Comparative Study of Nonlinear Modal Modeling Identification Techniques from Force Appropriation Experiments
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Pacini, Benjamin Robert↗
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Comparative Study of Nonlinear Modal Modeling Identification Techniques from Force Appropriation Experiments
Explore the source record for details and available documents.
Pacini, Benjamin Robert↗
Model Identification of Inverter Nonlinear Control Dynamics
To comprehensively predict in silico potential disruptive dynamic performance of converter-based generation and develop solutions, the application of electromagnetic transient programs is desirable. However, these accurate simulations highly depend on inverter models of actual field implementations, which are often unavailable because they are proprietary. To address this problem, we propose a time-domain model identification method that can be used to determine the control models of inverters in continuous time from multiple experimental studies. The focus is on identifying the dynamic representation of controls because they dominate the dynamic response of renewable assets. To illustrate the applicability of the technique, we consider a subclass of inverter controllers for autonomous grid applications that rely on nonlinear oscillators.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Sparse-identification-based model predictive control of nonlinear two-time-scale processes
Not Available
Abdullah, Fahim (ORCID:000000025094788X)↗
Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System
Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimization problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.
Lexicographic optimization↗
Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking
Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improve modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.
Blast furnace (BF)↗
Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *
Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs
In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.
creep-fatigue↗
gLaSDI: Parametric physics-informed greedy latent space dynamics identification
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.
97 MATHEMATICS AND COMPUTING↗
Sparsifying priors for Bayesian uncertainty quantification in model discovery
We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.
97 MATHEMATICS AND COMPUTING↗
Nonlinear elasticity and damping govern ultrafast dynamics in click beetles
Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge’s internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. Here, the tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.
59 BASIC BIOLOGICAL SCIENCES↗
Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System
Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Operable adaptive sparse identification of systems: Application to chemical processes
Not provided.
Engineering↗
Data-driven discovery of coordinates and governing equations
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.
97 MATHEMATICS AND COMPUTING↗
Automated identification of dominant physical processes
The identification of processes that locally and approximately dominate dynamical system behavior has enabled significant advances in understanding and modeling nonlinear differential dynamical systems. Conventional methods of dominant process identification involve piecemeal and ad hoc (non-rigorous, informal) scaling analyses to identify dominant balances of governing equation terms and to delineate the spatiotemporal boundaries (boundaries in space and/or time) of each dominant balance. For the first time, we present an objective global measure of the fit of dominant balances to observations, which is desirable for automation, and was previously undefined. Furthermore, we propose a formal definition of the dominant balance identification problem in the form of an optimization problem. Here, we show that the optimization can be performed by various machine learning algorithms, enabling the automatic identification of dominant balances. Our method is algorithm agnostic and it eliminates reliance upon expert knowledge to identify dominant balances which are not known beforehand.
42 ENGINEERING↗
Learning Physically Interpretable Atmospheric Models From Data With WSINDy
The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the weak-form sparse identification of nonlinear dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension.
58 GEOSCIENCES↗
Weak-Form Latent Space Dynamics Identification
This software showcases the enhanced capabilities of the Latent Space Dynamics Identification (LaSDI) algorithm through the application of the weak form, resulting in WLaSDI. WLaSDI first compresses the data, then projects it onto test functions, and subsequently learns the local latent space models. Notably, WLaSDI demonstrates significantly improved robustness to noise. Using weak-form equation learning techniques, WLaSDI achieves local latent space modeling. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form ensures robust and precise latent space recovery, enabling fast, robust, and accurate simulations. We demonstrate the efficacy of WLaSDI against LaSDI using several common benchmark examples, including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in 1D inviscid Burgers' simulations with up to 100% Gaussian white noise, WLaSDI maintains relative errors consistently below 6%, whereas LaSDI errors can exceed 10,000%. Similarly, in radial advection simulations, WLaSDI keeps relative errors below 16%, compared to potential errors of up to 10,000% with LaSDI. Additionally, WLaSDI achieves significant speedups, such as a 140X speedup in 1D Burgers' simulations compared to the corresponding full order model.
Choi, Youngsoo↗
Data-driven Identification and Prediction of Power System Dynamics Using Linear Operators
In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust approach for data-driven approximation of Koopman operator for the identification of nonlinear power system dynamics. The identified model is used for the prediction of state trajectories in the power system. The application of the framework is illustrated using an IEEE nine bus test system.
24 POWER TRANSMISSION AND DISTRIBUTION↗