Nonlinear System Identification Method Research Articles

Two-dimensional identification of time-varying batch nonlinear processes with input dead-zone nonlinearity

ABSTRACT In the time dimension, the batch process with input dead-zone nonlinearity often has the characteristics of short operation time and time-varying process parameters. A two-dimensional recursive least squares (2D-RLS) identification method for time-varying nonlinear systems with input dead zone is proposed. By mining system dynamic information from the time direction of the same batch and different batch directions, the identification parameters are updated. The proposed two-dimensional identification strategy converts the time-varying parameter estimation problem of time dimension into the equivalent time-invariant parameter estimation problem of batch dimension. Sufficient production data in batch dimension ensure that the proposed identification algorithm can eliminate the influence of random measurement noise. The identification strategy with unequal length of batch data is also given. The convergence of the proposed algorithm is analysed. Finally, numerical simulation and experimental tests are used to verify the effectiveness and superiority of the proposed algorithm.

Nonlinear system identification using modified variational autoencoders

This research proposes a methodology for identifying nonlinear systems using input/output data and deep learning generative models. Our framework integrates Variational Autoencoders (VAE) with Nonlinear Autoregressive with exogenous input (NARX) in a unified identification structure to address overfitting in nonlinear system identification using NARX structures. Specifically, we modify a variational autoencoder by replacing the decoder module with a NARX model using the latent space information captured from the VAE encoder module as one of the exogenous inputs. Following the training phase, the decoder module can be used as a nonlinear model of the system. We evaluate the efficacy of our approach by performing open-loop prediction tests on data from four nonlinear benchmark systems: Cascaded tanks, Gas furnace, Silverbox, and Wiener-Hammerstein. The proposed VAE-NARX method reported Root Mean Squared Error (RMSE) of 8.23×10−3, 16.69×10−3, 0.002×10−3 and 0.037×10−3 respectively. Our results demonstrate that our proposed method achieves similar and outperforms prediction performances to standard identification techniques and can enhance the performance of traditional nonlinear system identification methods based on multi-layer perceptron models.

Adaptive neural identification and non-singular control of pure-feedback nonlinear systems

This paper proposes a new constructive identification and adaptive control method for nonlinear pure-feedback systems, which remedies the ’explosion of complexity’ and potential control singularity encountered in the traditional adaptive backstepping controllers. First, to avoid using the backstepping recursive design, alternative state variables and the corresponding coordinate transformation are introduced to reformulate the pure-feedback system into an equivalent canonical model. Then, a high-order sliding mode (HOSM) observer is used to reconstruct the unknown states for this canonical model. To remedy the potential singularity in the control, the unknown system dynamics are lumped to derive an alternative identification structure and one-step control synthesis, where two radial basis function neural networks (RBFNN) are adopted to online estimate these lumped dynamics. In this framework, the online estimation of control gain is not in the denominator of controller, and thus the division by zero in the controllers is avoided. Finally, a new online learning algorithm is constructed to obtain the RBFNNs’ weights, ensuring the convergence to the neighborhood of true values and allowing accurate identification of unknown dynamics. Theoretical analysis elaborates that the convergence of both the tracking error and the estimation error is obtained simultaneously. Simulations and practical experiments on a hydraulic servo test-rig verify the effectiveness and utility of the suggested methods.

A robust sparse identification method for nonlinear dynamic systems affected by non-stationary noise.

In the field of science and engineering, identifying the nonlinear dynamics of systems from data is a significant yet challenging task. In practice, the collected data are often contaminated by noise, which often severely reduce the accuracy of the identification results. To address the issue of inaccurate identification induced by non-stationary noise in data, this paper proposes a method called weighted ℓ1-regularized and insensitive loss function-based sparse identification of dynamics. Specifically, the robust identification problem is formulated using a sparse identification mathematical model that takes into account the presence of non-stationary noise in a quantitative manner. Then, a novel weighted ℓ1-regularized and insensitive loss function is proposed to account for the nature of non-stationary noise. Compared to traditional loss functions like least squares and least absolute deviation, the proposed method can mitigate the adverse effects of non-stationary noise and better promote the sparsity of results, thereby enhancing the accuracy of identification. Third, to overcome the non-smooth nature of the objective function induced by the inclusion of loss and regularization terms, a smooth approximation of the non-smooth objective function is presented, and the alternating direction multiplier method is utilized to develop an efficient optimization algorithm. Finally, the robustness of the proposed method is verified by extensive experiments under different types of nonlinear dynamical systems. Compared to some state-of-the-art methods, the proposed method achieves better identification accuracy.

Fractional Order Learning Methods for Nonlinear System Identification Based on Fuzzy Neural Network

Fractional Order Learning Methods for Nonlinear System Identification Based on Fuzzy Neural Network

Nonlinear System Identification Using Audio-Inspired WaveNet Deep Neural Networks

Nonlinear system identification is a challenging task that requires accurate estimation of the structural model from observations of nonlinear behavior. The WaveNet, which was originally a neural network architecture for audio processing, has been modified and first introduced to the analysis of mechanical signals to capture long-term dependencies in mechanical systems and generate high-quality signals. A novel nonlinear system identification method has been proposed using a modified WaveNet-based approach that constructs a relationship between the vibration response and the nonlinear elements in the inverse model without the need for a definite structural model. This approach uses dilated convolution for feature extraction and a multilayer perceptron for feature transition, with the addition of average pooling along the time dimension for adaptive processing of varying length data, which are more computationally efficient and widely applicable. The 13-layer modified WaveNet models have been designed and applied to the problem. Comparisons with other baseline models were made to demonstrate the method’s superiority in terms of accuracy, effectiveness, and robustness. Additionally, the method has been applied to predict composite models of friction and elastic curves, demonstrating its ability to handle diverse and complex problems.

Kernel Regularization Based Volterra Series Identification Method for Time-delayed Nonlinear Systems with Unknown Structure

Kernel Regularization Based Volterra Series Identification Method for Time-delayed Nonlinear Systems with Unknown Structure

Predicting Nonlinear Modal Properties by Measuring Free Vibration Responses

AbstractIdentifying dynamical system models from measurements is a central challenge in the structural dynamics community. Nonlinear system identification, in particular, is a big challenge as there are many possible combinations of model structures, which requires expert knowledge to construct an appropriate model. Furthermore, traditional nonlinear system identification methods require a steady excitation input that is not always available in many practical applications. Recently, a technique referred to as the sparse identification of nonlinear dynamics (SINDy) algorithm was developed to discover mathematical models of general nonlinear systems. The SINDy method finds a generalized linear state-space model for an autonomous nonlinear system by analyzing the collected response data. In this work, the SINDy method is adapted and combined with the shooting method and the numerical continuation technique to form a system identification framework that can predict the nonlinear modal properties of mechanical oscillators. The proposed framework predicts the nonlinear normal modes (NNMs) of these systems by processing the noised data of the systems' free vibration response. In addition, the NNMs and the internal resonance of nonlinear systems at a high energy level can be captured using the proposed framework by processing the response data at a lower energy level. The proposed method is numerically demonstrated on a 2-degree-of-freedom mechanical oscillator. Furthermore, the effects of the measurement error and the excitation condition on NNM prediction are investigated. The NNM prediction framework presented in this paper is fairly general and is applicable to a variety of nonlinear systems.

Subspace State-Space Identification of Nonlinear Dynamical System Using Deep Neural Network with a Bottleneck

This paper proposes a new type of subspace state-space system identification method for nonlinear dynamical systems, which generates a model consisting of a state estimator and a predictor that can be directly used for model predictive control (MPC). The main feature of the proposed method is that it uses a neural network with a bottleneck layer between the state estimator and predictor to represent the input-output dynamics, and it is proven that the state of the dynamical system can be extracted from the bottleneck layer based on the observability of the target system. The training of the network is shown to be a natural nonlinear extension of the subspace state-space system identification method established for linear dynamical systems. This correspondence provides interpretability and optimality to the resulting model based on linear control theory. The usefulness of the proposed method and the interpretability of the model are demonstrated through an illustrative example of MPC.

Hybrid identification method for fractional-order nonlinear systems based on the multi-innovation principle

Hybrid identification method for fractional-order nonlinear systems based on the multi-innovation principle

A real-time identification method of network structure in complex network systems

This paper develops a real-time identification algorithm for structures of network systems. We have already proposed a structure identification method for nonlinear network systems with nonlinear couplings by combining Koopman operator theory and a sparse identification method. However, the proposed method is only applicable for offline use under the assumption that the state of an isolated system is available. To relax this assumption, this paper shows that the dynamical model of isolated systems can be extracted from measured data of interconnected systems under some weak restrictions on network structures. We also modify the identification algorithm to obtain real-time identification results with fewer calculation resources and analyse the convergence of the proposed methods. Numerical examples demonstrate that the proposed method can identify network structures in real-time and detect changes in networks correctly.

Volterra series based nonlinear system identification methods and modelling capabilities

Volterra series based nonlinear system identification methods and modelling capabilities

Volterra series based nonlinear system identification methods and modelling capabilities

Volterra series based nonlinear system identification methods and modelling capabilities

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data, Part I: Measurement of nonlinear dynamics

Jointed structures are ubiquitous constituents of engineering systems; however, their dynamic properties (e.g., natural frequencies and damping ratios) are challenging to identify correctly due to the complex, nonlinear nature of interfaces. This research seeks to extend the efficacy of traditional experimental methods for linear system identification (such as impact testing, shaker ringdown testing, random excitation, and force or amplitude-control stepped sine testing) on nonlinear jointed systems, e.g., the half Brake–Reußbeam, by augmenting them with full-field data collected by high-speed videography. The full-field response is acquired using high-speed cameras combined with Digital Image Correlation (DIC), which enables studying the spatial–temporal dynamic characteristics of the system. As this is a video-based experiment, additional constraints are attached to the beam at the node points to remove the rigid body motion, which ensures that the beam is in the view of the camera during the entire test. The use of a video-based method introduces new sources of experimental error, such as noise from the high-speed camera’s fan and electrical noise, and so the measurement accuracy of DIC is validated using accelerometer data. After validating the DIC data, the measurements are recorded for several types of excitation, including hammer testing, shaker ringdown testing, fixed sine testing, and stepped sine testing. Using the DIC data to augment standard nonlinear system identification techniques, modal coupling and the mode shapes’ evolution are investigated. The suitability of videography methods for nonlinear system identification of nonlinear beams is explored for the first time in this paper, and recommendations for techniques to facilitate this process are made. This article focuses on developing an accurate data collection methodology as well as recommendations for nonlinear testing with DIC, which paves the way for video-based investigation of nonlinear system identification. In Part-II (Jin et al., 2021) of this work, the same data set is used for a rigorous assessment of nonlinear system identification with full-field DIC data.

Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data; Part II - Nonlinear system identification

The dynamic responses of assembled structures are greatly affected by the mechanical joints, which are often the cause of nonlinear behavior. To better understand and, in the future, tailor the nonlinearities, accurate methods are needed to characterize the dynamic properties of jointed structures. In this paper, the nonlinear characteristics of a jointed beam is studied with the help of multiple identification methods, including the Hilbert Transform method, Peak Finding and Fitting method, Dynamic Mode Decomposition method, State-Space Spectral Submanifold, and Wavelet-Bounded Empirical Mode Decomposition method. The nonlinearities are identified by the responses that are measured via accelerometers in a series of experiments that consist of hammer testing, shaker ringdown testing, and response/force-control stepped sine testing. In addition to accelerometers, two high-speed cameras are used to capture the motion of the whole structure during the shaker ringdown testing. Digital Image Correlation (DIC) is then adopted to obtain the displacement responses and used to determine the mode shapes of the jointed beam. The accuracy of the DIC data is validated by the comparison between the identification results of acceleration and displacement signals. As enabled by full-field data, the energy-dependent characteristics of the structure are also presented. The setup of the different experiments is described in detail in Part I (Chen et al., 2021) of this research. The focus of this paper is to compare nonlinear system identification methods applied to different measurement techniques and to exploit the use of high spatial resolution data.

Nonlinear modal interactions in a beam-mass system tuned to 3:1 and combination internal resonances based on correspondence between MTS and NSI methods

In this article, a correspondence between multiple time scales (MTS) results and nonlinear system identification (NSI) method is established to identify nonlinear modal interactions in large amplitude vibrations of a coupled dynamical system. The system is a beam carrying a mass-spring-damper (MSD) system tuned to 3:1 and combination internal resonances caused by MSD parameters. The energy exchange mechanisms and modal interactions among the first three vibration modes are interpreted based on the modal amplitudes extracted by the MTS method. However, these amplitudes are not available in practical measured time series. Therefore, to detect the modal interactions based on measured data, time-frequency analysis beside NSI is employed. To this end, the mono-frequency components of the time series are studied by extracting intrinsic mode functions (IMFs), and a correspondence between the IMFs amplitudes and MTS results is determined to comprehend the energy exchanges in the system. Accordingly, by applying NSI for different values of excitation frequency, energy exchange among the modes is understood without the necessity of modal amplitudes. Moreover, the dominant dynamic behavior of the time response, i.e. periodic, quasi-periodic, and chaotic behaviors are determined, and beating-like phenomenon in the IMFs is investigated.

A nonlinear signal processing framework for rapid identification and diagnosis of structural freeplay

Structural freeplay due to loosened mechanical linkages is a discrete nonlinear event which occurs pseudo-routinely in modern aircraft, causing severe airframe vibration. This impacts fatigue life, and has serious implications for fleet management and Structural Health Monitoring (SHM). While the concepts which drive SHM for aircraft are traditionally based on reactive procedures, we are currently observing a major shift towards actionable and pro-active condition-based maintenance, known as Prognostics and Health Management (PHM), to significantly reduce fleet sustainment costs. Given this current paradigm shift, there is a demand for the development of novel strategies to address decades old SHM problems, where the adaptation of existing methods or the development of new and innovative techniques both play critical roles. In this paper a signal processing framework is presented, based upon well-established nonlinear system identification methods, to rapidly diagnose structural freeplay in aircraft systems with a focus on the requirements of PHM technology. The framework exploits the nonlinear dynamical characteristics of the structural freeplay anomaly in a transonic aeroelastic system by specifically targeting rich bilinear signatures that are encoded in time-domain sensory outputs, via the Higher-Order Spectra (HOS) and the Empirical Mode Decomposition (EMD). The characteristic freeplay signatures which were initially extracted from computational transonic aeroelastic models are shown to be analogous in a transonic flight-test case-study (an all-movable horizontal tail with actuator freeplay), presenting a rare and important opportunity to verify the practical freeplay identification research. Once verified, a comprehensive understanding of the fundamental bilinear signatures allows the HOS and EMD to be adapted and refined towards a structured freeplay diagnosis framework. Using the extensive flight-test dataset as a case study, it is shown that the freeplay location and magnitude information can be extracted with a high level of robustness, verified by making consistent predictions over a period of three years and several maintenance cycles, with a large variation in Mach number and angle-of-attack (predominantly high angle maneuvers). The paper is intended to communicate the fundamental principles and significance of the data-driven framework, highlighting revisiting and adapting existing well-established nonlinear identification tools, it is possible to address the requirements of contemporary SHM, although practical implementation requires ongoing research. Limitations of the data-driven approach are discussed, predominantly related to data acquisition requirements.

Identification and semi-active control of structures with abrupt stiffness degradations

This paper presents for variable stiffness tuned mass dampers (VS-TMDs) a vibration control algorithm combined with a nonlinear system identification method. The objective of the proposed approach is the control of multistory shear frame structures, which exhibit abrupt stiffness degradations. A stiffness variable control (SVC) algorithm is developed to control the stiffness of the VS-TMD, which is based on the mitigation of the potential energy of the structure. For the identification of the system parameters, an adaptive unscented Kalman filter (A-UKF) scheme is utilized. The paper describes the theoretical background of the proposed approach with its governing equations and conducts performance studies on a semi-actively controlled 2-story shear frame structure. Harmonic, white noise and earthquake excitation scenarios including seismic aftershock effects are investigated. Sensitivity studies are conducted. With the proposed approach, the abrupt stiffness changes of the structure are detected and the damper stiffness is adapted successfully. The results show that the SVC together with the A-UKF clearly outperforms the passive TMD control.

A Nonlinear System Identification Method Based on Adaptive Neural Network

Nonlinear system identification (NSI) is of great significance to modern scientific engineering and control engineering. Despite their identification ability, the existing analysis methods for nonlinear systems have several limitations. The neural network (NN) can overcome some of these limitations in NSI, but fail to achieve desirable accuracy or training speed. This paper puts forward an NSI method based on adaptive NN, with the aim to further improve the convergence speed and accuracy of NN-based NSI. Specifically, a generic model-based nonlinear system identifier was constructed, which integrates the error feedback and correction of predictive control with the generic model theory. Next, the radial basis function (RBF) NN was optimized by adaptive particle swarm optimization (PSO), and used to build an NSI model. The effectiveness and speed of our model were verified through experiments. The research results provide a reference for applying the adaptive PSO-optimized RBFNN in other fields.

NONLINEAR SYSTEM IDENTIFICATION OF WPC TERRACE WALL WITH HAMMERSTEIN-WIENER MODEL USING AMBIENT VIBRATION

Today, many advances in engineering field have been and are being made. Especially the predictions of the strengths and behavior of the models designed against external factors are of great importance. Elimination of negative effects and necessary updates on the model or in other words, strengthening works play the biggest role in the design stages. In addition to all these, the dynamically influenced situations of existing structures should be revealed. New methods have been developed for this and similar reasons. System identification is one of these methods. System identification is simply the estimation of the mathematical model of the building from the input and output vibration data obtained through the structures. Thanks to the predicted mathematical model, the reactions of the building to dynamic effects can be predicted. The aim of this study is to reveal the mathematical model of the WPC terrace wall with the nonlinear system identification method. Finally, nonlinear system identification of the WPC terrace wall results demonstrated that fit to estimation data was nearly 100 % and it can be concluded that Hammerstein–Wiener system identification method is efficient and accurate in identifying mathematical model of the WPC terrace wall.