Sparse Volterra Model Research Articles

Optimal Sparse Volterra Modeling for Transient Behavior of Turbofan Engines based on Internet of Things

In recent years, Internet of Things (IoT) technologies have been increasingly utilized to collect enormous volumes of performance data for intelligent analysis and modeling of aero-engines. This has aided in the development of numerous data-driven solutions so that a strong knowledge of the intricate operations within the equipment is no longer needed. To characterize the dynamic nonlinear transient behavior of turbofan engines, fast response changes have the possibility of being captured accurately through high-order, long-memory-length Volterra series. However, exponentially increasing coefficients are still challenging to be handled properly. For fast and reliable modeling of turbofan engines, an Optimal Sparse Volterra (OSV) model is developed in this paper by reconstructing sparse nonzero coefficients after a global selection through particle swarm optimization. The OSV model focuses on the optimal sparsity of the Volterra kernels while being insensitive to the signal length. Besides, noise reduction and the correlation analysis method are specifically designed for sensor measurements of low-bypass ratio turbofan engines. The OSV model, as well as retaining the powerful descriptive capability of the Volterra series for nonlinear characteristics, finds the most relevant sets of variables and the set of model parameters automatically under the minimum computing workload. According to the experimental results, when real test data are used for turbofan transient maneuvers, the OSV model ensures that the mean absolute error is less than [Formula: see text] for high-pressure rotor speed, thrust and exhaust temperature. Moreover, the nonzero identification coefficients produced by the OSV model in the experiments are less than 6% of the total coefficients. At the same time, the average running time required by the OSV model is less than 35% of that of traditional identification algorithms.

Modeling of human smooth pursuit by sparse Volterra models with functionally dependent parameters

This paper deals with the identification of Volterra models that capture the dynamics of smooth pursuit eye movements recorded by an eye tracker. The framework is motivated by neurological applications but can also be useful in biometrics. In healthy subjects, ocular dynamics are predominantly linear, while neurological conditions inflict nonlinearity on smooth pursuit eye movements. Besides overparameterization, Volterra models may also exhibit functional dependence among the model coefficients. A combination of sparse estimation and Principal Component Analysis is shown to be instrumental in estimating parsimonious Volterra models from eye-tracking data. The efficacy of the approach is demonstrated on experimental data collected from Parkinsonian patients as well as healthy controls.

Sparse Modeling of Nonlinear Secondary Path for Nonlinear Active Noise Control

In many practical active noise control systems, the nonlinear secondary path (NSP) model can offer broader applications than the linear secondary path (LSP) model for the widespread existence of nonlinearities in the secondary path. However, the computational burden often limits the application of the NSP algorithms. In this paper, we apply a sparse Volterra model for the LSP and NSP instead of the complete Volterra model, which may be over parameterized for the nonlinear active noise control (NANC) system. The developed new control algorithms greatly result in reduction of computational complexity. We also provide an analysis of the NANC system to show that the noise at the canceling point could be approximated by the function expansion filters when the secondary path is modeled as the second-order Volterra series. In addition, two new function expansion forms, the even mirror Fourier nonlinear filter with a linear finite-impulse response section and the Chebyshev filter, are explored to process the nonlinearities in the NANC system using the filtered-x least mean square and filtered-error least mean square algorithm structures. The computational complexity analysis and the computer simulations validate that the new control algorithms with a sparse Volterra model for the secondary path can significantly reduce computational load without sacrificing the control performance.

Sparse Volterra model based on optical single side-band NPAM-4 direct-detection system

Abstract Signal-to-signal beating interference (SSBI) is one of the main drawbacks in direct-detection based optical transmission systems. Volterra filter is a common equalization method to mitigate the nonlinear distortion. However, the computational complexity may be unacceptable as the transmission capacity increases. In this paper, we propose a sparse Volterra model combining the feed forward equalization (FFE) and higher order terms of a modified Volterra filter with Schmidt orthogonal searching to mitigate the linear and nonlinear interference and reduce the complexity significantly in an optical single-side band (SSB) Nyquist pulse-shaped four-level pulse amplitude (NPAM-4) system. The experimental results show that the sparse Volterra filter and full Volterra filter have comparable performance, but the former only needs half kernels of the latter.

Sparse modeling of super-resolution near-field structure read-out signals

In this study, super-RENS disc read-out signals were modeled with various nonlinear models. In the results of modeling the nonlinearity, DC offset, and domain bloom phenomena of the super-RENS channel with a second-order Volterra filter, it was identified that the number of significant quadratic coefficients was relatively small. Therefore, a sparse Volterra model and a truncated Volterra model are applied to effectively model the nonlinear channel. In addition, the Hammerstein-type asymmetric conversion model is employed to model the nonlinear channel for the purpose of comparison. The results demonstrate that the sparse model of a simplified polynomial form achieves good modeling performance for the super-RENS disc read-out signals.

Simulation of nonlinear bridge aerodynamics: A sparse third-order Volterra model

A sparse third-order Volterra model is utilized to simulate nonlinear bridge aerodynamics and attendant response under turbulent fluctuations. The Volterra model is pruned based on aerodynamic considerations, which significantly reduces computational effort needed for nonlinear analysis. The first-, second- and third-order Volterra kernels are identified using least-squares with the input–output pairs obtained from a numerical simulation and a wind-tunnel experiment. Both studies involving a simulation and an experiment show that the proposed sparse third-order Volterra model can adequately simulate nonlinear bridge aerodynamics with high fidelity. Finally, the robustness of the sparse Volterra model is verified by comparing it to an upgraded Volterra scheme.

A Compressed Sensing Approach for Modeling the Super-Resolution Near-Field Structure Disc System With a Sparse Volterra Filter

In this paper, we investigate the compressed sensing (CS) algorithms for modeling a super-resolution near-field structure (super-RENS) disc system with a sparse Volterra filter. It is well known that the super-RENS disc system has severe nonlinear inter-symbol interference (ISI). A nonlinear system with memory can be well described with the Volterra series. Furthermore, CS can restore sparse or compressed signals from measurements. For these reasons, we employ the CS algorithms to estimate a sparse super-RENS read-out channel. The evaluation results show that the CS algorithms can efficiently construct a sparse Volterra model for the super-RENS read-out channel and that observable nonlinear interactions take place among restricted components in the read-out channel.

Adaptive algorithms for sparse system identification

In this paper, identification of sparse linear and nonlinear systems is considered via compressive sensing methods. Efficient algorithms are developed based on Kalman filtering and Expectation-Maximization. The proposed algorithms are applied to linear and nonlinear channels which are represented by sparse Volterra models and incorporate the effect of power amplifiers. Simulation studies confirm significant performance gains in comparison to conventional non-sparse methods.

Estimating sparse Volterra models using group L1-regularization.

Sparse Volterra model (sVM) is defined as a Volterra model (VM) that contains only a subset of its all possible model coefficients corresponding to its significant inputs and the existing terms of those inputs. Compared with ordinary VM, sVM is more efficient and interpretable in representing sparsely connected multiple-input systems, e.g., neuronal networks. In this paper, we formulate a rigorous statistical method of estimating sVM based on the group L1-regularization. It allows simultaneous selection and estimation of the significant groups of coefficients of a VM and results in a sVM. Simulation results show that the actual structure of a sVM can be faithfully recovered even with short input-output data. This method can be extended and applied to the identification of the functional connectivity between neurons.

SOS-Based Blind Identification of Nonlinear Volterra Systems

Discrete Volterra models appear widely in various fields of signal processing, control and communication. In this paper, blind identification of a single-input single-output (SISO) Volterra system with finite order and memory is discussed in the second-order statistical sense. The assumption of inaccessible i.i.d. stationary input signals requires that the kernel estimation is achieved based only on the output observations and the statistical properties of the input signals. The systems are composed of linear moving average (MA) models, nonlinear quadratic, cubic models as well as higher-order nonlinear models. Volterra kernels of arbitrary order are derived as functions of system output observations and are expressed in a general matrix form. Based on this formulation, it is shown that while blind identification is not possible for full-sized Volterra systems, nontrivial kernel estimates can be obtained if the system is approximated by a sparse Volterra model. Results based on simulated and experimental data are provided to confirm results.

A sparse third-order orthogonal frequency-domain Volterra-like model

The purpose of this paper is twofold. The first objective is to develop a discrete frequency-domain orthogonal third-order Volterra model valid for both nonGaussian and Gaussian stationary random inputs in order to eliminate the presence of ‘interference’ terms. The second objective is to develop a sparse third-order frequency-domain Volterra model by identifying the most significant frequency-domain Volterra kernel coefficients using a given amount of raw experimental times series data. The concept of coherence function is extended to the orthogonal higher-order model in order to quantify the goodness of both the model and its constituent linear, quadratic, and cubic components and, then, is utilized as a criterion to select the most significant frequency-domain Volterra kernel coefficients to be included in the sparse Volterra model. Identification of the most significant frequency-domain Volterra coefficients is based upon a frequency-domain extension of the well-known orthogonal-search method. Finally, the practicality and feasibility of these approaches are demonstrated by utilizing them to model actual physical nonlinear systems given experimental input-output data from such systems.