by using the recorded features to navigate. Vision-Guided AGVs use Evidence Grid technology, an application of probabilistic volumetric sensing, and was invented and initially developed by Dr. Hans Moravec at Carnegie Mellon University. The Evidence Grid technology uses probabilities of occupancy for each point in space to compensate for the uncertainty in the performance of sensors and in the environment. The primary navigation sensors are specially designed stereo cameras. The vision-guided AGV uses 360-degree images to build a 3D map, which allows the vision-guided AGVs to follow a trained route without human assistance or the addition of special features, landmarks or positioning systems.
Geoguidance.
A geoguided AGV recognizes its environment to establish its location. Without any infrastructure, the forklift equipped with geoguidance technology detects and identifies columns, racks and walls within the warehouse. Using these fixed references, it can position itself, in real time and determine its route. There are no limitations on distances to cover number of pick-up or drop-off locations. Routes are infinitely modifiable.
Steering control.
To help an AGV navigate it can use three different steer control systems. The differential speed control is the most common. In this method there are two independent drive wheels. Each drive is driven at different speeds in order to turn or the same speed to allow the AGV to go forwards or backwards. The AGV turns in a similar fashion to a tank. This method of steering is the simplest as it does not require additional steering motors and mechanism. More often than not, this is seen on an AGV that is used to transport and turn in tight spaces or when the AGV is working near machines. This setup for the wheels is not used in towing applications because the AGV would cause the trailer to jackknife when it turned.
The second type of steering used is steered wheel control AGV. This type of steering can be similar to a car's steering. But this is not very manoeuvrable. It is more common to use a three-wheeled vehicle similar to a conventional three wheeled forklift. The drive wheel is the turning wheel. It is more precise in following the programmed path than the differential speed controlled method. This type of AGV has smoother turning. Steered wheel control AGV can be used in all applications; unlike the differential controlled. Steered wheel control is used for towing and can also at times have an operator control it.
The third type is a combination of differential and steered. Two independent steer/drive motors are placed on diagonal corners of the AGV and swivelling castors are placed on the other corners. It can turn like a car (rotating in an arc) in any direction. It can crab in any direction and it can drive in differential mode in any direction.
Path Decision.
AGVs have to make decisions on path selection. This is done through different methods: frequency select mode (wired navigation only), and path select mode (wireless navigation only) or via a magnetic tape on the floor not only to guide the AGV but also to issue steering commands and speed commands.
Frequency select mode.
Frequency select mode bases its decision on the frequencies being emitted from the floor. When an AGV approaches a point on the wire which splits the AGV detects the two frequencies and through a table stored in its memory decides on the best path. The different frequencies are required only at the decision point for the AGV. The frequencies can change back to one set signal after this point. This method is not easily expandable and requires extra cutting meaning more money.
Path select mode.
An AGV using the path select mode chooses a path based on preprogrammed paths. It uses the measurements taken from the sensors and compares them to values given to them by programmers. When an AGV approaches a decision point it only has to decide whether to follow path 1, 2, 3, etc. This decision is rather simple since it already knows its path from its programming. This method can increase the cost of an AGV because it is required to have a team of programmers to program the AGV with the correct paths and change the paths when necessary. This method is easy to change and set up.
Magnetic tape mode.
The magnetic tape is laid on the surface of the floor or buried in a 10mm channel; not only does it provide the path for the AGV to follow but also strips of the tape in different combinations of polarity, sequence, and distance laid alongside the track tell the AGV to change lane, speed up, slow down, and stop.
Traffic control.
Flexible manufacturing systems containing more than one AGV may require it to have traffic control so the AGV's will not run into one another. Traffic control can be carried out locally or by software running on a fixed computer elsewhere in the facility. Local methods include zone control, forward sensing control, and combination control. Each method has its advantages and disadvantages.
Zone control.
Zone control is the favorite of most environments because it is simple to install and easy to expand. Zone control uses a wireless transmitter to transmit a signal in a fixed area. Each AGV contains a sensing device to receive this signal and transmit back to the transmitter. If the area is clear the signal is set at "clear" allowing any AGV to enter and pass through the area. When an AGV is in the area the "stop" signal is sent and all AGV attempting to enter the area stop and wait for their turn. Once the AGV in the zone has moved out beyond the zone the "clear" signal is sent to one of the waiting AGVs. Another way to set up zone control traffic management is to equip each individual robot with its own small transmitter/receiver. The individual AGV then sends its own "do not enter" message to all the AGVs getting too close to its zone in the area. A problem with this method is if one zone goes down all the AGV's are at risk to collide with any other AGV. Zone control is a cost efficient way to control the AGV in an area.
Collision avoidance.
Forward sensing control uses collision avoidance sensors to avoid collisions with other AGV in the area. These sensors include: sonic, which work like radar; optical, which uses an infrared sensor; and bumper, physical contact sensor. Most AGV's are equipped with a bumper sensor of some sort as a fail-safe. Sonic sensors send a "chirp" or high frequency signal out and then wait for a reply from the outline of the reply the AGV can determine if an object is ahead of it and take the necessary actions to avoid collision. The optical uses an infrared transmitter/receiver and sends an infrared signal which then gets reflected back; working on a similar concept as the sonic sensor. The problems with these are they can only protect the AGV from so many sides. They are relatively hard to install and work with as well.
Combination control.
Combination control sensing is using collision avoidance sensors as well as the zone control sensors. The combination of the two helps to prevent collisions in any situation. For normal operation the zone control is used with the collision avoidance as a fail safe. For example, if the zone control system is down, the collision avoidance system would prevent the AGV from colliding.
System management.
Industries with AGVs need to have some sort of control over the AGVs. There are three main ways to control the AGV: locator panel, CRT color graphics display, and central logging and report.
A locator panel is a simple panel used to see which area the AGV is in. If the AGV is in one area for too long, it could mean it is stuck or broken down. CRT color graphics display shows real time where each vehicle is. It also gives a status of the AGV, its battery voltage, unique identifier, and can show blocked spots. Central logging used to keep track of the history of all the AGVs in the system. Central logging stores all the data and history from these vehicles which can be printed out for technical support or logged to check for up time.
AGV is a system often used in FMS to keep up, transport, and connect smaller subsystems into one large production unit. AGVs employ a lot of technology to ensure they do not hit one another and make sure they get to their destination. Loading and transportation of materials from one area to another is the main task of the AGV. AGV require a lot of money to get started with, but they do their jobs with high efficiency. In places such as Japan automation has increased and is now considered to be twice as efficient as factories in America. For a huge initial cost the total cost over time decreases.
Common applications.
Automated Guided Vehicles can be used in a wide variety of applications to transport many different types of material including pallets, rolls, racks, carts, and containers. AGVs excel in applications with the following characteristics:
Handling raw materials.
AGVs are commonly used to transport raw materials such as paper, steel, rubber, metal, and plastic. This includes transporting materials from receiving to the warehouse, and delivering materials directly to production lines.
Work-in-process movement.
Work-in-Process movement is one of the first applications where automated guided vehicles were used, and includes the repetitive movement of materials throughout the manufacturing process. AGVs can be used to move material from the warehouse to production/processing lines or from one process to another.
Pallet handling.
Pallet handling is an extremely popular application for AGVs as repetitive movement of pallets is very common in manufacturing and distribution facilities. AGVs can move pallets from the palletizer to stretch wrapping to the warehouse/storage or to the outbound shipping docks.
Finished product handling.
Moving finished goods from manufacturing to storage or shipping is the final movement of materials before they are delivered to customers. These movements often require the gentlest material handling because the products are complete and subject to damage from rough handling. Because AGVs operate with precisely controlled navigation and acceleration and deceleration this minimizes the potential for damage making them an excellent choice for this type of application
Trailer loading.
Automatic loading of trailers is a relatively new application for automated guided vehicles and becoming increasingly popular. AGVs are used to transport and load pallets of finished goods directly into standard, over-the-road trailers without any special dock equipment. AGVs can pick up pallets from conveyors, racking, or staging lanes and deliver them into the trailer in the specified loading pattern. Some Automatic Trailer Loading AGVs utilize Natural Targeting to view the walls of the trailer for navigation. These types of ATL AGVs can be either completely driverless or hybrid vehicles.
Roll handling.
AGVs are used to transport rolls in many types of plant including paper mills, converters, printers, newspapers, steel producers, and plastics manufacturers. AGVs can store and stack rolls on the floor, in racking, and can even automatically load printing presses with rolls of paper.
Container handling.
AGVs are used to move sea containers in some port container terminals. The main benefits are reduced labour costs and a more reliable (less variable) performance. This use of AGVs was pioneered in 1993 at the Port of Rotterdam in the Netherlands. By 2014 there were 20 automated or semi-automated port container terminals around the world which use either or both automated-guideway vehicles and automated-stacking-cranes. The original AGVs used diesel power with either hydraulic or electric drives. However more AGV use battery power and automated battery swap, which reduces emissions and lowers refueling costs but cost more to purchase and have shorter range.
Primary application industries.
Efficient, cost effective movement of materials is an important, and common element in improving operations in many manufacturing plants and warehouses. Because automatic guided vehicles (AGVs) can deliver efficient, cost effective movement of materials, AGVs can be applied to various industries in standard or customized designs to best suit an industry's requirements. Industries currently utilizing AGVs include (but are not limited to):
Pharmaceutical.
AGVs are a preferred method of moving materials in the pharmaceutical industry. Because an AGV system tracks all movement provided by the AGVs, it supports process validation and cGMP (current Good Manufacturing Practice).
Chemical.
AGVs deliver raw materials, move materials to curing storage warehouses, and provide transportation to other processing cells and stations. Common industries include rubber, plastics, and specialty chemicals.
Manufacturing.
AGVs are often used in general manufacturing of products. AGVs can typically be found delivering raw materials, transporting work-in process, moving finished goods, removing scrap materials, and supplying packaging materials.
Automotive.
AGV installations are found in Stamping Plants, Power Train (Engine and Transmission) Plants, and Assembly Plants delivering raw materials, transporting work-in process, and moving finished goods. AGVs are also used to supply specialized tooling which must be changed.
Paper and print.
AGVs can move paper rolls, pallets, and waste bins to provide all routine material movement in the production and warehousing (storage/retrieval) of paper, newspaper, printing, corrugating, converting, and plastic film.
Food and beverage.
AGVs can be applied to move materials in food processing (such as the loading of food or trays into sterilizers) and at the "end of line," linking the palletizer, stretch wrapper, and the warehouse. AGVs can load standard, over-the-road trailers with finished goods, and unload trailers to supply raw materials or packaging materials to the plant. AGVs can also store and retrieve pallets in the warehouse.
Hospital.
AGVs are becoming increasingly popular in the healthcare industry for efficient transport, and are programmed to be fully integrated to automatically operate doors, elevators/lifts, cart washers, trash dumpers, etc. AGVs typically move linens, trash, regulated medical waste, patient meals, soiled food trays, and surgical case carts.
Warehousing.
AGVs used in Warehouses and Distribution Centers logically move loads around the warehouses and prepare them for shipping/loading or receiving or move them from an induction conveyor to logical storage locations within the warehouse. Often, this type of use is accompanied by customized warehouse management software. To avoid damage to fragile goods, AGVs are preferred in warehouses that handle fragile items since human errors are reduced to almost zero. Warehouses with hazardous goods have primarily adopted this technology as they can operate in extreme conditions like passing through freezers.
Theme parks.
In recent years, the theme park industry has begun using AGVs for rides. One of the earliest AGV ride systems was for Epcot's Universe of Energy, opened in 1982. The ride used wired navigation to drive the 'Traveling Theatre' through the ride. Many rides use wired navigation, especially when employees must frequently walk over the ride path such as at (the now-closed attraction) The Great Movie Ride at Disney's Hollywood Studios. Another ride at Hollywood Studios that uses wired navigation is The Twilight Zone Tower of Terror, a combined drop tower/dark ride. The elevator cars are AGVs that lock into place inside separate vertical motion cabs to move vertically. When it reaches a floor requiring horizontal movement, the AGV unlocks from the vertical cab and drives itself out of the elevator.
A recent trend in theme parks is a so-called trackless ride system, AGV rides that use LPS, Wi-Fi, or RFID to move around. The advantage of this system is that the ride can execute seemingly random movements, giving a different ride experience each time.
Battery charging.
AGVs utilize a number of battery charging options. Each option is dependent on the users preference.
Battery swap.
"Battery swap technology" requires an operator to manually remove the discharged battery from the AGV and place a fully charged battery in its place after approximately 8 – 12 hours (about one shift) of AGVs operation. 5 – 10 minutes is required to perform this with each AGV in the fleet.
Automatic and opportunity charging.
"Automatic and opportunity battery charging" allows for continuous operation. On average an AGV charges for 12 minutes every hour for automatic charging and no manual intervention is required. If opportunity is being utilized the AGV will receive a charge whenever the opportunity arises.
When a battery pack gets to a predetermined level the AGV will finish the current job that it has been assigned before it goes to the charging station.
Automatic battery swap.
Automatic battery swap is an alternative to manual battery swap. It might require an additional piece of automation machinery, an automatic battery changer, to the overall AGV system. AGVs will pull up to the battery swap station and have their batteries automatically replaced with fully charged batteries. The automatic battery changer then places the removed batteries into a charging slot for automatic recharging. The automatic battery changer keeps track of the batteries in the system and pulls them only when they are fully charged.
Other versions of automatic battery swap allow AGVs to change each other's batteries.
While a battery swap system reduces the manpower required to swap batteries, recent developments in battery charging technology allow batteries to be charged more quickly and efficiently potentially eliminating the need to swap batteries.


Process Window Index

Process Window Index (PWI) is a statistical measure that quantifies the robustness of a manufacturing process, e.g. one which involves heating and cooling, known as a thermal process. In manufacturing industry, PWI values are used to calibrate the heating and cooling of soldering jobs (known as a thermal profile) while baked in a reflow oven.
PWI measures how well a process fits into a user-defined process limit known as the specification limit. The specification limit is the tolerance allowed for the process and may be statistically determined. Industrially, these specification limits are known as the "process window", and values that a plotted inside or outside this window are known as the process window index.
Using PWI values, processes can be accurately measured, analyzed, compared, and tracked at the same level of statistical process control and quality control available to other manufacturing processes.
Statistical process control.
Process capability is the ability of a process to produce output within specified limits. To help determine whether a manufacturing or business process is in a state of statistical control, process engineers use control charts, which help to predict the future performance of the process based on the current process.
To help determine the capability of a process, statistically determined upper and lower limits are drawn on either side of a process mean on the control chart. The control limits are set at three standard deviations on either side of the process mean, and are known as the upper control limit (UCL) and lower control limit (LCL) respectively. If the process data plotted on the control chart remains within the control limits over an extended period, then the process is said to be stable.
The tolerance values specified by the end-user are known as specification limits – the upper specification limit (USL) and lower specification limit (LSL) respectively. If the process data plotted on a control chart remains within these specification limits, then the process is considered a capable process, denoted by formula_1.
Manufacturing industry has developed customized specification limits known as Process Windows. Within this process window, values are plotted. The values relative to the process mean of the window are known as the Process Window Index. By using PWI values, processes can be accurately measured, analyzed, compared, and tracked at the same level of statistical process control and quality control available to other manufacturing processes.
Control limits.
Control limits, also known as natural process limits, are horizontal lines drawn on a statistical process control chart, usually at a distance of ±3 standard deviations of the plotted statistic's mean, used to judge the stability of a process.
Control limits should not be confused with "tolerance limits" or "specifications," which are completely independent of the distribution of the plotted sample statistic. Control limits describe what a process is capable of producing (sometimes referred to as the “voice of the process”), while tolerances and specifications describe how the product should perform to meet the customer's expectations (referred to as the “voice of the customer”).
Use.
Control limits are used to detect signals in process data that indicate that a process is not in control and, therefore, not operating predictably. A value in excess of the control limit indicates a special cause is affecting the process.
To detect signals one of several rule sets may be used . One specification outlines that a signal is defined as any single point outside of the control limits. A process is also considered out of control if there are seven consecutive points, still inside the control limits but on one single side of the mean.
For normally distributed statistics, the area bracketed by the control limits will on average contain 99.73% of all the plot points on the chart, as long as the process is and remains in statistical control. A false-detection rate of at least 0.27% is therefore expected.
It is often not known whether a particular process generates data that conform to particular distributions, but the Chebyshev's inequality and the Vysochanskij–Petunin inequality allow the inference that for any unimodal distribution at least 95% of the data will be encapsulated by limits placed at 3 sigma.
PWI in electronics manufacturing.
An example of a process to which the PWI concept may be applied is soldering. In soldering, a thermal profile is the set of time-temperature values for a variety of processes such as slope, thermal soak, reflow, and peak.
Each thermal profile is ranked on how it fits in a process window (the specification or tolerance limit). Raw temperature values are normalized in terms of a percentage relative to both the process mean and the window limits. The center of the process window is defined as zero, and the extreme edges of the process window are ±99%. A PWI greater than or equal to 100% indicates that the profile does not process the product within specification. A PWI of 99% indicates that the profile runs at the edge of the process window. For example, if the process mean is set at 200 °C, with the process window calibrated at 180 °C and 220 °C respectively; then a measured value of 188 °C translates to a process window index of −60%. A lower PWI value indicates a more robust profile. For maximum efficiency, separate PWI values are computed for peak, slope, reflow, and soak processes of a thermal profile.
To avoid thermal shock affecting production, the steepest slope in the thermal profile is determined and leveled. Manufacturers use custom-built software to accurately determine and decrease the steepness of the slope. In addition, the software also automatically recalibrates the PWI values for the peak, slope, reflow, and soak processes. By setting PWI values, engineers can ensure that the reflow soldering work does not overheat or cool too quickly.
Formula.
The Process Window Index is calculated as the worst case (i.e. highest number) in the set of thermal profile data. For each profile statistic the percentage used of the respective process window is calculated, and the worst case (i.e. highest percentage) is the PWI.
For example, a thermal profile with three thermocouples, with four profile statistics logged for each thermocouple, would have a set of twelve statistics for that thermal profile. In this case, the PWI would be the highest value among the twelve percentages of the respective process windows.
The formula to calculate PWI is:
where:


Teaching dimension

In computational learning theory, the teaching dimension of a concept class "C" is defined to be formula_1, where formula_2 is the minimum size of a witness set for "c" in "C". Intuitively, this measures the number of instances that are needed to identify a concept in the class, using supervised learning with examples provided by a helpful teacher who is trying to convey the concept as succinctly as possible. This definition was formulated in 1995 by Sally Goldman and Michael Kearns, based on earlier work by Goldman, Ron Rivest, and Robert Schapire.
The teaching dimension of a finite concept class can be used to give a lower and an upper bound on the membership query cost of the concept class.
In Stasys Jukna's book "Extremal Combinatorics", a lower bound is given for the teaching dimension in general:
Let "C" be a concept class over a finite domain "X". If the size of "C" is greater than
then the teaching dimension of "C" is greater than "k".
However, there are more specific teaching models that make assumptions about teacher or learner, and can get lower values for the teaching dimension. For instance, several models are the classical teaching (CT) model, the optimal teacher (OT) model, recursive teaching (RT), preference-based teaching (PBT), and non-clashing teaching (NCT).


Die casting

Die casting is a metal casting process that is characterized by forcing molten metal under high pressure into a mold cavity. The mold cavity is created using two hardened tool steel dies which have been machined into shape and work similarly to an injection mold during the process. Most die castings are made from non-ferrous metals, specifically zinc, copper, aluminium, magnesium, lead, pewter, and tin-based alloys. Depending on the type of metal being cast, a hot- or cold-chamber machine is used.
The casting equipment and the metal dies represent large capital costs and this tends to limit the process to high-volume production. Manufacture of parts using die casting is relatively simple, involving only four main steps, which keeps the incremental cost per item low. It is especially suited for a large quantity of small- to medium-sized castings, which is why die casting produces more castings than any other casting process. Die castings are characterized by a very good surface finish (by casting standards) and dimensional consistency.
History.
Die casting equipment was invented in 1838 for the purpose of producing movable type for the printing industry. The first die casting-related patent was granted in 1849 for a small hand-operated machine for the purpose of mechanized printing type production. In 1885 Ottmar Mergenthaler invented the Linotype machine, which cast an entire line of type as a single unit, using a die casting process. It nearly completely replaced setting type by hand in the publishing industry. The Soss die-casting machine, manufactured in Brooklyn, NY, was the first machine to be sold in the open market in North America. Other applications grew rapidly, with die casting facilitating the growth of consumer goods, and appliances, by greatly reducing the production cost of intricate parts in high volumes. In 1966, General Motors released the "Acurad" process.
Cast metal.
The main die casting alloys are: zinc, aluminium, magnesium, copper, lead, and tin; although uncommon, ferrous die casting is also possible. Specific die casting alloys include: zinc aluminium; aluminium to, e.g. The Aluminum Association (AA) standards: AA 380, AA 384, AA 386, AA 390; and AZ91D magnesium. The following is a summary of the advantages of each alloy:
, maximum weight limits for aluminium, brass, magnesium, and zinc castings are estimated at approximately , and , respectively. By late-2019, press machines capable of die casting single pieces over- were being used to produce aluminium chassis components for cars.
The material used defines the minimum section thickness and minimum draft required for a casting as outlined in the table below. The thickest section should be less than , but can be greater.
Design geometry.
There are a number of geometric features to be considered when creating a parametric model of a die casting:
Equipment.
There are two basic types of die casting machines: "hot-chamber machines" and "cold-chamber machines". These are rated by how much clamping force they can apply. Typical ratings are between .
Hot-chamber die casting.
Hot-chamber die casting, also known as "gooseneck machines", rely upon a pool of molten metal to feed the die. At the beginning of the cycle the piston of the machine is retracted, which allows the molten metal to fill the "gooseneck". The pneumatic- or hydraulic-powered piston then forces this metal out of the gooseneck into the die. The advantages of this system include fast cycle times (approximately 15 cycles a minute) and the convenience of melting the metal in the casting machine. The disadvantages of this system are that it is limited to use with low-melting point metals and that aluminium cannot be used because it picks up some of the iron while in the molten pool. Therefore, hot-chamber machines are primarily used with zinc-, tin-, and lead-based alloys.
Cold-chamber die casting.
These are used when the casting alloy cannot be used in hot-chamber machines; these include aluminium, zinc alloys with a large composition of aluminium, magnesium and copper. The process for these machines start with melting the metal in a separate furnace. Then a precise amount of molten metal is transported to the cold-chamber machine where it is fed into an unheated shot chamber (or injection cylinder). This shot is then driven into the die by a hydraulic or mechanical piston. The biggest disadvantage of this system is the slower cycle time due to the need to transfer the molten metal from the furnace to the cold-chamber machine.
Mold or tooling.
Two dies are used in die casting; one is called the "cover die half" and the other the "ejector die half". Where they meet is called the parting line. The cover die contains the sprue (for hot-chamber machines) or shot hole (for cold-chamber machines), which allows the molten metal to flow into the dies; this feature matches up with the injector nozzle on the hot-chamber machines or the shot chamber in the cold-chamber machines. The ejector die contains the ejector pins and usually the runner, which is the path from the sprue or shot hole to the mould cavity. The cover die is secured to the stationary, or front, platen of the casting machine, while the ejector die is attached to the movable platen. The mould cavity is cut into two "cavity inserts", which are separate pieces that can be replaced relatively easily and bolt into the die halves.
The dies are designed so that the finished casting will slide off the cover half of the die and stay in the ejector half as the dies are opened. This assures that the casting will be ejected every cycle because the ejector half contains the "ejector pins" to push the casting out of that die half. The ejector pins are driven by an "ejector pin plate", which accurately drives all of the pins at the same time and with the same force, so that the casting is not damaged. The ejector pin plate also retracts the pins after ejecting the casting to prepare for the next shot. There must be enough ejector pins to keep the overall force on each pin low, because the casting is still hot and can be damaged by excessive force. The pins still leave a mark, so they must be located in places where these marks will not hamper the casting's purpose.
Other die components include "cores" and "slides". Cores are components that usually produce holes or opening, but they can be used to create other details as well. There are three types of cores: fixed, movable, and loose. Fixed cores are ones that are oriented parallel to the pull direction of the dies (i.e. the direction the dies open), therefore they are fixed, or permanently attached to the die. Movable cores are ones that are oriented in any other way than parallel to the pull direction. These cores must be removed from the die cavity after the shot solidifies, but before the dies open, using a separate mechanism. Slides are similar to movable cores, except they are used to form undercut surfaces. The use of movable cores and slides greatly increases the cost of the dies. Loose cores, also called "pick-outs", are used to cast intricate features, such as threaded holes. These loose cores are inserted into the die by hand before each cycle and then ejected with the part at the end of the cycle. The core then must be removed by hand. Loose cores are the most expensive type of core, because of the extra labor and increased cycle time. Other features in the dies include water-cooling passages and vents along the parting lines. These vents are usually wide and thin (approximately ) so that when the molten metal starts filling them the metal quickly solidifies and minimizes scrap. No risers are used because the high pressure ensures a continuous feed of metal from the gate.
The most important material properties for the dies are thermal shock resistance and softening at elevated temperature; other important properties include hardenability, machinability, heat checking resistance, weldability, availability (especially for larger dies), and cost. The longevity of a die is directly dependent on the temperature of the molten metal and the cycle time. The dies used in die casting are usually made out of hardened tool steels, because cast iron cannot withstand the high pressures involved, therefore the dies are very expensive, resulting in high start-up costs. Metals that are cast at higher temperatures require dies made from higher alloy steels.
The main failure mode for die casting dies is wear or erosion. Other failure modes are "heat checking" and "thermal fatigue". Heat checking is when surface cracks occur on the die due to a large temperature change on every cycle. Thermal fatigue is when surface cracks occur on the die due to a large number of cycles.
Process.
The following are the four steps in "traditional die casting", also known as "", these are also the basis for any of the die casting variations: die preparation, filling, ejection, and shakeout. The dies are prepared by spraying the mould cavity with lubricant. The lubricant both helps control the temperature of the die and it also assists in the removal of the casting. The dies are then closed and molten metal is injected into the dies under high pressure; between . Once the mould cavity is filled, the pressure is maintained until the casting solidifies. The dies are then opened and the shot (shots are different from castings because there can be multiple cavities in a die, yielding multiple castings per shot) is ejected by the ejector pins. Finally, the shakeout involves separating the scrap, which includes the gate, runners, sprues and flash, from the shot. This is often done using a special trim die in a power press or hydraulic press. Other methods of shaking out include sawing and grinding. A less labor-intensive method is to tumble shots if gates are thin and easily broken; separation of gates from finished parts must follow. This scrap is recycled by remelting it. The yield is approximately 67%.
The high-pressure injection leads to a quick fill of the die, which is required so the entire cavity fills before any part of the casting solidifies. In this way, discontinuities are avoided, even if the shape requires difficult-to-fill thin sections. This creates the problem of air entrapment, because when the mould is filled quickly there is little time for the air to escape. This problem is minimized by including vents along the parting lines, however, even in a highly refined process there will still be some porosity in the center of the casting.
Most die casters perform other secondary operations to produce features not readily castable, such as tapping a hole, polishing, plating, buffing, or painting.
Inspection.
After the shakeout of the casting it is inspected for defects. The most common defects are misruns and cold shuts. These defects can be caused by cold dies, low metal temperature, dirty metal, lack of venting, or too much lubricant. Other possible defects are gas porosity, shrinkage porosity, hot tears, and flow marks. "Flow marks" are marks left on the surface of the casting due to poor gating, sharp corners, or excessive lubricant.
Lubricants.
Water-based lubricants are the most used type of lubricant, because of health, environmental, and safety reasons. Unlike solvent-based lubricants, if water is properly treated to remove all minerals from it, it will not leave any by-product in the dies. If the water is not properly treated, then the minerals can cause surface defects and discontinuities.
Today "water-in-oil" and "oil-in-water" emulsions are used, because, when the lubricant is applied, the water cools the die surface by evaporating depositing the oil that helps release the shot. A common mixture for this type of emulsion is thirty parts water to one part oil, however in extreme cases a ratio of one-hundred to one is used. Oils that are used include heavy residual oil (HRO), animal fat, vegetable fat, synthetic oil, and all sorts of mixtures of these. HROs are gelatinous at room temperature, but at the high temperatures found in die casting, they form a thin film. Other substances are added to control the viscosity and thermal properties of these emulsions, e.g. graphite, aluminium, mica. Other chemical additives are used to inhibit rusting and oxidation. In addition emulsifiers are added to improve the emulsion manufacturing process, e.g. soap, alcohol esters, ethylene oxides.
Historically, solvent-based lubricants, such as diesel fuel and kerosene, were commonly used. These were good at releasing the part from the die, but a small explosion occurred during each shot, which led to a build-up of carbon on the mould cavity walls. However, they were easier to apply evenly than water-based lubricants.
Advantages.
Advantages of die casting:
Disadvantages.
The main disadvantage to die casting is the very high capital cost. Both the casting equipment required and the dies and related components are very costly, as compared to most other casting processes. Therefore, to make die casting an economic process, a large production volume is needed. Other disadvantages are:
Variants.
Acurad.
Acurad was a die casting process developed by General Motors in the late 1950s and 1960s. The name is an acronym for accurate, reliable, and dense. It was developed to combine a stable fill and directional solidification with the fast cycle times of the traditional die casting process. The process pioneered four breakthrough technologies for die casting: thermal analysis, flow and fill modeling, heat treatable and high integrity die castings, and indirect squeeze casting (explained below).
The thermal analysis was the first done for any casting process. This was done by creating an electrical analog of the thermal system. A cross-section of the dies were drawn on Teledeltos paper and then thermal loads and cooling patterns were drawn onto the paper. Water lines were represented by magnets of various sizes. The thermal conductivity was represented by the reciprocal of the resistivity of the paper.
The Acurad system employed a bottom fill system that required a stable flow-front. Logical thought processes and trial and error were used because computerized analysis did not exist yet; however this modeling was the precursor to computerized flow and fill modeling.
The Acurad system was the first die casting process that could successfully cast low-iron aluminium alloys, such as A356 and A357. In a traditional die casting process these alloys would solder to the die. Similarly, Acurad castings could be heat treated and meet the U.S. military specification .
Finally, the Acurad system employed a patented double shot piston design. The idea was to use a second piston (located within the primary piston) to apply pressure after the shot had partially solidified around the perimeter of the casting cavity and shot sleeve. While the system was not very effective, it did lead the manufacturer of the Acurad machines, Ube Industries, to discover that it was just as effective to apply sufficient pressure at the right time later in the cycle with the primary piston; this is indirect squeeze casting.
Pore-free.
When no porosity is allowed in a cast part then the pore-free casting process is used. It is identical to the standard process except oxygen is injected into the die before each shot to purge any air from the mould cavity. This causes small dispersed oxides to form when the molten metal fills the die, which virtually eliminates gas porosity. An added advantage to this is greater strength. Unlike standard die castings, these castings can be heat treated and welded. This process can be performed on aluminium, zinc, and lead alloys.
Vacuum-assisted high-pressure die casting.
In vacuum assisted high pressure die casting, a.k.a. vacuum high pressure die casting (VHPDC), a vacuum pump removes air and gases from die cavity and metal delivery system before and during injection. Vacuum die casting reduces porosity, allows heat treating and welding, improves surface finish, and can increase strength.
Heated-manifold direct-injection.
Heated-manifold direct-injection die casting, also known as direct-injection die casting or runnerless die casting, is a zinc die casting process where molten zinc is forced through a heated manifold and then through heated mini-nozzles, which lead into the moulding cavity. This process has the advantages of lower cost per part, through the reduction of scrap (by the elimination of sprues, gates, and runners) and energy conservation, and better surface quality through slower cooling cycles.
Semi-solid.
"Semi-solid die casting" uses metal that is heated between its liquidus and either solidus or eutectic temperature, so that it is in its "mushy region". This allows for more complex parts and thinner walls.
Low Pressure Die Casting (LPDC) uses compressed air instead of a piston to inject molten metal into the die. The process begins with the preparation of the die. The die is preheated to a temperature that will ensure good metal flow and avoid premature solidification of the molten metal. A holding furnace (crucible) filled with molten metal is located beneath the sealed die. The furnace is pressurized to inject the molten metal into the die cavity through a tube. The pressure is usually around 7 to 15 psi. The molten metal is left to solidify in the die. This takes anywhere from a few seconds to a few minutes, depending on the size and complexity of the part being cast. Once the casting has solidified, the die is opened, and the casting is ejected or removed manually.


Oracle Health Sciences

Oracle Health Sciences is a family of software developed by Oracle Corporation which is primarily used to create clinical trials and to conduct pharmacovigilance based on the database created with it.
Oracle Argus.
Oracle Argus is a pharmacovigilance product line that includes Oracle Argus Affiliate, Oracle Argus Analytics, Oracle Argus Dossier, Oracle Argus Insight, Oracle Argus Reconciliation, Oracle Argus Intercange, and Oracle Argus Safety.


Robocup Rescue Simulation

Robocup Rescue Simulation is an education and research project intended to promote the development of robotic agents for search and rescue. The project was initiated in reaction to the Great Hanshin earthquake, which hit Hyōgo Prefecture, Japan, on 17 January 1995, killing more than six thousand people, most of them in the city of Kobe.
According to event organizers, "The intention of the RoboCup Rescue project is to promote research and development in this socially significant domain at various levels involving multi-agent team work coordination, physical robotic agents for search and rescue, information infrastructures, personal digital assistants, a standard simulator and decision support systems, evaluation benchmarks for rescue strategies and robotic systems that [can] all [be] integrated into comprehensive systems in future."
The RoboCup Rescue Simulation Project challenges teams of researchers to design virtual robots to solve various challenges, or to build real, autonomous robots, which are evaluated in specially designed rescue simulations.
The project is one of several competitions operated by RoboCup, which is best known for the Robot Soccer World Cup.


Abrasive flow machining

Abrasive flow machining (AFM), also known as abrasive flow deburring or extrude honing, is an interior surface finishing process characterized by flowing an abrasive-laden fluid through a workpiece. This fluid is typically very viscous, having the consistency of putty, or dough. AFM smooths and finishes rough surfaces, and is specifically used to remove burrs, polish surfaces, form radii, and even remove material. The nature of AFM makes it ideal for interior surfaces, slots, holes, cavities, and other areas that may be difficult to reach with other polishing or grinding processes. Due to its low material removal rate, AFM is not typically used for large stock-removal operations, although it can be.
Abrasive flow machining was first patented by the Extrude Hone Corporation in 1970.
Process.
In abrasive flow machining, the abrasive fluid flows through the workpiece, effectively performing erosion. Abrasive particles in the fluid contact raised features on the surface of the workpiece and remove them. The fluid is forced through the workpiece by a hydraulic ram, where it acts as a flexible file, or slug, molding itself precisely to the shape of the workpiece. The highest amount of material removal occurs in areas where the flow of the fluid is restricted; according to Bernoulli's Principle, the flow speed and pressure of the fluid decrease in these areas, facilitating a higher material removal rate (MRR). The pressure exerted by the fluid on all contacting surfaces also results in a very uniform finish.
AFM may be performed once, as a one-way flow process, or repeatedly as a two-way flow process. In the two-way flow process, a reservoir of medium exists at either end of the workpiece, and the medium flows back and forth through the workpiece from reservoir to reservoir.
Equipment.
An abrasive flow machine normally includes two medium chambers equipped with hydraulic rams, a fixture for holding the workpiece, and a clamping system that holds all the components tightly together. Most machines allow for the loading of different types of abrasive medium, and include the capacity to adjust the pressure used in extruding the medium through the workpiece. They may be manually operated, or automated using CNC. For machines designed to accommodate high production volumes, accessories such as part-cleaning stations, unloading and reloading stations, media refeed devices, and media heat exchangers may be included.


Pendulum-and-hydrostat control

Pendulum-and-hydrostat control is a control mechanism developed originally for depth control of the Whitehead torpedo. It is an early example of what is now known as proportional and derivative control.
The hydrostat is a mechanism that senses pressure; the torpedo's depth is proportional to pressure. However, with only a hydrostat controlling the depth fins in a negative feedback loop, the torpedo tends to oscillate around the desired depth rather than settling to the desired depth. The addition of a pendulum allows the torpedo to sense the pitch of the torpedo. The pitch information is combined with the depth information to set the torpedo's depth control fins. The pitch information provides a damping term to the depth control response and suppresses the depth oscillations.
Operation.
In control theory the effect of the addition of the pendulum can be explained as turning the simple proportional controller into a proportional-derivative controller since the depth keeping is not controlled by the depth alone anymore but also by the derivative (rate of change) of the depth which is roughly proportional to the angle of the machine. The relative gain of the proportional and derivative functions could be altered by adjusting the linkages.
It was mainly used to control the depth of torpedoes until the end of the Second World War, and it reduced depth errors from ±40 feet (12 meters) to as little as ±6 inches (0.15 m).
The pendulum and hydrostat control was invented by Robert Whitehead. It was an important advance in torpedo technology, and it was nicknamed "The Secret".


NiuTrans

NiuTrans is a machine translation system. It has a platform, an API, and two open-source translation systems.
It is developed by the Natural Language Processing Group at Northeastern University (China).
Translation systems.
NiuTrans.SMT is an open-source statistical machine translation system jointly developed by the Natural Language Processing Laboratory of Northeastern University and Shenyang Yayi Network Technology Co., Ltd.
NiuTrans.NMT is a lightweight and efficient Transformer-based neural machine translation system. It is implemented with pure C++ and it is heavily optimized for fast decoding. The system can run with various systems and devices


Karen Rudie

Karen Gail Rudie (born 1963) is a Canadian control theorist and electrical engineer known for her work on the decentralized control of discrete event dynamic systems. She is a professor of electrical and computer engineering in Queen's University at Kingston.
Education and career.
Rudie majored in mathematics and engineering as an undergraduate at Queen's University, specializing in control and communication; she graduated in 1985. She has a Ph.D. from the University of Toronto, completed in 1992; Her dissertation, "Decentralized Control of Discrete-Event Systems", was supervised by Walter Murray Wonham.
She returned to Queen's University as a faculty member in 1993, after postdoctoral research at the Institute for Mathematics and its Applications.
Recognition.
In 2018, Rudie was named an IEEE Fellow, as a member of the IEEE Control Systems Society, "for contributions to the supervisory control theory of discrete event systems".


Universal measuring machine

Universal measuring machines (UMM) are measurement devices used for objects in which geometric relationships are the most critical element, with dimensions specified from geometric locations (see GD&T) rather than absolute coordinates. The very first uses for these machines was the inspection of gauges and parts produced by jig grinding. While bearing some resemblance to a coordinate-measuring machine (CMM) its usage and accuracy envelope differs significantly. While CMMs typically move in three dimensions and measure with a touch probe, a UMM aligns a spindle (4th axis) with a part geometry using a continuous scanning probe.
Originally, universal measuring machines were created to fill a need to continuously measure geometric features in both an absolute and comparative capacity, rather than a point based coordinate measuring system. A CMM provides a rapid method for inspecting absolute points, but geometric relationships, such as runout, parallelism, perpendicularity, etc., must be calculated rather than measured directly. By aligning an accurate spindle with an electronic test indicator with a geometric feature of interest, rather than using non-scanning cartesian probe to estimate an alignment, a universal measuring machine fills this need. The indicator can be accurately controlled and moved across a part, either along a linear axis or radially around the spindle, to continuously record profile and determine geometry. This gives the universal machine a very strong advantage over non-scanning measuring methods when profiling flats, radii, contours, and holes, as the detail of the feature can be of at the resolution of the probe. More modern CMMs do have scanning probes and thus can determine geometry similarly.
In practice, the 1970s-era universal measuring machine is a very slow machine that requires a highly skilled and patient operator to use, and the accuracy built into these machines far outstripped the needs of most industries. As a result, the universal measuring machine today is uncommon, only found as a special-purpose machine in metrology laboratories. Because the machine can make comparative length measurements without moving linear axes, it is a valuable tool in comparing master gauges and length standards. While universal measuring machines were never a mass-produced item, they are no longer available on a production basis, and are produced on a to-order basis tailored to the needs of the metrology lab purchasing it. Manufacturers that perform work that must be measured on such a machine will frequently opt to subcontract the measurement to a laboratory which specializes in such.
Universal measuring machines placed under corrected interferometric control and using non-contact gauge heads can measure features to millionths of an inch across the entire machine's envelope, where other types of machine are limited either in number of axes or accuracy of the measurement. The accuracy of the machine itself is negligible, as the environment the machine is the limiting factor to effective accuracy. The earlier mechanical machines were built to hold 10 to 20 millionths of an inch accuracy across the entire machine envelope, and due to incredible machine design and forethought, remain as accurate today without computer compensation.