Online machine learning

In computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update the best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the entire training data set at once. Online learning is a common technique used in areas of machine learning where it is computationally infeasible to train over the entire dataset, requiring the need of out-of-core algorithms. It is also used in situations where it is necessary for the algorithm to dynamically adapt to new patterns in the data, or when the data itself is generated as a function of time, e.g., stock price prediction.
Online learning algorithms may be prone to catastrophic interference, a problem that can be addressed by incremental learning approaches.
Introduction.
In the setting of supervised learning, a function of formula_1 is to be learned, where formula_2 is thought of as a space of inputs and formula_3 as a space of outputs, that predicts well on instances that are drawn from a joint probability distribution formula_4 on formula_5. In reality, the learner never knows the true distribution formula_4 over instances. Instead, the learner usually has access to a training set of examples formula_7. In this setting, the loss function is given as formula_8, such that formula_9 measures the difference between the predicted value formula_10 and the true value formula_11. The ideal goal is to select a function formula_12, where formula_13 is a space of functions called a hypothesis space, so that some notion of total loss is minimised. Depending on the type of model (statistical or adversarial), one can devise different notions of loss, which lead to different learning algorithms.
Statistical view of online learning.
In statistical learning models, the training sample formula_14 are assumed to have been drawn from the true distribution formula_4 and the objective is to minimize the expected "risk"
A common paradigm in this situation is to estimate a function formula_17 through empirical risk minimization or regularized empirical risk minimization (usually Tikhonov regularization). The choice of loss function here gives rise to several well-known learning algorithms such as regularized least squares and support vector machines.
A purely online model in this category would learn based on just the new input formula_18, the current best predictor formula_19 and some extra stored information (which is usually expected to have storage requirements independent of training data size). For many formulations, for example nonlinear kernel methods, true online learning is not possible, though a form of hybrid online learning with recursive algorithms can be used where formula_20 is permitted to depend on formula_21 and all previous data points formula_22. In this case, the space requirements are no longer guaranteed to be constant since it requires storing all previous data points, but the solution may take less time to compute with the addition of a new data point, as compared to batch learning techniques.
A common strategy to overcome the above issues is to learn using mini-batches, which process a small batch of formula_23 data points at a time, this can be considered as pseudo-online learning for formula_24 much smaller than the total number of training points. Mini-batch techniques are used with repeated passing over the training data to obtain optimized out-of-core versions of machine learning algorithms, for example, stochastic gradient descent. When combined with backpropagation, this is currently the de facto training method for training artificial neural networks.
Example: linear least squares.
The simple example of linear least squares is used to explain a variety of ideas in online learning. The ideas are general enough to be applied to other settings, for example, with other convex loss functions.
Batch learning.
Consider the setting of supervised learning with formula_25 being a linear function to be learned:
where formula_27 is a vector of inputs (data points) and formula_28 is a linear filter vector.
The goal is to compute the filter vector formula_29.
To this end, a square loss function
is used to compute the vector formula_29 that minimizes the empirical loss
where
Let formula_2 be the formula_35 data matrix and formula_36 is the column vector of target values after the arrival of the first formula_37 data points.
Assuming that the covariance matrix formula_38 is invertible (otherwise it is preferential to proceed in a similar fashion with Tikhonov regularization), the best solution formula_39 to the linear least squares problem is given by
Now, calculating the covariance matrix formula_41 takes time formula_42, inverting the formula_43 matrix takes time formula_44, while the rest of the multiplication takes time formula_45, giving a total time of formula_46. When there are formula_47 total points in the dataset, to recompute the solution after the arrival of every datapoint formula_48, the naive approach will have a total complexity formula_49. Note that when storing the matrix formula_50, then updating it at each step needs only adding formula_51, which takes formula_52 time, reducing the total time to formula_53, but with an additional storage space of formula_52 to store formula_50.
Online learning: recursive least squares.
The recursive least squares (RLS) algorithm considers an online approach to the least squares problem. It can be shown that by initialising formula_56 and formula_57, the solution of the linear least squares problem given in the previous section can be computed by the following iteration:
The above iteration algorithm can be proved using induction on formula_60. The proof also shows that formula_61.
One can look at RLS also in the context of adaptive filters (see RLS).
The complexity for formula_47 steps of this algorithm is formula_63, which is an order of magnitude faster than the corresponding batch learning complexity. The storage requirements at every step formula_37 here are to store the matrix formula_65, which is constant at formula_45. For the case when formula_50 is not invertible, consider the regularised version of the problem
loss function formula_68. Then, it's easy to show that the same algorithm works with formula_69, and the iterations proceed to give formula_70.
Stochastic gradient descent.
When this
is replaced by
or formula_73 by formula_74, this becomes the stochastic gradient descent algorithm. In this case, the complexity for formula_47 steps of this algorithm reduces to formula_76. The storage requirements at every step formula_37 are constant at formula_78.
However, the stepsize formula_79 needs to be chosen carefully to solve the expected risk minimization problem, as detailed above. By choosing a decaying step size formula_80 one can prove the convergence of the average iterate formula_81. This setting is a special case of stochastic optimization, a well known problem in optimization.
Incremental stochastic gradient descent.
In practice, one can perform multiple stochastic gradient passes (also called cycles or epochs) over the data. The algorithm thus obtained is
called incremental gradient method and corresponds to an iteration
The main difference with the stochastic gradient method is that here a sequence formula_83 is chosen to decide which training point is visited in the formula_60-th step. Such a sequence can be stochastic or deterministic. The number of iterations is then decoupled to the number of points (each point can be considered more than once). The incremental gradient method can be shown to provide a minimizer to the empirical risk. Incremental techniques can be advantageous when considering objective functions made up of a sum of many terms e.g. an empirical error corresponding to a very large dataset.
Kernel methods.
Kernels can be used to extend the above algorithms to non-parametric models (or models where the parameters form an infinite dimensional space). The corresponding procedure will no longer be truly online and instead involve storing all the data points, but is still faster than the brute force method.
This discussion is restricted to the case of the square loss, though it can be extended to any convex loss. It can be shown by an easy induction that if formula_85 is the data matrix and formula_86 is the output after formula_60 steps of the SGD algorithm, then,
where formula_89 and the sequence formula_90 satisfies the recursion:
Notice that here formula_94 is just the standard Kernel on formula_95, and the predictor is of the form
Now, if a general kernel formula_97 is introduced instead and let the predictor be
then the same proof will also show that predictor minimising the least squares loss is obtained by changing the above recursion to
The above expression requires storing all the data for updating formula_90. The total time complexity for the recursion when evaluating for the formula_101-th datapoint is formula_102, where formula_103 is the cost of evaluating the kernel on a single pair of points.
Thus, the use of the kernel has allowed the movement from a finite dimensional parameter space formula_104 to a possibly infinite dimensional feature represented by a kernel formula_97 by instead performing the recursion on the space of parameters formula_106, whose dimension is the same as the size of the training dataset. In general, this is a consequence of the representer theorem.
Online convex optimization.
Online convex optimization (OCO) is a general framework for decision making which leverages convex optimization to allow for efficient algorithms. The framework is that of repeated game playing as follows:
For formula_107
The goal is to minimize regret, or the difference between cumulative loss and the loss of the best fixed point formula_113 in hindsight.
As an example, consider the case of online least squares linear regression. Here, the weight vectors come from the convex set formula_114, and nature sends back the convex loss function formula_115. Note here that formula_116 is implicitly sent with formula_117.
Some online prediction problems however cannot fit in the framework of OCO. For example, in online classification, the prediction domain and the loss functions are not convex. In such scenarios, two simple techniques for convexification are used: randomisation and surrogate loss functions.
Some simple online convex optimisation algorithms are:
Follow the leader (FTL).
The simplest learning rule to try is to select (at the current step) the hypothesis that has the least loss over all past rounds. This algorithm is called Follow the leader, and is simply given round formula_118 by:
This method can thus be looked as a greedy algorithm. For the case of online quadratic optimization (where the loss function is formula_120), one can show a regret bound that grows as formula_121. However, similar bounds cannot be obtained for the FTL algorithm for other important families of models like online linear optimization. To do so, one modifies FTL by adding regularisation.
Follow the regularised leader (FTRL).
This is a natural modification of FTL that is used to stabilise the FTL solutions and obtain better regret bounds. A regularisation function formula_122 is chosen and learning performed in round as follows:
As a special example, consider the case of online linear optimisation i.e. where nature sends back loss functions of the form formula_124. Also, let formula_114. Suppose the regularisation function formula_126 is chosen for some positive number formula_127. Then, one can show that the regret minimising iteration becomes
Note that this can be rewritten as formula_129, which looks exactly like online gradient descent.
If is instead some convex subspace of formula_95, would need to be projected onto, leading to the modified update rule
This algorithm is known as lazy projection, as the vector formula_132 accumulates the gradients. It is also known as Nesterov's dual averaging algorithm. In this scenario of linear loss functions and quadratic regularisation, the regret is bounded by formula_133, and thus the average regret goes to as desired.
Online subgradient descent (OSD).
The above proved a regret bound for linear loss functions formula_134. To generalise the algorithm to any convex loss function, the subgradient formula_135 of formula_117 is used as a linear approximation to formula_117 near formula_109, leading to the online subgradient descent algorithm:
Initialise parameter formula_139
For formula_107
One can use the OSD algorithm to derive formula_133 regret bounds for the online version of SVM's for classification, which use the hinge lossformula_150
Other algorithms.
Quadratically regularised FTRL algorithms lead to lazily projected gradient algorithms as described above. To use the above for arbitrary convex functions and regularisers, one uses online mirror descent. The optimal regularization in hindsight can be derived for linear loss functions, this leads to the AdaGrad algorithm.
For the Euclidean regularisation, one can show a regret bound of formula_133, which can be improved further to a formula_152 for strongly convex and exp-concave loss functions.
Continual learning.
Continual learning means constantly improving the learned model by processing continuous
streams of information.
Continual learning capabilities are essential for software systems and autonomous agents interacting in an ever changing real world.
However, continual learning is a challenge for machine learning and neural network models since the continual acquisition of incrementally available information from non-stationary data distributions
generally leads to catastrophic forgetting.
Interpretations of online learning.
The paradigm of online learning has different interpretations depending on the choice of the learning model, each of which has distinct implications about the predictive quality of the sequence of functions formula_153. The prototypical stochastic gradient descent algorithm is used for this discussion. As noted above, its recursion is given by
The first interpretation consider the stochastic gradient descent method as applied to the problem of minimizing the expected risk formula_155 defined above. Indeed, in the case of an infinite stream of data, since the examples formula_156 are assumed to be drawn i.i.d. from the distribution formula_4, the sequence of gradients of formula_158 in the above iteration are an i.i.d. sample of stochastic estimates of the gradient of the expected risk formula_155 and therefore one can apply complexity results for the stochastic gradient descent method to bound the deviation formula_160, where formula_161 is the minimizer of formula_155. This interpretation is also valid in the case of a finite training set; although with multiple passes through the data the gradients are no longer independent, still complexity results can be obtained in special cases.
The second interpretation applies to the case of a finite training set and considers the SGD algorithm as an instance of incremental gradient descent method. In this case, one instead looks at the empirical risk:
Since the gradients of formula_158 in the incremental gradient descent iterations are also stochastic estimates of the gradient of formula_165, this interpretation is also related to the stochastic gradient descent method, but applied to minimize the empirical risk as opposed to the expected risk. Since this interpretation concerns the empirical risk and not the expected risk, multiple passes through the data are readily allowed and actually lead to tighter bounds on the deviations formula_166, where formula_167 is the minimizer of formula_165.
See also.
Learning paradigms
General algorithms
Learning models


Transfer function

In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. They are widely used in electronic engineering tools like circuit simulators and control systems. In some simple cases, this function can be represented as two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.
The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric current applied to the device; the transfer function of a photodetector might be the output voltage as a function of the luminous intensity of incident light of a given wavelength.
The term "transfer function" is also used in the frequency domain analysis of systems using transform methods such as the Laplace transform; here it means the amplitude of the output as a function of the frequency of the input signal. For example, the transfer function of an electronic filter is the voltage amplitude at the output as a function of the frequency of a constant amplitude sine wave applied to the input. For optical imaging devices, the optical transfer function is the Fourier transform of the point spread function (hence a function of spatial frequency).
Linear time-invariant systems.
Transfer functions are commonly used in the analysis of systems such as single-input single-output filters in the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear time-invariant (LTI) systems. Most real systems have non-linear input/output characteristics, but many systems, when operated within nominal parameters (not "over-driven") have behavior close enough to linear that LTI system theory is an acceptable representation of the input/output behavior.
The descriptions below are given in terms of a complex variable, formula_1, which bears a brief explanation. In many applications, it is sufficient to define formula_2 (thus formula_3), which reduces the Laplace transforms with complex arguments to Fourier transforms with real argument ω. The applications where this is common are ones where there is interest only in the steady-state response of an LTI system, not the fleeting turn-on and turn-off behaviors or stability issues. That is usually the case for signal processing and communication theory.
Thus, for continuous-time input signal formula_4 and output formula_5, the transfer function formula_6 is the linear mapping of the Laplace transform of the input, formula_7, to the Laplace transform of the output formula_8:
or
In discrete-time systems, the relation between an input signal formula_4 and output formula_5 is dealt with using the z-transform, and then the transfer function is similarly written as formula_13 and this is often referred to as the pulse-transfer function.
Direct derivation from differential equations.
Consider a linear differential equation with constant coefficients
where "u" and "r" are suitably smooth functions of "t", and "L" is the operator defined on the relevant function space, that transforms "u" into "r". That kind of equation can be used to constrain the output function "u" in terms of the "forcing" function "r". The transfer function can be used to define an operator formula_15 that serves as a right inverse of "L", meaning that formula_16.
Solutions of the "homogeneous", constant-coefficient differential equation formula_17 can be found by trying formula_18. That substitution yields the characteristic polynomial
The inhomogeneous case can be easily solved if the input function "r" is also of the form formula_20. In that case, by substituting formula_21 one finds that formula_22 if we define
Taking that as the definition of the transfer function requires careful disambiguation between complex vs. real values, which is traditionally influenced by the interpretation of abs("H"("s")) as the gain and −atan("H"("s")) as the phase lag. Other definitions of the transfer function are used: for example formula_24
Gain, transient behavior and stability.
A general sinusoidal input to a system of frequency formula_25 may be written formula_26. The response of a system to a sinusoidal input beginning at time formula_27 will consist of the sum of the steady-state response and a transient response. The steady-state response is the output of the system in the limit of infinite time, and the transient response is the difference between the response and the steady state response (it corresponds to the homogeneous solution of the above differential equation). The transfer function for an LTI system may be written as the product:
where "sPi" are the "N" roots of the characteristic polynomial and will therefore be the poles of the transfer function. Consider the case of a transfer function with a single pole formula_29 where formula_30. The Laplace transform of a general sinusoid of unit amplitude will be formula_31. The Laplace transform of the output will be formula_32 and the temporal output will be the inverse Laplace transform of that function:
The second term in the numerator is the transient response, and in the limit of infinite time it will diverge to infinity if "σP" is positive. In order for a system to be stable, its transfer function must have no poles whose real parts are positive. If the transfer function is strictly stable, the real parts of all poles will be negative, and the transient behavior will tend to zero in the limit of infinite time. The steady-state output will be:
The frequency response (or "gain") "G" of the system is defined as the absolute value of the ratio of the output amplitude to the steady-state input amplitude:
which is just the absolute value of the transfer function formula_36 evaluated at formula_37. This result can be shown to be valid for any number of transfer function poles.
Signal processing.
Let formula_38 be the input to a general linear time-invariant system, and formula_39 be the output, and the bilateral Laplace transform of formula_38 and formula_39 be
Then the output is related to the input by the transfer function formula_36 as
and the transfer function itself is therefore
In particular, if a complex harmonic signal with a sinusoidal component with amplitude formula_46, angular frequency formula_47 and phase formula_48, where arg is the argument
is input to a linear time-invariant system, then the corresponding component in the output is:
Note that, in a linear time-invariant system, the input frequency formula_52 has not changed, only the amplitude and the phase angle of the sinusoid has been changed by the system. The frequency response formula_53 describes this change for every frequency formula_52 in terms of "gain":
and "phase shift":
The phase delay (i.e., the frequency-dependent amount of delay introduced to the sinusoid by the transfer function) is:
The group delay (i.e., the frequency-dependent amount of delay introduced to the envelope of the sinusoid by the transfer function) is found by computing the derivative of the phase shift with respect to angular frequency formula_52,
The transfer function can also be shown using the Fourier transform which is only a special case of the bilateral Laplace transform for the case where formula_60.
Common transfer function families.
While any LTI system can be described by some transfer function or another, there are certain "families" of special transfer functions that are commonly used.
Some common transfer function families and their particular characteristics are:
Control engineering.
In control engineering and control theory the transfer function is derived using the Laplace transform.
The transfer function was the primary tool used in classical control engineering. However, it has proven to be unwieldy for the analysis of multiple-input multiple-output (MIMO) systems, and has been largely supplanted by state space representations for such systems. In spite of this, a transfer matrix can always be obtained for any linear system, in order to analyze its dynamics and other properties: each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.
A useful representation bridging state space and transfer function methods was proposed by Howard H. Rosenbrock and is referred to as Rosenbrock system matrix.
Optics.
In optics, modulation transfer function indicates the capability of optical contrast transmission.
For example, when observing a series of black-white-light fringes drawn with a specific spatial frequency, the image quality may decay. White fringes fade while black ones turn brighter.
The modulation transfer function in a specific spatial frequency is defined by
where modulation (M) is computed from the following image or light brightness:
Imaging.
In imaging, transfer functions are used to describe the relationship between the scene light, the image signal and the displayed light.
Non-linear systems.
Transfer functions do not properly exist for many non-linear systems. For example, they do not exist for relaxation oscillators; however, describing functions can sometimes be used to approximate such nonlinear time-invariant systems.


The Richard E. Bellman Control Heritage Award is an annual award (since 1979) given by the American Automatic Control Council (AACC) for achievements in control theory, named after the applied mathematician Richard E. Bellman. The award is given for "distinguished career contributions to the theory or applications of automatic control", and it is the "highest recognition of professional achievement for U.S. control systems engineers and scientists".
The original name was Control Heritage Award, and it was initially only given for the engineering side of control.
Recipients.
The following individuals have received the AACC Richard E. Bellman Control Heritage Award:


American Automatic Control Council

The American Automatic Control Council (AACC) is an organization founded in 1957 for research in control theory. AACC is a member of the International Federation of Automatic Control (IFAC) and is an association of the control systems divisions of nine member societies:
American Control Conference.
The American Control Conference (ACC) is an annual research conference sponsored by the AACC and is one of the most prestigious conferences in the field of control theory. Dating back to 1960, the attendees of the ACC are about 50% from the Americas and about 50% from other countries, consisting mostly of researchers with a large portion being students.
Awards.
The AACC issues five awards for achievements in control theory:


Reishauer

Reishauer is a Swiss machine tool builder based in Wallisellen, which manufactures gear grinding machines.
The company was founded in 1788 by the toolmaker Hans Jakob Däniker as a craft enterprise in Zurich. In 1870, the company was officially registered as a tool factory. In 1945, the first continuous generating gear grinding machine, ZA, was launched on the market, introducing a form of gear grinding that is today known as the Reishauer process. Soon after this, production expanded to gear parts outside machine-tool-engineering and met the requirements of the aircraft industry and the automotive industry. Reishauer AG is a subsidiary of Reishauer Beteiligungen AG, to which the German Felsomat AG has been a part of since 2010. The most important customers are the automotive industry and its suppliers.
Reishauer manufactures: gear grinding machines, grinding and dressing tools, clamping systems, and automation solutions. All components are supplied from one source with more than 80% vertical integration. Reishauer describes its performance system as a Circle of Competence, in which all machine components, tooling, and automation are manufactured in-house.
History.
Foundation as a toolmaker (from 1788).
The company was founded in 1788 by the toolmaker Hans Jakob Däniker as a craft enterprise in Zurich. Däniker's son Gottfried Reishauer trained as a toolmaker in the business and took over the management in 1824. In 1870, the company was officially registered as a tool factory. In 1882, the "Aktiengesellschaft für Fabrikation Reishauer'scher Werkzeuge" was founded, and the portfolio was expanded to include thread gauges in addition to thread cutting tools.
The step to mechanical engineering (from 1924).
As the thread grinding machines that were currently available on the market did not meet Reishauer's requirements, they designed their own thread grinding machine in 1924. The "RK Gewinde" started to work in the factory in 1928 and marked the step towards becoming a machine tool manufacturer. In 1931, the first in-house made machine for grinding taps was put into operation. Soon Reishauer began to produce the machines not only for his own needs but also to sell them to other companies. This enabled the company to bridge the declining demand for tools in the years after 1929.
The introduction of the continuous generating grinding process and the rise to become an international company (from 1945).
In 1945, the first continuous generating gear grinding machine, ZA, was launched on the market, introducing a form of gear grinding, today known as the Reishauer process. This machine had been preceded by a 15-year development period, as Reishauer wanted to find a more accurate, faster, and cheaper method of manufacturing gears. 1968, the AZA, a new gear grinding machine, was produced. The AZA was based on the same continuous generating process but allowed one person to operate several grinders at the same time, thanks to streamlining the operating process. Reishauer thus took the first step towards automating the gear grinding process. At the same time, production at Reishauer’s customers expanded to gear parts outside machine tool engineering, andt included gears for printing machines, trucks, tractors, and pumps. The electronic generating gearbox, introduced in 1977 with the RZ300E, ensured a level of precision that met the requirements of the aircraft industry. In 1986, the RZ301S enhanced generating grinding with shift grinding, which enabled constant grinding forces and higher profile accuracy. In 1993, the RZ362A, the first high-performance gear grinding machine, made its entry into the automotive industry. With this machine, Reishauer introduces the Low Noise Shifting (LNS) process, which reduced unwanted gear noise. In 1998, the company started its own diamond tool production and laid the foundation for its performance system, the Circle of Competence.
Universal machine and technological development (from 2001).
In 2001, the RZ400, the first universal machine, was launched on the market. It included the electronic generating gearbox developed by Reishauer with interfering signal suppression and extremely high drive rigidity. Furthermore, the RZ400 featured a Windows user interface, safety monitoring of the drive axes, and grinding at 63 m/s cutting speed and dressing of and grinding with multi-start threaded grinding wheels. With the RZ150, developed in 2003, two-spindle technology was introduced, which achieved a further increase in productivity. The machine was specially designed for automotive transmission gears. 2006 saw the launch of the RZ1000, which, just like the RZ400, was particularly adapted to job shops.
In 2008, Reishauer started the production of vitrified grinding wheels and built a new fully automated plant for this purpose in Pfaffnau, the canton of Lucerne, Switzerland. In 2009, the RZ60 series (RZ60, 160, 260) was designed, mainly for the automotive industry, but also for job shops, and further increased the productivity of the Reishauer process. In 2010, Reishauer started the development of clamping devices, which were launched in 2012. In 2014, Reishauer automation was introduced as part of the company's own performance system.
Corporate structure.
Reishauer AG is a subsidiary of Reishauer Beteiligungen AG, to which the German Felsomat AG has been part since 2010. The most important customers are the automotive industry and its suppliers. Reishauer has branches in Germany, France, Japan, China, and the USA.
Products.
Reishauer manufactures gear grinding machines, grinding and dressing tools, clamping systems, and automation solutions. All components are supplied from one source with more than 80% vertical integration. Machines specifically customized for each customer. Reishauer offers complete systems for the production of high-quality gears, including loading and unloading systems for its gear grinding machines. Almost 100% of the products are exported. Reishauer describes its performance system as a Circle of Competence, in which all machine components, tooling, and automation are manufactured in-house.
See also.


Maria Domenica Di Benedetto

Maria Domenica Di Benedetto (born 1953) is an Italian electrical engineer and control theorist whose interests include the control of hybrid systems, embedded control systems, automotive engine control, and aerospace flight control. She is Professor of Automatic Control at the University of L'Aquila, president of the European Embedded Control Institute, and the former president of the Italian Society of researchers in Automatic Control.
She should be distinguished from Maria-Gabriella Di Benedetto, another Italian electrical engineer with similar career details.
Education and career.
Di Benedetto earned a master's degree (Dr. Ing.) at Sapienza University of Rome in 1976. She earned a French doctorate of engineering at Paris-Sud University in 1981 and a state doctorate there in 1987.
She worked as a research engineer for IBM in Paris and Rome from 1979 to 1983, as an assistant professor at Sapienza University from 1983 to 1987, as an associate professor at the Parthenope University of Naples (then called the Istituto Universitario Navale) from 1987 to 1990, and again at Sapienza University from 1990 to 1993. She joined the Department of Information Engineering at the University of L'Aquila as Professor of Automatic Control in 1994. At L'Aquila, she directs the Center of Excellence for Research in Design methodologies of Embedded controllers, Wireless interconnect and Systems-on-chip (DEWS).
She has headed the European Embedded Control Institute (EECI) since 2009, and served as president of the Italian Society of researchers in Automatic Control (SIDRA) from 2013 to 2019.
Book.
With Elena De Santis, Di Benedetto is the coauthor of the book "Observability of Hybrid Dynamical Systems" (Now Publishers, 2016).
Recognition.
Di Benedetto was named an IEEE Fellow in the class of 2002, affiliated with the IEEE Control Systems Society, "for contributions to the theory of nonlinear and hybrid control system design". She was named a Fellow of the International Federation of Automatic Control in 2019, "for contributions to nonlinear and hybrid system theory and leadership in control research and education".


Multiple models

In control theory, multiple models is an approach to improve efficiency of adaptive system or observer system. It uses large number of models, which are distributed in the region of uncertainty, and based on the responses of the plant and the models. One model is chosen at every instant, which is closest to the plant according to some metric. The method offers satisfactory performance when no restrictions are put on the number of available models.
Approaches.
There are two multiple model methods:
Applications.
Multiple model method can be used for:


Armature Controlled DC Motor

An armature controlled DC motor is a direct current (DC) motor that uses a permanent magnet driven by the armature coils only.
Basic operation of DC motor.
A motor is an actuator, converting electrical energy in to rotational mechanical energy. A motor requiring a DC power supply for operation is termed a DC motor. DC motors are widely used in control applications like robotics, tape drives, machines and many more.
Separately excited DC motors are suitable for control applications because of separate field and armature circuit. Two ways to control DC separately excited motors are: Armature Control and Field Control.
A DC motor consists of two parts: a rotor and a stator. The stator consists of field windings while the rotor (also called the armature) consists of an armature winding. When both the armature and the field windings are excited by a DC supply, current flows through the windings and a magnetic flux proportional to the current is produced. When the flux from the field interacts with the flux from the armature, it results in motion of the rotor. Armature control is the most common control technique for DC motors. In order to implement this control, the stator flux must be kept constant. To achieve this, either the stator voltage is kept constant or the stator coils are replaced by a permanent magnet. In the latter case, the motor is said to be a permanent magnet DC motor and is driven by the armature coils only.
Equations for motor operation.
Equations governing the operation of motor are made linear by simplifying the effects of the magnetic field from the stator to only its flux, formula_1, and a term that describes the effect of the stator field on the rotor, formula_2. formula_2 is unlikely to be a constant and may be a function of formula_1:
formula_5 (1)
where formula_6 is motor torque and formula_7 is armature current. When field flux is constant, equation (1) becomes
formula_8 (2)
where formula_9 as formula_1 is constant.
In addition, the motor has an intrinsic negative feedback structure, hence at the steady state, the speed ω is proportional to the reference input Va.
These two facts, in addition to the cheaper price of a permanent magnet motor with respect to a standard DC motor (because only the rotor coils need to be wound), are the main reasons why armature controlled motors are widely used. However, several disadvantages arise from this control technique, of which major is the flow of large currents during transients. For example, when started speed ω is zero initially, hence back EMF (electromotive force) governed by the following relation, would be zero.
formula_11 (3)
Also, armature current is given by formula_12(4)
which will be very high causing increase in heating of machine and it may damage the insulation.
Equations for transfer function.
Essential Equations for transfer function:
formula_11 in Laplace domain formula_14(5)
formula_12 in Laplace domain formula_16 (6)
formula_5 in Laplace domain formula_18 (7)
formula_19 in Laplace domain formula_20 (8)
Various parameters in figure are described as
The transfer matrix of the system may be written as
formula_28 (9)
where formula_29 (10)
formula_30 (11)


Belur Industrial Area

Belur Industrial Area (Abbreviation : BIA) is an industrial area of the Dharwad city in India and it is one of the biggest industrial areas in Karnataka. lies on the Dharwad-Belgaum Highway. It houses small, medium, and large-scale industries. The industrial area is known for engineering, electrical goods such as: CNC Machine tools, GDC dies & moulds transformers, motors and generators, textile (silk), hydraulics, machine tool industries and Rubber moulding industries.


Moldflow

Moldflow is a producer of simulation software for high-end plastic injection molding computer-aided engineering. It is owned by Autodesk.
Autodesk stable release is Moldflow 2023.
Moldflow was founded in Melbourne, Australia as Moldflow Pty. Ltd. in 1978 by Colin Austin. In 2008 Moldflow was acquired by Autodesk for $297M.
Products.
Moldflow has two core products: Moldflow Adviser which provides manufacturability guidance and directional feedback for standard part and mold design, and Moldflow Insight which provides definitive results for flow, cooling, and warpage along with support for specialized molding processes. In addition, Autodesk produces Moldflow Design, Moldflow CAD Doctor, Moldflow synergy, Moldflow Magics STL Expert, and Moldflow Structural Alliance that serve as connectivity tools for other CAD and CAE software. They also have a free results viewer, Moldflow Communicator.


Geometric programming

A geometric program (GP) is an optimization problem of the form
where formula_2 are posynomials and formula_3 are monomials. In the context of geometric programming (unlike standard mathematics), a monomial is a function from formula_4 to formula_5 defined as
where formula_7 and formula_8. A posynomial is any sum of monomials.
Geometric programming is
closely related to convex optimization: any GP can be made convex by means of a change of variables. GPs have numerous applications, including component sizing in IC design, aircraft design, maximum likelihood estimation for logistic regression in statistics, and parameter tuning of positive linear systems in control theory.
Convex form.
Geometric programs are not in general convex optimization problems, but they can be transformed to convex problems by a change of variables and a transformation of the objective and constraint functions. In particular, after performing the change of variables formula_9 and taking the log of the objective and constraint functions, the functions formula_10, i.e., the posynomials, are transformed into log-sum-exp functions, which are convex, and the functions formula_11, i.e., the monomials, become affine. Hence, this transformation transforms every GP into an equivalent convex program. In fact, this log-log transformation can be used to convert a larger class of problems, known as log-log convex programming (LLCP), into an equivalent convex form.
Software.
Several software packages exist to assist with formulating and solving geometric programs.


TP model transformation in control theory

Baranyi and Yam proposed the TP model transformation as a new concept in quasi-LPV (qLPV) based control, which plays a central role in the highly desirable bridging between identification and polytopic systems theories. It is also used as a TS (Takagi-Sugeno) fuzzy model transformation. It is uniquely effective in manipulating the convex hull of polytopic forms (or TS fuzzy models), and, hence, has revealed and proved the fact that convex hull manipulation is a necessary and crucial step in achieving optimal solutions and decreasing conservativeness in modern linear matrix inequality based control theory. Thus, although it is a transformation in a mathematical sense, it has established a conceptually new direction in control theory and has laid the ground for further new approaches towards optimality.
For details please visit: TP model transformation.
A free MATLAB implementation of the TP model transformation can be downloaded at or an old version of the toolbox is available at MATLAB Central . Be careful, in the MATLAB toolbox the assignments of the dimensions of the core tensor is in the opposite way in contrast to the notation used in the related literature. In some variants of the ToolBox, the first two dimension of the core tensor is assigned to the vertex systems. In the TP model literature the last two. A simple example is given below.
Related definitions.
with input formula_2, output formula_3 and state
vector formula_4. The system matrix formula_5 is a parameter-varying object, where formula_6 is a time varying formula_7-dimensional parameter vector which is an element of
closed hypercube formula_8. As a matter of fact, further parameter dependent channels can be inserted to formula_9 that represent various control performance requirements.
formula_10 in the above LPV model can also include some elements of the state vector
formula_4, and, hence this model belongs to the class of non-linear systems, and is also referred to as a quasi LPV (qLPV) model.
with input formula_2, output formula_3 and state
vector formula_4. The system matrix formula_16 is a parameter-varying object, where formula_6 is a time varying formula_7-dimensional parameter vector which is an element of
closed hypercube formula_8, and the weighting functions formula_20 are the elements of vector formula_21. Core tensor contains elements formula_22 which are the vertexes of the system.
As a matter of fact, further parameter dependent channels can be inserted to formula_9 that represent various control performance requirements.
Here
This means that formula_26 is within the vertexes formula_22 of the system (within the convex hull defined by the vertexes) for all formula_28.
Note that the TP type polytopic model can always be given in the form
where the vertexes are the same as in the TP type polytopic form and the multi variable weighting functions are the product of the one variable weighting functions according to the TP type polytopic form, and r is the linear index equivalent of the multi-linear indexing formula_30.
Assume a given qLPV model formula_31, where formula_32, whose TP polytopic structure may be unknown (e.g. it is given by neural networks). The TP model transformation determines its TP polytopic structure as
namely it generates core tensor formula_34 and weighting functions of formula_35 for all formula_36. Its free MATLAB implementation is downloadable at or at MATLAB Central .
If the given model does not have (finite element) TP polytopic structure, then the TP model transformation determines its approximation:
where trade-off is offered by the TP model transformation between complexity (number of vertexes stored in the core tensor or the number of weighting functions) and the approximation accuracy. The TP model can be generated according to various constrains. Typical TP models generated by the TP model transformation are:
TP model based control design.
Since the TP type polytopic model is a subset of the polytopic model representations, the analysis and design methodologies developed for polytopic representations are applicable for the TP type polytopic models as well.
One typical way is to search the nonlinear controller in the form:
where the vertexes formula_39 of the controller is calculated from formula_40. Typically, the vertexes formula_40 are substituted into Linear Matrix Inequalities in order to determine formula_39.
In TP type polytopic form the controller is:
where the vertexes formula_44 stored in the core tensor formula_45 are determined from the vertexes formula_46 stored in formula_34. Note that the polytopic observer or other components can be generated in similar way, such as these vertexes are also generated from formula_48.
The polytopic representation of a given qLPV model is not invariant. I.e. a given formula_49 has formula_50 number of different representation as:
where formula_52. In order to generate an optimal control of the given model formula_49 we apply, for instance LMIs. Thus, if we apply the selected LMIs to the above polytopic model we arrive at:
Since the LMIs realize a non-linear mapping between the vertexes in formula_48 and formula_56 we may find very different controllers for each formula_52. This means that we have formula_58 different number of "optimal" controllers to the same system formula_49. Thus, the question is: which one of the "optimal" controllers is really the optimal one. The TP model transformation let us to manipulate the weighting functions systematically that is equivalent to the manipulation of the vertexes. The geometrical meaning of this manipulation is the manipulation of the convex hull defined by the vertexes. We can easily demonstrate the following facts:
of a given model formula_49, then we can generate a controller as
then we solved the control problem of all systems formula_63 that can be given by the same vertexes, but with different weighting functions as:
where
If one of these systems are very hardly controllable (or even uncontrollable) then we arrive at a very conservative solution (or unfeasible LMIs). Therefore, we expect that during tightening the convex hull we exclude such problematic systems.


IEC 61360

IEC 61360, with the title "Standard data element types with associated classification scheme", is a series of standard documents defining a general purpose vocabulary in terms of a reference dictionary published by the International Electrotechnical Commission.
Intended use.
The vocabulary specified in IEC 61360 may be used to define ontologies for use in the field of electrotechnology, electronics and related domains.
Structure.
The IEC 61360 series is structured into different parts:
IEC 61360-1 provides a detailed introduction to the structure of the dictionary and its use.
IEC 61360-2 specifies the detailed dictionary data model and IEC 61360-6 stipulates quality criteria for the content of the dictionary.
The data model defined in IEC 61360-2 is also published in ISO 13584-42.
The IEC provides a technical dictionary for the use in the electro-technical and electronic domain which is published as IEC 61360-4. This dictionary is called IEC Common Data Dictionary (IEC CDD) and can be accessed as a web page (https://cdd.iec.ch).
See also.
IEC 61360 also defines the base for other product taxonomies like eCl@ss.
Industrie 4.0 uses product property description based on IEC 61360.


Predictive state representation

In computer science, a predictive state representation (PSR) is a way to model a state of controlled dynamical system from a history of actions taken and resulting observations. PSR captures the state of a system as a vector of predictions for future tests (experiments) that can be done on the system. A test is a sequence of action-observation pairs and its prediction is the probability of the test's observation-sequence happening if the test's action-sequence were to be executed on the system. One of the advantage of using PSR is that the predictions are directly related to observable quantities. This is in contrast to other models of dynamical systems, such as partially observable Markov decision processes (POMDPs) where the state of the system is represented as a probability distribution over unobserved nominal states.


Small control property

For applied mathematics, in nonlinear control theory, a non-linear system of the form formula_1 is said to satisfy the small control property if for every formula_2 there exists a formula_3 so that for all formula_4 there exists a formula_5 so that the time derivative of the system's Lyapunov function is negative definite at that point.
In other words, even if the control input is arbitrarily small, a starting configuration close enough to the origin of the system can be found that is asymptotically stabilizable by such an input.


Smart Metrology

Smart Metrology is the modern approach to industrial metrology. The name was introduced by Jean-Michel Pou and Laurent Leblond, a French meteorologist and a French statistician. The term was coined in their book "La Smart Metrology: De la métrologie des instruments... à la métrologie des décisions". It was immediately adopted by Deltamu, a French company providing services in the field of industrial metrology, to promote its vision of metrology.
The modern approach promoted by Smart Metrology consists, mainly, in the full exploitation of all available data and information, including that provided by Big Data, to implement a correct, pertinent and efficient approach to the three pillars of metrology (uncertainty, calibration and traceability) in the industrial applications
The Smart Metrology approach.
The approach suggested by Smart Metrology is fully framed inside the ISO 9001 recommendations that any industry using a measuring instrument must keep them under control.
The traditional approach.
The traditional approach to industrial metrology tends to follow these steps:
So, the actual results of the calibration may not even be used in the decision-making process. This way, metrology is often regarded as a pure cost and is actually not following the ISO 9001 quality standards.
Smart metrology innovation.
Smart metrology follows a different approach to keeping the instruments under control. This new approach is aimed at achieving a higher efficiency according to the following steps:
According to the above steps, metrology does no longer represent an useless cost, afforded mainly to satisfy the standards. Instead, it can be regarded as an investment to enhance the quality of industrial production. It makes full use of the measurement results and makes use of measurement uncertainty in the decision-making process.


Mengchu Zhou

Mengchu Zhou (; born 31 October 1963) is a Chinese Distinguished Professor of electrical and computer engineering in the Helen and John C. Hartmann Dept. of Electrical and Computer Engineering at New Jersey Institute of Technology (NJIT) and at Macau University of Science and Technology. He is the Chairman of IKAS Industries of Shenzhen in China and a Board Member of OneSmart Education Group headquartered in China.
He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE), a Fellow of the International Federation of Automatic Control (IFAC), a Fellow of the American Association for the Advancement of Science (AAAS) and a Fellow of the Chinese Association of Automation (CAA). Zhou is the Founding Editor-in-Chief of the IEEE/Wiley Book Series on Systems Science and Engineering and the Editor-in-Chief of the IEEE/CAA Journal of Automatica Sinica. In 2015, he received the Norbert Wiener Award for "fundamental contributions to the area of Petri net theory and applications to discrete event systems," from the IEEE Systems, Man, and Cybernetics Society which also awarded him the Franklin V. Taylor Memorial Award for Best Paper award in 2010. In 2000, Zhou received the Humboldt Research Award for US Senior Scientists, Alexander von Humboldt Foundation, Germany. In 1994, he received the Society of Manufacturing Engineers, Computer-Integrated Manufacturing UNIVERSITY-LEAD Award (Leadership and Excellence in the Application and Development of integrated manufacturing). The number of his publications receiving 200 or more citations is 24 according to Google Scholar. He is one of the world's Highly Cited Researchers in Web of Science and has a total of more than 34,000 citations with an h- index of 89.
Education.
Zhou earned his Ph.D. in Computer & Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, 1990. He completed his M. S. in Automatic Control, Beijing Institute of Technology, Beijing, China, 1986 following the completion of his B. S. in Control Engineering, Nanjing University of Science & Technology, Nanjing, China, 1983.
Career.
In 2000, Zhou joined the faculty of New Jersey Institute of Technology where in 2013, Zhou became a Distinguished Professor at The Helen and John C. Hartmann Department of Electrical and Computer Engineering at the New Jersey Institute of Technology. There, he serves as researcher of Petri Nets and their applications, Director of the M.S. Program in Power and Energy Systems, Director of the M.S. Program in Computer Engineering, Director of Discrete Event Systems Laboratory, Director of CRRC-ZIC Laboratory for Rail System Network and Information Technologies, and Area Coordinator of Intelligent Systems. Previous to his career as professor, Zhou worked at Beijing Institute of Computer Applications, where he was an assistant engineer responsible for the development of CAD/CAM for vehicles.
Significant contributions.
Petri nets are a modeling tool playing the same role in event- driven systems as the differential/difference equations in continuous dynamic systems. As the size and complexity of automated systems increase, ad hoc methods lose their effectiveness, and a strong need arises for systematic methods of analysis and design. Zhou's work is about such methods - including their modeling, analysis, and synthesis of various automated systems.
In 1991, Zhou provided the theoretical basis for Petri net synthesis methods that model systems with shared resources. He formulated two new resource- sharing concepts: parallel mutual exclusion (PME) and sequential mutual exclusion (SME). PME models a resource shared by distinct independent processes. SME is a sequential composition of PMEs, modeling a resource shared by sequentially related processes. Zhou derived the conditions under which a net containing such structures will not have a total system shut down (deadlock). His approach enabled flexible design of systems that met constraints, and optimized performance. The synthesized models could be converted to supervisory controllers for automated systems. To simplify the optimal control design for any given automated system, his work invented the elementary and dependent siphons of Petri nets - important structural objects for characterizing deadlocks. He also invented several deadlock control methods for automated systems. Their use reduced the structural complexity of supervisory controllers - - they became linear with respect to system size. For certain systems, optimal controllers were developed with polynomially complex algorithms, thereby allowing for the first time, on- line deployment of optimal control methods. Thousands of researchers and engineers use his methods in various applications for automated system design, analysis, and control. Factories which use Zhou’s methods are thereby able to both prevent deadlock and simultaneously operate at maximum productivity - a rare combination in complex automated systems.
Zhou was among the pioneers of Petri net- based methods for semiconductor manufacturing, in particular, robotic cells called cluster tools, widely used in today’s semiconductor wafer fabrication plants. His survey- type papers popularized and greatly increased acceptance of Petri nets in system designs and applications (e.g., work published in IEEE Transactions on Industrial Electronics, IEEE Transactions on Semiconductor Manufacturing, IEEE Transactions on Automation Science and Engineering, and IEEE Robotics and Automation Magaz ine). Several of his patents have been licensed to dozens of industrial firms and put into industrial use, generating significant economic outcomes. Helping substantially improve the productivity of manufacturing semiconductor wafers and chips, this has a direct impact on lowering manufacturing costs and significantly increasing bottom line profitability in the semiconductor manufacturing industry.
Zhou has made contributions to the advancement of Petri net theory and their applications in automated systems. He has published over 400 papers in IEEE Transactions and Journals (majority being regular papers) and over 100 in other journals. He has authored/coathored 12 patents, 12 books, 29 book chapters and over 300 conference- proceeding papers. He is the world’s most cited researcher on Petri nets, and one of the overall leading researchers in automated manufacturing systems (Scopus). Web of Science ranked Zhou in 2012 as the number one most highly cited scholar in engineering worldwide and has listed him as a "highly cited scholar" in engineering since then. His recognition includes four Fellow designations - by IEEE for contributions to Petri nets and their applications; by AAAS for distinguished contributions to Petri nets, discrete event systems, and their applications to manufacturing, transportation, workflow, disassembly, web services, and software design; by the International Federation of Automatic Control (IFAC) for seminal contributions to the theory of Petri nets and their application in manufacturing, transportation, and web services; and by Chinese Association of Automation for contributions to the field of automation.


Robot welding

Robot welding is the use of mechanized programmable tools (robots), which completely automate a welding process by both performing the weld and handling the part. Processes such as gas metal arc welding, while often automated, are not necessarily equivalent to robot welding, since a human operator sometimes prepares the materials to be welded. Robot welding is commonly used for resistance spot welding and arc welding in high production applications, such as the automotive industry.
History.
Robot welding is a relatively new application of robotics, even though robots were first introduced into U.S. industry during the 1960s. The use of robots in welding did not take off until the 1980s, when the automotive industry began using robots extensively for spot welding. Since then, both the number of robots used in industry and the number of their applications has grown greatly. In 2005, more than 120,000 robots were in use in North American industry, about half of them for welding. Growth is primarily limited by high equipment costs, and the resulting restriction to high-production applications.
Robot arc welding has begun growing quickly just recently, and already it commands about 20 percent of industrial robot applications. The major components of arc welding robots are the manipulator or the mechanical unit and the controller, which acts as the robot's "brain". The manipulator is what makes the robot move, and the design of these systems can be categorized into several common types, such as SCARA and cartesian coordinate robot, which use different coordinate systems to direct the arms of the machine.
The robot may weld a pre-programmed position, be guided by machine vision, or by a combination of the two methods. However, the many benefits of robotic welding have proven to make it a technology that helps many original equipment manufacturers increase accuracy, repeat-ability, and throughput One welding robot can do the work of several human welders. For example, in arc welding, which produces hot sparks and smoke, a human welder can keep his torch on the work for roughly thirty percent of the time; for robots, the percentage is about 90.
The technology of signature image processing has been developed since the late 1990s for analyzing electrical data in real time collected from automated, robotic welding, thus enabling the optimization of welds.
Advantages.
Advantages of robot welding include:
Disadvantages.
Disadvantages of robot welding include:


Rate gyro

A rate gyro is a type of gyroscope, which rather than indicating direction, indicates the rate of change of angle with time. If a gyro has only one gimbal ring, with consequently only one plane of freedom, it can be adapted for use as a rate gyro to measure a rate of angular movement.
Rate gyros are used in rate integrating gyroscopes, and in attitude control systems for vehicles, and in combination with other sensors to make inertial navigation systems.
The advantage of rate gyros over other types of gyros is the fast response rate and their relatively low cost.
Principles.
Spinning.
The traditional type of rate gyro employs relatively conventional gyroscopes with viscous couplings to transfer the spin rate to allow it to be read.
Vibrating structure gyroscope.
MEMS gyros are cheap and have no moving parts. They often work by sonic resonance effects driven by piezoelectric transducers, that provide a signal when a rotation occurs.


Hobby injection molding

Hobby injection molding machines, also known as benchtop injectors, hold molds on a smaller scale. Benchtop injectors have become more common as inexpensive CNC milling machines have reduced the cost of producing molds in a home workshop.
In hobby injectors injection pressure is generated manually by the operator, with a lever or gear translating the operator's effort to the required pressure. The most common hobby injection machine uses a handle to press down with. This enables the user to generate roughly of downward force, through the use of leverage.
History.
It is not known when the first hobby injection molder was constructed. Before the development of inexpensive CNC milling machines, producing a metal mold was prohibitively expensive for most hobbyists. With a small CNC mill and personal CAD tools, though, even complex shapes can be cut easily and accurately.
Applications.
Hobby injection molding has a variety of applications including the creation of low cost prototypes, new inventions, replication of lost or broken parts, and provides homeowners the opportunity to build anything. Hobby injection molding is a low cost method of repeatable production.
Materials.
Polyethylene (both LDPE and HDPE), polypropylene, and polystyrene (including HIPS) have all been used successfully with lever-actuated benchtop injectors.
Equipment.
Benchtop injectors are smaller and simpler than their larger industrious counterparts because they rely on the operator to manually inject melted polymer into the mold and remove the finished part from the mold. Production injectors automatically inject melted polymer at a prescribed rate into the mold, cool the mold to rapidly solidify the polymer, then eject the part from the mold once it's cool. The two halves of the mold must be pressed together with great force to prevent a flash in the part where the two halves meet, and the nozzle of the injector must be pressed tightly against the inlet port of the mold to prevent the escape of melted polymer and a defect in the finished part. In a benchtop injector this is done manually by clamping or bolting the mold together and clamping the complete mold into the injector. In a production injector this is accomplished with hydraulic or pneumatic actuators, which increase the cost of the machine but dramatically reduce the labor required to produce a finished part.
Molds.
Metal molds.
Low cost benchtop CNC milling machines allow home enthusiasts to machine molds out of softer metals. Rather than P20 tool steel, most grades of aluminum can be machined into working molds capable of 1000 plus cycles. Mic 6 cast aluminum is more stable post machining and during cycles than hot extruded grades like 6061 and is easy to machine however it has worse mechanical properties. 7000 series like 7050 and 7075 are preferred for the best mechanical properties in aluminum, they are comparable to low to mid carbon steel molds. Copper alloys, like pewter, or bismuth alloy molds can be cast around a model to create strong molds with higher molding temperatures than epoxy molds. The casting around a model to create each mold part produces complex molds quickly. The parts can also capture detailed surface finishes.
Epoxy Molds.
Epoxy molds typically mix epoxy with a metal powder (generally aluminum) to form a mold. Atomized aluminum allows for the distribution of heat from the mold surface outward toward the edges. This typically preserves the surface quality for 50-100 cycles on a single epoxy mold.
Due to the nature of oxygen entrapment in epoxy during the pouring and curing period it is common to have distortions and cavitation in the final injection mold. Pressurizing the epoxy during the curing period is a form of surface quality retention. External pressures can be created with the use of a pressure pot connected to an air compressor to crush air trapped inside the epoxy mold during curing. As time passes over a 24-hour period the oxygen bubbles will not be able to escape and will cure directly inside the mold. With sufficient pressure these small cavities will be invisible to the naked eye.
Degassing the epoxy during the curing period can also be done using a vacuum chamber and will require a pressure of 100 kPa (29 inHg) in order to create near vacuum conditions. This can be achieved with the use of a 2-stage vacuum pump that is capable of 2 Pa (15 μmHg).
Single use molds.
Single use injection molds can be achieved through the use of plaster of Paris. The mold breaks down after the first shot and will rarely allow for the injection of a second shot.


IEEE Robotics and Automation Award

The IEEE Robotics and Automation Award is a Technical Field Award of the Institute of Electrical and Electronics Engineers (IEEE) that was established by the IEEE Board of Directors in 2002. This award is presented for contributions in the field of robotics and automation.
This award may be presented to an individual or team of up to three people.
Recipients of this award receive a bronze medal, certificate, and honorarium.


SOS-convexity

A multivariate polynomial is SOS-convex (or sum of squares convex) if its Hessian matrix H can be factored as H("x") = "S"T("x")"S"("x") where "S" is a matrix (possibly rectangular) which entries are polynomials in "x". In other words, the Hessian matrix is a SOS matrix polynomial.
An equivalent definition is that the form defined as "g"("x","y") = "y"TH("x")"y" is a sum of squares of forms.
Connection with convexity.
If a polynomial is SOS-convex, then it is also convex. Since establishing whether a polynomial is SOS-convex amounts to solving a semidefinite programming problem, SOS-convexity can be used as a proxy to establishing if a polynomial is convex. In contrast, deciding if a generic polynomial of degree large than four is convex is a NP-hard problem.
The first counterexample of a polynomial which is convex but not SOS-convex was constructed by Amir Ali Ahmadi and Pablo Parrilo in 2009. The polynomial is a homogeneous polynomial that is sum-of-squares and given by:
formula_1
In the same year, Grigoriy Blekherman proved in a non-constructive manner that there exist convex forms that is not representable as sum of squares. An explicit example of a convex form (with degree 4 and 272 variables) that is not a sum of squares was claimed by James Saunderson in 2021.
Connection with non-negativity and sum-of-squares.
In 2013 Amir Ali Ahmadi and Pablo Parrilo showed that every convex homogeneous polynomial in "n" variables and degree 2"d" is SOS-convex if and only if either (a) "n" = 2 or (b) 2"d" = 2 or (c) "n" = 3 and 2"d" = 4. Impressively, the same relation is valid for non-negative homogeneous polynomial in "n" variables and degree 2"d" that can be represented as sum of squares polynomials (See Hilbert's seventeenth problem).


Spindle (tool)

In machine tools, a spindle is a rotating axis of the machine, which often has a shaft at its heart. The shaft itself is called a spindle, but also, in shop-floor practice, the word often is used metonymically to refer to the entire rotary unit, including not only the shaft itself, but its bearings and anything attached to it (chuck, etc.). Spindles are electrically or pneumatically powered and come in various sizes. They are versatile in terms of material it can work with. Materials that spindles work with include embroidery, foam, glass, wood, and etc.
A machine tool may have several spindles, such as the headstock and tailstock spindles on a bench lathe. The main spindle is usually the biggest one. References to "the spindle" without further qualification imply the main spindle. Some machine tools that specialize in high-volume mass production have a group of 4, 6, or even more main spindles. These are called multispindle machines. For example, gang drills and many screw machines are multispindle machines. Although a bench lathe has more than one spindle (counting the tailstock), it is not called a multispindle machine; it has one main spindle.
Examples of spindles include
High speed spindle.
High speed spindles are used strictly in machines, like CNC mills, designed for metal work. There are two types of high speed spindles, each with different designs:
Belt-driven spindle.
Consisting of spindle and bearing shafts held within the spindle housing, the belt-driven spindle is powered by an external motor connected via a belt-pulley system.
Integral motor spindle.
A main component of this spindle is the motor, stored internally.
Both types, the belt-driven and the integral motor spindles, have advantages and disadvantages according to their design. Which one is more desirable depends on the purpose of the machine and product(s) being produced.
CNC machines used with spindles.
The type of CNC machine being used with your spindle will vary. Common CNC machines used are:
Being that there are a variety of CNC machines available, it is important to choose the right one that fits your specifities.


Drawing (manufacturing)

Drawing is a metalworking process that uses tensile forces to elongate metal, glass, or plastic. As the material is drawn (pulled), it stretches and becomes thinner, achieving a desired shape and thickness. Drawing is classified into two types: sheet metal drawing and wire, bar, and tube drawing. Sheet metal drawing is defined as a plastic deformation over a curved axis. For wire, bar, and tube drawing, the starting stock is drawn through a die to reduce its diameter and increase its length. Drawing is usually performed at room temperature, thus classified as a cold working process; however, drawing may also be performed at higher temperatures to hot work large wires, rods, or hollow tubes in order to reduce forces.
Drawing differs from rolling in that pressure is not applied by the turning action of a mill but instead depends on force applied locally near the area of compression. This means the maximal drawing force is limited by the tensile strength of the material, a fact particularly evident when drawing thin wires.
The starting point of cold drawing is hot-rolled stock of a suitable size.
Metal.
Successful drawing depends on the flow and stretch of the material. Steels, copper alloys, and aluminium alloys are commonly drawn metals.
In sheet metal drawing, as a die forms a shape from a flat sheet of metal (the "blank"), the material is forced to move and conform to the die. The flow of material is controlled through pressure applied to the blank and lubrication applied to the die or the blank. If the form moves too easily, wrinkles will occur in the part. To correct this, more pressure or less lubrication is applied to the blank to limit the flow of material and cause the material to stretch or set thin. If too much pressure is applied, the part will become too thin and break. Drawing metal requires finding the correct balance between wrinkles and breaking to achieve a successful part.
Sheet metal drawing becomes deep drawing when the workpiece is longer than its diameter. It is common that the workpiece is also processed using other forming processes, such as piercing, ironing, necking, rolling, and beading. In shallow drawing, the depth of drawing is less than the smallest dimension of the hole.
Bar, tube, and wire drawing all work upon the same principle: the starting stock is drawn through a die to reduce its diameter and increase its length. Usually, the die is mounted on a draw bench. The starting end of the workpiece is narrowed or pointed to get the end through the die. The end is then placed in grips which pull the rest of the workpiece through the die.
Drawing can also be used to cold form a shaped cross-section. Cold drawn cross-sections are more precise and have a better surface finish than hot extruded parts. Inexpensive materials can be used instead of expensive alloys for strength requirements, due to work hardening. Bars or rods that are drawn cannot be coiled; therefore, straight-pull draw benches are used. Chain drives are used to draw workpieces up to . Hydraulic cylinders are used for shorter length workpieces. The reduction in area is usually restricted to between 20% and 50%, because greater reductions would exceed the tensile strength of the material, depending on its ductility. To achieve a certain size or shape, multiple passes through progressively smaller dies and intermediate anneals may be required. Tube drawing is very similar to bar drawing, except the beginning stock is a tube. It is used to decrease the diameter, improve surface finish, and improve dimensional accuracy. A mandrel may or may not be used depending on the specific process used. A floating plug may also be inserted into the inside diameter of the tube to control the wall thickness. Wire drawing has long been used to produce flexible metal wire by drawing the material through a series of dies of decreasing size. These dies are manufactured from a number of materials, the most common being tungsten carbide and diamond.
The cold drawing process for steel bars and wire is as follows:
Glass.
Similar drawing processes are applied in glassblowing and in making glass and plastic optical fiber.
Plastics.
Plastic drawing, sometimes referred to as "cold drawing", is the same process as used on metal bars, applied to plastics. Plastic drawing is primarily used in manufacturing plastic fibers. The process was discovered by Julian W. Hill in 1930 while trying to make fibers from an early polyester.
It is performed after the material has been "spun" into filaments; by extruding the polymer melt through pores of a spinneret. During this process, the individual polymer chains tend to somewhat align because of viscous flow. These filaments still have an amorphous structure, so they are drawn to align the fibers further, thus increasing crystallinity, tensile strength, and stiffness. This is done on a draw twister machine. For nylon, the fiber is stretched to four times its spun length. The crystals formed during drawing are held together by hydrogen bonds between the amide hydrogens of one chain and the carbonyl oxygens of another chain. Polyethylene terephthalate (PET) sheet is drawn in two dimensions to make BoPET (biaxially-oriented polyethylene terephthalate) with improved mechanical properties.


Western Electric rules

The Western Electric rules are decision rules in statistical process control for detecting out-of-control or non-random conditions on control charts. Locations of the observations relative to the control chart control limits (typically at ±3 standard deviations) and centerline indicate whether the process in question should be investigated for assignable causes. The Western Electric rules were codified by a specially-appointed committee of the manufacturing division of the Western Electric Company and appeared in the first edition of a 1956 handbook, that became a standard text of the field. Their purpose was to ensure that line workers and engineers interpret control charts in a uniform way.
Motivation.
The rules attempt to distinguish unnatural patterns from natural patterns based on several criteria:
The absence of points near the centerline is identified as a mixture pattern.
The absence of points near the control limits is identified as a stratification pattern.
The presence of points outside the control limits is identified as an instability pattern.
Other unnatural patterns are categorized as systematic (autocorrelative), repetition, or trend patterns.
This classification divides the chart of observations into zones, measured in units of standard deviation (σ) between the centerline and control limits, as follows:
Zones A, B, and C are sometimes called the "three sigma zone", "two sigma zone", and "one sigma zone", respectively.
Zone rules.
An important aspect of the Western Electric rules are the zone rules, designed to detect process instability, and the presence of assignable causes.
Data sets of observations are appraised by four basic rules, that categorize the occurrence of data samples in a set of zones defined by multiples of the standard deviation.
These rules are evaluated for one side of the center line (one half of the control band) at a time (e.g., first the centerline to the upper control limit, then the centerline to the lower control limit).
Data satisfying any of these conditions as indicated by the control chart provide the justification for investigating the process to discover whether assignable causes are present and can be removed. Note that there is always a possibility of false positives: Assuming observations are normally distributed, one expects Rule 1 to be triggered by chance one out of every 370 observations on average. The false alarm rate rises to one out of every 91.75 observations when evaluating all four rules.
Asymmetric control limits.
The zone rules presented above apply to control charts with symmetric control limits. The handbook provides additional guidelines for control charts where the control limits are not symmetrical, as for R charts and p-charts.
For formula_1 and R charts (which plot the behavior of the subgroup range), the Handbook recommends using the zone rules above for subgroups of sufficient size (five or more). For small sample subgroups, the Handbook recommends:
For other control charts based on skewed distributions, the Handbook recommends:
Other unnatural patterns.
The handbook also identifies patterns that require consideration of both the upper and lower halves of the control chart together for identification:


Local tangent space alignment

Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned. It begins by computing the "k"-nearest neighbors of every point. It computes the tangent space at every point by computing the "d"-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by data samples, and thus can not be used for classification directly.


Energy-shaping control

Energy-shaping control for energy systems considers the plant and its controller as energy-transformation devices. The control strategy is formulated in terms of interconnection (in a power-preserving manner) in order to achieve a desired behavior.


Tidepool (company)

Tidepool is a nonprofit company founded in 2013 which makes open-source tools to help people better manage diabetes. The company works together with Medtronic to create an interoperable automated insulin pump system.


Trailer stability assist

Trailer Stability Assist (TSA), also known as Electronic Trailer Sway Control, is designed to control individual wheel slip to correct potential trailer swing before there is an accident. Although similar to Electronic Stability Control (ESC), TSA is programmed differently and is designed to detect yaw in the tow-vehicle and take specific corrective actions to eliminate trailer sway. Most ESC systems are not designed to detect such movement nor take the correct actions to control both trailer and tow-vehicle; so not all ESC equipped vehicles have TSA capabilities.
TSA systems detect when a trailer is starting to oscillate while under tow and corrects any dangerous trailer swing through a combination of either torque reduction and/or individual wheel braking to bring the trailer and tow-vehicle back under control. While towing heavy trailers, such as travel trailer, an unwanted wallow of the whole assembly may occur. Without the help of electronics, regaining stability requires focused attention by the driver.


Sparse matrix–vector multiplication

Sparse matrix–vector multiplication (SpMV) of the form is a widely used computational kernel existing in many scientific applications. The input matrix is sparse. The input vector and the output vector are dense. In the case of a repeated operation involving the same input matrix but possibly changing numerical values of its elements, can be preprocessed to reduce both the parallel and sequential run time of the SpMV kernel.


Bang–bang control

In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a furnace that is either completely on or completely off. Most common residential thermostats are bang–bang controllers. The Heaviside step function in its discrete form is an example of a bang–bang control signal. Due to the discontinuous control signal, systems that include bang–bang controllers are variable structure systems, and bang–bang controllers are thus variable structure controllers.
Bang–bang solutions in optimal control.
In optimal control problems, it is sometimes the case that a control is restricted to be between a lower and an upper bound. If the optimal control switches from one extreme to the other (i.e., is strictly never in between the bounds), then that control is referred to as a bang-bang solution.
Bang–bang controls frequently arise in minimum-time problems. For example, if it is desired for a car starting at rest to arrive at a certain position ahead of the car in the shortest possible time, the solution is to apply maximum acceleration until the unique "switching point", and then apply maximum braking to come to rest exactly at the desired position.
A familiar everyday example is bringing water to a boil in the shortest time, which is achieved by applying full heat, then turning it off when the water reaches a boil. A closed-loop household example is most thermostats, wherein the heating element or air conditioning compressor is either running or not, depending upon whether the measured temperature is above or below the setpoint.
Bang–bang solutions also arise when the Hamiltonian is linear in the control variable; application of Pontryagin's minimum or maximum principle will then lead to pushing the control to its upper or lower bound depending on the sign of the coefficient of "u" in the Hamiltonian.
In summary, bang–bang controls are actually "optimal" controls in some cases, although they are also often implemented because of simplicity or convenience.
Practical implications of bang-bang control.
Mathematically or within a computing context there may
be no problems, but the physical realization of bang-bang
control systems gives rise to several complications.
First, depending on the width of the hysteresis gap and inertia in the process, there will be an oscillating error signal around the desired set point value (e.g., temperature), often saw-tooth shaped. Room temperature may become uncomfortable just before the next switch 'ON' event. Alternatively, a narrow hysteresis gap will lead to frequent
on/off switching, which is often undesirable (e.g. an electrically ignited gas heater).
Second, the onset of the step function may entail, for example, a high electrical current and/or sudden heating and expansion of metal vessels, ultimately leading to metal fatigue or other wear-and-tear effects. Where possible, continuous control, such as in PID control will avoid problems caused by the brisk state transitions that are the consequence of bang-bang control.
Pulse-width modulation.
A PID controller can send pulse-width modulation control signals that reduce switching of motors, solenoids, etc. by setting "minimum ON times" and "minimum OFF times".


Giorgio Quazza Medal

The Giorgio Quazza Medal is an award given by the International Federation of Automatic Control (IFAC) to a distinguished control engineer, presented at each IFAC Triennial International World Congress. It was established in 1979, as a memorial to the late Giorgio Quazza, a leading Italian electrical and control engineer who served IFAC in many capacities in a most distinguished manner. The award is given for "outstanding lifetime contributions of a researcher and/or engineer to conceptual foundations in the field of systems and control."


Iron roughneck

An iron roughneck is a piece of hydraulic machinery used to "handle" (connect and disconnect) segments of pipe in a modern drilling rig. The segments can be manipulated as they are hoisted into and out of a borehole. This type of work was previously performed manually by workers using tongs, and was one of the most dangerous jobs in a drilling operation. However, with iron roughnecks and modern technology, much of this can be done remotely with minimal manual handling.
Automated roughnecks became common in deep-water drilling and were later adopted by onshore rigs.


Bending machine (manufacturing)

A bending machine is a forming machine tool (DIN 8586). Its purpose is to assemble a bend on a workpiece. A bend is manufactured by using a bending tool during a linear or rotating move.
The detailed classification can be done with the help of the kinematics.
CNC bending.
CNC bending machines are developed for high flexibility and low setup times. Those machines are able to bend single pieces as well as small batches with the same precision and efficiency as series-produced parts in an economical way.
Universal bending machines – modular construction.
Universal bending machines consists of a basic machine that can be adjusted with little effort and used for a variety of bends. A simple plug-in system supports quick and easy exchange of tools.
The basic machine consists of a CNC-operated side stop, a work bench, and software for programming and operating. Its modular construction offers an affordable entry into the bending technology, because after an initial investment the machine can be customized and extended later without any conversion. That means the basic machine delivers a bending stroke, and the tool determines the kind of bending.
Bending tools.
In the case of bending tools they are classified by the kind of generated bends. They can be constructed to adjust the bending angle by reference, stroke measurement or angle measurement.
CNC machines usually abstain from a reference part. They grant a high bending accuracy starting with the first work piece.
Standard bends.
All bends without an extraordinary geometry belong to standard bends. The distance between a bend and the material end is quite high providing an adequate bearing area. The same with one bend to the next.
Typical tools are a so-called bending former combined with a prisms with electronic angular measurement or an ordinary prism.
U-bending.
For U-bends where tight and narrow bends are necessary, the bending former is replaced by a bending mandrel. A bending mandrel has a narrow geometry.
Offset bending.
Offset bending tools are used to assemble two bends with a small distance between in one step.
Edgewise bending.
Edge bending tools are used if the bending axis is placed parallel to the tight side of the work piece. Tools for bending on edge may include electronic angular measurement allowing a high bending accuracy.
Torsion bending.
Torsion tools are able to rotate the workpiece on the longitudinal axis. Alternatives are complex assembly groups with standard bends.
Angular measurement and spring back compensation.
For producing single pieces as well as small batches with the same precision and efficiency as series-produced parts, a spring back compensation is helpful. A bending accuracy of +/- 0.2° starting
from the first work piece is achieved due to calculated spring back compensation and the use
of electronic tools.
Operating mode angular measurement.
Bending prisms with electronic angular measurement technology are equipped with two flattened bending bolds. That bold rotate while bending giving a signal to the angle measurement. The measuring accuracy is about 0.1º. The computer then calculates the required final stroke and spring back of every bend is compensated regardless of material type. A high angle accuracy of +/- 0.2º is achieved instantly with the first workpiece without adjustments. Compared to adjustment by reference, material waste amounts are decreased, because even inconsistencies within a single piece of material are automatically adjusted .
Operating mode stroke measurement.
Wherever bending prisms with electronic angular measurement are not suitable, a small distance between the bends might be a reason, bending prisms without electronic angle measurement are applied.
In that case the control unit can be switched from angular measurement to stroke measurement. This method allows the pre-selection of the stroke of the bending ram in mm and therefore the immersion depth of the punch into the prism. Setting accuracy is +/- 0.1 mm. A final stroke is usually not required. Further development of the stroke system enables the user to specify an angle from which the stroke is calculated by using stored stroke functions. Bending accuracy in that case is dependent on material properties such as thickness, hardness, etc. which may differ from one work piece to another.
Programming and principle of operation.
Programming is done on a PC equipped with dedicated software, which is part of the machine or connected to an external workstation. For generating a new program engineering data can be imported or pasted per mouse and keyboard. Through a graphic and menu-driven user interface previous CNC programming skills are not required. The software asks for all necessary values and checks all figures. Inputs can be corrected at any time and minimum distances are checked instantly to guard against improper inputs. The software automatically calculates the flat length of each part being bent and determines the exact position of the side stop. The part is shown on a screen.
Ideally each program is stored in one database, so it is easy to recover them by search and sort functions.
Networking with the whole production line.
A lot of organizational effort and interface management is saved, if the CNC bending machine is connected to the previous and subsequent process. For a connection to other machines and external workstations corporate interfaces have to be established.
Networking with a punching machine.
If a part is bended, in most cases a prior process was inserting holes to mount it in an assembly group.
Therefore, a punching machine is an option. Some programs enable the operator to program both step by one software tool.