Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression pr...Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges.This study proposes the adaptive backward stepwise selection of fast SINDy(ABSS-FSINDy),which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time.This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points,particularly in the context of backward stepwise selection(BSS).By decoding predefined features into textual expressions,ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods.We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems,including Lotka-Volterra,hyperchaotic Rossler,coupled Lorenz,and Lorenz 96 benchmark systems.The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework,overcoming the curse of dimensionality in high-dimensional simulations.This improvement is substantial across both lowand high-dimensional systems,yielding efficiency gains of one to three orders of magnitude.For instance,in a 20D dynamical system,the simulation time is reduced from 107.63 s to just 0.093 s,resulting in a 3-order-of-magnitude improvement in simulation efficiency.This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.展开更多
We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (...We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.展开更多
Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SIND...Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SINDy)rule to restore nonlinear equations,there also exist obstacles.One is the excessive dependence on empirical parameters,which increases the difficulty of data pre-processing.Another one is the coexistence of multiple coefficient vectors,which causes the optimal solution to be drowned in multiple solutions.The third one is the composition of basic function,which is exclusively applicable to specific equations.In this article,a local sparse screening identification algorithm(LSSI)is proposed to identify nonlinear systems.First,we present the k-neighbor parameter to replace all empirical parameters in data filtering.Second,we combine the mean error screening method with the SINDy algorithm to select the optimal one from multiple solutions.Third,the time variable t is introduced to expand the scope of the SINDy algorithm.Finally,the LSSI algorithm is applied to recover a classic ODE and a bi-stable energy harvester system.The results show that the new algorithm improves the ability of noise immunity and optimal parameters identification provides a desired foundation for nonlinear analyses.展开更多
Dear Editor,This letter presents a novel approach to the data-driven control of unknown nonlinear systems.By leveraging online sparse identification based on the Koopman operator,a high-dimensional linear system model...Dear Editor,This letter presents a novel approach to the data-driven control of unknown nonlinear systems.By leveraging online sparse identification based on the Koopman operator,a high-dimensional linear system model approximating the actual system is obtained online.The upper bound of the discrepancy between the identified model and the actual system is estimated using real-time prediction error,which is then utilized in the design of a tube-based robust model predictive controller.The effectiveness of the proposed approach is validated by numerical simulation.展开更多
Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuato...Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuators.Existing methods for fitting hysteresis loops include operator class,differential equation class,and machine learning class.The modeling cost of operator class and differential equation class methods is high,the model complexity is high,and the process of machine learning,such as neural network calculation,is opaque.The physical model framework cannot be directly extracted.Therefore,the sparse identification of nonlinear dynamics(SINDy)algorithm is proposed to fit hysteresis loops.Furthermore,the SINDy algorithm is improved.While the SINDy algorithm builds an orthogonal candidate database for modeling,the sparse regression model is simplified,and the Relay operator is introduced for piecewise fitting to solve the distortion problem of the SINDy algorithm fitting singularities.The Relay-SINDy algorithm proposed in this paper is applied to fitting hysteresis loops.Good performance is obtained with the experimental results of open and closed loops.Compared with the existing methods,the modeling cost and model complexity are reduced,and the modeling accuracy of the hysteresis loop is improved.展开更多
The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality ...The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry,including green production and the use of fewer resources;thus,traditional stability control is no longer suitable for multi-objective control tasks.Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics(CFD)simulation models to study its dynamics,these models cannot be directly applied to process control due to their high computational complexity.To address these issues,this paper proposes a multi-objective adaptive optimization model predictive control(MAO-MPC)method based on sparse identification.More specifically,with a large amount of data collected from a CFD model,a sparse regression problem is first formulated and solved to obtain a reduction model.Then,a two-layered control framework including real-time optimization(RTO)and model predictive control(MPC)is designed.In the RTO layer,an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up.By solving the optimization problem in real time,a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state.Our experiments show the strength and reliability of the proposed method,which reduces the usage of coal while maintaining high profits.展开更多
In this paper, we demonstrate a new model identification-based control method for spacecraft rendezvous with limited amount of data of data. We use the method of sparse identification for nonlinear dynamics(SINDy) to ...In this paper, we demonstrate a new model identification-based control method for spacecraft rendezvous with limited amount of data of data. We use the method of sparse identification for nonlinear dynamics(SINDy) to identify the high-order nonlinear gravitational acceleration in the motion dynamics of spacecraft rendezvous. The control has a feedforward plus feedback structure. The feedforward control uses the nonlinear functions identified by SINDy to compensate the nonlinear highorder acceleration terms, while the feedback control designed by solving a standard linear quadratic regulator(LQR) problem is used to guarantee the stability of the closed-loop system. Numerical results show the effectiveness of the proposed control scheme for spacecraft rendezvous mission. With few state samplings, the dynamics identified based on SINDy achieve better state prediction performance than Clohessy–Wiltshire(CW) equations and the dynamics identified by BP neural networks. Considering the computation and storage burden brought by the data amount in identification, the proposed method is promising in improving the autonomy of spacecraft in missions with complex and uncertain dynamics environment.展开更多
This paper shows hidden information from the plastic deformation of metallic glasses using machine learning.Ni_(62)Nb_(38)(at.%)metallic glass(MG)film and Zr_(64.13)Cu_(15.75)Al_(10)Ni_(10.12)(at.%)BMG,as two model ma...This paper shows hidden information from the plastic deformation of metallic glasses using machine learning.Ni_(62)Nb_(38)(at.%)metallic glass(MG)film and Zr_(64.13)Cu_(15.75)Al_(10)Ni_(10.12)(at.%)BMG,as two model materials,are considered for nano-scratching and compression experiment,respectively.The interconnectedness among variables is probed using correlation analysis.The evolvement mechanism and governing system of plastic deformation are explored by combining dynamical neural networks and sparse identification.The governing system has the same basis function for different experiments,and the coefficient error is≤0.14%under repeated experiments,revealing the intrinsic quality in metallic glasses.Furthermore,the governing system is conducted based on the preceding result to predict the deformation behavior.This shows that the prediction agrees well with the real value for the deformation process.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12172291,12472357,and 12232015)the Shaanxi Province Outstanding Youth Fund Project(No.2024JC-JCQN-05)the 111 Project(No.BP0719007)。
文摘Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges.This study proposes the adaptive backward stepwise selection of fast SINDy(ABSS-FSINDy),which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time.This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points,particularly in the context of backward stepwise selection(BSS).By decoding predefined features into textual expressions,ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods.We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems,including Lotka-Volterra,hyperchaotic Rossler,coupled Lorenz,and Lorenz 96 benchmark systems.The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework,overcoming the curse of dimensionality in high-dimensional simulations.This improvement is substantial across both lowand high-dimensional systems,yielding efficiency gains of one to three orders of magnitude.For instance,in a 20D dynamical system,the simulation time is reduced from 107.63 s to just 0.093 s,resulting in a 3-order-of-magnitude improvement in simulation efficiency.This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.
文摘We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.
基金The work was supported by the National Science Foundation of China(grant nos.11772218 and 11872044)China-UK NSFC-RS Joint Project(grant nos.11911530177 in China and IE181496 in the UK)Tianjin Research Program of Application Foundation and Advanced Technology(grant no.17JCYBJC18900).
文摘Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SINDy)rule to restore nonlinear equations,there also exist obstacles.One is the excessive dependence on empirical parameters,which increases the difficulty of data pre-processing.Another one is the coexistence of multiple coefficient vectors,which causes the optimal solution to be drowned in multiple solutions.The third one is the composition of basic function,which is exclusively applicable to specific equations.In this article,a local sparse screening identification algorithm(LSSI)is proposed to identify nonlinear systems.First,we present the k-neighbor parameter to replace all empirical parameters in data filtering.Second,we combine the mean error screening method with the SINDy algorithm to select the optimal one from multiple solutions.Third,the time variable t is introduced to expand the scope of the SINDy algorithm.Finally,the LSSI algorithm is applied to recover a classic ODE and a bi-stable energy harvester system.The results show that the new algorithm improves the ability of noise immunity and optimal parameters identification provides a desired foundation for nonlinear analyses.
基金supported by the National Natural Science Foundation of China(62473020).
文摘Dear Editor,This letter presents a novel approach to the data-driven control of unknown nonlinear systems.By leveraging online sparse identification based on the Koopman operator,a high-dimensional linear system model approximating the actual system is obtained online.The upper bound of the discrepancy between the identified model and the actual system is estimated using real-time prediction error,which is then utilized in the design of a tube-based robust model predictive controller.The effectiveness of the proposed approach is validated by numerical simulation.
基金National Natural Science Foundation of China(62203118)。
文摘Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuators.Existing methods for fitting hysteresis loops include operator class,differential equation class,and machine learning class.The modeling cost of operator class and differential equation class methods is high,the model complexity is high,and the process of machine learning,such as neural network calculation,is opaque.The physical model framework cannot be directly extracted.Therefore,the sparse identification of nonlinear dynamics(SINDy)algorithm is proposed to fit hysteresis loops.Furthermore,the SINDy algorithm is improved.While the SINDy algorithm builds an orthogonal candidate database for modeling,the sparse regression model is simplified,and the Relay operator is introduced for piecewise fitting to solve the distortion problem of the SINDy algorithm fitting singularities.The Relay-SINDy algorithm proposed in this paper is applied to fitting hysteresis loops.Good performance is obtained with the experimental results of open and closed loops.Compared with the existing methods,the modeling cost and model complexity are reduced,and the modeling accuracy of the hysteresis loop is improved.
基金supported in part by the National Key Research and Development Program of China(2022YFB3304900)in part by the National Natural Science Foundation of China(61988101,62073340,and 61860206014)+2 种基金in part by the Major Key Project of Peng Cheng Laboratory(PCL)(PCL2021A09)in part by the Science and Technology Innovation Program of Hunan Province(2022JJ10083,2021RC3018,and 2021RC4054)in part by the Innovation-Driven Project of Central South University,China(2019CX020)。
文摘The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry,including green production and the use of fewer resources;thus,traditional stability control is no longer suitable for multi-objective control tasks.Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics(CFD)simulation models to study its dynamics,these models cannot be directly applied to process control due to their high computational complexity.To address these issues,this paper proposes a multi-objective adaptive optimization model predictive control(MAO-MPC)method based on sparse identification.More specifically,with a large amount of data collected from a CFD model,a sparse regression problem is first formulated and solved to obtain a reduction model.Then,a two-layered control framework including real-time optimization(RTO)and model predictive control(MPC)is designed.In the RTO layer,an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up.By solving the optimization problem in real time,a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state.Our experiments show the strength and reliability of the proposed method,which reduces the usage of coal while maintaining high profits.
基金supported in part by the National Natural Science Foundation of China(No.62303337)Sichuan Science and Technology Program(No.2024NSFSC1494)+1 种基金National Laboratory of Space Intelligent Control(Nos.HTKJ2023KL502005 and HTKJ2024KL502007)the opening project of Robotic Satellite Laboratory
文摘In this paper, we demonstrate a new model identification-based control method for spacecraft rendezvous with limited amount of data of data. We use the method of sparse identification for nonlinear dynamics(SINDy) to identify the high-order nonlinear gravitational acceleration in the motion dynamics of spacecraft rendezvous. The control has a feedforward plus feedback structure. The feedforward control uses the nonlinear functions identified by SINDy to compensate the nonlinear highorder acceleration terms, while the feedback control designed by solving a standard linear quadratic regulator(LQR) problem is used to guarantee the stability of the closed-loop system. Numerical results show the effectiveness of the proposed control scheme for spacecraft rendezvous mission. With few state samplings, the dynamics identified based on SINDy achieve better state prediction performance than Clohessy–Wiltshire(CW) equations and the dynamics identified by BP neural networks. Considering the computation and storage burden brought by the data amount in identification, the proposed method is promising in improving the autonomy of spacecraft in missions with complex and uncertain dynamics environment.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.52071298,and 11771407)the ZhongYuan Science and Technology Innovation Leadership Program(Grant No.214200510010)+2 种基金the China Postdoctoral Science Foundation funded project(Grant No.2019M651600)the Innovative Funds Plan of Henan University of Technol-ogy(Grant No.2020ZKCJ09)the Research Foundation for Advanced Talents of Henan University of Technology(Grant No.2018BS027).
文摘This paper shows hidden information from the plastic deformation of metallic glasses using machine learning.Ni_(62)Nb_(38)(at.%)metallic glass(MG)film and Zr_(64.13)Cu_(15.75)Al_(10)Ni_(10.12)(at.%)BMG,as two model materials,are considered for nano-scratching and compression experiment,respectively.The interconnectedness among variables is probed using correlation analysis.The evolvement mechanism and governing system of plastic deformation are explored by combining dynamical neural networks and sparse identification.The governing system has the same basis function for different experiments,and the coefficient error is≤0.14%under repeated experiments,revealing the intrinsic quality in metallic glasses.Furthermore,the governing system is conducted based on the preceding result to predict the deformation behavior.This shows that the prediction agrees well with the real value for the deformation process.
