Model Identification Algorithm Research Articles

Model reduction of dynamical systems with a novel data-driven approach: The RC-HAVOK algorithm.

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC-HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size of the linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-like systems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function, and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven model identification algorithms, particularly when applied to commonly used Lorenz time series data.

Koopman operator-based multi-model for predictive control

AbstractThis work describes a new model structure developed for prediction in Model Predictive Control (MPC). The model has a multi-model structure in which independent sub-models are employed for the consecutive sampling instants. The model lifts process states into a high-dimensional space in which a linear process description is applied. Depending on the influence of the manipulated variables on lifted states, three general model versions are described and model identification algorithms are derived. As a result of the multi-model structure, model parameters are found analytically from computationally uncomplicated least squares problems using the Extended Dynamic Mode Decomposition algorithm, but the evolution of states over the horizon used in MPC is taken into account. Next, the MPC algorithm for the described model is derived. It requires solving online simple quadratic optimisation tasks. The effectiveness of three considered model configurations and three versions of the lifting functions is examined for a nonlinear DC motor benchmark. Their impact on model accuracy, complexity, possible control accuracy and MPC calculation time is thoroughly discussed. Finally, a more complex polymerisation reactor process is considered to showcase the practical applicability of the presented approach to modelling and MPC.

Parameter identification algorithm for ship manoeuvrability and wave peak model based multi-innovation stochastic gradient algorithm use data filtering technique

This paper addresses the issue of identifying ship motion parameters and wave peak frequency. Utilising the Euler discretisation principle, we establish a discrete-time auto-regressive moving average model with exogenous input (ARMAX) for the ship-wave system. Furthermore, we develop a filtering-based stochastic gradient algorithm for the system by applying filtering techniques and auxiliary model identification idea. A filtering-based multi-innovation stochastic gradient algorithm, utilizing the multi-innovation identification theory, was developed to enhance the convergence rate and accuracy of parameter identification. This approach was found to be more effective than the filtering-based stochastic gradient algorithm. Simulation results validate the efficacy of the proposed algorithm in parameter identification.

Young Duality for Variational Inequalities and Nonparametric Method of Demand Analysis in Input–Output Models with Inputs Substitution: Application for Kazakhstan Economy

The global macroeconomic shocks of the last decade entail the restructuring of national production networks and induce processes of input substitution. We suggest mathematical tools of Young duality for variational inequalities for studying these processes. Based on the tools we provide, a new mathematical model of a production network with several final consumers is created. The model is formulated as a pair of conjugated problems: a complementarity problem for optimal resource allocation with neoclassical production functions and the Young dual problem for equilibrium price indices on network products. The solution of these problems gives an equilibrium point in the space of network inter-industry flows and price indices on goods. Based on our previous results, we suggest an algorithm for model identification with an official economic statistic in the case of constant elasticity of substitution production functions. We give an explicit solution to the complementarity problems in this case and develop the algorithm of the inter-industry flows scenario projection. Since the algorithm needs the scenario projection of final sales structure as its input, we suggest a modified methodology that allows the calculation of scenario shifts in final consumer spending. To do this, we employ the generalized nonparametric method of demand analysis. As a result, we develop new technology for scenario calculation of a national input–output table, including shifts in final consumer spending. The technology takes into account a substitution of inputs in the network and is based on officially published national statistics data. The application of the methodology to study tax collection scenarios for Kazakhstan’s production network is demonstrated.

Friction modelling and the use of a physics-informed neural network for estimating frictional torque characteristics

This paper presents an exploration of friction modeling encompassing theoretical and practical aspects, utilizing a planar or 2D contact system. Various white-box friction models, including static and dynamic variants, are introduced, highlighting the superior capability of dynamic models in comprehensively capturing friction effects, substantiated through numerical simulation. Practical aspects of friction measurement and data-driven friction modeling are elucidated. The discourse extends to the development of grey-box and black-box friction models. A significant contribution lies in the proposition of a physics-informed neural network-based friction modeling approach, presenting it as an advanced and preferable alternative for friction estimation. To exemplify its efficacy, a case study of a torsion-based frictional contact scenario, employing Physics-Informed Neural Network (PINN) and the Nelder–Mead (N–M) algorithm for concurrent dynamics and friction model identification, was examined. Experimental data from a double torsion pendulum system, characterized by discontinuous dynamics, is employed for training. Results demonstrate the PINN’s superiority, providing more accurate representation of stick–slip phases at the contact zone and exhibiting faster performance compared to the N–M algorithm. The paper concludes by deliberating on challenges, prospects, and future directions in friction modeling.

Parameter identification algorithm for dynamic modeling of industrial-scale vanadium redox flow batteries

In this work, we propose a two-stage parameter identification algorithm for the zero-dimensional model of vanadium redox flow battery (VRFB) based on the fitting of the available experimental data. Specifically, in the first stage, the parameters of overpotentials are obtained from the discharge polarization curve at the state of charge of 50%. In the second stage, the parameters of capacity loss and crossover are identified by the minimization of square error between the predicted and experimental charge-discharge curves at a certain value of load current. The algorithm allows to assess the degree of degradation of the battery components, and capture the effects associated with crossover and mass transfer limitations at high load currents and low flow rates. We verify this algorithm with a reference simulation considering the most interesting practical cases of battery use and validate it with three experimental VRFB systems with power and capacity ratings in the range of 5–10 kW and 5–100 kWh, correspondingly. The results show a good agreement with experimental data having an average error value of less than 1%. The results of the study are an important step in further developments of advanced control algorithms for large-scale energy storage systems.

Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered.

Linear Time-Invariant Model Identification Algorithm for Mechatronic Systems Based on MIMO Frequency Response Data

This article describes a new frequency- domain multi-input multioutput linear time-invariant (LTI) system identification algorithm for accurate model construction suitable for motion control systems. The proposed method can capture the effects of time-delay, lightly damped poles (structural resonances), as well as highly damped complex or real poles, and direct or derivative-like terms. The effectiveness of the algorithm has been validated using experimental frequency response measurements obtained from different types of motion control mechanisms. The proposed algorithm has also been compared with “ <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tfest</monospace> ” and “ <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modalfit</monospace> ” functions in MATLAB. Over these methods, nearly two orders of magnitude improvement is observed in the closeness of the model prediction, in terms of root mean square of the frequencywise modeling error.

A real-time unmeasured dynamic response prediction for nuclear facility pressure pipeline system

A real-time unmeasured dynamic response prediction process for the nuclear power plant pressure pipeline is proposed and its performance is tested in the test-loop system (KAERI). The aim of the process is to predict unmeasurable or unreachable dynamic responses such as acceleration, velocity, and displacement by using a limited amount of directly measured physical responses. It is achieved by combining a well-constructed finite element model and robust inverse force identification algorithm. The pressure pipeline system is described by using the displacement-pressure vibro-acoustic formulation to consider fully filled liquid effect inside the pipeline structure. A robust multiphysics modal projection technique is employed for the real-time sensor synchronized prediction. The inverse force identification method is also derived and employed by using Bathe's time integration method to identify the full-field responses of the target system from the modal domain computation. To validate the performance of the proposed process, an experimental test is extensively performed on the nuclear power plant pressure pipeline test-loop under operation conditions. The results show that the proposed identification process could well estimate the unmeasured acceleration in both frequency and time domain faster than 32,768 samples per sec.

A regularised fast recursive algorithm for fraction model identification of nonlinear dynamic systems

The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown model parameters. This is achieved first by transforming the fraction form to a linear combination of nonlinear model terms. Then the terms in the denominator are used to form a regularisation term in the cost function to offset the bias induced by the linear transformation. According to the structural risk minimisation principle based on the new cost function, the model terms are selected based on their contributions to the cost function and the coefficients are then identified recursively without explicitly solving the inverse matrix. The proposed method is proved to have low computational complexity. Simulation results confirm the efficacy of the method in fast identification of the true fraction models for the targeted nonlinear systems.

Data-Driven Model Identification and Control of the Inertial Systems

In the synthesis of the control algorithm for complex systems, we are often faced with imprecise or unknown mathematical models of the dynamical systems, or even with problems in finding a mathematical model of the system in the open loop. To tackle these difficulties, an approach of data-driven model identification and control algorithm design based on the maximum stability degree criterion is proposed in this paper. The data-driven model identification procedure supposes the finding of the mathematical model of the system based on the undamped transient response of the closed-loop system. The system is approximated with the inertial model, where the coefficients are calculated based on the values of the critical transfer coefficient, oscillation amplitude and period of the underdamped response of the closed-loop system. The data driven control design supposes that the tuning parameters of the controller are calculated based on the parameters obtained from the previous step of system identification and there are presented the expressions for the calculation of the tuning parameters. The obtained results of data-driven model identification and algorithm for synthesis the controller were verified by computer simulation.

Online Tracking of Maneuvering Target Trajectory Based on Chaotic Time Series Prediction.

Online prediction of maneuvering target trajectory is one of the most popular research directions at present. Specifically, the primary factors balancing, between prediction accuracy and response time, will give the research substance. This paper presents an online trajectory prediction algorithm based on small sample chaotic time series (OTP-SSCT). First, we optimize in terms of data breadth. The dynamic split window is built according to the motion characteristics of the maneuvering target, thus realizing trajectory segmentation and constructing a small sample chaotic time series prediction set. Second, since fully considering the motion patterns of maneuvering targets, we introduce the spatiotemporal features into the particle swarm optimization (PSO) model identification algorithm, which improves the identification sensitivity of key trajectory data points. Furthermore, we propose a feedback optimization strategy of residual compensation to correct the trajectory prediction values to improve the prediction accuracy. For the initial value sensitivity problem of the PSO model identification algorithm, we propose a new initial population strategy, which improves the effectiveness of initial parameters on model identification. Through simulation experiment analysis, it is verified that the proposed OTP-SSCT algorithm achieves better prediction accuracy and faster response time.

Multi-spectral radiation thermometry based on an Alpha spectrum-LM algorithm under the background of high temperature and intense reflection.

In order to meet the needs of multi-spectral radiation temperature measurement under high temperature background, this paper studies the problems of reflected radiation interference and spectral emissivity difficult to obtain in high temperature and intense reflection environment. First, using discrete triangular surface elements and radiation angle coefficients, an analysis model of high temperature background reflected radiation is constructed to describe the variation characteristics of high temperature background reflected radiation. Secondly, the least squares support vector machine (LSSVM) is optimized by particle swarm optimization (PSO) algorithm, and an emissivity model identification algorithm based on Alpha spectrum-Levenberg Marquarelt (LM) algorithm is proposed, which has stronger applicability and accuracy than existing emissivity model identification methods. Finally, the high temperature background radiation and the emissivity model are combined to construct and solve the multi-spectral target equation, so as to realize the reflected radiation error correction and radiation temperature measurement under the high temperature and intense reflection background. The simulation and experimental comparison with the existing methods show that the temperature measurement error of the radiation temperature measurement method proposed in this paper is below 9.5K, which can effectively correct the reflected radiation error and further improve the temperature measurement accuracy.

Analyzing Efficacy and Safety of Anti-Fungal Blue Light Therapy via Kernel-Based Modeling the Reactive Oxygen Species Induced by Light.

The goal of this study is to investigate the efficacy, safety, and mechanism of ABL for inactivating Candida albicans (C. albicans), and to determine the best wavelength for treating candida infected disease, by experimental measurements and dynamic modeling. The changes in reactive oxygen species (ROS) in C. albicans and human host cells under the irradiation of 385, 405, and 415 nm wavelengths light with irradiance of 50 mW/cm2 were measured. Moreover, a kernel-based nonlinear dynamic model, i.e., nonlinear autoregressive with exogenous inputs (NARX), was developed and applied to predict the concentration of light-induced ROS, whose kernels were selected by a newly developed algorithm based on particle swarm optimization (PSO). The ROS concentration was increased respectively about 10-12 times in C. albicans and about 3-6 times in human epithelial cells by the ABL treatment with the same fluence of 90 J/cm2. The NARX models were respectively fitted to the data from the experiments on both types of cells. Besides, four different kernel functions, including Gaussian, Laplace, linear and polynomial kernels, were compared in their fitting accuracies. The errors with the Laplace kernel turned out to be only 0.2704 and 0.0593, as respectively fitted to the experimental data of the C. albicans and human host cells. The results demonstrated the effectiveness of the NARX modeling approach, and revealed that the 415 nm light was more effective as an anti-fungal treatment with less damage to the host cells than the 405 or 385 nm light. The kernel-based NARX model identification algorithm offers opportunities for determining the effective and safe light dosages in treating various fungal infection diseases.

Research on broadband equivalent modeling for the dielectric response of transformer bushings based on the improved artificial bee colony algorithm

As a new nondestructive diagnosis method of insulation state, frequency domain spectroscopy (FDS) has been widely used in the field detection of power equipment. However, the quantitative correlation between FDS measurement results and insulation state is not clear for transformer bushing, which seriously affects its detection effect. In order to solve this problem, the FDS modeling and parameter identification of transformer bushing has been studied in this paper. Firstly, the transformer bushing model was built in the laboratory, and the FDS measurement data of transformer bushings with different water content were collected. Then, a fusion algorithm of improved artificial bee colony algorithm and sequential quadratic programming algorithm was used to identify the parameters of transformer bushing model. After modeling and analyzing the FDS measured data, it is found that there is a good consistency between the measured spectrum of complex capacitance and the reconstructed spectrum of the model, and the goodness of fit of the model to the measured FDS exceeds 0.95. In addition, the identified values of resistance and capacitance in the equivalent model are within the reasonable range of 109Ω and 10−9F respectively. These results show that the extended Debye model and parameter identification algorithm can accurately model the frequency domain dielectric response of transformer bushing in a wide frequency range, and can provide an effective tool for more accurate analysis of transformer bushings insulation state.

Adaptive model predictive control for actuation dynamics compensation in real-time hybrid simulation

Hybrid simulation is used to obtain the dynamic response of a system whose components consist of physical and numerical substructures. The coupling of these substructures is achieved by actuation systems, which are commanded in closed-loop control setting. To ensure high fidelity of such hybrid simulations, performing them in real-time is necessary. However, real-time hybrid simulation poses challenges since the inherent dynamics of the actuation system introduce time delays, thus modifying the dynamic response of the investigated system. Therefore, a tracking controller is required to adequately compensate for such time delays. In this study, a novel tracking controller is proposed for dynamics compensation in real-time hybrid simulations. It is based on adaptive model predictive control, a linear time-varying Kalman filter, and a real-time model identification algorithm. Within the latter, auto-regressive exogenous polynomial models are identified in real-time to estimate the changing plant dynamics. A parametric virtual case study, encompassing a virtual motorcycle, is used to validate the performance and robustness of the proposed controller. Results demonstrate the effectiveness of the proposed controller for real-time hybrid simulations.

Data-driven identification of dynamical models using adaptive parameter sets

This paper presents two data-driven model identification techniques for dynamical systems with fixed point attractors. Both strategies implement adaptive parameter update rules to limit truncation errors in the inferred dynamical models. The first strategy can be considered an extension of the dynamic mode decomposition with control (DMDc) algorithm. The second strategy uses a reduced order isostable coordinate basis that captures the behavior of the slowest decaying modes of the Koopman operator. The accuracy and robustness of both model identification algorithms is considered in a simple model with dynamics near a Hopf bifurcation. A more complicated model for nonlinear convective flow past an obstacle is also considered. In these examples, the proposed strategies outperform a collection of other commonly used data-driven model identification algorithms including Koopman model predictive control, Galerkin projection, and DMDc.

Detection of sludge bulking using adaptive fuzzy neural network and mechanism model

The frequent occurrence of sludge bulking can influence the effluent qualities and destroy the stable operation of activated sludge process (ASP). In order to accurately detect the sludge bulking, a detection method, based on adaptive fuzzy neural network and mechanism model, is proposed in this paper. First, a novel detection scheme is designed, where hybrid detection model and intelligent identification algorithm, are designed to describe the dynamics of sludge bulking. Second, an error compensation model, by using adaptive fuzzy neural network, is established to make up for the errors caused by the assumptions set in hybrid detection model. Finally, an error-assisted detection strategy is designed to evaluate sludge bulking. To verify the effectiveness of the proposed detection method, operating data from ASP are applied. The results show that this proposed method can efficiently detect sludge bulking.

Integrated Passive-Active Model Identification With Tunable Model Discrimination for Affine Discrete-Time Systems

This letter proposes a passive-active model identification algorithm for affine discrete-time systems that integrates active model discrimination (AMD) and model invalidation (MI). A look-up tree consisting of control inputs is constructed offline for this integrated model identification (IMI) technique to discriminate among models in a time-varying model set, which is only known at run time when repeatedly applying MI online. Furthermore, a novel tunable AMD (TAMD), with its mixed-integer linear programming (MILP) formulation, is proposed and combined with the IMI algorithm, which can improve model discrimination performance. The effectiveness of the proposed IMI algorithm is demonstrated through simulations for identifying intention models of human-driven vehicles in a lane changing scenario.

A Wiener Model Identification for Creep and Vibration Linear and Hysteresis Nonlinear Dynamics of Piezoelectric Actuator

The piezoelectric actuator exhibits both linear dynamics of creep and vibration and nonlinear dynamics of hysteresis. The model identification from experiments can compensate uncertainties in the model and get a satisfactory model for the control. Block-oriented nonlinear model is suitable for modeling this kind of linear and nonlinear hybrid dynamics. In this study, a Wiener model identification method for the piezoelectric actuator is proposed to model the linear and nonlinear dynamics together from the data. The model is called two-linear(linear+linear)-nonlinear (TLN) Wiener model, where two additive linear dynamic models are used to identify the creep and vibration dynamics, and a nonlinear dynamic model is followed to identify the hysteresis nonlinear features. The TLN-Wiener model is parameterized using Laguerre functions and Prandtl-Ishlinskii (PI) model, and the model identification algorithm is proposed. The experiments on piezoelectric actuators show that the TLN-Wiener model identification method can model the creep, vibration and hysteresis dynamics. The method is applicable to model the rate-dependency dynamics of the piezoelectric actuator.