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The smooth variable structure filter (SVSF) is a recently proposed predictor-corrector filter for state and parameter estimation. The SVSF is based on the sliding mode control concept. It defines a hyperplane in terms of the state trajectory and then applies a discontinuous corrective action that forces the estimate to go back and forth across that hyperplane. The SVSF is robust and stable to modeling uncertainties making it suitable for fault detection application. The discontinuous action of the SVSF results in a chattering effect that can be used to correct modeling errors and uncertainties in conjunction with adaptive strategies. In this paper, the SVSF is complemented with a novel parameter estimation technique referred to as the iterative bi-section/shooting method (IBSS). This combined strategy is used for estimating model parameters and states for systems in which only the model structure is known. This combination improves the performance of the SVSF in terms of rate of convergence, robustness, and stability. The benefits of the proposed estimation method are demonstrated by its application to an electrohydrostatic actuator. [ABSTRACT FROM AUTHOR]

In this paper, a new method for state estimation, referred to as the smooth variable structure filter (SVSF), is presented. The SVSF method is model based and applies to smooth nonlinear dynamic systems. It allows for the explicit definition of the source of uncertainty and can guarantee stability given an upper bound for uncertainties and noise levels. The performance of the SVSF improves with more refined definition of upper bounds on parameter variations or uncertainties. Furthermore, most filtering methods provide as their measure of performance the filter innovation vector or (output) estimation error. However in addition to the innovation vector, the SVSF has a secondary set of performance indicators that correlate to the modeling errors specific to each state or parameter that is being estimated. The combined robustness and multiple indicators of performance allow for dynamic refinement of internal models in the SVSF. Dynamic refinement and robustness are features that are particularly advantageous in fault diagnosis and prediction. In this paper, the applications of the SVSF to linear and nonlinear systems, including one pertaining to fault detection, are provided. The characteristics of this filter in terms of its accuracy and rate of convergence are discussed. [ABSTRACT FROM AUTHOR]

Highlights • Robust estimation strategies are critical for the safe and reliable control of mechanical and electrical systems. • Presents a novel robust estimation method based on sliding mode concepts and the smooth variable structure filter (SVSF). • A mathematical proof of stability is provided based on Lyapunov theory. • The proposed nonlinear second‐order (NSO) filtering strategy is applied on an aerospace actuator. • The results are compared with the popular Kalman and extended Kalman filter, as well as the SVSF. Abstract In this paper, a new strategy referred to as the nonlinear second-order (NSO) filter is presented and used for estimation of linear and nonlinear systems in the presence of uncertainties. Similar to the popular Kalman filter estimation strategy, the proposed strategy is model-based and formulated as a predictor-corrector. The NSO filter is based on variable structure theory that utilizes a switching term and gain that ensures some level of estimation stability. It offers improvements in terms of robustness to modeling uncertainties and errors. The proof of stability is derived based on Lyapunov that demonstrates convergence of estimates towards the true state values. The proposed filtering strategy is based on a second-order Markov process that utilizes information from the current and past two time steps. An experimental system was setup and characterized in order to demonstrate the proposed filtering strategy's performance. The strategy was compared with the popular Kalman filter (and its nonlinear form) and the smooth variable structure filter (SVSF). Experimental results demonstrate that the proposed nonlinear second-order filter provides improvements in terms of state estimation accuracy and robustness to modeling uncertainties and external disturbances. [ABSTRACT FROM AUTHOR]

Abstract Deep-Learning has become a leading strategy for artificial intelligence and is being applied in many fields due to its excellent performance that has surpassed human cognitive abilities in a number of classification and control problems (Ciregan, Meier, & Schmidhuber, 2012; Mnih et al., 2015). However, the training process of Deep-Learning is usually slow and requires high-performance computing, capable of handling large datasets. The optimization of the training method can improve the learning rate of the Deep-Learning networks and result in a higher performance while using the same number of training epochs (cycles). This paper considers the use of estimation theory for training of large neural networks and in particular Deep-Learning networks. Two estimation strategies namely the Extended Kalman Filter (EKF) and the Smooth Variable Structure Filter (SVSF) have been revised (subsequently referred to as RSVSF and REKF) and used for network training. They are applied to several benchmark datasets and comparatively evaluated. Highlights • Two Deep-Learning training algorithms are introduced, called REKF and RSVSF. • REKF and RSVSF allow Deep-Learning networks to learn fast. • REKF and RSVSF use less memory than current adaptive methods. [ABSTRACT FROM AUTHOR]

A method that is often used for parameter estimation is the extended Kalman filter (EKF). EKF is a model-based strategy that implicitly considers the effect of modeling uncertainties. This implicit consideration often leads to the tuning of the filter by trial and error. When formulated for parameter estimation, the "tuned" EKF becomes sensitive to uncertainties in its internal model. The EKF's robustness can be improved by combining it with the recently proposed variable structure filter (VSF) concept. In a combined form, the modeling uncertainties no longer affect stability, but impact the performance and the quality of the estimation process. Furthermore, the VSF concept provides a secondary set of indicators of performance that is in addition to the estimation error and that pertains to the range of parametric uncertainties. As such, the robustness of the combined method and its multiple indicators of performance allow the use of intelligent adaptation for improving the performance of the estimation process. For real-time applications, online neural network adaptation may be used to improve the performance by progressively reducing specific modeling uncertainties in the system. In this paper, a new parameter estimation method that uses concepts associated with the EKF, the VSF, and neural network adaptation is introduced. The performance of this method is considered and discussed for applications that involve parameter estimation such as fault detection. [ABSTRACT FROM AUTHOR]

This paper introduces a reliable strategy for the state of charge (SOC) and the state of health (SOH) estimation of healthy and aged Lithium polymer cells. Dynamics of the cell are modeled using some equivalent circuit models and parameters of each model are calculated by adaptive particle swarm optimization. The modeling process involves modeling and parametric uncertainties as well as measurement and instrumentation noise. They may degrade the performance of an optimal filter for SOC and SOH estimation. To alleviate effects of such uncertain factors, the smooth variable structure filter (SVSF) is implemented. The SVSF is a novel robust state estimation method that benefits from the robustness property of variable structure systems. The performance of the SVSF is compared with the extended Kalman filter (EKF) for real-time SOC estimation of a healthy and an aged Lithium polymer cell. The paper moreover presents a novel method for SOH estimation using the SVSF’s chattering signal and without the need for modeling the cell undergoes aging. Experiments show performance benefits of the SVSF for reliable SOC and SOH estimation of healthy and aged Lithium polymer cells. [ABSTRACT FROM AUTHOR]