Algorithm For Nonlinear System Identification Research Articles

Concurrent Learning-Based Two-Stage Predefined-Time System Identification

This paper proposes a novel two-stage predefined-time system identification algorithm for uncertain nonlinear systems based on concurrent learning. The main feature of the algorithm is that the convergence time of estimation error is an exact predefined parameter, which can be known and adjusted directly by users. Historic identification data are stored in the first stage to guarantee that a finite-rank condition is satisfied. In the second stage, the estimation error converges to zero for linearly parameterized uncertain systems, or it is regulated into the neighborhood of zero for unknown systems modeled by neural networks. The identification algorithm takes effect without the restrictive requirement of the persistent excitation condition. Simulation examples verify the effectiveness of the proposed method.

Nonlinear Identification through eXtended Outputs (NIXO) with numerical and experimental validation using geometrically nonlinear structures

This work presents a novel technique for nonlinear system identification that operates in the frequency domain and fits a model to measured spectra to estimate the parameters in a modal domain nonlinear equation of motion (EOM). Nonlinear terms are added to the linear EOM in the form of polynomials, and the proposed algorithm estimates the polynomial coefficients as well as the underlying linear Frequency Response Function (FRF). This method is an extension to a popular nonlinear system identification algorithm called NIFO, from Nonlinear Identification through Feedback of the Outputs. However, NIFO identifies the nonlinear parameters as complex numbers that may be different at each frequency line, even though the mechanical system is expected to be governed by an EOM in which the nonlinear parameters are real and constant with frequency. This might be problematic, because any variation in the identified nonlinear parameters will distort the linear FRFs estimated by NIFO, and those linear FRFs are important to tell the user whether all of the significant nonlinearity has been extracted from the system. The proposed algorithm, here dubbed Nonlinear Identification through eXtended Outputs (NIXO), estimates the nonlinear parameters as frequency-independent and real. Additionally, it is demonstrated that for the systems studied here that the algorithm works when random and swept-sine inputs are used to excite the tested structure, while NIFO only worked well when random inputs were used. The method is first evaluated numerically using benchmark case studies, starting with the SDOF equation and then reduced models of a clamped-clamped flat beam, and the results are compared to those obtained with NIFO. Then the algorithm is applied to swept-sine measurements from a 3D-printed flat beam and the results are validated by computing the primary nonlinear normal mode of the identified model and comparing it with measurements.

A Novel Second-OrderSine-Cost-Function-Derived Kernel Adaptive Algorithm for Non-Linear System Identification

A novel kernel recursive second-order sine adaptive (KRSOSA) algorithm was devised for identifying non-linear systems, which was constructed using a symmetry squared sine function to develop a novel kernel loss function and recursive scheme. In the proposed KRSOSA algorithm, the squared sine function provides resistance to impulsive noise due to the sine operation, which was well-derived and investigated in the framework of kernel adaptive filtering (KAF). The behavior of the proposed KRSOSA algorithm was investigated and analyzed using computer simulations, which provided good performance for identifying non-linear systems under impulsive noises.

Interval type-2 fuzzy neural networks with asymmetric MFs based on the twice optimization algorithm for nonlinear system identification

This paper proposes a novel algorithm twice optimization for interval type-2 fuzzy neural networks with asymmetric membership functions (TOIT2FNN-AMF), for nonlinear system identification problems. The proposed TOIT2FNN-AMF uses an asymmetric Gaussian interval type-2 membership function to enhance the network’s ability to describe and solve nonlinear and uncertain problems. The twice optimization algorithm consists of structure learning and parameter learning. Firstly, this paper proposes a multi-strategy adaptive differential evolution (MSADE) algorithm as the first optimization algorithm, which is used to determine the structure and the initial values of the parameters of the TOIT2FNN-AMF. It applies the root mean square error (RMSE) of the TOIT2FNN-AMF as the fitness function to determine the structure (number of rules) and initial parameters of the IT2FNN by searching for the RMSE values under different structures. When the fitness value reaches the minimum, that is, the RMSE value of the TOIT2FNN-AMF, the corresponding number will become the optimal one of fuzzy rules of the TOIT2FNN-AMF. Then, the second optimization algorithm of the TOIT2FNN-AMF turns into a hybrid optimization algorithm composed of an adaptive moment estimation (Adam) algorithm and recursive least squares (RLS) algorithm. Adam is used to optimize the antecedent parameters of TOIT2FNN-AMF rules, so as to maintain rapid convergence without generating oscillation during the training process; RLS is used to optimize the consequent parameters of TOIT2FNN-AMF rules, so that the network parameters can be optimized rapidly. In this way, the problems of excessive parameters to be adjusted and excessive slow convergence of the network can be solved. Finally, this paper evaluates the proposed TOIT2FNN-AMF by testing on problems of nonlinear system identification and chaotic time-series prediction. The simulation results are compared with those of similar methods in the existing literatures, which demonstrates that the proposed TOIT2FNN-AMF model yields a lower RMSE value and a simpler network structure than the other type-2 fuzzy neural networks (T2FNNs).

A New Neural Network Training Algorithm Based on Artificial Bee Colony Algorithm for Nonlinear System Identification

Artificial neural networks (ANNs), one of the most important artificial intelligence techniques, are used extensively in modeling many types of problems. A successful training process is required to create effective models with ANN. An effective training algorithm is essential for a successful training process. In this study, a new neural network training algorithm called the hybrid artificial bee colony algorithm based on effective scout bee stage (HABCES) was proposed. The HABCES algorithm includes four fundamental changes. Arithmetic crossover was used in the solution generation mechanisms of the employed bee and onlooker bee stages. The knowledge of the global best solution was utilized by arithmetic crossover. Again, this solution generation mechanism also has an adaptive step size. Limit is an important control parameter. In the standard ABC algorithm, it is constant throughout the optimization. In the HABCES algorithm, it was determined dynamically depending on the number of generations. Unlike the standard ABC algorithm, the HABCES algorithm used a solution generation mechanism based on the global best solution in the scout bee stage. Through these features, the HABCES algorithm has a strong local and global convergence ability. Firstly, the performance of the HABCES algorithm was analyzed on the solution of global optimization problems. Then, applications on the training of the ANN were carried out. ANN was trained using the HABCES algorithm for the identification of nonlinear static and dynamic systems. The performance of the HABCES algorithm was compared with the standard ABC, aABC and ABCES algorithms. The results showed that the performance of the HABCES algorithm was better in terms of solution quality and convergence speed. A performance increase of up to 69.57% was achieved by using the HABCES algorithm in the identification of static systems. This rate is 46.82% for the identification of dynamic systems.

Recursive Maximum Correntropy Algorithms for Second-Order Volterra Filtering

As a special case of the Volterra system, the second-order Volterra (SOV) filter is very efficient for nonlinear system identification. The improved correntorpy based on the generalized Gaussian density function has been proven robust against impulsive noise. In this brief, we propose several SOV filters based on a recursive maximum correntropy (RMC) algorithm for nonlinear system identification. We first introduce a basic RMC algorithm, which faces a trade-off between filtering accuracy and tracking capability due to the use of a fixed forgetting factor (FFF). Two RMCs with variable FF (VFF) are further proposed to enhance the tracking ability. Simulation results demonstrate that our proposed algorithms outperform existing ones in impulsive noise environments and/or in time-varying systems.

Echo state networks for online, multi-step MPC relevant identification

This paper presents an online nonlinear system identification algorithm for model predictive control relevant identification, based on an echo state network (ESN) trained using the recursive least squares method with a directional forgetting factor. The proposed online ESN architecture is formed by a reservoir, with fixed recurrent connections, and a reservoir readout mechanism, which is updated online to define the network output. The ESN is used to perform a multi-step prediction task, which can be used for model-predictive control purposes. The proposed online identification algorithm is evaluated in simulation using a conical tank level process and compared with the results of other approaches from the literature. The results show that the proposed algorithm is able to identify the nonlinear characteristics of the process without considering any prior information about it. In addition, the results for long-range predictions are better than the ones obtained with a model linear in its parameters and several baseline ESN models from literature, after the adaptation phase of the proposed algorithm.

Robust spline adaptive filtering based on accelerated gradient learning: Design and performance analysis

This paper proposes a novel spline adaptive filtering (SAF) algorithm for nonlinear system identification under impulsive noise environments. This algorithm combines the logarithmic hyperbolic cosine (LHC) cost function and the modified Nesterov accelerated gradient (MNAG) learning method, which is called the SAF-LHC-MNAG algorithm. The LHC cost function can reduce the sensitivity of SAF to large outliers and improve the robustness to impulsive noises. Additionally, the MNAG method can further accelerate the convergence under the premise of low steady-state error. Performance analysis of this algorithm is carried out and supported by simulations. Numerical results show that the SAF-LHC-MNAG algorithm has better convergence performance than some existing SAF algorithms. Besides, experimental results confirm the effectiveness of SAF-LHC-MNAG for the accurate identification of nonlinear hysteresis system.

Data-Driven Discovery of Block-Oriented Nonlinear Models Using Sparse Null-Subspace Methods.

This article develops an identification algorithm for nonlinear systems. Specifically, the nonlinear system identification problem is formulated as a sparse recovery problem of a homogeneous variant searching for the sparsest vector in the null subspace. An augmented Lagrangian function is utilized to relax the nonconvex optimization. Thereafter, an algorithm based on the alternating direction method and a regularization technique is proposed to solve the sparse recovery problem. The convergence of the proposed algorithm can be guaranteed through theoretical analysis. Moreover, by the proposed sparse identification method, redundant terms in nonlinear functional forms are removed and the computational efficiency is thus substantially enhanced. Numerical simulations are presented to verify the effectiveness and superiority of the present algorithm.

Robust extended recursive least squares identification algorithm for Hammerstein systems with dynamic disturbances

This paper derives an identification algorithm for Hammerstein nonlinear systems with dynamic disturbances and measurement noise. The dynamic disturbance is viewed as a time-varying sequence to be estimated and its model structure and excitation signal are not considered. By extending the parameter and information vector, an extended recursive least squares algorithm is proposed first time to identify recursively both the system parameters and dynamic disturbance of a Hammerstein output error model. By constructing matrix forgetting factor, the dot product operation is used to update covariance matrix, which improves the estimation accuracy of time-invariant system parameters and the tracking performance of dynamic disturbance. The auxiliary model technique ensures that consistent estimation of model parameters can be obtained. The adaptive forgetting factor improves the convergence rate of the algorithm under finite sampling data. Numerical example with Monte-Carlo simulation test is used to verify the superiority of the proposed algorithm.

Nonlinear system modeling using self-organizing fuzzy neural networks for industrial applications

In this paper, a novel self-organizing fuzzy neural network with an adaptive learning algorithm (SOFNN-ALA) for nonlinear system modeling and identification in industrial processes is proposed. To efficiently enhance the generalization capability, the proposed SOFNN-ALA is designed by using both structure identification and parameter estimation simultaneously in the learning process. In the structure identification phase, the rule neuron with the highest neuronal activity will be split into two new rule neurons. Meanwhile, the redundant rule neurons with small singular values will be removed to simplify the network structure. In the parameter estimation phase, an adaptive learning algorithm (ALA), which is designed based on the widely used Levenberg-Marquardt (LM) optimization algorithm, is adopted to optimize the network parameters. The ALA-based learning algorithm can not only speed up the convergence speed but also enhance the modeling performance. Moreover, we carefully analyze the convergence of the proposed SOFNN-ALA to guarantee its successful practical application. Finally, the effectiveness and efficiency of the proposed SOFNN-ALA is validated by several examples. The experimental results demonstrate that the proposed SOFNN-ALA exhibits a better comprehensive performance than some other state-of-the-art SOFNNs for nonlinear system modeling in industrial applications. The source code can be downloaded from https://github.com/hyitzhb/SOFNN-ALA.git.

Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model

Fractional calculus extends the scope of adaptive algorithms supporting the design of novel fractional methods that outperform standard strategies in various applications arising in applied physics and engineering. In this study, a momentum fractional least-mean-square (M-FLMS) algorithm for nonlinear system identification using a first and fractional-order gradient information is proposed. The M-FLMS avoids being trapped in local minima and provides faster convergence than the standard FLMS. The convergence and complexity analysis of the M-FLMS are given along with simulation results of a benchmark nonlinear system identification problem. The M-FLMS accuracy is verified through a parameter estimation problem for a nonlinear Hammerstein structure, modeling an electrically stimulated muscle (ESM) for rehabilitation of paralyzed muscles. The proposed method is studied in detail for different levels of noise variance, fractional orders and proportion of gradients used in the current update.

Experimental identification of distributed nonlinearities in the modal domain

This paper deals with the nonlinear system identification of structures exhibiting distributed nonlinearities, which has become of great interest recently, due to the continuous interest to improve the performance of structures. This brings the need for designing lighter and more flexible structural elements, which are usually characterized by moderate and large deformation, resulting in a distributed nonlinear behavior. In this framework, system identification remains a particularly challenging problem, especially when experimental measurements are considered. This work proposes a method to perform such a task, based on a convenient model order reduction of the considered structure, followed by a nonlinear system identification algorithm. The methodology is validated on a very thin beam undergoing large-amplitude oscillations, firstly using numerical data and then considering an experimental test bench. On the experimental side, the nonlinearity is first characterized using just the measured data, in order to acquire information that would help the identification process. Eventually, nonlinear system identification is performed in the reduced-order domain. An ad-hoc version of the nonlinear subspace identification (NSI) algorithm is used, but the presented methodology can also be applied with other nonlinear identification tools. Results confirm the goodness of the identification strategy in obtaining a reliable model which takes into account the distributed nonlinear behavior.

Fractional-order Hammerstein state-space modeling of nonlinear dynamic systems from input–output measurements

This paper introduces a continuous-time fractional-order Hammerstein state-space model with a systematic identification algorithm for modeling nonlinear dynamic systems. The proposed model consists of a radial-basis function neural network followed by a fractional-order system. The proposed identification scheme is accomplished in two stages. The structural parameters of the fractional-order system (i.e. the values of the fractional order and the degree of the denominator in the fractional-order system) are estimated in the frequency domain. Then, the synaptic weights of the radial-basis function neural network and the coefficients of the fractional-order system are determined in the time domain via the Lyapunov stability theory, which guarantees stability of the given method and its convergence under a mild condition. Three examples are provided to show the effectiveness of the proposed method.

Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper we develop a path-following interior point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the data set. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.

Neural predictive control of broiler chicken and pig growth

Active control of the growth of broiler chickens and pigs has potential benefits for farmers in terms of improved production efficiency, as well as for animal welfare in terms of improved leg health in broiler chickens. In this work, a differential recurrent neural network (DRNN) was identified from experimental data to represent animal growth using a nonlinear system identification algorithm. The DRNN model was then used as the internal model for nonlinear model predictive control (NMPC) to achieve a group of desired growth curves. The experimental results demonstrated that the DRNN model captured the underlying dynamics of the broiler and pig growth process reasonably well. The DRNN based NMPC was able to specify feed intakes in real time so that the broiler and pig weights accurately followed the desired growth curves ranging from −12% to +12% and −20% to +20% of the standard curve for broiler chickens and pigs, respectively. The overall mean relative error between the desired and achieved broiler or pig weight was 1.8% for the period from day 12 to day 51 and 10.5% for the period from week 5 to week 21, respectively.

A New Parameter Identification Algorithm for a Class of Second Order Nonlinear Systems: An On-line Closed-loop Approach

This paper presents a novel on-line closed-loop parameter identification algorithm for second order nonlinear systems. Parameter convergence of the proposed methodology is ensured by means of a rigorous Lyapunov-based analysis. The estimated parameters are obtained using the actual and an estimation system. Algebraic techniques are applied for estimating velocity and acceleration signals, which are required in the proposed algorithm. A comparative analysis allows assessing the performance of the new parameter identification algorithm with respect to on-line and off-line least squares algorithms. Numerical simulations indicate that the proposed methodology allows estimating different types of non-linearities, converges faster than other methodologies, is robust against disturbances, outperforms on-line techniques, and provides similar estimates as an off-line technique, but without requiring any type of data pre-processing.

Application of interacting multiple model-based fault detection method on a hydraulic two-tank system

This paper addresses the problem of designing a fault identification and detection algorithm for non-linear systems. Timely identification and detection of a fault in a system is crucial in condition monitoring systems. However, finding the source of the failure is not trivial in systems with large numbers of components and complex component relationships. In this paper, an efficient scheme to detect adverse changes in system reliability and find the failed component is proposed, based on the interacting multiple model (IMM) algorithm, with fault detection and diagnosis formulated as a hybrid multiple model estimation scheme. The proposed approach provides an integrated framework for fault detection, diagnosis and state estimation. Its performance is illustrated for fault detection of a non-linear two-tank system. The proposed method can be used with different kinds of filters, using the confusion matrix and classification accuracy as comparison metrics. A particle filter is used with the IMM algorithm and its performance is compared to the linear Kalman filter as a comparative case concerning the improvement that can be achieved when going beyond the consideration that the system is linear.

A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation

Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms.

Type-2 fuzzy neural network using grey wolf optimizer learning algorithm for nonlinear system identification

Real systems with nonlinearity and valuable information always have unpredictable meaning and chaos properties in nature. It is often difficult to obtain the system model based on set of stimulus and response samples due to its complexity. This paper proposes the type-2 fuzzy neural network (T2FNN) and its learning method using grey wolf optimizer (GWO) for system identification. The structure of T2FNN is a combination between a type-2 fuzzy logic system with human-like IF–THEN rule thinking properties and neural networks (NN) with learning and optimization capability. The GWO is a meta-heuristic algorithm inspired from the social hunting behavior of grey wolves as search agents. This method is investigated by strategy, which maintains a proper balance between exploration and exploitation processes and gives more importance to the fittest to find the new position of search agent during the iterations. The GWO algorithm is considered for learning method due to its advantages, including high accuracy, very effective and more competitive. To evaluate the proposed system, the T2FNN with GWO learning method is employed by several nonlinear problems, including single-input single-output systems and multi-input multi-output (MIMO) systems. They are Mackey–Glass chaotic data series, nonlinear plant, nonlinear dynamical time-varying plant, and two MIMO systems. The merits of the proposed learning algorithm can be defined through experiments of the model and compared with existing learning PSO and GA algorithms and previous studies in literature. Based on the experimental results and performance comparisons, the proposed GWO algorithm indeed obtains the enhanced performance and capability in terms of the root mean squared error for nonlinear system identification applications.