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
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
With the rapid increase of observational,experimental and simulated data for stochastic systems,tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems.Despite the ...With the rapid increase of observational,experimental and simulated data for stochastic systems,tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems.Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena,the data-driven approaches to extracting stochastic dynamics with Levy noise are relatively few.In this work,we propose aWeak Collocation Regression(WCR)to explicitly reveal unknown stochastic dynamical systems,i.e.,the Stochastic Differential Equation(SDE)with bothα-stable Levy noise and Gaussian noise,from discrete aggregate data.This method utilizes the evolution equation of the probability distribution function,i.e.,the Fokker-Planck(FP)equation.With the weak form of the FP equation,the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations.Then,the unknown parameters are obtained by a sparse linear regression.For a SDE with Levy noise,the corresponding FP equation is a partial integro-differential equation(PIDE),which contains nonlocal terms,and is difficult to deal with.The weak form can avoid complicated multiple integrals.Our approach can simultaneously distinguish mixed noise types,even in multi-dimensional problems.Numerical experiments demonstrate that our method is accurate and computationally efficient.展开更多
In recent years,developing Artificial Intelligence(AI)models for complex system has become a popular research area.There have been several successful AI models for predicting the Selective Non-Catalytic Reduction(SNCR...In recent years,developing Artificial Intelligence(AI)models for complex system has become a popular research area.There have been several successful AI models for predicting the Selective Non-Catalytic Reduction(SNCR)system in power plants and large boilers.However,all these models are in essence black box models and lack of explainability,which are not able to give new knowledge.In this study,a novel explainable AI(XAI)model that combines the polynomial kernel method with Sparse Identification of Nonlinear Dynamics(SINDy)model is proposed to find the governing equation of SNCR system based on 5-year operation data from a power plant.This proposed model identifies the system’s governing equation in a simple polynomial format with polynomial order of 1 and only 1 independent variable among original 68 input variables.In addition,the explainable AI model achieves a considerable accuracy with less than 21%deviation from base-line models of partial least squares model and artificial neural network model.展开更多
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.
基金supported by the National Key R&D Program of China(Grant No.2021YFA0719200).
文摘With the rapid increase of observational,experimental and simulated data for stochastic systems,tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems.Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena,the data-driven approaches to extracting stochastic dynamics with Levy noise are relatively few.In this work,we propose aWeak Collocation Regression(WCR)to explicitly reveal unknown stochastic dynamical systems,i.e.,the Stochastic Differential Equation(SDE)with bothα-stable Levy noise and Gaussian noise,from discrete aggregate data.This method utilizes the evolution equation of the probability distribution function,i.e.,the Fokker-Planck(FP)equation.With the weak form of the FP equation,the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations.Then,the unknown parameters are obtained by a sparse linear regression.For a SDE with Levy noise,the corresponding FP equation is a partial integro-differential equation(PIDE),which contains nonlocal terms,and is difficult to deal with.The weak form can avoid complicated multiple integrals.Our approach can simultaneously distinguish mixed noise types,even in multi-dimensional problems.Numerical experiments demonstrate that our method is accurate and computationally efficient.
文摘In recent years,developing Artificial Intelligence(AI)models for complex system has become a popular research area.There have been several successful AI models for predicting the Selective Non-Catalytic Reduction(SNCR)system in power plants and large boilers.However,all these models are in essence black box models and lack of explainability,which are not able to give new knowledge.In this study,a novel explainable AI(XAI)model that combines the polynomial kernel method with Sparse Identification of Nonlinear Dynamics(SINDy)model is proposed to find the governing equation of SNCR system based on 5-year operation data from a power plant.This proposed model identifies the system’s governing equation in a simple polynomial format with polynomial order of 1 and only 1 independent variable among original 68 input variables.In addition,the explainable AI model achieves a considerable accuracy with less than 21%deviation from base-line models of partial least squares model and artificial neural network model.
