Hierarchical Stochastic Gradient Research Articles

Auxiliary model-based hierarchical stochastic gradient methods for multiple-input multiple-output systems

This paper presents a hierarchical identification model for multiple-input multiple-output (MIMO) systems. An auxiliary model-based hierarchical stochastic gradient (AM-HSG) algorithm is derived by means of the auxiliary model identification idea and the hierarchical identification principle. Furthermore, an auxiliary model-based hierarchical multi-innovation stochastic gradient (AM-HMISG) algorithm is derived by utilizing the multi-innovation identification theory. In order to compare the computational efficiency of the AM-HSG and AM-HMISG algorithms for identifying MIMO systems, this paper gives the existing traditional gradient algorithms and discusses the complexity of these algorithms in detail. Finally, the simulation example tests the effectiveness of all four algorithms.

A Hierarchical Identification Method for Lithium-Ion Battery SOC Based on the Hammerstein Model

Two-input one-output Hammerstein model consists of two parallel nonlinear static blocks followed by a linear dynamic part. By using Hammerstein structure to map relation between a battery State of Charge (SOC) and its terminal voltage/current, a hierarchical stochastic gradient algorithm is studied to estimate parameters of Hammerstein SOC model, so as to predict battery SOC. Firstly, the Hammerstein model is transformed into a bilinear parameter system with the least number of required parameters. Then, a hierarchical stochastic gradient algorithm with a forgetting factor is used to update the two sets of model parameters of the bilinear parameter system, so as to realize SOC estimation. Furthermore, the experiment platform of lithium-ion battery was built and the data of the urban dynamometer driving schedule (UDDS) profile and the Los Angeles 92 (LA92) profile were collected. Finally, the MATLAB simulation results show that the proposed parameter optimized method based Hammerstein model has the advantages of fast convergence speed and high SOC estimation accuracy.

Hierarchical multi-innovation stochastic gradient identification algorithm for estimating a bilinear state-space model with moving average noise

This paper considers the combined parameter and state estimation problem of a bilinear state space system with moving average noise. There are product terms of state variables and control variables in bilinear systems, which brings difficulties to parameter and state estimation. By designing a bilinear state estimator based on Kalman filter and using input–output data to estimate the state, a hierarchical multi-innovation stochastic gradient (i.e., H-MISG) algorithm based on the state estimator is proposed to jointly estimate unknown states and parameters. In addition, compared with the hierarchical stochastic gradient algorithm, H-MISG algorithm introduces the innovation length parameter, makes full use of the system input and output data information, and improves the accuracy of parameter estimation. Numerical simulation examples verify the effectiveness of the proposed algorithm.

Identification of the nonlinear systems based on the kernel functions

AbstractConstructing an appropriate membership function is significant in fuzzy logic control. Based on the multi‐model control theory, this article constructs a novel kernel function which can implement the fuzzification and defuzzification processes and reflect the dynamic quality of the nonlinear systems accurately. Then we focus on the identification problems of the nonlinear systems based on the kernel functions. Applying the hierarchical identification principle, we present the hierarchical stochastic gradient algorithm for the nonlinear systems. Meanwhile, the one‐dimensional search methods are proposed to solve the problem of determining the optimal step sizes. In order to improve the parameter estimation accuracy, we propose the hierarchical multi‐innovation forgetting factor stochastic gradient algorithm by introducing the forgetting factor and using the multi‐innovation identification theory. The simulation example is provided to test the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance.

Weighted hierarchical stochastic gradient identification algorithms for ARX models

In this paper, a weighted hierarchical stochastic gradient algorithm and a latest estimation-based weighted hierarchical stochastic gradient algorithm for ARX models are proposed. Different from some existing stochastic gradient algorithms, the correction term of the developed algorithms is in a weighted form of the correction terms in the current and last recursive steps of the hierarchical stochastic gradient algorithm. Further, the convergence property of the presented latest estimation-based weighted hierarchical stochastic gradient algorithm is analysed. It is illustrated by a numerical example that both the weighted hierarchical stochastic gradient and the latest estimation-based weighted hierarchical stochastic gradient algorithms possess higher convergence accuracy compared with some existing hierarchical stochastic gradient algorithms if the weighting factor is appropriately chosen.

Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

SummaryThis paper is concerned with the joint estimation of states and parameters of a special class of nonlinear systems, ie, bilinear systems. The key is to investigate new estimation methods for interactive state and parameter estimation of the considered system based on the interactive estimation theory. Because the system states are unknown, a bilinear state observer is established based on the Kalman filtering principle. Then, the unavailable states are updated by the state observer outputs recursively. Once the state estimates are obtained, the bilinear state observer–based hierarchical stochastic gradient algorithm is developed by using the gradient search. For the purpose of improving the convergence rate and the parameter estimation accuracy, a bilinear state observer–based hierarchical multi‐innovation stochastic gradient algorithm is proposed by expanding a scalar innovation to an innovation vector. The convergence analysis indicates that the parameter estimates can converge to their true values. The numerical example illustrates the effectiveness of the proposed algorithms.

High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning

Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has been developed based on distributed gradient descent. Based on the approach, stochastic gradients are computed at edge devices and then transmitted to an edge server for updating a global AI model. Since each stochastic gradient is typically high-dimensional (with millions to billions of coefficients), communication overhead becomes a bottleneck for edge learning. To address this issue, we propose in this work a novel framework of hierarchical stochastic gradient quantization and study its effect on the learning performance. First, the framework features a practical hierarchical architecture for decomposing the stochastic gradient into its norm and normalized block gradients, and efficiently quantizes them using a uniform quantizer and a low-dimensional codebook on a Grassmann manifold, respectively. Subsequently, the quantized normalized block gradients are scaled and cascaded to yield the quantized normalized stochastic gradient using a so-called hinge vector designed under the criterion of minimum distortion. The hinge vector is also efficiently compressed using another low-dimensional Grassmannian quantizer. The other feature of the framework is a bit-allocation scheme for reducing the quantization error. The scheme determines the resolutions of the low-dimensional quantizers in the proposed framework. The framework is proved to guarantee model convergency by analyzing the convergence rate as a function of the quantization bits. Furthermore, by simulation, our design is shown to substantially reduce the communication overhead compared with the state-of-the-art signSGD scheme, while both achieve similar learning accuracies.

Modeling a nonlinear process using the exponential autoregressive time series model

The parameter estimation methods for the nonlinear exponential autoregressive (ExpAR) model are investigated in this work. Combining the hierarchical identification principle with the negative gradient search, we derive a hierarchical stochastic gradient algorithm. Inspired by the multi-innovation identification theory, we develop a hierarchical-based multi-innovation identification algorithm for the ExpAR model. Introducing two forgetting factors, a variant of the hierarchical-based multi-innovation identification algorithm is proposed. Moreover, to compare and demonstrate the serviceability of these algorithms, a nonlinear ExpAR process is taken as an example in the simulation.

Gradient-Based Recursive Identification Methods for Input Nonlinear Equation Error Closed-Loop Systems

The identification problem of closed-loop or feedback nonlinear systems is a hot topic. Based on the hierarchical identification principle, this paper presents a hierarchical stochastic gradient algorithm and a hierarchical multi-innovation stochastic gradient algorithm for feedback nonlinear systems. The simulation results show that the hierarchical multi-innovation stochastic gradient can more effectively estimate the parameters of the feedback nonlinear systems than the hierarchical stochastic gradient algorithm.

Hierarchical Stochastic Gradient Algorithm and its Performance Analysis for a Class of Bilinear-in-Parameter Systems

This paper considers the parameter identification for a special class of nonlinear systems, i.e., bilinear-in-parameter systems. Based on the hierarchical identification principle, a hierarchical stochastic gradient (HSG) estimation algorithm is presented. The basic idea is to decompose a bilinear-in-parameter system into two subsystems and to derive the HSG identification algorithm for estimating the system parameters by replacing the unknown variables in the information vectors with their estimates obtained at the previous time. The convergence analysis of the proposed algorithm indicates that the parameter estimation errors converge to zero under persistent excitation conditions. The simulation results show that the proposed algorithm is effective.

The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique

On the basis of the auxiliary model identification idea, this paper studies the filtering based parameter estimation issues for a class of multivariable control systems with colored noise. An auxiliary model based hierarchical stochastic gradient (AM-HSG) algorithm is given for comparison and a data filtering AM-HSG identification algorithm is derived by using the data filtering technique. Its main key is to decompose a multivariable system into two subsystems and to coordinate the associate items between two subsystem identification algorithms. The convergence analysis indicates that the parameter estimates given by the presented algorithms converge to the true values under proper conditions by using the stochastic process theory. The simulation results show that the proposed hierarchical stochastic gradient estimation algorithms are effective.

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

This paper focuses on the identification problem of an input nonlinear state space system with colored noise. Based on the observability canonical form, an identification model is derived and a state observer is designed. By using the hierarchical identification principle, a state observer based hierarchical stochastic gradient algorithm is presented for estimating the parameter vectors and states jointly. Furthermore, by using the multi-innovation identification theory, a state observer based hierarchical multi-innovation stochastic gradient algorithm is proposed for improving the convergence rate. The analysis indicates that the parameter estimates given by the proposed algorithms converge to the true values under persistent excitation conditions. Two numerical examples are offered to demonstrate the effectiveness of the proposed algorithms.

DATA FILTERING BASED STOCHASTIC GRADIENT ALGORITHMS FOR MULTIVARIABLE CARAR-LIKE SYSTEMS

This paper considers identification problems for a multivariable controlled autoregressive system with autoregressive noises. A hierarchical generalized stochastic gradient algorithm and a filtering based hierarchical stochastic gradient algorithm are presented to estimate the parameter vectors and parameter matrix of such multivariable colored noise systems, by using the hierarchical identification principle. The simulation results show that the proposed hierarchical gradient estimation algorithms are effective.

Hierarchical gradient-based identification of multivariable discrete-time systems

In this paper, we use a hierarchical identification principle to study identification problems for multivariable discrete-time systems. We propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation. The proposed algorithms can be applied to identification of systems involving non-stationary signals and have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms by simulation and show their effectiveness.