code/t4_structural_dynamics.py

"""Validated AgentFEM pilot for structural dynamics and virtual sensing.

The pilot deliberately starts from a slender, clamped plane-stress cantilever:
its first bending frequency has an independent Euler--Bernoulli reference.  A
modal solve supplies the frequency scale and Rayleigh damping anchors, while
implicit Newmark trajectories retain full displacement, velocity and
acceleration fields plus five sparse displacement sensors.
"""

from __future__ import annotations

import argparse
import json
import math
from pathlib import Path
from time import perf_counter

import h5py
import numpy as np
from dolfinx import fem
from mpi4py import MPI
from petsc4py import PETSc

from agentfem import (
    amplitudes,
    constitutive,
    dynamics as dynamics_api,
    fields,
    mesh,
    models,
    operators,
    results,
    studies,
)
from agentfem.solvers import prepare_linear_problem


ROOT = Path(__file__).resolve().parents[1]
DEFAULT_CONFIG = ROOT / "configs" / "t4_structural_dynamics_pilot.json"


def load_config(path: Path = DEFAULT_CONFIG) -> dict:
    return json.loads(path.read_text(encoding="utf-8"))


def analytical_first_frequency(config: dict) -> float:
    geometry = config["geometry"]
    material = config["material"]
    beta_1 = 1.875104068711961
    length = float(geometry["length_m"])
    height = float(geometry["height_m"])
    return float(
        beta_1**2
        / (2.0 * math.pi)
        * math.sqrt(
            float(material["young_pa"])
            * height**2
            / (12.0 * float(material["density_kg_m3"]) * length**4)
        )
    )


def _base_model(config: dict, *, analysis: str, cells: tuple[int, int] | None = None):
    geometry = config["geometry"]
    material = config["material"]
    selected_cells = tuple(cells or geometry["cells"])
    if analysis == "modal":
        study = studies.modal_solid(dimension=2, assumption=geometry["assumption"])
    elif analysis == "transient":
        study = studies.dynamic_solid(
            dimension=2,
            assumption=geometry["assumption"],
            method=config["dynamics"]["method"],
        )
    else:
        raise ValueError(f"Unknown analysis {analysis!r}.")
    domain = mesh.rectangle(
        (0.0, 0.0),
        (float(geometry["length_m"]), float(geometry["height_m"])),
        selected_cells,
        comm=MPI.COMM_SELF,
        cell_type=geometry["cell_type"],
    )
    model = models.create(study=study, mesh=domain, name=f"t4_cantilever_{analysis}")
    displacement = model.field(
        fields.displacement(domain, degree=int(geometry["displacement_degree"]))
    )
    model.material(
        constitutive.isotropic_elastic(
            young=float(material["young_pa"]),
            poisson=float(material["poisson"]),
            density=float(material["density_kg_m3"]),
            name=material["name"],
        )
    )
    left = mesh.face(domain, axis="x", value=0.0, name="fixed_end", tag=1)
    right = mesh.face(
        domain,
        axis="x",
        value=float(geometry["length_m"]),
        name="loaded_end",
        tag=2,
    )
    model.clamp(displacement, on=left)
    return model, displacement, right


def solve_modes(config: dict, *, cells: tuple[int, int] | None = None, modes: int = 4):
    model, displacement, _ = _base_model(config, analysis="modal", cells=cells)
    result = model.step(target=displacement, modes=modes).solve_result()
    return result


def rayleigh_coefficients(frequencies_hz: np.ndarray, damping_ratio: float) -> tuple[float, float]:
    omega_1, omega_2 = 2.0 * math.pi * np.asarray(frequencies_hz[:2], dtype=float)
    system = np.array([[1.0 / omega_1, omega_1], [1.0 / omega_2, omega_2]])
    alpha, beta = np.linalg.solve(system, np.full(2, 2.0 * float(damping_ratio)))
    return float(alpha), float(beta)


def component_preserving_zero_bcs(model) -> list:
    """Create zero kinematic BCs without expanding component subspaces.

    AgentFEM 0.3.7 reconstructs acceleration constraints on the parent vector
    space, which expands each component BC to all vector components.  Keep this
    campaign-side compatibility shim until the core implementation preserves
    ``bc.function_space`` itself.
    """

    result = []
    for item in model.constraints:
        source_bcs = item.bcs if hasattr(item, "bcs") else [item.bc]
        for bc in source_bcs:
            zero = fem.Constant(model.mesh, PETSc.ScalarType(0.0))
            indices = bc.dof_indices()
            dofs = indices[0] if isinstance(indices, tuple) else indices
            result.append(fem.dirichletbc(zero, dofs, bc.function_space))
    return result


def excitation_amplitude(spec: dict, *, first_frequency_hz: float, duration: float, dt: float):
    kind = spec["kind"]
    name = spec["name"]
    if kind == "sine":
        return amplitudes.sine(
            amplitude=1.0,
            frequency=float(spec["frequency_factor"]) * first_frequency_hz,
            name=name,
        )
    times = np.arange(0.0, duration + 0.5 * dt, dt)
    if kind == "half_sine_pulse":
        pulse_duration = 0.5 / first_frequency_hz
        values = np.where(
            times <= pulse_duration,
            np.sin(math.pi * times / pulse_duration),
            0.0,
        )
    elif kind == "chirp":
        f0 = float(spec["start_frequency_factor"]) * first_frequency_hz
        f1 = float(spec["end_frequency_factor"]) * first_frequency_hz
        rate = (f1 - f0) / duration
        phase = 2.0 * math.pi * (f0 * times + 0.5 * rate * times**2)
        envelope = np.sin(math.pi * np.clip(times / duration, 0.0, 1.0)) ** 2
        values = envelope * np.sin(phase)
    else:
        raise ValueError(f"Unknown excitation kind {kind!r}.")
    return amplitudes.tabular(times, values, name=name, left=0.0, right=0.0)


def run_trajectory(
    config: dict,
    spec: dict,
    *,
    frequencies_hz: np.ndarray,
    output_dir: Path,
    dt: float | None = None,
    save_fields: bool = True,
) -> dict:
    dynamics = config["dynamics"]
    geometry = config["geometry"]
    selected_dt = float(dynamics["dt_s"] if dt is None else dt)
    duration = float(dynamics["duration_s"])
    steps = int(round(duration / selected_dt))
    model, displacement, right = _base_model(config, analysis="transient")
    amplitude = excitation_amplitude(
        spec,
        first_frequency_hz=float(frequencies_hz[0]),
        duration=duration,
        dt=selected_dt,
    )
    traction = float(dynamics["traction_amplitude_pa"])
    driven_load = model.traction(
        (0.0, -traction), on=right, amplitude=amplitude
    )
    stiffness = model.stiffness(displacement)
    mass = model.mass(displacement)
    force = model.external_force(displacement)
    # The spatial load shape is fixed and only its scalar amplitude changes.
    # Assemble that shape once; reassembling the full FE vector in every
    # accepted-step history callback is both unnecessary and very expensive.
    driven_load.scale.value = PETSc.ScalarType(1.0)
    unit_force_vector = operators.assemble_vector(force)
    driven_load.scale.value = PETSc.ScalarType(amplitude(0.0))
    alpha, beta = rayleigh_coefficients(
        frequencies_hz,
        float(dynamics["target_damping_ratio"]),
    )
    damping = operators.rayleigh_damping(
        mass,
        stiffness,
        mass_coefficient=alpha,
        stiffness_coefficient=beta,
    )
    compiled_damping = damping.assemble_matrix()
    sensor_history = tuple(
        results.probe_history(
            f"sensor_{index:02d}_uy",
            at=tuple(point),
            component=1,
            unit="m",
        )
        for index, point in enumerate(config["sensors"])
    )
    power_history = (
        results.history(
            "external_power_w_per_m",
            lambda accepted_step, time: float(
                np.real(
                    accepted_step.state.v.value.x.petsc_vec.dot(
                        unit_force_vector
                    )
                )
                * amplitude(time)
            ),
            unit="W/m",
        ),
        results.history(
            "damping_power_w_per_m",
            lambda accepted_step, time: operators.bilinear_form(
                compiled_damping,
                accepted_step.state.v,
                accepted_step.state.v,
            ),
            unit="W/m",
        ),
    )
    history = sensor_history + power_history
    output_dir.mkdir(parents=True, exist_ok=True)
    output = output_dir / f"{spec['name']}.xdmf" if save_fields else None
    step = model.step(
        target=displacement,
        M=mass,
        C=damping,
        K=stiffness,
        F=force,
        dt=selected_dt,
        steps=steps,
        save_every=int(dynamics["save_every"]),
        print_every=max(1, steps // 5),
        progress=False,
        name=f"newmark_{spec['name']}",
    )
    # Linear Newmark has a constant effective operator for this fixed-step,
    # time-invariant model. Reuse AgentFEM's public prepared-linear lifecycle;
    # only the right-hand side changes with predictors and load amplitude.
    original_problem = step.problem
    corrected_bcs = component_preserving_zero_bcs(model)
    step.problem = prepare_linear_problem(
        original_problem.bilinear_form,
        original_problem.linear_form,
        original_problem.solution,
        bcs=corrected_bcs,
        options=original_problem.solver_options,
    )
    # Preserve the inspection attribute expected by the transient summary.
    step.problem.solver_options = original_problem.solver_options
    started = perf_counter()
    result = step.solve_result(output=output, history=history)
    wall = perf_counter() - started
    time = np.asarray(result.histories[sensor_history[0].name].abscissa, dtype=float)
    sensors = np.column_stack(
        [
            np.asarray(result.histories[item.name].values, dtype=float)
            for item in sensor_history
        ]
    )
    force_scale = np.asarray([amplitude(item) for item in time], dtype=float)
    strain_energy = np.asarray(result.histories["strain_energy"].values)
    kinetic_energy = np.asarray(result.histories["kinetic_energy"].values)
    external_power = np.asarray(result.histories["external_power_w_per_m"].values)
    damping_power = np.asarray(result.histories["damping_power_w_per_m"].values)
    increments = np.diff(time)
    external_work = np.concatenate(
        ([0.0], np.cumsum(0.5 * increments * (external_power[:-1] + external_power[1:])))
    )
    damping_dissipation = np.concatenate(
        ([0.0], np.cumsum(0.5 * increments * (damping_power[:-1] + damping_power[1:])))
    )
    mechanical_energy = strain_energy + kinetic_energy
    energy_balance_residual = (
        mechanical_energy
        - mechanical_energy[0]
        + damping_dissipation
        - external_work
    )
    # Use one trajectory-level reference scale. A pointwise denominator is
    # nearly zero during the first load increments and can turn a negligible
    # absolute residual into a misleadingly large percentage.
    energy_reference_scale = max(
        float(np.max(np.abs(mechanical_energy - mechanical_energy[0]))),
        float(np.max(np.abs(damping_dissipation))),
        float(np.max(np.abs(external_work))),
        float(np.finfo(float).eps),
    )
    return {
        "name": spec["name"],
        "spec": spec,
        "dt_s": selected_dt,
        "steps": steps,
        "time_s": time,
        "force_scale": force_scale,
        "sensor_displacement_m": sensors,
        "strain_energy_j_per_m": strain_energy,
        "kinetic_energy_j_per_m": kinetic_energy,
        "external_power_w_per_m": external_power,
        "damping_power_w_per_m": damping_power,
        "external_work_j_per_m": external_work,
        "damping_dissipation_j_per_m": damping_dissipation,
        "energy_balance_residual_j_per_m": energy_balance_residual,
        "energy_balance_reference_j_per_m": energy_reference_scale,
        "energy_balance_relative_residual": (
            energy_balance_residual / energy_reference_scale
        ),
        "rayleigh_mass_coefficient_per_s": alpha,
        "rayleigh_stiffness_coefficient_s": beta,
        "wall_time_s": wall,
        "field_hdf5": (
            None
            if not save_fields
            else str(Path(result.artifacts["fields_hdf5"]).resolve())
        ),
        "field_xdmf": (
            None
            if not save_fields
            else str(Path(result.artifacts["fields_xdmf"]).resolve())
        ),
        "dof_count": int(step.state.u.value.x.array.size),
        "kinematic_bc_scalar_dof_count": int(
            sum(bc.dof_indices()[1] for bc in corrected_bcs)
        ),
        "final_displacement_norm": float(np.linalg.norm(step.state.u.value.x.array)),
        "final_velocity_norm": float(np.linalg.norm(step.state.v.value.x.array)),
        "final_acceleration_norm": float(np.linalg.norm(step.state.a.value.x.array)),
        "geometry": geometry,
    }


def read_field_history(path: str | Path) -> dict[str, np.ndarray]:
    """Read AgentFEM's scientific HDF5 field history into dense arrays."""

    with h5py.File(path, "r") as h5:
        frame_names = sorted(h5["Frames"])
        return {
            "time_s": np.asarray(
                [h5[f"Frames/{name}"].attrs["coordinate"] for name in frame_names],
                dtype=float,
            ),
            "reference_geometry_m": np.asarray(h5["Mesh/ReferenceGeometry"]),
            "topology": np.asarray(h5["Mesh/Topology"]),
            "displacement_m": np.stack(
                [np.asarray(h5[f"Frames/{name}/Point/U"]) for name in frame_names]
            ),
            "velocity_m_per_s": np.stack(
                [
                    np.asarray(h5[f"Frames/{name}/Point/Velocity"])
                    for name in frame_names
                ]
            ),
            "acceleration_m_per_s2": np.stack(
                [
                    np.asarray(h5[f"Frames/{name}/Point/Acceleration"])
                    for name in frame_names
                ]
            ),
        }


def write_pilot_hdf5(path: Path, config: dict, modal: dict, trajectories: list[dict]) -> None:
    path.parent.mkdir(parents=True, exist_ok=True)
    with h5py.File(path, "w") as h5:
        h5.attrs["schema"] = "agentfem.physics-data.structural-dynamics-pilot"
        h5.attrs["schema_version"] = "0.1.0"
        h5.attrs["trajectory_count"] = len(trajectories)
        h5.attrs["config_json"] = json.dumps(config, sort_keys=True)
        modal_group = h5.create_group("modal")
        for key, value in modal.items():
            modal_group.create_dataset(key, data=np.asarray(value))
        root = h5.create_group("trajectories")
        common_written = False
        for trajectory in trajectories:
            group = root.create_group(trajectory["name"])
            group.attrs["spec_json"] = json.dumps(trajectory["spec"], sort_keys=True)
            for key in (
                "dt_s",
                "steps",
                "rayleigh_mass_coefficient_per_s",
                "rayleigh_stiffness_coefficient_s",
                "wall_time_s",
                "dof_count",
                "final_displacement_norm",
                "final_velocity_norm",
                "final_acceleration_norm",
                "energy_balance_reference_j_per_m",
            ):
                group.attrs[key] = trajectory[key]
            for key in (
                "time_s",
                "force_scale",
                "sensor_displacement_m",
                "strain_energy_j_per_m",
                "kinetic_energy_j_per_m",
                "external_power_w_per_m",
                "damping_power_w_per_m",
                "external_work_j_per_m",
                "damping_dissipation_j_per_m",
                "energy_balance_residual_j_per_m",
                "energy_balance_relative_residual",
            ):
                group.create_dataset(key, data=trajectory[key], compression="gzip")
            for key in ("field_hdf5", "field_xdmf"):
                if trajectory[key] is not None:
                    group.attrs[key] = trajectory[key]
            if trajectory["field_hdf5"] is not None:
                fields_data = read_field_history(trajectory["field_hdf5"])
                if not common_written:
                    common = h5.create_group("common")
                    common.create_dataset(
                        "reference_geometry_m",
                        data=fields_data["reference_geometry_m"],
                    )
                    common.create_dataset("topology", data=fields_data["topology"])
                    common.create_dataset(
                        "sensor_coordinates_m",
                        data=np.asarray(config["sensors"], dtype=float),
                    )
                    common_written = True
                field_group = group.create_group("fields")
                for key in (
                    "time_s",
                    "displacement_m",
                    "velocity_m_per_s",
                    "acceleration_m_per_s2",
                ):
                    field_group.create_dataset(
                        key,
                        data=fields_data[key],
                        compression="gzip",
                        shuffle=True,
                    )


def make_preview(
    path: Path,
    config: dict,
    modal_array: np.ndarray,
    trajectories: list[dict],
) -> None:
    import matplotlib.pyplot as plt

    figure, axes = plt.subplots(2, 2, figsize=(12.5, 8.0), constrained_layout=True)
    cells = np.asarray(config["verification"]["modal_meshes"], dtype=float)[:, 0]
    axes[0, 0].plot(cells, modal_array[:, 0], "o-", label="AgentFEM Q2")
    axes[0, 0].axhline(
        analytical_first_frequency(config),
        color="black",
        linestyle="--",
        label="Euler--Bernoulli",
    )
    axes[0, 0].set(
        xlabel="longitudinal cells",
        ylabel="first frequency (Hz)",
        title="Modal verification",
    )
    axes[0, 0].legend(frameon=False)

    for trajectory in trajectories:
        axes[0, 1].plot(
            trajectory["time_s"],
            trajectory["force_scale"],
            label=trajectory["name"].replace("_", " "),
        )
    axes[0, 1].set(
        xlabel="time (s)",
        ylabel="normalized load",
        title="Four excitation histories",
    )
    axes[0, 1].legend(frameon=False, fontsize=8)

    for trajectory in trajectories:
        axes[1, 0].plot(
            trajectory["time_s"],
            1.0e3 * trajectory["sensor_displacement_m"][:, -1],
            label=trajectory["name"].replace("_", " "),
        )
    axes[1, 0].set(
        xlabel="time (s)",
        ylabel="tip displacement (mm)",
        title="Virtual tip sensor",
    )

    selected = trajectories[0]
    field = read_field_history(selected["field_hdf5"])
    magnitudes = np.linalg.norm(field["displacement_m"][:, :, :2], axis=2)
    frame = int(np.argmax(np.max(magnitudes, axis=1)))
    coordinates = field["reference_geometry_m"]
    color = field["displacement_m"][frame, :, 1]
    scatter = axes[1, 1].scatter(
        coordinates[:, 0],
        coordinates[:, 1],
        c=color,
        s=26,
        cmap="coolwarm",
    )
    axes[1, 1].set_aspect("equal")
    axes[1, 1].set(
        title=f"Full-field vertical displacement, t={field['time_s'][frame]:.4f} s",
        xlabel="x (m)",
        ylabel="y (m)",
    )
    figure.colorbar(scatter, ax=axes[1, 1], label="vertical displacement (m)")
    figure.suptitle(
        "AgentFEM T4 structural dynamics and virtual sensing pilot",
        fontsize=15,
    )
    figure.savefig(path, dpi=180)
    plt.close(figure)


def run_pilot(config_path: Path, *, smoke: bool = False) -> dict:
    config = load_config(config_path)
    output_dir = ROOT / "data" / "t4_structural_dynamics_pilot"
    fields_dir = output_dir / "fields"
    modal_meshes = [tuple(item) for item in config["verification"]["modal_meshes"]]
    modal_frequencies = []
    for cells in modal_meshes:
        result = solve_modes(config, cells=cells, modes=4)
        modal_frequencies.append(np.asarray(result.quantity("frequencies"), dtype=float))
    selected_frequencies = modal_frequencies[1]
    specs = config["excitations"][:1] if smoke else config["excitations"]
    trajectories = [
        run_trajectory(
            config,
            spec,
            frequencies_hz=selected_frequencies,
            output_dir=fields_dir,
        )
        for spec in specs
    ]
    time_refinement_relative_l2 = None
    dominant_frequency_hz = None
    damping_estimate = None
    if not smoke:
        coarse = trajectories[0]
        fine_dt = float(config["verification"]["time_refinement_dt_s"][-1])
        fine = run_trajectory(
            config,
            config["excitations"][0],
            frequencies_hz=selected_frequencies,
            output_dir=fields_dir,
            dt=fine_dt,
            save_fields=False,
        )
        fine_on_coarse = np.column_stack(
            [
                np.interp(
                    coarse["time_s"],
                    fine["time_s"],
                    fine["sensor_displacement_m"][:, index],
                )
                for index in range(fine["sensor_displacement_m"].shape[1])
            ]
        )
        time_refinement_relative_l2 = float(
            np.linalg.norm(coarse["sensor_displacement_m"] - fine_on_coarse)
            / max(np.linalg.norm(fine_on_coarse), np.finfo(float).eps)
        )
        tip = coarse["sensor_displacement_m"][:, -1]
        spectrum = dynamics_api.spectrum(coarse["time_s"], tip, window="hann")
        dominant_frequency_hz = float(spectrum.dominant_frequency)
        pulse_duration = 0.5 / float(selected_frequencies[0])
        free_tip = tip[coarse["time_s"] >= pulse_duration]
        if free_tip.size >= 8:
            try:
                damping_estimate = float(
                    dynamics_api.damping_from_free_decay(free_tip).damping_ratio
                )
            except ValueError:
                damping_estimate = None
    analytical = analytical_first_frequency(config)
    modal_array = np.vstack(modal_frequencies)
    quality = {
        "analytical_first_frequency_hz": analytical,
        "modal_cells": modal_meshes,
        "modal_frequencies_hz": modal_array.tolist(),
        "finest_first_frequency_relative_error": float(
            abs(modal_array[-1, 0] - analytical) / analytical
        ),
        "last_modal_mesh_relative_change": float(
            abs(modal_array[-1, 0] - modal_array[-2, 0]) / modal_array[-1, 0]
        ),
        "trajectory_count": len(trajectories),
        "all_finite": bool(
            all(
                np.all(np.isfinite(item["sensor_displacement_m"]))
                and np.all(np.isfinite(item["force_scale"]))
                and np.all(np.isfinite(item["energy_balance_relative_residual"]))
                for item in trajectories
            )
        ),
        "maximum_energy_balance_relative_residual": float(
            max(
                np.max(np.abs(item["energy_balance_relative_residual"]))
                for item in trajectories
            )
        ),
        "trajectory_energy_balance_relative_residual": {
            item["name"]: float(
                np.max(np.abs(item["energy_balance_relative_residual"]))
            )
            for item in trajectories
        },
        "time_refinement_tip_history_relative_l2": time_refinement_relative_l2,
        "pulse_tip_dominant_frequency_hz": dominant_frequency_hz,
        "pulse_free_decay_damping_ratio_estimate": damping_estimate,
        "target_damping_ratio": float(config["dynamics"]["target_damping_ratio"]),
    }
    gates = {
        "analytical_frequency": quality["finest_first_frequency_relative_error"]
        <= float(
            config["verification"][
                "maximum_first_frequency_analytical_relative_error"
            ]
        ),
        "modal_mesh": quality["last_modal_mesh_relative_change"]
        <= float(config["verification"]["maximum_modal_mesh_relative_change"]),
        "time_refinement": smoke
        or quality["time_refinement_tip_history_relative_l2"]
        <= float(
            config["verification"]["maximum_tip_history_relative_l2_change"]
        ),
        "finite": quality["all_finite"],
        "energy_balance": quality["maximum_energy_balance_relative_residual"]
        <= float(
            config["verification"]["maximum_energy_balance_relative_residual"]
        ),
    }
    quality["gates"] = gates
    quality["passed"] = bool(all(gates.values()))
    output_dir.mkdir(parents=True, exist_ok=True)
    (output_dir / "quality.json").write_text(
        json.dumps(quality, indent=2, ensure_ascii=False), encoding="utf-8"
    )
    modal = {
        "cells": np.asarray(modal_meshes, dtype=int),
        "frequencies_hz": modal_array,
        "analytical_first_frequency_hz": np.asarray([analytical]),
    }
    write_pilot_hdf5(output_dir / "pilot.h5", config, modal, trajectories)
    if not smoke:
        make_preview(output_dir / "preview.png", config, modal_array, trajectories)
    return quality


def main() -> None:
    parser = argparse.ArgumentParser()
    parser.add_argument("--config", type=Path, default=DEFAULT_CONFIG)
    parser.add_argument("--smoke", action="store_true")
    args = parser.parse_args()
    quality = run_pilot(args.config, smoke=args.smoke)
    if MPI.COMM_WORLD.rank == 0:
        print(json.dumps(quality, indent=2, ensure_ascii=False))


if __name__ == "__main__":
    main()