scholarly journals Nonlinear System Identification in coherence with Nonlinearity measure for Dynamic Physical systems- Case Studies

2021 ◽  
Author(s):  
Joanofarc Xavier ◽  
Rames C Panda ◽  
SK Patnaik
Keyword(s):  
Nonlinear Dynamics ◽  
System Identification ◽  
Nonlinear System ◽  
Case Studies ◽  
Nonlinear System Identification ◽  
Least Square ◽  
Measurement Tool ◽  
Identification Methods ◽  
Physical Systems ◽  
Highly Nonlinear

Abstract With the recent success of using the time series to vast applications, one would expect its boundless adaptation to problems like nonlinear control and nonlinearity quantification. Though there exist many system identification methods, finding suitable method for identifying a given process is still cryptic. Moreover, to this notch, research on their usage to nonlinear system identification and classification of nonlinearity remains limited. This article hovers around the central idea of developing a ‘kSINDYc’ (key term based Sparse Identification of Nonlinear Dynamics with control) algorithm to capture the nonlinear dynamics of typical physical systems. Furthermore, existing two reliable identification methods namely NL2SQ (Nonlinear least square method) and N3ARX (Neural network based nonlinear auto regressive exogenous input scheme) are also considered for all the physical process-case studies. The primary spotlight of present research is to encapsulate the nonlinear dynamics identified for any process with its nonlinearity level through a mathematical measurement tool. The nonlinear metric Convergence Area based Nonlinear Measure (CANM) calculates the process nonlinearity in the dynamic physical systems and classifies them under mild, medium and highly nonlinear categories. Simulation studies are carried-out on five industrial systems with divergent nonlinear dynamics. The user can make a flawless choice of specific identification methods suitable for given process by finding the nonlinear metric (Δ0). Finally, parametric sensitivity on the measurement has been studied on CSTR and Bioreactor to evaluate the efficacy of kSINDYc on system identification.

scholarly journals Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Lan Wang ◽  
Yu Cheng ◽  
Jinglu Hu ◽  
Jinling Liang ◽  
Abdullah M. Dobaie
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Radial Basis Function Network ◽  
Nonlinear System Identification ◽  
Support Vector ◽  
Identification Procedure ◽  
Identification Methods ◽  
Nonlinear Parameter Identification ◽  
And Control ◽  
Function Network

Quasi-linear autoregressive with exogenous inputs (Quasi-ARX) models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN) model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.

Nonlinear System Identification Technique for a Base-Excited Structure Based on Modal Space Formulation

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Sushil Doranga ◽  
Christine Q. Wu
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Nonlinear System Identification ◽  
Model Space ◽  
Least Square ◽  
Closed Form Expression ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Modal Space

Most of the nonlinear system identification techniques described in the existing literature required force and response information at all excitation degrees-of-freedom (DOFs). For cases, where the excitation comes from base motion, those methods cannot be applied as it is not feasible to obtain the measurements of motion at all DOFs from an experiment. The objective of this research is to develop the methodology for the nonlinear system identification of continuous, multimode, and lightly damped systems, where the excitation comes from the moving base. For this purpose, the closed-form expression for the equivalent force also known as the pseudo force from the measured data for the base-excited structure is developed. A hybrid model space is developed to find out the nonlinear restoring force at the nonlinear DOFs. Once the nonlinear restoring force is obtained, the nonlinear parameters are extracted using “multilinear least square regression” in a modal space. A modal space is chosen to express the direct and cross-coupling nonlinearities. Using a cantilever beam as an example, the proposed methodology is demonstrated, where the experimental setup, testing procedure, data acquisition, and data processing are presented. The example shows that the method proposed here is systematic and constructive for nonlinear parameter identification for base-excited structure.

Modeling and Identification of a Nonlinear SDOF Moored Structure, Part 1—Hydrodynamic Models and Algorithms

2004 ◽  
Vol 126 (2) ◽  
pp. 175-182 ◽  
Author(s):  
S. Narayanan ◽  
S. C. S. Yim
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Small Body ◽  
Nonlinear System Identification ◽  
Ocean Waves ◽  
System Response ◽  
Restoring Force ◽  
Nonlinear Structure ◽  
Submerged Sphere ◽  
Highly Nonlinear

The highly nonlinear responses of compliant ocean structures characterized by a large-geometry restoring force and coupled fluid-structure interaction excitation are of great interest to ocean and coastal engineers. Practical modeling, parameter identification, and incorporation of the inherent nonlinear dynamics in the design of these systems are essential and challenging. The general approach of a nonlinear system technique using very simple models has been presented in the literature by Bendat. In Part 1 of this two-part study, two specific nonlinear small-body hydrodynamic Morison type formulations: (A) with a relative-velocity (RV) model, and (B) with an independent flow-field (IFF) model, are formulated. Their associated nonlinear system-identification algorithms based on the reverse multiple-input/single-output (R-MI/SO) system-identification technique: (A.1) nonlinear-structure linearly damped, and (A.2) nonlinear-structure coupled hydrodynamically damped for the RV model, and (B.1) nonlinear-structure nonlinearly damped for the IFF model, are developed for a specific experimental submerged-sphere mooring system under ocean waves exhibiting such highly nonlinear response behaviors. In Part 2, using the measured input wave and output system response data, the algorithms derived based on the MI/SO linear analysis of the reverse dynamic systems are applied to identify the properties of the highly nonlinear system. Practical issues on the application of the R-MI/SO technique based on limited available experimental data are addressed.

scholarly journals Nonlinear System Identification via Tensor Completion

2020 ◽  
Vol 34 (04) ◽  
pp. 4420-4427
Author(s):  
Nikos Kargas ◽  
Nicholas D. Sidiropoulos
Keyword(s):  
Neural Networks ◽  
System Identification ◽  
Nonlinear System ◽  
Nonlinear System Identification ◽  
Nonlinear Function ◽  
Low Rank ◽  
Tensor Completion ◽  
Input Output ◽  
Completion Problem ◽  
Highly Nonlinear

Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general nonlinear system, as they have proven to be very effective in approximating complex highly nonlinear functions. In this work, we show that identifying a general nonlinear function y = ƒ(x1,…,xN) from input-output examples can be formulated as a tensor completion problem and under certain conditions provably correct nonlinear system identification is possible. Specifically, we model the interactions between the N input variables and the scalar output of a system by a single N-way tensor, and setup a weighted low-rank tensor completion problem with smoothness regularization which we tackle using a block coordinate descent algorithm. We extend our method to the multi-output setting and the case of partially observed data, which cannot be readily handled by neural networks. Finally, we demonstrate the effectiveness of the approach using several regression tasks including some standard benchmarks and a challenging student grade prediction task.

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