Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be wr...Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.展开更多
Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonanc...Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.展开更多
This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging...This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.展开更多
Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting ...Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.展开更多
The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break...The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the l...Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.展开更多
The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this...The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this study proposes an innovative hybrid approach that integrates wavelet neural network(WNN)with chaos analysis.By leveraging the Cross-Correlation(C−C)method,the minimum embedding dimension for phase space reconstruction is systematically calculated and then adopted as the input node configuration for the WNN.Simulation results demonstrate the remarkable effectiveness of this integrated method in predicting pressure drop signals,advancing our understanding of the intricate dynamic phenomena occurring with V−L−S fluidized bed evaporators.Moreover,this study offers a novel perspective on applying advanced data-driven techniques to handle the complexities of multi-phase flow systems and highlights the potential for improved operational prediction and control in industrial settings.展开更多
We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise durin...We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise during the photoelectric detection and analog-digital conversion,the varying of output optical power would change the signal to noise ratio,then impact time delay signature identification and the random bit generation.Our results show that,when the optical power is less than-14 dBm,with the decreasing of the optical power,the actual identified time delay signature degrades and the entropy of the chaotic signal increases.Moreover,the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.展开更多
As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effect...As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effects.In this paper,we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model.It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions,and the Husimi Q function are more dispersed in phase space.Moreover,we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space.Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.展开更多
The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous contr...The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.展开更多
Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines...Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.展开更多
Polynomial Chaos Expansion(PCE)has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis.However,traditional PCE suffers from two major drawbacks.First,the ortho...Polynomial Chaos Expansion(PCE)has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis.However,traditional PCE suffers from two major drawbacks.First,the orthogonality of polynomial basis functions holds only for independent input variables,limiting the model’s ability to propagate uncertainty in dependent variables.Second,PCE encounters the"curse of dimensionality"due to the high computational cost of training the model with numerous polynomial coefficients.In practical manufacturing,compressor blades are subject to machining precision limitations,leading to deviations from their ideal geometric shapes.These deviations require a large number of geometric parameters to describe,and exhibit significant correlations.To efficiently quantify the impact of high-dimensional dependent geometric deviations on the aerodynamic performance of compressor blades,this paper firstly introduces a novel approach called Data-driven Sparse PCE(DSPCE).The proposed method addresses the aforementioned challenges by employing a decorrelation algorithm to directly create multivariate basis functions,accommodating both independent and dependent random variables.Furthermore,the method utilizes an iterative Diffeomorphic Modulation under Observable Response Preserving Homotopy regression algorithm to solve the unknown coefficients,achieving model sparsity while maintaining fitting accuracy.Then,the study investigates the simultaneous effects of seven dependent geometric deviations on the aerodynamics of a high subsonic compressor cascade by using the DSPCE method proposed and sensitivity analysis of covariance.The joint distribution of the dependent geometric deviations is determined using Quantile-Quantile plots and normal copula functions based on finite measurement data.The results demonstrate that the correlations between geometric deviations significantly impact the variance of aerodynamic performance and the flow field.Therefore,it is crucial to consider these correlations for accurately assessing the aerodynamic uncertainty.展开更多
The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)frac...The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.展开更多
Despite their strategic hydrological importance for neighbouring areas,the Polish Carpathians are experiencing spatial chaos,which may weaken their adaptability to the progressive climate change.The article attempts t...Despite their strategic hydrological importance for neighbouring areas,the Polish Carpathians are experiencing spatial chaos,which may weaken their adaptability to the progressive climate change.The article attempts to answer the question of whether spatial planning,which is supposed to guarantee spatial order,fulfils its role and whether the knowledge of the natural conditions of spatial development is respected in the spatial planning process.Using GIS techniques,up to 238 communes were analysed in terms of their spatial coverage,the degree of scattered settlement,and the violation of natural barriers by location of buildings in areas that are threatened with mass movements or floods;by settlement on excessively inclined slopes and in areas with adverse climatic conditions.Spearman non-parametric rank correlation analysis and the multidimensional Principal Component Analysis(PCA)technique were performed to investigate relations between spatial chaos indicators and the planning situation.The analysis of the data has revealed that spatial planning does not fulfil its role.Serious errors in location of buildings have been noted even though the communes are covered by local spatial development plans.Scientific knowledge is not sufficiently transferred into planning documents,and bottom-up initiatives cannot replace systemic solutions.There is a need for strengthening the role of environmental studies documents in the spatial planning system.This would facilitate the transfer of scientific knowledge into the planning process and help to protect mountain areas.The development of a special spatial strategy for the Polish Carpathians in compliance with the Carpathian Convention is also recommended.展开更多
Full lifecycle high fidelity digital twin is a complex model set contains multiple functions with high dimensions and multiple variables.Quantifying uncertainty for such complex models often encounters time-consuming ...Full lifecycle high fidelity digital twin is a complex model set contains multiple functions with high dimensions and multiple variables.Quantifying uncertainty for such complex models often encounters time-consuming challenges,as the number of calculated terms increases exponentially with the dimensionality of the input.This paper based on the multi-stage model and high time consumption problem of digital twins,proposed a sparse polynomial chaos expansions method to generate the digital twin dynamic-polymorphic uncertainty surrogate model,striving to strike a balance between the accuracy and time consumption of models used for digital twin uncertainty quantification.Firstly,an analysis and clarification were conducted on the dynamic-polymorphic uncertainty of the full lifetime running digital twins.Secondly,a sparse polynomial chaos expansions model response was developed based on partial least squares technology with the effectively quantified and selected basis polynomials which sorted by significant influence.In the end,the accuracy of the proxy model is evaluated by leave-one-out cross-validation.The effectiveness of this method was verified through examples,and the results showed that it achieved a balance between maintaining model accuracy and complexity.展开更多
To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on ...To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.展开更多
Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-s...Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.展开更多
This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a gen...This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.展开更多
In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is a...In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.12122515(HH)Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(Grant No.2022B1212010008)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023B1515040023)。
文摘Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.
文摘Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.
基金supported by Young Talents from Longyuan,Gansu Province(Liwei Liu),the Fundamental Research Funds for the Central Universities,Northwest Minzu University(Grant No.31920230134)Teaching Achievement Cultivation Project of Gansu Province Department of Education(Grant No.2022GSJXCGPY-46)+1 种基金Special research topic on curriculum and teaching materials for primary,secondary and higher schools,Gansu Province Department of Education(Grant No.GSJC-Y2024204)Quality improvement project for undergraduate talent training,Northwest Minzu University(Grant Nos.2024YBJG-04 and 2024FCTD-03).
文摘This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.
基金Dalian Municipal Natural Science Foundation under Grant No.2019RD01。
文摘Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.
基金support from the National Natural Science Foundation of China(Nos.12102242 and 12172086)the Educational Foundation of Liaoning Province(No.JYTQN2023261)the Key R&D Program of Shandong Province of China(No.2022SFGC0801).
文摘The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
文摘This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
基金funded by Taif University,Saudi Arabia,Project No.(TU-DSPP-2024-52).
文摘Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.
基金supported by the open foundation of State Key Laboratory of Chemical Engineering(SKL-ChE-22B01)the Natural Science Foundation of China(22008169).
文摘The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this study proposes an innovative hybrid approach that integrates wavelet neural network(WNN)with chaos analysis.By leveraging the Cross-Correlation(C−C)method,the minimum embedding dimension for phase space reconstruction is systematically calculated and then adopted as the input node configuration for the WNN.Simulation results demonstrate the remarkable effectiveness of this integrated method in predicting pressure drop signals,advancing our understanding of the intricate dynamic phenomena occurring with V−L−S fluidized bed evaporators.Moreover,this study offers a novel perspective on applying advanced data-driven techniques to handle the complexities of multi-phase flow systems and highlights the potential for improved operational prediction and control in industrial settings.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.62005129 and 62175116)。
文摘We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise during the photoelectric detection and analog-digital conversion,the varying of output optical power would change the signal to noise ratio,then impact time delay signature identification and the random bit generation.Our results show that,when the optical power is less than-14 dBm,with the decreasing of the optical power,the actual identified time delay signature degrades and the entropy of the chaotic signal increases.Moreover,the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.
基金supported by the National Natural Science Foundation of China under Grant Nos.12275078,11875026,12035005 and 2020YFC2201400Science Foundation of Hengyang Normal University of China under Contract No.2020QD24sponsored by the innovative research group of Hunan Province under Grant No.2024JJ1006。
文摘As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effects.In this paper,we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model.It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions,and the Husimi Q function are more dispersed in phase space.Moreover,we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space.Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.
文摘The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.
基金supported by Science and Technology Project of Yunnan Provincial Transportation Department(Grant No.25 of 2018)the National Natural Science Foundation of China(Grant No.52279107)The authors are grateful for the support by the China Scholarship Council(CSC No.202206260203 and No.201906690049).
文摘Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.
基金the National Science and Technology Major Project of China(No.J2019-I-0011)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX2023057)for supporting the research work.
文摘Polynomial Chaos Expansion(PCE)has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis.However,traditional PCE suffers from two major drawbacks.First,the orthogonality of polynomial basis functions holds only for independent input variables,limiting the model’s ability to propagate uncertainty in dependent variables.Second,PCE encounters the"curse of dimensionality"due to the high computational cost of training the model with numerous polynomial coefficients.In practical manufacturing,compressor blades are subject to machining precision limitations,leading to deviations from their ideal geometric shapes.These deviations require a large number of geometric parameters to describe,and exhibit significant correlations.To efficiently quantify the impact of high-dimensional dependent geometric deviations on the aerodynamic performance of compressor blades,this paper firstly introduces a novel approach called Data-driven Sparse PCE(DSPCE).The proposed method addresses the aforementioned challenges by employing a decorrelation algorithm to directly create multivariate basis functions,accommodating both independent and dependent random variables.Furthermore,the method utilizes an iterative Diffeomorphic Modulation under Observable Response Preserving Homotopy regression algorithm to solve the unknown coefficients,achieving model sparsity while maintaining fitting accuracy.Then,the study investigates the simultaneous effects of seven dependent geometric deviations on the aerodynamics of a high subsonic compressor cascade by using the DSPCE method proposed and sensitivity analysis of covariance.The joint distribution of the dependent geometric deviations is determined using Quantile-Quantile plots and normal copula functions based on finite measurement data.The results demonstrate that the correlations between geometric deviations significantly impact the variance of aerodynamic performance and the flow field.Therefore,it is crucial to consider these correlations for accurately assessing the aerodynamic uncertainty.
文摘The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.
基金supported by the Minister of Science of the Republic of Poland under the Programme“Regional initiative of excellence”.Agreement No.RID/SP/0010/2024/1.
文摘Despite their strategic hydrological importance for neighbouring areas,the Polish Carpathians are experiencing spatial chaos,which may weaken their adaptability to the progressive climate change.The article attempts to answer the question of whether spatial planning,which is supposed to guarantee spatial order,fulfils its role and whether the knowledge of the natural conditions of spatial development is respected in the spatial planning process.Using GIS techniques,up to 238 communes were analysed in terms of their spatial coverage,the degree of scattered settlement,and the violation of natural barriers by location of buildings in areas that are threatened with mass movements or floods;by settlement on excessively inclined slopes and in areas with adverse climatic conditions.Spearman non-parametric rank correlation analysis and the multidimensional Principal Component Analysis(PCA)technique were performed to investigate relations between spatial chaos indicators and the planning situation.The analysis of the data has revealed that spatial planning does not fulfil its role.Serious errors in location of buildings have been noted even though the communes are covered by local spatial development plans.Scientific knowledge is not sufficiently transferred into planning documents,and bottom-up initiatives cannot replace systemic solutions.There is a need for strengthening the role of environmental studies documents in the spatial planning system.This would facilitate the transfer of scientific knowledge into the planning process and help to protect mountain areas.The development of a special spatial strategy for the Polish Carpathians in compliance with the Carpathian Convention is also recommended.
基金co-supported by the National Natural Science Foundation of China(Nos.51875014,U2233212 and 51875015)the Natural Science Foundation of Beijing Municipality,China(No.L221008)+1 种基金the Science,Technology Innovation 2025 Major Project of Ningbo of China(No.2022Z005)the Tianmushan Laboratory Project,China(No.TK-2023-B-001).
文摘Full lifecycle high fidelity digital twin is a complex model set contains multiple functions with high dimensions and multiple variables.Quantifying uncertainty for such complex models often encounters time-consuming challenges,as the number of calculated terms increases exponentially with the dimensionality of the input.This paper based on the multi-stage model and high time consumption problem of digital twins,proposed a sparse polynomial chaos expansions method to generate the digital twin dynamic-polymorphic uncertainty surrogate model,striving to strike a balance between the accuracy and time consumption of models used for digital twin uncertainty quantification.Firstly,an analysis and clarification were conducted on the dynamic-polymorphic uncertainty of the full lifetime running digital twins.Secondly,a sparse polynomial chaos expansions model response was developed based on partial least squares technology with the effectively quantified and selected basis polynomials which sorted by significant influence.In the end,the accuracy of the proxy model is evaluated by leave-one-out cross-validation.The effectiveness of this method was verified through examples,and the results showed that it achieved a balance between maintaining model accuracy and complexity.
基金Project([2018]3010)supported by the Guizhou Provincial Science and Technology Major Project,China。
文摘To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.
基金The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups(Grant Number RGP.2/246/44),B.B.,and https://www.kku.edu.sa/en.
文摘Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.
基金Project supported by the National Research Foundation of Korea(Nos.NRF-2020R1C1C1011970 and NRF-2018R1A5A7023490)。
文摘This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(No.62102444)a Major Research Project in Higher Education Institutions in Henan Province(No.23A560015).
文摘In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.
