Online Parameter Estimation of Hydraulic System Based on Stochastic Gradient Descent

2020 ◽  
Author(s):  
Takashi Yamada ◽  
Matthew Howard
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Hydraulic System ◽  
Gradient Descent ◽  
Estimation Error ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Estimation Methods ◽  
Hydraulic Systems ◽  
Parameter Estimation Methods

Abstract In this paper, offline and online parameter estimation methods for hydraulic systems based on stochastic gradient descent are presented. In contrast to conventional approaches, the proposed methods can estimate any parameter in mathematical models based on multi-step prediction error. These advantages are achieved by calculating the gradient of the multi-step error against the estimated parameters using Lagrange multipliers and the calculus of variations, and by forming differentiable models of hydraulic systems. In experiments on a physical hydraulic system, the proposed methods with three different gradient decent methods (normal gradient descent, Nesterov’s Accelerated Gradient (NAG), and Adam) are compared with conventional least squares. In the offline experiment, the proposed method with NAG achieves estimation error about 95% lower than that of least squares. In online estimation, the proposed method with NAG produces predictive models with about 20% lower error than that of the offline method. These results suggest the proposed method is a practical alternative to more conventional parameter estimation methods.

Parameter Estimation of Linear Sensorimotor Synchronization Models: Phase Correction, Period Correction, and Ensemble Synchronization

2015 ◽  
Vol 3 (1-2) ◽  
pp. 52-87 ◽  
Author(s):  
Nori Jacoby ◽  
Naftali Tishby ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Peter E. Keller
Keyword(s):  
Experimental Data ◽  
Parameter Estimation ◽  
Linear Models ◽  
Estimation Error ◽  
Phase Correction ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Single Subject ◽  
Novel Method ◽  
Parameter Estimation Methods

Linear models have been used in several contexts to study the mechanisms that underpin sensorimotor synchronization. Given that their parameters are often linked to psychological processes such as phase correction and period correction, the fit of the parameters to experimental data is an important practical question. We present a unified method for parameter estimation of linear sensorimotor synchronization models that extends available techniques and enhances their usability. This method enables reliable and efficient analysis of experimental data for single subject and multi-person synchronization. In a previous paper (Jacoby et al., 2015), we showed how to significantly reduce the estimation error and eliminate the bias of parameter estimation methods by adding a simple and empirically justified constraint on the parameter space. By applying this constraint in conjunction with the tools of matrix algebra, we here develop a novel method for estimating the parameters of most linear models described in the literature. Through extensive simulations, we demonstrate that our method reliably and efficiently recovers the parameters of two influential linear models: Vorberg and Wing (1996), and Schulze et al. (2005), together with their multi-person generalization to ensemble synchronization. We discuss how our method can be applied to include the study of individual differences in sensorimotor synchronization ability, for example, in clinical populations and ensemble musicians.

scholarly journals Optimal survey schemes for stochastic gradient descent with applications to M-estimation

2019 ◽  
Vol 23 ◽  
pp. 310-337 ◽  
Author(s):  
Stephan Clémençon ◽  
Patrice Bertail ◽  
Emilie Chautru ◽  
Guillaume Papa
Keyword(s):  
Gradient Descent ◽  
A Priori ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Estimation Methods ◽  
Full Data ◽  
Predictive Learning ◽  
Inclusion Probabilities ◽  
Estimation Problems ◽  
The Impact

Iterative stochastic approximation methods are widely used to solve M-estimation problems, in the context of predictive learning in particular. In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural and popular approach to gradient descent in this context consists in substituting the “full data” statistics with their counterparts based on subsamples picked at random of manageable size. It is the main purpose of this paper to investigate the impact of survey sampling with unequal inclusion probabilities on stochastic gradient descent-based M-estimation methods. Precisely, we prove that, in presence of some a priori information, one may significantly increase statistical accuracy in terms of limit variance, when choosing appropriate first order inclusion probabilities. These results are described by asymptotic theorems and are also supported by illustrative numerical experiments.

scholarly journals Tikhonov Regularized Variable Projection Algorithms for Separable Nonlinear Least Squares Problems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Zhengqing Fu ◽  
Lanlan Guo
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Linear Parameter ◽  
Nonlinear Parameters ◽  
Marquardt Algorithm ◽  
Tikhonov Regularisation ◽  
Parameter Estimation Methods

This paper considers the classical separable nonlinear least squares problem. Such problems can be expressed as a linear combination of nonlinear functions, and both linear and nonlinear parameters are to be estimated. Among the existing results, ill-conditioned problems are less often considered. Hence, this paper focuses on an algorithm for ill-conditioned problems. In the proposed linear parameter estimation process, the sensitivity of the model to disturbance is reduced using Tikhonov regularisation. The Levenberg–Marquardt algorithm is used to estimate the nonlinear parameters. The Jacobian matrix required by LM is calculated by the Golub and Pereyra, Kaufman, and Ruano methods. Combining the nonlinear and linear parameter estimation methods, three estimation models are obtained and the feasibility and stability of the model estimation are demonstrated. The model is validated by simulation data and real data. The experimental results also illustrate the feasibility and stability of the model.

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