Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Analysis of Some Approaches to Modeling Nonlinear Dynamical Systems Using Polynomial Operators

The problem of mathematical description of nonlinear dynamical systems remains relevant today, especially given the need to build modern surveillance systems for complex technical objects, such as power plants. The use of polynomial operators obtained with the help of shortened Volterra series to solve this problem, as practice has shown, proved to be promising, because this method allows to display in the mathematical model both nonlinear and dynamic properties of systems. For further development of the method, it is advisable to analyze diffe­rent approaches in order to build effective algorithms for obtaining and applying in the problems of monitoring the functioning of nonlinear systems.

A Bivariate Volterra Series Model for the Design of Power Amplifier Digital Predistorters

The operation of the power amplifier (PA) in wireless transmitters presents a trade-off between linearity and power efficiency, being more efficient when the device exhibits the highest nonlinearity. Its modeling and linearization performance depend on the quality of the underlying Volterra models that are characterized by the presence of relevant terms amongst the enormous amount of regressors that these models generate. The presence of PA mechanisms that generate an internal state variable motivates the adoption of a bivariate Volterra series perspective with the aim of enhancing modeling capabilities through the inclussion of beneficial terms. In this paper, the conventional Volterra-based models are enhanced by the addition of terms, including cross products of the input signal and the new internal variable. The bivariate versions of the general full Volterra (FV) model and one of its pruned versions, referred to as the circuit-knowledge based Volterra (CKV) model, are derived by considering the signal envelope as the internal variable and applying the proposed methodology to the univariate models. A comparative assessment of the bivariate models versus their conventional counterparts is experimentally performed for the modeling of two PAs driven by a 30 MHz 5G New Radio signal: a class AB PA and a class J PA. The results for the digital predistortion of the class AB PA under a direct learning architecture reveal the benefits in linearization performance produced by the bivariate CKV model structure compared to that of the univariate CKV model.

Comparison of Feature Selection Techniques for Power Amplifier Behavioral Modeling and Digital Predistortion Linearization

The power amplifier (PA) is the most critical subsystem in terms of linearity and power efficiency. Digital predistortion (DPD) is commonly used to mitigate nonlinearities while the PA operates at levels close to saturation, where the device presents its highest power efficiency. Since the DPD is generally based on Volterra series models, its number of coefficients is high, producing ill-conditioned and over-fitted estimations. Recently, a plethora of techniques have been independently proposed for reducing their dimensionality. This paper is devoted to presenting a fair benchmark of the most relevant order reduction techniques present in the literature categorized by the following: (i) greedy pursuits, including Orthogonal Matching Pursuit (OMP), Doubly Orthogonal Matching Pursuit (DOMP), Subspace Pursuit (SP) and Random Forest (RF); (ii) regularization techniques, including ridge regression and least absolute shrinkage and selection operator (LASSO); (iii) heuristic local search methods, including hill climbing (HC) and dynamic model sizing (DMS); and (iv) global probabilistic optimization algorithms, including simulated annealing (SA), genetic algorithms (GA) and adaptive Lipschitz optimization (adaLIPO). The comparison is carried out with modeling and linearization performance and in terms of runtime. The results show that greedy pursuits, particularly the DOMP, provide the best trade-off between execution time and linearization robustness against dimensionality reduction.

Robust Flow Field Signal Estimation Method for Flow Sensing by Underwater Robotics

The flow field is difficult to evaluate, and underwater robotics can only partly adapt to the submarine environment. However, fish can sense the complex underwater environment by their lateral line system. In order to reveal the fish flow sensing mechanism, a robust nonlinear signal estimation method based on the Volterra series model with the Kautz kernel function is provided, which is named KKF-VSM. The flow field signal around a square target is used as the original signal. The sinusoidal noise and the signal around a triangular obstacle are considered undesired signals, and the predicting performance of KKF-VSM is analyzed after introducing them locally in the original signals. Compared to the radial basis function neural network model (RBF-NNM), the advantages of KKF-VSM are not only its robustness but also its higher sensitivity to weak signals and its predicting accuracy. It is confirmed that even for strong nonlinear signals, such as pressure responses in the flow field, KKF-VSM is more efficient than the commonly used RBF-NNM. It can provide a reference for the application of the artificial lateral line system on underwater robotics, improving its adaptability in complex environments based on flow field information.

Integral Equations Related to Volterra Series and Inverse Problems: Elements of Theory and Applications in Heat Power Engineering

The paper considers two types of Volterra integral equations of the first kind, arising in the study of inverse problems of the dynamics of controlled heat power systems. The main focus of the work is aimed at studying the specifics of the classes of Volterra equations of the first kind that arise when describing nonlinear dynamics using the apparatus of Volterra integro-power series. The subject area of the research is represented by a simulation model of a heat exchange unit element, which describes the change in enthalpy with arbitrary changes in fluid flow and heat supply. The numerical results of solving the problem of identification of transient characteristics are presented. They illustrate the fundamental importance of practical recommendations based on sufficient conditions for the solvability of linear multidimensional Volterra equations of the first kind. A new class of nonlinear systems of integro-algebraic equations of the first kind, related to the problem of automatic control of technical objects with vector inputs and outputs, is distinguished. For such systems, sufficient conditions are given for the existence of a unique, sufficiently smooth solution. A review of the literature on these problem types is given.