摘要 :
Nonlinear factors existing in engineering structures have drawn considerable attention, and nonlinear identification is a competent technique to understand the dynamic characteristics of nonlinear structures. Therefore, in this pa...
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Nonlinear factors existing in engineering structures have drawn considerable attention, and nonlinear identification is a competent technique to understand the dynamic characteristics of nonlinear structures. Therefore, in this paper, a novel nonlinear separation subspace identification (NSSI) algorithm based on subspace algorithm and nonlinear separation strategy is proposed to conduct nonlinear parameter identification of nonlinear structures. For the proposed NSSI algorithm, the low-level excitation test is firstly conducted to obtain the transfer matrix in the linear response formula. Then, the obtained transfer matrix is used in the high-level excitation test to calculate the nonlinear response part by the proposed nonlinear separation strategy, and the subspace algorithm is utilized to identify the nonlinear parameter on the modified state-space model including only the nonlinear part. The proposed NSSI algorithm can reduce the coupling error caused by simultaneously processing both the large number part (corresponding to the linear part) and small number part (corresponding to the nonlinear part) in the traditional nonlinear subspace identification (NSI) algorithm. At last, two numerical experiments are given to validate the effectiveness of the developed novel nonlinear identification method. Furthermore, some influence factors are discussed to show the stability of the identification algorithm, and some comparisons between the proposed NSSI method and traditional NSI method are also conducted to demonstrate the advantages of the novel method.
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Clearance which is a typical nonlinear factor is unavoidable in the engineering structure. Clearance would constantly change during service, thus exceeding the reasonable design range. The improper clearance can change the contact...
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Clearance which is a typical nonlinear factor is unavoidable in the engineering structure. Clearance would constantly change during service, thus exceeding the reasonable design range. The improper clearance can change the contact state of parts to degrade the dynamical performance of the mechanical system. Nonlinear parameter identification is an efficient tool for understanding the characteristic of clearance nonlinearity and contributing significantly to control the clearance effect. In this paper, the simultaneous identification algorithm is proposed to simultaneously identify two clearance parameters, clearance value and effective stiffness, and the transfer error existing in the previous multi-step identification method (Li et al., 2015) can be avoided so as to improve the identification accuracy. For the proposed simultaneous identification algorithm, on the one hand, Tikhonov regularization method is used to solve a nonlinear force calculation formula which is formed by the transmission characteristic of the clearance-type system to directly obtain the nonlinear force. On the other hand, clearance nonlinear force can also be predicted by the mechanics characteristic of clearance nonlinearity. And then, the clearance parameters can be simultaneously obtained by an iterative parametric optimization process, wherein the objective is to minimize the error between the calculated and predicted nonlinear forces. The feasibility of simultaneous identification algorithm is verified by simulation data from a cantilever with clearance nonlinearity. The influence factors, including initial guess, non-equivalence clearance parameters and other nonlinearities, are fully discussed to illustrate the robustness of simultaneous identification algorithm. The experimental data from the clearance test-bed are utilized to verify the effectiveness of the simultaneous identification algorithm. Numerical and experimental studies show that the proposed identification algorithm can precisely and simultaneously identify the clearance value and effective stiffness, and compared with previous multi-step identification method, simultaneous identification algorithm is more accurate and stable.
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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. T...
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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. (C) 2019 Elsevier Ltd. All rights reserved.
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New multi-directional model validation tests are derived to provide improved statistical validation test procedures for a wide crass of non-linear modelling methods. [References: 11]
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This article presents a nonlinear system identification approach that uses a two-dimensional (2-D) wavelet-based state-dependent parameter (SDP) model. In this method, differing from our previous approach, the SDP is a function wi...
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This article presents a nonlinear system identification approach that uses a two-dimensional (2-D) wavelet-based state-dependent parameter (SDP) model. In this method, differing from our previous approach, the SDP is a function with respect to two different state variables, which is realised by the use of a 2-D wavelet series expansion. Here, an optimised model structure selection is accomplished using a PRESS-based procedure in conjunction with orthogonal decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. Two simulation examples are provided to demonstrate the merits of the proposed approach.
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Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisti...
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Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites may require nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, in most of the applications in structural dynamics, linear FRF matrices constructed from experimental measurements will not be complete. These handicaps make most of the methods given in the literature difficult to apply to engineering structures. The aim of this study is to improve a previously developed method considering these practical limitations. The approach proposed can be used for detection, localization, characterization and parametric identification of nonlinear elements by using incomplete FRF data. In order to reduce the effort and avoid the limitations in using footprint graphs for identification of nonlinearity, describing function inversion is used. Thus, it is made possible to identify the restoring force of more than one type of nonlinearity which may co-exist at the same location. The validation of the method is demonstrated with case studies based on simulated experiments, as well as real experiments with two nonlinear structures. It is concluded in this study that the approach proposed improves the previously developed method by avoiding the use of footprint graphs in nonlinear identification and also by making it possible to identify more than one type of nonlinearity that may co-exist at the same location.
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To identify multiple degree-of-freedom vibrating structures with local nonlinearities, a two-stage time domain approach based on the subspace method is proposed in this study. The locally nonlinear system to-be-identified is divid...
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To identify multiple degree-of-freedom vibrating structures with local nonlinearities, a two-stage time domain approach based on the subspace method is proposed in this study. The locally nonlinear system to-be-identified is divided into an underlying linear part described by the FRF and a local nonlinear part described by nonlinear coefficients. The identification process of the proposed approach is not the same as the existing single-stage method. It identifies the underlying linear system before the local nonlinearities. The proposed approach reduces the dimensions of matrices which are used to calculate the system's state-space model and also gives a more appropriate estimation of the order of the underlying linear system with the utilization of classical spectrum estimation techniques. Both numerical and experimental examples are given to verify the performance of the method. Results show that the method is more accurate and reliable than the single-stage method, especially in a noisy environment.
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Summary This paper investigates the identification problem of an output‐error nonlinear system with saturation and dead‐zone nonlinearity. Introducing a switching function and by means of the auxiliary model identification idea,...
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Summary This paper investigates the identification problem of an output‐error nonlinear system with saturation and dead‐zone nonlinearity. Introducing a switching function and by means of the auxiliary model identification idea, an auxiliary model hierarchical least squares‐based iterative algorithm is proposed for estimating the parameters of the nonlinear system. Based on the hierarchical identification model, an auxiliary model hierarchical gradient‐based iterative algorithm is presented for the nonlinear system by utilizing the gradient search. In order to take full advantage of the system data, an auxiliary model hierarchical multi‐innovation gradient‐based iterative algorithm is derived for the nonlinear system according to the multi‐innovation identification theory. Finally, the numerical simulation results illustrate the effectiveness of the proposed algorithms.
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This paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded-error context. This method is based on functions which consists of the difference of two convex functions, called DC functions. ...
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This paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded-error context. This method is based on functions which consists of the difference of two convex functions, called DC functions. The method considers DC representations of the functional form of the dynamic system to obtain an outer bound of the set of parameters that are consistent with the measurements, the system and the considered bounded error. At each iteration, the proposed algorithm solves several convex optimization problems to discard from the initial search region subregions that are proved not consistent. This operation is repeated while the obtained solution is improved. Four examples are provided to clarify the proposed identification algorithm.
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Within Hybrid systems, piecewise affine systems are a common class to be identified from input/output data. In this paper an improved algorithm for identifying piecewise affine systems is developed. The algorithm stems from cluste...
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Within Hybrid systems, piecewise affine systems are a common class to be identified from input/output data. In this paper an improved algorithm for identifying piecewise affine systems is developed. The algorithm stems from clustering-based system identification. An affine output error algorithm is used to identify final models. The performance of the new Piecewise Affine Output Error (PWA-OE) algorithm is demonstrated using experimental data from a Radio Frequency MicroElectroMechanical Systems switch. Compared to the existing state-of-the-art, the PWA-OE algorithm generates a potential 62% improvement in model coefficient accuracy. Furthermore the PWA-OE algorithm is less sensitive to two additional input parameter selections.
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