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Overview of Research Status
Published in Jingchang Nan, Mingming Gao, Nonlinear Modeling Analysis and Predistortion Algorithm Research of Radio Frequency Power Amplifiers, 2021
The Volterra series method is one of the methods to describe nonlinear systems. It can explain the physical meaning of a nonlinear system more clearly and accurately. However, its disadvantage lies in that the number of model coefficients grows exponentially with the increase of the nonlinearity and memory depth of the system, resulting in an extremely complicated identification process of model coefficients. In most cases, the Volterra series method cannot meet the requirements of model accuracy and complexity at the same time, and is usually used only in PA modeling with weak nonlinearity. To solve these problems of the Volterra series model, some simplified Volterra series models are often selected for PA modeling in recent years. The most frequently used models are Wiener model, Hammerstein model, memory polynomial (MP) model, generalized memory polynomial (GMP) model, etc. Compared with the Volterra series model, the above simplified models greatly reduce the computational complexity and better adapt to modern wireless communication systems.
Estimation of Volterra kernel coefficients of a nonlinear dynamic system
Published in J. Parunov, C. Guedes Soares, Trends in the Analysis and Design of Marine Structures, 2019
Considering the nonlinear responses of ships and offshore structures in harsh environmental loads is crucial in the design of ships and offshore structures, and this requires a long-term response analysis that considers nonlinear. And a solution is needed to overcome the long-term response analysis, as there are time-consuming losses that require performing a very large number of nonlinear analyses of short-term sea conditions. The identification of nonlinear systems based on data among the various methods is attracting attention as an approach to shorten the analysis time required for long-term response analysis. System identification is the method by which the system is defined through the prepared input and output values to derive output data for any input value. The model structures used to identify nonlinear systems include NARX (Nonlinear autoregressive exogenous) models, NLHW (Nonlinear Hammerstein-Wiener) models and Volterra series, etc. In this study, the Volterra Series, a technique widely used to identify dynamic nonlinear systems, was used to model nonlinear properties efficiently according to the order of responses. The Volterra series has a kernel based on the order of responses, and the n-th order kernel derives the n-th order response.
Nonlinear Systems Analysis in Vision: Overview of Kernel Methods
Published in Robert B. Pinter, Bahram Nabet, Nonlinear Vision: Determination of Neural Receptive Fields, Function, and Networks, 1992
These idealized examples point out that a Wiener series for a nonlinearity with a singularity such as a sharp corner cannot be converted into a Volterra series. The distinction between Volterra and Wiener approximations is of practical importance, even though the typical biological nonlinearity, when regarded on a sufficiently small scale, is likely to be smooth rather than abrupt. This is because for some nonlinearities, a signal size small enough to be sensitive to the “smoothness” of the nonlinearity may result in a response which is lost in the noise. Stated another way, a sequence of Wiener approximations built on inputs of successively smaller variances will approach a Volterra limit, provided that the contributions from higher-order components become sufficiently small as the variance decreases. This is the behavior which characterizes an “analytic” nonlinearity (such as y = ex). For a “nonanalytic” nonlinearity (such as y = max{0,x}), higher-order contributions do not become negligible as the variance decreases. An example of a nonlinearity that appears nonanalytic for signals of limitingly small size is that of the Y cell of the cat retina (Victor and Shapley 1979), whose response consists of second- and fourth-order components down to a contrast on the order of 1%.
Volterra and Wiener Model Based Temporally and Spatio-Temporally Coupled Nonlinear System Identification: A Synthesized Review
Published in IETE Technical Review, 2021
Saurav Gupta, Ajit Kumar Sahoo, Upendra Kumar Sahoo
It is one of the powerful mathematical tools for nonlinear system characterization and analysis. Volterra model is the representation of nonlinear system dynamics in terms of Volterra series that differs from well-known Taylor series because of the capability to capture memory effects. Volterra model can well approximate the output of any nonlinear system of the form [30, 31] where is the nonlinear operator with finite memory length (M), is the output for input with present and past sequences, and represents the process disturbance of the system.
Volterra-series-based equivalent nonlinear system method for subharmonic vibration systems
Published in International Journal of Systems Science, 2019
Bin Xiao, Zhen-dong Lu, Shuang-xia Shi, Chao Gao, Li-hua Cao
The Volterra series has been widely applied in the representation and analysis of nonlinear systems. However, when subharmonic generates in the nonlinear system, traditional single finite Volterra series cannot generally represent it. In this paper, a new approach is presented which is an alternative Volterra-series-based method to analyse subharmonic vibration systems over whole concerned input amplitude range where subharmonic generates. By pre-compensating the subharmonic vibration system with a super-harmonic model, the virtual source and the equivalent nonlinear system were obtained, which can be represented by a truncated Volterra series. Truncated order of Volterra series and predominant Volterra kernels of the equivalent nonlinear system were identified by the OLS method. The MGFRFs of the equivalent nonlinear system are obtained from the data of the virtual source and response, and verified by comparing the response estimated by the MGFRFs with its true value. Therefore, the aimed subharmonic vibration system can be analysed by taking advantage of a truncated Volterra series based on the equivalent nonlinear system.
Nonlinear modeling of industrial boiler NOx emissions
Published in Journal of the Air & Waste Management Association, 2022
Guillermo Ronquillo-Lomeli, Noé Amir Rodríguez-Olivares, Leonardo Barriga-Rodríguez, Antonio Ramírez-Martínez, Jorge Alberto Soto-Cajiga, Luciano Nava-Balanzar
The Volterra series has been used successfully in the nonlinear system identification (Schmidt et al. 2014; Wray and Green 1994) and modeling (Cheng et al. 2017; Ronquillo-Lomeli et al. 2018), controllers design, and model structure detection with online parameter estimation (Liu 2001). In this method, the orthogonal least squares (OLS) algorithm is applied for model structure detection and size control using an online model structure selection. The online structure selection is used to graduate the network complexity and make it suitable for providing a system approximation uniform with the actual data values that are being received, and we also developed an algorithm for recursive parameter estimation using the Lyapunov synthesis.