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Optimization of the recursive least squares algorithm for capacitive strain sensing

ENGINEERING RESEARCH EXPRESS 2020年第4期2卷

作者： Bohnker, Jillian Breuer, Kenneth Naval Undersea Warfare Ctr Newport RI 02841 USA Brown Univ Sch Engn Providence RI 02912 USA

The use of dielectric elastomers as integrated actuators and strain sensors offers a simple approach for closed-loop control in a wide range of applications. While a number of approaches for self-sensing have been proposed, the adaptive online algorithm offers an appealing combination of high accuracy and low computational cost. In this work, the recursive least squares algorithm will be applied to capacitive deformation sensing of dielectric elastomers. With the goal of minimizing sampling rate while achieving a set accuracy over a desired range of deformation frequencies, the probe frequency, sampling frequency, and forgetting factor will be optimized. It will be shown that the accuracy is primarily determined by a nondimensionalized variable, (W) over bar, which defines the proportion of a hypothetical deformation cycle that is weighted more heavily by the algorithm. Ultimately, this optimized algorithm will be validated by variably inflating a dielectric elastomer membrane and comparing the algorithm output to membrane deformation measured by video.

关键词： dielectric elastomer actuator recursive least squares algorithm optimization capacitive self sensing

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Modified recursive least squares (RLS) algorithm for neural networks using piecewise linear function

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IEE PROCEEDINGS-CIRCUITS DEVICES AND SYSTEMS 2004年第6期151卷 510-518页

作者： Gokhale, AP Nawghare, PM Visvesvaraya Natl Inst Technol Dept Elect & Comp Sci Nagpur 440011 Maharashtra India

The recursive least squares (RLS) learning algorithm for multilayer feedforward neural networks uses a sigmoid nonlinearity at node outputs. It is shown that by using a piecewise linear function at node outputs, the algorithm becomes faster. The modified algorithm improves computational efficiency and by preserving matrix symmetry it is possible to avoid explosive divergence, which is normally seen in the conventional RLS algorithm due to the finite precision effects. Also the use of this piecewise linear function avoids the approximation, which is otherwise necessary in the derivation of the conventional algorithm with sigmoid nonlinearity. Simulation results on the XOR problem, 4-2-4 encoder and function approximation problem indicate that the modified algorithm reduces the occurrence of local minima and improves the convergence speed compared to the conventional RLS algorithm. A nonlinear system identification and control problem is considered to demonstrate the application of the algorithm to complex problems.

关键词： recursive least squares algorithm matrix symmetry piecewise linear function node outputs multilayer feedforward neural networks function approximation piecewise linear techniques convergence speed RLS algorithm explosive divergence feedforward neural nets least squares approximations XOR problem computational efficiency 4-2-4 encoder sigmoid nonlinearity finite precision effects local minima recursive functions

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Improved recursive least squares algorithm Based on Echo State Neural Network for Nonlinear System Identification

Improved Recursive Least Squares Algorithm Based on Echo Sta...

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第三十届中国控制会议

作者： SONG Qingsong~(1,2),ZHAO Xiangmo~1,FENG Zuren~2 1.School of Information Engineering,Chang'an University,Xi'an 710064,P.R.China 2.Systems Engineering Institute,Xi'an Jiaotong University,Xi'an 710049,P.R.China

In order to model nonlinear systems with more accuracy,and to further exploit the potential capacities of recurrent neural networks,we propose a novel recursive least square(RLS) algorithm based on echo state network(ESN),and note it as RLSESN in this *** is a new paradigm for using recurrent neural networks(RNN) with a simpler training *** proposed RLSESN consists of three main components:an ESN,a recursive least square(RLS) algorithm with adaptive forgetting factor and a change detection *** first,the change detection module modifies the forgetting factor online according to ESN output *** then,the RLS algorithm regulates the ESN output connection *** simulation experiment results show that RLSESN can model nonlinear systems very well;the modeling performances are significantly better than those traditional ARMA model based filters.

关键词： Neural Networks System Identification recursive least squares algorithm Filtering

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Identifying Time-Varying Neuromuscular System with a recursive least-squares algorithm: a Monte-Carlo Simulation Study

Identifying Time-Varying Neuromuscular System with a Recursi...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Olivari, Mario Nieuwenhuizen, Frank M. Buelthoff, Heinrich H. Pollini, Lorenzo Max Planck Inst Biol Cybernet Dept Human Percept Cognit & Action D-72012 Tubingen Germany Univ Pisa Fac Automat Engn Dipartimento Ingn Informaz I-56100 Pisa Italy Korea Univ Dept Brain & Cognit Engn Seoul South Korea

ISBN: (纸本)9781479938407

A human-centered design of haptic aids aims at tuning the force feedback based on the effect it has on human behavior. For this goal, a better understanding of the influence of haptic aids on the pilot neuromuscular response becomes crucial. In realistic scenarios, the neuromuscular response can continuously vary depending on many factors, such as environmental factors or pilot fatigue. This paper presents a method that online estimates time-varying neuromuscular dynamics during force-related tasks. This method is based on a recursive least squares (RLS) algorithm and assumes that the neuromuscular response can be approximated by a Finite Impulse Response filter. The reliability and the robustness of the method were investigated by performing a set of Monte-Carlo simulations with increasing level or remnant noise. Even with high level of remnant noise, the RLS algorithm provided accurate estimates when the neuromuscular dynamics were constant or changed slowly. With instantaneous changes, the RLS algorithm needed almost 8s to converge to a reliable estimate. These results seem to indicate that RLS algorithm is a valid tool for estimating online time-varying admittance.

关键词： FIR filters Monte Carlo methods force feedback haptic interfaces least squares approximations medical signal processing neuromuscular stimulation Monte Carlo simulation RLS algorithm environmental factors finite impulse response filter haptic aids human-centered design neuromuscular response pilot fatigue recursive least squares algorithm time-varying neuromuscular system Admittance Dynamics Force Haptic interfaces Heuristic algorithms least squares approximations Neuromuscular

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Identifying Time-Varying Neuromuscular Response: a recursive least-squares algorithm with Pseudoinverse

Identifying Time-Varying Neuromuscular Response: a Recursive...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Olivari, Mario Nieuwenhuizen, Frank M. Buelthoff, Heinrich H. Pollini, Lorenzo Max Planck Inst Biol Cybernet Dept Human Percept Cognit & Act Spemannstr 38 D-72076 Tubingen Germany Univ Pisa Fac Automat Engn Dipartimento Ingn Informaz I-56122 Pisa Italy Korea Univ Dept Brain & Cognit Engn Seoul 1367601 South Korea

ISBN: (纸本)9781479986965

Effectiveness of haptic guidance systems depends on how humans adapt their neuromuscular response to the force feedback. A quantitative insight into adaptation of neuromuscular response can be obtained by identifying neuromuscular dynamics. Since humans are likely to vary their neuromuscular response during realistic control scenarios, there is a need for methods that can identify time-varying neuromuscular dynamics. In this work an identification method is developed which estimates the impulse response of time-varying neuromuscular system by using a recursive least squares (RLS) method. The proposed method extends the commonly used RLS-based method by employing the pseudoinverse operator instead of the inverse operator. This results in improved robustness to external noise. The method was validated in a human in-the-loop experiment. The neuromuscular estimates given by the proposed method were more accurate than those obtained with the commonly used RLS-based method.

关键词： Haptic aids neuromuscular system time-varying identification recursive least squares algorithm

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On Bias Compensated recursive least-squares algorithm for FIR Adaptive Filtering

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IFAC Proceedings Volumes 2001年第14期34卷 347-352页

作者： L.-J. Jia C.-Z. Jin K. Wada Department of Electrical and Electronic System Engineering Kyushu University Fukuoka 812-8581 JAPAN Tel: +81-92-642-3958； Fax:+81-92-642-3939

It is known that recursive least squares (RLS) algorithm or least mean square (LMS) algorithm leads to biased FIR filter coefficients in the presence of input and output noise. In this paper, a new type of bias compensated recursive least squares (BCRLS) algorithm is proposed to produce consistent results for adaptive FIR filtering in the input and output noise case. The proposed algorithm introduces an auxiliary estimator to estimate unknown input noise variance. Owing to this, the bias of the RLS solution due to the input noise can be compensated to yield the consistent filter coefficients. Computational simulations indicate that the proposed algorithm is very efficient

关键词： Linear systems adaptive filters recursive least squares algorithm noisy systems system identification bias compensation

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Dynamic-spread assessment and kink detection in the early mpox outbreak

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APPLIED MATHEMATICAL MODELLING 2025年 143卷

作者： Cai, Junyang Xu, Rui Zhou, Jian Gu, Haoran Techn Israel Inst Technol Fac Data & Decis Sci IL-3200003 Haifa Israel Univ Penn Philadelphia PA 19104 USA Shanghai Univ Sch Management Shanghai 200444 Peoples R China Univ Bahrain Confucius Inst Manama Bahrain Univ Alberta Dept Math & Stat Sci Edmonton AB T6G 2G1 Canada

This paper proposes a varying coefficient Susceptible-Exposed-Infected-Removed (vSEIR) model to dynamically simulate the early mpox epidemic. We incorporate a time-varying infection rate and smallpox vaccination protection to capture real-time changes in transmission influenced by non-pharmaceutical interventions, setting our work apart from studies relying on fixed rates. To this end, we apply the recursive least squares algorithm with a forgetting factor for real-time identification of time-varying infection rate. The sparse Hodrick-Prescott (HP) filter, tuned with leave-one-out cross-validation, captures mpox epidemic kinks via the effective reproduction number RI obtained from the discrete vSEIR model. This allows for accurate segmentation of epidemic phases, better evaluation of intervention effectiveness, and insights that can guide preparedness for future possible outbreaks. We analyze the mpox and COVID19 outbreaks in four countries using the proposed kink-based framework. The results show that the mpox epidemic generally entered its decline phase earlier than COVID-19, despite weaker interventions. Additionally, the early mpox epidemic exhibited more inflection points compared to the early COVID-19 pandemic, reflecting stronger non-pharmacological controls during the latter. Sensitivity analyses further indicate that mpox infections would have increased by 12% without smallpox vaccination, and data uncertainty significantly impacts RI estimates. Finally, our proposed systematic framework can also be extended to other early outbreaks of human-to- human epidemics, especially in the absence of reliable medical data on contact rates.

关键词： Mpox vSEIR model recursive least squares algorithm Kink Sparse HP filter

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Contemporary Sinusoidal Disturbance Detection and Nano Parameters Identification Using Data Scaling Based on recursive least squares algorithms

Contemporary Sinusoidal Disturbance Detection and Nano Param...

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2nd International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Schimmack, Manuel Mercorelli, Paolo Leuphana Univ Lueneburg Inst Prod & Proc Innovat D-21339 Luneburg Germany

ISBN: (纸本)9781479967735

Single-input and single-output (SISO) controlled autoregressive moving average system by using a scalar factor input-output data is considered. Through data scaling, a simple identification technique is obtained. Using input-output scaling factors a data recursive least squares (RLS) method for estimating the parameters of a linear model and contemporary sinusoidal disturbance detection is deduced. For estimating parameters of a model in nano range a very high frequency input signal with a very small sampling rate is needed. The main contribution of this work consists of the use of a scaled recursive least Square with a forgetting factor. Using this proposed technique, a low input signal frequency and a wider sampling rate can be used to identify the parameters. In the meantime, the scaling technique reduces the effect of the external disturbance so that RLS can be applied to identify the disturbance without considering a model of it. The proposed technique is quite general and can be applied to any kind of linear systems. The simulation results indicate that the proposed algorithm is effective.

关键词： autoregressive moving average processes least mean squares methods linear systems RLS method autoregressive moving average system contemporary sinusoidal disturbance detection data scaling forgetting factor input-output scaling factor linear model nanoparameters identification recursive least squares algorithm scalar factor input-output data single-input-single-output system Autoregressive processes Estimation Frequency modulation least squares approximations Mathematical model Noise Vectors autoregressive moving average processes least squares method autoregressive processes least squares approximations linear models Frequency modulation Linear system Mathematical Model Noise recursive least squares disturbance input signal

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recursive least squares with linear inequality constraints

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OPTIMIZATION AND ENGINEERING 2015年第1期16卷 1-26页

作者： Engel, Konrad Engel, Sebastian Univ Rostock Inst Math D-18057 Rostock Germany Univ Kassel Dept Elect Engn & Comp Sci D-34121 Kassel Germany

A new recursive algorithm for the least squares problem subject to linear equality and inequality constraints is presented. It is applicable for problems with a large number of inequalities. The algorithm combines three types of recursion: time-, order-, and active-set-recursion. Each recursion step has time-complexity , where is the dimension of the data vectors. An -refreshment of the corresponding inverse matrices after each time-period of length makes the algorithm numerically very stable, such that it can handle arbitrarily many data vectors without significant rounding errors. Processing a new data vector (which usually only slightly changes the instance of the optimization problem) has time complexity , provided that the active set method only requires steps for the update until the optimum is found. In a series of examples with randomly generated data sets and with either convex constraints or with randomly generated linear constraints, the set of active constraints remains relatively stable after the inclusion of each new data vector.

关键词： recursive least squares algorithm Linear constraints Active set method Convex constraints

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Fault estimation for a quadrotor unmanned aerial vehicle by integrating the parity space approach with recursive least squares

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2018年第4期232卷 783-796页

作者： Han, Weixin Wang, Zhenhua Shen, Yi Harbin Inst Technol Sch Astronaut Harbin 150001 Heilongjiang Peoples R China

This paper studies actuator fault detection and estimation for a quadrotor unmanned aerial vehicle. By combining a parity space approach and a recursive least squares algorithm, we propose a novel fault detection and estimation method strategy for a quadrotor unmanned aerial vehicle, which is described by a linear time-varying system. Specifically, the parity space approach is used to generate a residual in fault detection, and then the magnitude of the fault is estimated by a recursive least squares algorithm with a variable forgetting factor based on the parity. Numerical simulations of a quadrotor unmanned aerial vehicle are conducted to verify the effectiveness of the proposed method.

关键词： Quadrotor unmanned aerial vehicle fault estimation parity space approach variable forgetting factor recursive least squares algorithm

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