Papers by Keyword: Volterra Series

Abstract: Volterra series take important role in nonlinear vibration analysis. For material hysteresis, it is proposed Bouc-Wen model to estimate frequency response function by using Volterra series in this paper: first, the component of hysteretic linear parameters was identified, then complex function was calculated, finally the differential equation of hysteretic systems was solved based on Harmonic detection method. It is not only for fast-identifying system parameters, but also providing for nonlinear seismic response.

Abstract: Strong Electromagnetic Pulses (EMP) as a new idea weapon has caused many effects like malfunctions, performance degradation, interferences, and destructions in electronic and electrical systems. EMP coupling model research is the foundation of effect evolution and protection. In this paper, a new modeling method on the base of combination system identification theory and Volterra series algorithm was utilized to analyze the electromagnetic coupling process from an external field to an inner electric system. First, we will analyze the theory foundation of non-parameters model evolution. And then, using input and output test data, we presented commonly Voleterra series expression of EMP electromagnetic coupling model. Then, we analyze coupling models several important characteristics in detail. Finally, we approach High Order Spectrum algorithms to identify Volterra kernel functions. Theoretical results show that the Volterra kernel function will be used as an efficient method in EMP coupling model research and can apply this method to character the nonlinear behavior of the EMP electromagnetic coupling. The model described above was assigned under certain assumptions, moreover describes the effects in theory only and does not consider the time variation of the parameters of the system. From this reason it appears as more convenient to characterize the electromagnetic coupling process, by a more universal mathematical approach.

Abstract: This paper gives a low-order approximations of multi-input Volterra series as a nonlinear reduced-order model (ROM) based on wavelet multiresolution analysis. The band-limited pseudorandom multilevel sequence (PRMS) is used as the identification signal and the QR decomposition recursive least square (QRD-RLS) method is utilized as identification method. At last, the ROM is applied to model the nonlinear aerodynamic moment of an airfoil undergoing simultaneous forced pitch and plunge harmonic oscillation. The results show that including the second-order Volterra cross kernels in ROM can capture the coupling effect which significantly improves accuracy in predicting nonlinear aerodynamics under simultaneous motion. And the wavelet multiresolution analysis efficiently reduces the number of identification coefficients for Volterra kernels.

Abstract: Structural damage identification is basically a nonlinear phenomenon; however, nonlinearprocedures are not used currently in practical applications due to the complexity and difficulty forimplementation of such techniques. Therefore, the development of techniques that consider the nonlinearbehavior of structures for damage detection is a research of major importance since nonlineardynamical effects can be erroneously treated as damage in the structure by classical metrics. Thispaper proposes the discrete-time Volterra series for modeling the nonlinear convolution between theinput and output signals in a benchmark nonlinear system. The prediction error of the model in anunknown structural condition is compared with the values of the reference structure in healthy conditionfor evaluating the method of damage detection. Since the Volterra series separate the responseof the system in linear and nonlinear contributions, these indexes are used to show the importanceof considering the nonlinear behavior of the structure. The paper concludes pointing out the mainadvantages and drawbacks of this damage detection methodology.

Abstract: The Volterra series are a functional series.Its kernals both in time domain and frequency domain have definite physical significance and are independent with the system input. Thus the kernals can reflect intrinsic nature of the system. Thus the Volterra series can be used to analyze the nonlinear analog circuit.The fault feature can be extracted based on the direct analysis on the frequency response of nonlinear analog circuit so as to detect the fault in nonlinear analog circuit.

Abstract: For the purpose of addressing non-stationary, poor repeatability, abundant information in the speed-up and speed-down process of a rotor-bearing system, combining with volterra series (VS) and neighborhood rough sets (NRS), a new hybrid intelligent diagnosis method is proposed. The VS is a type of nonparametric model of a nonlinear system, it can model a wide range of nonlinear systems, and can get the volterra kernel that includes the related characteristics of the system through identification. The NRS extracts useful information based only on the data itself, and is used for redundant attributes reduction to make the selected features more objective. In this paper, speed signal and vibration peak-peak value were selected as input and output signals, identified volterra kernels were applied as fault features first, then the NRS was applied for feature selection, and finally support vector machine(SVM) was used as a classifier to recognize faults of the speed-up and speed-down process. The experiment results demonstrate the proposed model not only identifies the fault type, but also identifies the fault severity.

Abstract: Volterra series kernel coefficient calculation of non-linear system is a difficult problem. In this paper, we introduce some way, which can get kernel coefficient. With the increasing of memory length and identification order, it can make calculation complex and hard to rebuild system non-linear model. This article introduces some conventional Volterra series kernel calculation ways, and introduces a kind of method to get Volterra series kernel through using Hilbert space method emphasis, this method can transform Volterra series kernel coefficient calculation problem into reproducing kernel coefficient problem, which has largely simple calculation rate and can get any order Volterra series kernel coefficient in theory.

Abstract: With the development of analysis and identification way to nonlinear dynamic system, people uses many different method to build up mathematics model to simulate nonlinear dynamic system. This paper introduces some important nonlinear system identification ways and a kind of Volterra series expression type in detail. This kind of way adopts Hilbert reproducing kernel method to build up nonlinear dynamic system model. Hilbert space provides a kind of effective expression type for Fourier series and transfer based on anyorthogonal polynomial. Volterra series function has very strict theory basic, which can be applied into many nonlinear dynamic system analysis and identification filed, and has broad practicality and application prospect.

Abstract: In the present study, a nonlinear system identification approach known as NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous Inputs) modelling method and the NOFRF (Nonlinear Output Frequency Response Function) are introduced to detect damage in plate. A set of NOFRF-based damage features is proposed, and the procedure about how to extract the features from the measured response data is presented in detail. An experimental application to the detection of damages in aluminium plates demonstrates the effectiveness and engineering significance of the new damage detection technique.

Abstract: A new bearing fault recognition method based on volterra series and HMM is proposed. In the proposed method, first the feature vectors are extracted from amplitude demodulated signals obtained from normal, ball, inner and outer faulty bearings. The feature vectors are based on the volterra series of the vibration signals, which is obtained by the subspace method. Then these feature vectors are input to each fault’s HMM to be recognized. The result of experiment shows that the proposed method is very effective. The proposed method is tested with the experiment data sampled from drive end ball bearing of an induction motor driven mechanical system.