System Identification Problem Research Articles

UKF-Based Neural Training for Nonlinear Systems Identification and Control Improvement

Numerous academic works have addressed the identification and control problem for complex dynamic systems. In recent decades, the use of control algorithms based on neural networks (NNs) has been highlighted, which have shown satisfactory results in the trajectory tracking control for a class of discrete-time nonlinear systems. The present work proposes an efficient learning law for discrete-time recurrent high order neural networks (RHONNs), using a training algorithm based on an unscented Kalman filter (UKF). This learning law is applied through a decentralized neural block control using UKF (DNBC-UKF), for trajectory tracking control of a class of discrete-time nonlinear systems. The proposed controller is experimentally evaluated by means of real-time tests in a two degrees of freedom (DOF) vertical direct-drive robotic manipulator against a decentralized neural block control using EKF (DNBC-EKF). The Lyapunov stability theory is used to show that the identification errors of RHONNs are semi-globally uniformly ultimately bounded (SGUUB), the RHONN weights remains bounded, and the closed-loop tracking errors go to zero.

Zero-Attracting Kernel Maximum Versoria Criterion Algorithm for Nonlinear Sparse System Identification

Sparsity-induced kernel adaptive filters have emerged as a promising candidate for a nonlinear sparse system identification (SSI) problem. The existing zero-attracting kernel least mean square (ZA-KLMS) algorithm relies on minimum mean square error criterion, which considers only second order statistics of error, thereby resulting in suboptimal performance in the presence of non-Gaussian/impulsive distortions. In this letter, we propose a novel random Fourier features (RFF) based ZA kernel maximum Versoria criterion (ZA-KMVC) algorithm, and their variants, which are robust for nonlinear SSI in the presence of non-Gaussian distortions over both stationary and time-varying environments. Furthermore, the mean-square convergence analysis of the proposed RFF-ZA-KMVC algorithm is performed. It has been observed from the simulation results that the proposed algorithm delivers better convergence performance as compared to the existing state-of-art approaches.

Identification of Parallel Wiener-Hammerstein Systems

This paper is focused on the problem of system identification for a class of nonlinear systems constituted of a Wiener subsystem and Hammerstein subsystem connected in parallel. Most of existing works on the identification of compound systems, involving Wiener and Hammerstein subsystems, have been focused on series connections. Presently, we present a frequency identification approach to determine estimates of the different components of the considered parallel Wiener-Hammerstein system. The approach comes in two versions. The first one consists in using repeatedly a one-frequency sine input experiment, with different frequencies in the various experiments. The second version consists in performing a signal experiment involving a sufficiently rich multi-sine excitation. The applicability of the approach and its relevance are highlighted by simulation.

Identification of Room Acoustic Impulse Responses via Kronecker Product Decompositions

The identification of room acoustic impulse responses represents a challenging problem in the framework of many important applications related to the acoustic environment, like echo cancellation, noise reduction, and microphone arrays, among others. In this context, the main issues are related to the long length of such impulse responses and their time-variant nature. These raise significant difficulties in terms of the convergence rate, computational complexity, and accuracy of the solution. Recently, a decomposition-based approach was developed for the identification of low-rank systems, which can also be applied (to some extent) for the identification of acoustic impulse responses. This approach exploits the nearest Kronecker product decomposition of the impulse response and solves a high-dimension system identification problem using a combination of low-dimension solutions (provided by shorter filters), thus gaining in terms of both performance and complexity. Nevertheless, it does not consider the intrinsic nature of the room acoustic impulse responses, which contain specific components (e.g., early reflections and late reverberation) that can be very different in nature. In this paper, we propose an improved decomposition-based method (via the Kronecker product) that takes into account these specific components and processes them separately, in order to better exploit their important low-rank features. Following this approach, an iterative Wiener filter is firstly developed, followed by a recursive least-squares (RLS) algorithm designed in the same framework. Both solutions outperform the conventional benchmarks, i.e., the conventional Wiener filter and the RLS algorithm, respectively. Moreover, they achieve superior performances as compared to the recently developed versions based on the nearest Kronecker product decomposition, also owning lower computational complexities than their previous counterparts. Simulations are performed in the framework of acoustic echo cancellation and the obtained results support the performance features of the proposed algorithms.

An Innovative Transient Analysis of Adaptive Filter With Maximum Correntropy Criterion

The adaptive filtering algorithm based on the maximum correntropy criterion (MCC) is very effective in suppressing non-Gaussian noises and therefore attracts widespread attentions. At present, some works have been done for study the convergence and steady-state performance analysis of the MCC algorithm, but its transient performance analysis is still an open problem. To provide a comprehensive theoretical foundation for the MCC algorithm, we propose a method for transient performance analysis based on moment generating function (MGF). Since this method can efficiently calculate the expected value of the exponential term in the iterative update equation, it can avoid the discrepancies caused by introducing some approximation methods such as Taylor expansions in the analysis process. To date, there is no precedent for using this method to analyze the transient performance of the MCC algorithm. In addition, the steady-state performance and stability conditions of the MCC algorithm are discussed based on this method. Finally, the proposed analytical method is applied to the system identification problem, and the results show that the theoretical analysis results are agree well with the Monte Carlo simulation results.

Robust Fault Detection using Zonotopic Parameter Estimation

This paper addresses the system identification problem, as well as its application to robust fault detection, considering parametric uncertainty and using zonotopes. As a result, a Zonotopic Recursive Least Squares (ZRLS) estimator is proposed and compared with the Setmembership (SM) approach when applied to fault detection, taking as a reference the minimum detectable fault generated in the worst-case. To illustrate the effectiveness of the proposed robust parameter estimation and fault detection methodologies, a quadruple tank process is employed

Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle

Recently, a quasi-fractional order gradient descent (QFGD) algorithm was proposed and successfully applied to solve system identification problem. The QFGD suffers from the overparameterization problem and results in estimating the redundant parameters instead of identifying only the actual parameters of the system. This study develops a novel hierarchical QFDS (HQFGD) algorithm by introducing the concepts of hierarchical identification principle and key term separation idea. The proposed HQFGD is effectively applied to solve the parameter estimation problem of input nonlinear autoregressive with exogeneous noise (INARX) system. A detailed investigation about the performance of HQFGD is conducted under different disturbance conditions considering different fractional orders and learning rate variations. The simulation results validate the better performance of the HQFGD over the standard counterpart in terms of estimation accuracy, convergence speed and robustness.

A New Neural Networks Approach Used to Improve Wind Speed Time Series Forecasting

Generally, wind turbines convert the energy of wind into electricity. In this order, it is essential to predict accurately this source’s availability and intensity at the same location and height where wind electric generators will be installed, and therefore obtain reliable time-series data. The problem of meteorological time series prediction can be formulated as a system identification problem. To improve the prediction of these meteorological time series, we describe then use an application of a new neural networks approach in this paper. This novel, robust, and reliable forecasting method is based on the application of a new learning algorithm that allows a renewal of learning data, with time. For our algorithm a neural network is developed to estimate just one value y (t+1), then it is taken up with a new learning set enriched by data freshly measured. The obtained results showed a good agreement between measured and predicted series, and the mean relative error over the whole data set, which are not exceeding 5 %.

Maximum-Likelihood-Based Adaptive and Intelligent Computing for Nonlinear System Identification

Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence.

Sample Complexity of Block-Sparse System Identification Problem

In this article, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state data samples. We characterize the properties of this estimator under high-dimensional scaling, where the growth rate of the system dimension is comparable to or even faster than that of the number of available sample trajectories. In particular, using contemporary results on high-dimensional statistics, we show that the proposed estimator results in a small elementwise error, provided that the number of sample trajectories is above a threshold. This threshold depends polynomially on the size of each block and the number of nonzero elements at different rows of input and state matrices, but only logarithmically on the system dimension. A by product of this result is that the number of sample trajectories required for sparse system identification is significantly smaller than the dimension of the system. Furthermore, we show that, unlike the recently celebrated least-squares estimators for system identification problems, the method developed in this work is capable of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exact recovery</i> of the underlying sparsity structure of the system with the aforementioned number of data samples. Extensive case studies on switching networks and power systems are offered to demonstrate the effectiveness of the proposed method.

Fault identification in nonlinear dynamic systems not satisfying matching, minimum phase, and detectability conditions

The paper studies the fault identification problem for nonlinear control systems under unmatched disturbances. A novel approach to construct a sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation, in particular matching condition, minimum phase condition, and detectability conditions. The suggested approach is based on the reduced order model of the original system and on the canonical form of matrices describing such a model. This allows to reduce the complexity of sliding mode observers and relax the limitations imposed on the original system. Three different cases for disturbances are considered and the appropriate solutions are suggested.

Online Interval Type-2 Fuzzy Extreme Learning Machine applied to 3D path following for Remotely Operated Underwater Vehicles

In marine missions that involve 3D path following tasks, the overall goal of Underwater Vehicles (UVs) is the successful completion of a path previously specified by the operator. This implies that the path must be followed by the UV as closely as possible and arrive at a location for collection by a vessel. In this paper, an Online Interval Type-2 Fuzzy Extreme Learning Machine (OIT2-FELM) is suggested to achieve a robust following behaviour along a predefined 3D path using a Remotely Operated Underwater Vehicle (ROV). The proposed machine is a fast sequential learning scheme to the training of a more generalised model of TSK Interval Type-2 Fuzzy Inference Systems (TSK IT2 FISs) equivalent to Single Layer Feedforward Neural Networks (SLFNs). Learning new input data in the OIT2-FELM can be done one-by-one or chunk-by-chunk with a fixed or varying size. The OIT2-FELM is implemented in a hierarchical navigation strategy (HNS) as the main guidance mechanism to infer local control motions and to provide the ROV with the necessary autonomy to complete a predefined 3D path. For local path-planning, the OIT2-FELM performs signal classification for obstacle avoidance and target detection based on data collected by an on-board scan sonar. To evaluate the performance of the proposed OIT2-FELM, two different experiments are suggested. First, a number of benchmark problems in the field of non-linear system identification, regression and classification problems are used. Secondly, a number of experiments to the completion of a predefined 3D path using an ROV is implemented. Compared to other fuzzy strategies, the OIT2-FELM offered two significant capabilities. On the one hand, the OIT2-FELM provides a better treatment of uncertainty and noisy signals in underwater environments while improving the ROV’s performance. Secondly, online learning in OIT2-FELM allows continuous knowledge discovery from survey data to infer the surroundings of the ROV. Experiment results to the completion of 3D paths show the effectiveness of the proposed approach to handle uncertainty and produce reasonable classification predictions (∼90.5% accuracy in testing data).

Supply chain security evaluation model and index system based on a 5G information system.

Currently, the supply chain management model has been widely adopted worldwide. Internationally renowned companies such as IBM and Walmart have made significant achievements in supply chain management and have played a greater role in promoting the growth of their interests. However, while they are enjoying their own interests, they are also facing various risks in the supply chain. From the perspective of systems engineering, this paper uses complex network theory as a research tool to study supply chain networks and systematically study the important issues of supply chain network risks. This paper analyzes the new characteristics of the relationship between enterprises and suppliers in the supply chain and which indicators should be selected as the basis for evaluating suppliers from the perspective of cooperation and development, which more comprehensively reflects the characteristics of the new enterprise–supplier relationship in the supply chain environment. This highlights the evaluation of the supplier’s cooperation ability and development ability. Aiming at the problem of supply chain network system identification and integrated evaluation, a supply chain security evaluation model and index system research framework model are proposed, and the intercompany business risk and supply chain in supply chain network evaluation are introduced. As a model for evaluating transition parameters, the study of supply chain risk propagation introduces the theory of dynamic propagation in complex networks, the law of evolution, and the supplier's dynamic supply chain risk model. The experimental results of this paper show that when the global reputation value is 0.5 and the local reputation value is 0.8 and 0.7, the trust degree changes with the change of the confidence factor; when the value of the confidence factor decreases, the degree of trust converges more and more to the global reputation and vice versa. It can be seen that this model has high feasibility.

Auxiliary Model-Based Multi-Innovation Fractional Stochastic Gradient Algorithm for Hammerstein Output-Error Systems

This paper focuses on the nonlinear system identification problem, which is a basic premise of control and fault diagnosis. For Hammerstein output-error nonlinear systems, we propose an auxiliary model-based multi-innovation fractional stochastic gradient method. The scalar innovation is extended to the innovation vector for increasing the data use based on the multi-innovation identification theory. By establishing appropriate auxiliary models, the unknown variables are estimated and the improvement in the performance of parameter estimation is achieved owing to the fractional-order calculus theory. Compared with the conventional multi-innovation stochastic gradient algorithm, the proposed method is validated to obtain better estimation accuracy by the simulation results.

Statistical Inference for Piecewise Affine System Identification

This short note studies the problem of piecewise affine system identification, being a special nonlinear system based on our previous contribution on it. Two different identification strategies are proposed to achieve our mission, such as centralized identification and distributed identification. More specifically, for centralized identification, the total observed input-output data are used to estimate all unknown parameter vectors simultaneously without any consideration on the classification process. But for distributed identification, after the whole observed input-output data are classified into their own right subregions, then part input-output data, belonging to the same subregion, are applied to estimate the unknown parameter vector. Whatever the centralized identification and distributed identification, the final decision is to determine the unknown parameter vector in one linear form, so the recursive least squares algorithm and its modified form with the dead zone are studied to deal with the statistical noise and bounded noise, respectively. Finally, one simulation example is used to compare the identification accuracy for our considered two identification strategies.

Online Identification of Piecewise Affine Systems Using Integral Concurrent Learning

Piecewise affine (PWA) systems are attractive models that can represent various hybrid systems with local affine subsystems and polyhedral regions due to their universal approximation properties. The identification problem of PWA systems amounts to estimating the number of subsystems, parameters of each subsystem, and the corresponding polyhedral partitions via state-input vectors. In this paper, we propose a novel approach to address the online identification problem of continuous-time PWA systems in state-space form. Specifically, an online active mode recognition algorithm and a generalized integral concurrent learning identifier are presented to acquire the number of subsystems, the switching sequence, and the parameter of each subsystem. In addition, we develop the optimization problem for the polyhedral partition estimation, which is solved by using the estimated switching sequence and subsystem parameters. The effectiveness of the proposed identification approach is demonstrated via simulation results.

Low-Complexity Recursive Least-Squares Adaptive Algorithm Based on Tensorial Forms

Modern solutions for system identification problems employ multilinear forms, which are based on multiple-order tensor decomposition (of rank one). Recently, such a solution was introduced based on the recursive least-squares (RLS) algorithm. Despite their potential for adaptive systems, the classical RLS methods require a prohibitive amount of arithmetic resources and are sometimes prone to numerical stability issues. This paper proposes a new algorithm for multiple-input/single-output (MISO) system identification based on the combination between the exponentially weighted RLS algorithm and the dichotomous descent iterations in order to implement a low-complexity stable solution with performance similar to the classical RLS methods.

A new multivariate equation-error autoregressive moving average system with conditional heteroscedastic noise: Maximum likelihood identification

The aim of this paper is to deal with the problem of conditional heteroscedastic noise in multivariate systems. In this regard, a new multivariate equation-error system with colored noise is introduced, in which the noise conditional variance varies with time and the noise exhibits a GARCH process. Thus, in this our new approach, both the time dependency and probability distribution of noise samples shall be identified. Based on the maximum likelihood principle and orthogonality of parameters, the problem of multivariate system identification is reduced into two separate maximum likelihood problems. An iterative algorithm is proposed, which can efficiently estimate the problem parameters based on gradient reduction and nonlinear optimization. Besides, a bootstrap algorithm is applied for assessing the accuracy of estimators. Also, some asymptotic result of proposed method in large sample size is provided. According to bootstrap simulation results, the proposed algorithm can effectively estimate the parameters of the system with conditional heteroscedastic noise and provides more accurate parameter estimates with a much lower confidence interval, compared to the least square method.

Nonnegative least mean mixed-norm algorithm: Analysis and performance

Adaptive filter has been successfully considered for the system identifications. Under some circumstances, due to the unknown system's intrinsic characteristics, nonnegativity is an desired constraint imposed on the parameters to be estimated, which will affect the performance of devised adaptive filtering. This paper studies a nonnegative least mean mixed-norm algorithm (NNLMMN) with fourth-order moment error and square-order error, which are jointly considered and devised to design a new cost function for dealing with the system identification problems with a nonnegativity constraint in mixed Gaussian noise environment. We also provide the theoretical behavior prediction of the mean weight, the transient analysis and steady-state excess mean square error (EMSE) of the NNLMMN algorithm. Experiment results show that the superior performance of the NNLMMN algorithm and verify the effectiveness of the presented theory analysis.

An Insightful Overview of the Wiener Filter for System Identification

Efficiently solving a system identification problem represents an important step in numerous important applications. In this framework, some of the most popular solutions rely on the Wiener filter, which is widely used in practice. Moreover, it also represents a benchmark for other related optimization problems. In this paper, new insights into the regularization of the Wiener filter are provided, which is a must in real-world scenarios. A proper regularization technique is of great importance, especially in challenging conditions, e.g., when operating in noisy environments and/or when only a low quantity of data is available for the estimation of the statistics. Different regularization methods are investigated in this paper, including several new solutions that fit very well for the identification of sparse and low-rank systems. Experimental results support the theoretical developments and indicate the efficiency of the proposed techniques.