Identification Of Dynamic Systems Research Articles

Data-driven reconstruction of chaotic dynamical equations: The Hénon–Heiles type system

In this study, the classical two-dimensional potential VN=12mω2r2+1NrNsin(Nθ), N∈Z+, is considered. At N=1,2, the system is superintegrable and integrable, respectively, whereas for N>2 it exhibits a richer chaotic dynamics. For instance, at N=3 it coincides with the Hénon–Heiles system. The periodic, quasi-periodic and chaotic motions are systematically characterized employing time series, Poincaré sections, symmetry lines and the largest Lyapunov exponent as a function of the energy E and the parameter N. Concrete results for the lowest cases N=3,4 are presented in complete detail. This model is used as a benchmark system to estimate the accuracy of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method, a data-driven algorithm which reconstructs the underlying governing dynamical equations. We pay special attention at the transition from regular motion to chaos and how this influences the precision of the algorithm. In particular, it is shown that SINDy is a robust and stable tool possessing the ability to generate non-trivial approximate analytical expressions for periodic trajectories as well.

Identification of nonlinear dynamical system based on adaptive radial basis function neural networks

Identification of nonlinear dynamical system based on adaptive radial basis function neural networks

Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities

Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities

Dynamic system with correlated noise

Developing mathematical models for dynamic systems presents challenges in selecting state variables, crucial for minimizing computational operations during filter implementation. The paper addresses active identification of dynamic systems amid noise and measurement errors, using the Fisher information matrix. Additionally, it introduces Cholesky decomposition for generating correlated noise, demonstrating its applicability in practical problem-solving.

Identification of Continuous-Time Dynamic Systems With Uncertainties Measured by Fuzzy Sets Subject to Model Structure Errors

Identification of Continuous-Time Dynamic Systems With Uncertainties Measured by Fuzzy Sets Subject to Model Structure Errors

Identification of unknown dynamic system as a way to determine the transient characteristic of the inverse acoustic path

Identification of unknown dynamic system as a way to determine the transient characteristic of the inverse acoustic path

Recurrent context layered radial basis function neural network for the identification of nonlinear dynamical systems

This paper proposes a novel recurrent context layered radial basis function neural network (RCLRBFNN) for the identification of nonlinear dynamical systems. The proposed model consists of an additional context layer in which the nodes represent the unit-delayed outputs of the hidden layer radial centers. These delayed outputs undergo a nonlinear transformation by applying a tangent hyperbolic function. These transformed signals connect to the output layer neuron through the adjustable context layered weights. To tune the parameters of the proposed model the update equations are derived using the dynamic back-propagation algorithm. Further, an adaptive learning rate scheme is proposed to improve the performance of the learning algorithm. In the simulation experiment, a total of two examples are considered to test the efficacy and performance of the proposed model. The performance comparison is made with the conventional structure of the radial basis function neural network (RBFNN), Jordan Recurrent neural network (JRNN), and the feed-forward neural network (FFNN) (which is nothing but a single-layered multi-layered perceptron). Both the disturbance signal as well as system’s uncertainty scenarios are considered to test the robustness shown by the proposed model. The results showed that the proposed model has delivered a better identification accuracy as compared to the other neural models.

A data-driven implicit deep adaptive neuro-fuzzy inference system capable of manifold learning for function approximation

Fuzzy Neural Networks (FNN) have the ability of decision-making based on constructing semi-ellipsoidal clusters in the input space as the antecedent parts of their fuzzy rules. To determine the output value for each input instance, FNNs consider its membership degree to different sub-regions of the input space. However, forming such meaningful sub-regions is not possible in all applications due to the nonlinear interactions among input variables and their low information gain. Indeed, the samples could be distributed on a manifold in the input space. Therefore, to cover the input space, we need lots of rules, each representing a small region of input space. This issue decreases the generalization ability of the model along with its explainability. Consequently, to efficiently form fuzzy rules, first, it is necessary to unfold the manifold by mapping the samples to an appropriate embedding space. Next, the fuzzy rules in the form of semi-ellipsoidal regions should be constructed in this extracted feature space. Deep Fuzzy Neural Networks address this problem by representation learning through stacking multiple cascade mapping layers. In this paper, we propose a novel approach for nonlinear function approximation and time-series prediction problems, based on using the kernel trick to implicitly learn the mapping function to the new feature space. Moreover, to initialize the fuzzy rules, a KNN-based method using the kernel trick is proposed. A hierarchical Levenberg–Marquardt approach is applied to learn the model’s parameters. The performance and structure of the proposed method are studied and compared with some other relevant methods in synthetic and real-world benchmarks. Based on these experiments, the proposed method has the best performance with the most parsimonious architecture. According to these experiments, the test RMSE of the proposed method is 0.002 for Mc-Glass chaotic time-series prediction, 0.015 for a Nonlinear dynamic system identification, 0.0345 for Box–Jenkins nonlinear system identification, 0.0609 for Fuel consumption prediction of automobiles, 10.24 for Sydney stock price tracking, and 0.595 for California housing.

A kernel framework for learning differential equations and their solution operators

This article presents a three-step kernel framework for regression of the functional form of differential equations (DEs) and learning their solution operators. Given a training set consisting of pairs of noisy DE solutions and source/boundary terms on a mesh: (i) kernel smoothing is utilized to denoise the data and approximate derivatives of the solution; (ii) This information is then used in a kernel regression model to learn the functional form of the DE; (iii) The learned DE is then used within a numerical solver to approximate the solution of the DE with a new source term or initial data, thereby constituting an operator learning framework. Numerical experiments compare the method to state-of-the-art algorithms. In DE learning our framework matches the performance of Sparse Identification of nonlinear Dynamical Systems (SINDy) while in operator learning the method has superior performance compared to well-established neural network methods in low training data regimes.

Automatic identification of dynamical system excited by time-dependent factor without prior information

Automatic identification of dynamical system excited by time-dependent factor without prior information

An efficient method for generalised Wiener series estimation of nonlinear systems using Gaussian processes

System identification of dynamical systems aims to predict the output of a system for a given input by inferring model details from data. This is particularly challenging for nonlinear vibrating systems with long memory, which often have complex dynamics for which the physics is not fully understood. However, in many engineering applications, it is important to capture as much of the nonlinearity in the response as possible. The Wiener series is a classical data-driven technique that decomposes the system response into a set of orthogonal functionals of increasing order. Unlike standard black-box algorithms, such as neural networks, the series is highly interpretable and can offer insight into the nonlinearities present. However, current methods require vast quantities of data to calculate higher order terms in the Wiener series. In this paper, a novel generalised formulation of the Wiener series is developed by framing the series explicitly as a QR decomposition. Then by placing a Gaussian process prior over the kernels, their inherent structure is exploited to significantly reduce the quantity of data required for inference. Initial investigations were carried out using two systems: first pre-defined kernels and second an idealised nonlinear oscillatory system with unknown kernels. It is demonstrated that the Gaussian Process Generalised Wiener Series (GPGWS) enables the calculation of up to and including the third order kernel for systems with long memory and improves the robustness to noise.

Data-driven identification for nonlinear dynamic systems

Data-driven identification for nonlinear dynamic systems

Data-driven identification for nonlinear dynamic systems

Data-driven identification for nonlinear dynamic systems

Integration of Vehicle Dynamic Model and System Identification Model for Extending the Navigation Service Under Sensor Failures

Accurate and reliable localization is of great importance for autonomous vehicles (AV). Mainstream localization approaches in autonomous vehicles (AV) are limited by the reliability of onboard sensors, which could be vulnerable to sensor failure, such as signal outages of the camera and signal spoofing of the global navigation satellite systems (GNSS). Different from these active or passive sensors, the vehicle dynamic model (VDM), which is the application of physical laws to a vehicle in motion, is environmentally independent and is capable of providing vehicle motion estimation continuously. However, the performance of the VDM-based motion estimation is dominated by the accuracy of the system dynamics model. To tackle this issue, this study proposes a sensor-free localization method VDM-SI by integrating system identification into the design of vehicle dynamic models (VDM). A system identification process based on low-order process models is proposed to identify the system dynamics of the AV, where the identified system responses are taken as the control input of VDM to estimate the vehicular positioning. The localization experiments in two scenarios show that the mean absolute translation error of VDM-SI can be reduced by 70% compared to conventional VDM methods. In addition, VDM-SI is experimentally proven to improve the localization performance of sensor fusion-based localization systems with high noise levels. Furthermore, in the application of re-localization after sensors fail and recover, VDM-SI shows strength in enhancing the security of AVs in extreme conditions.

Application of the evolutionary approach to structural and parametric identification of dynamic objects

The paper examines the evolutionary approach to structural and parametric identification of dynamic systems in the form of differential equations. The approach is based on a genetic programming algorithm to determine a structure of the equation and differential evolution method for parameters selection. The author proposed approach based on such evolutionary algorithms as genetic programming and differential evolution. The search for the structure is carried out by genetic programming. The selection of numerical parameters and initial conditions is implemented by a method of differential evolution. The problem of finding a model that describes changes in the efficiency of a hydraulic system is solved with the help of this approach. The proposed approach is compared with a recurrent neural network and a nonparametric kernel regression estimation.

Sparse identification of dynamical systems by reweighted [formula omitted]-regularized least absolute deviation regression

This work proposes a generalized methodology for sparse identification of dynamical systems (SID), utilizing reweighted l1-regularized least absolute deviation (LAD) regression to recover the governing equation of dynamical systems. To programmatically implement the proposed method, a stabilized and efficient resolution scheme is developed by combining the solution method of the classical LAD-based least absolute shrinkage and selection operator (LAD-lasso) and the threshold iterative idea of the sequentially thresholded least-squares (STLS) method. The new method relaxes the assumption of normality for the error terms in the linear regression model employed by traditional SID techniques. Additionally, it overcomes the low identification accuracy deficiency of the recently proposed regularized least absolute deviation-based sparse identification of dynamics method (RLAD-SID) under some poor data conditions. The performance of the proposed approach is investigated by simulations of two well-known dynamical systems, that is, the Lorenz system and the Duffing system. The reliability of this approach in recovering the governing equation of dynamical systems from noise-contaminated datasets is firstly demonstrated. Furthermore, the advantage of the proposed method is illustrated by comparing it with four traditional techniques in relatively poor data environments. Finally, we display the robustness of the new method when the time derivative dataset is affected by different types of noise, and reveal its superiority compared to the traditional RLAD-SID.

Identification of Linear Dynamic Systems in State Sate

System identification has been growing in an engineering community over the last 60 years, and an intensive research has been published in this field. This study presents an identification method of a linear time-invariant continuous dynamic system directly from time series data. The considered system is represented in a state space form. All states are assumed to be measured. The proposed identification algorithm is demonstrated and investigated, with noise-free data and noisy data, on a MATLAB simulation environment. The results confirm that the simple procedures of the proposed algorithm give an effective and successful estimation of the system parameter matrices.

Real-time multi-variable optimization of the interstage subcooling vapor-injection based transcritical CO2 HPWH: An integrated model predictive control approach

The interstage subcooling vapor-injection technique has been introduced to transcritical CO2 heat pumps to alleviate performance degradation under conditions of low ambient temperature and high water-outlet temperature. This type of solution holds considerable appeal and finds utility across a wide range of applications. However, the efficacy and efficiency of such systems are contingent upon their management, which frequently requires the implementation of suitable control systems. The primary objective is to enhance the overall system operational performance, resulting in tangible advantages in terms of economic viability, energy conservation, and environmental sustainability. To achieve these objectives, one can utilize both explicit and implicit optimization methods ranging from Model Predictive Control (MPC) to Extremum Seeking Control (ESC), each with its strengths and weaknesses. This paper compares the performance of an ad hoc integrated MPC strategy and a multi-variable ESC one. Based on the results of the system operation employing the latter strategy, a significant linear correlation was discovered between the optimal medium pressure and the optimal discharge and suction pressure. Consequently, an intrinsic self-optimization strategy for the medium pressure was developed. Subsequently, a dynamic system identification was performed on the new system, incorporating this proposed strategy. To optimize the system Coefficient of Performance (COP) while maintaining the water outlet temperature, ensuring the thermal load constraint, the MPC strategy was employed. The main focus of the MPC was to determine the optimal Electronic Expansion Valve (EEV) opening degree and water pump settings. The integrated MPC strategy was evaluated and compared to the multi-variable ESC strategy under various conditions, including fixed design conditions, changing ambient conditions, and step-change water outlet temperature. The results clearly demonstrated the effectiveness and superiority of the integrated MPC.

A New Method for Dynamical System Identification by Optimizing the Control Parameters of Legendre Multiwavelet Neural Network

Wavelet neural networks have been widely applied to dynamical system identification fields. The most difficult issue lies in selecting the optimal control parameters (the wavelet base type and corresponding resolution level) of the network structure. This paper utilizes the advantages of Legendre multiwavelet (LW) bases to construct a Legendre multiwavelet neural network (LWNN), whose simple structure consists of an input layer, hidden layer, and output layer. It is noted that the activation functions in the hidden layer are adopted as LW bases. This selection if based on the its rich properties of LW bases, such as piecewise polynomials, orthogonality, various regularities, and more. These properties contribute to making LWNNs more effective in approximating the complex characteristics exhibited by uncertainties, step, nonlinear, and ramp in the dynamical systems compared to traditional wavelet neural networks. Then, the number of selection LW bases and the corresponding resolution level are effectively optimized by the simple Genetic Algorithm, and the improved gradient descent algorithm is implemented to learn the weight coefficients of LWNN. Finally, four nonlinear dynamical system identification problems are applied to validate the efficiency and feasibility of the proposed LWNN-GA method. The experiment results indicate that the LWNN-GA method achieves better identification accuracy with a simpler network structure than other existing methods.

A recurrent neural network-based identification of complex nonlinear dynamical systems: a novel structure, stability analysis and a comparative study

A recurrent neural network-based identification of complex nonlinear dynamical systems: a novel structure, stability analysis and a comparative study