Stochastic Excitation Research Articles

Research on control parameters of high-speed maglev train under stochastic track irregularities

During operational phases, maglev trains encounter track irregularities, presenting a formidable challenge to the integrity of their control systems owing to the inherently stochastic nature, a challenge accentuated in the context of high-speed maglev trains. This study aims to comprehensively examine control parameters within the context of stochastic excitation resulting from track irregularities. Through the development of a rigorous stochastic response analysis model utilizing the pseudo excitation method, the investigation delves into the dynamics of an EMS-type high-speed maglev train-rigid track system. Evaluation indices, derived from the power spectral density of the maglev train's response, are established to quantify both control stability and operational stability. Subsequently, based on these indices, a recommended range of PD control parameters is proposed, accounting for the requirements stipulated by the evaluation metrics. The study elucidates that variation in PD control parameters exert discernible effects on the system's stability, primarily altering the nature frequency and damping ratio. Specifically, control stability demonstrates a positive correlation with increasing PD control parameters, while operational stability exhibits a nuanced relationship—initially bolstered by escalating proportional coefficients but subsequently tempered, albeit gradually, with heightened derivative coefficients. The delineated range of values for PD control parameters is meticulously determined, considering pertinent physical parameters of the electromagnetic system, such as mass, static suspension current, and static suspension gap, alongside factors like the Sperling indicator and suspension gap variation.

Nonstationary response statistics of structures with hysteretic damping to evolutionary stochastic excitation

The damping of a structure has often been modeled as linear hysteretic damping (LHD), so its corresponding equation of motion (EOM) is an integro-differential equation that involves the Hilbert transform of response displacement. As a result, the system is non-causal in nature, and it is challenging to compute its nonstationary response statistics under evolutionary stochastic excitation. This article develops an efficient solution method to obtain closed-form solutions for various nonstationary response statistics, including the evolutionary power spectrum (EPS), correlation function and mean square values. The novel solution method utilizes the concept of causalization time to introduce a “causalized” impulse response function (IRF), by which causal response statistics are computed based on a pole-residue approach. This approach requires obtaining a pole-residue form of the transfer function (TF) from the frequency response function (FRF) of the system, which is readily obtained from the EOM. Subsequently, the desired response statistics are obtained by shifting the causal response statistics back to the original time. To obtain the pole-residue form of the TF, two steps are necessary: (1) taking the inverse Fourier transform of the FRF of the oscillator to obtain a discrete IRF and (2) using the Prony-SS method to decompose this discrete IRF to obtain the pole residues associated with the TF. The correctness of the proposed method is numerically verified by Monte Carlo simulations through examples of hysteretic damping and mixed viscous-hysteretic damping oscillators that are subjected to white noise, modulated white noise and modulated Kanai–Tajimi model random excitations.

Theoretical study of a novel resettable‐inertia damper: Dynamic modeling, equivalent linearization, and performance assessment

AbstractTo passively achieve an inertial device with unidirectional force transmission similar to Bang Bang control, this study introduces a novel energy dissipation device known as the resettable‐inertia damper (RID). The ingenious motion principles of the RID, encompassing a rack‐and‐pinion, bevel gear commutation system, speed transmission, and eddy current damping, are elucidated in detail. In particular, a unidirectional rotational flywheel within the device selectively engages when the primary structure reciprocates. The physical mass of the flywheel undergoes conversion into an amplified inertia through the rack‐and‐pinion mechanism, which enables the enhancement of damping effects coupling the flywheel rotation and eddy current configuration. A coupled multibody dynamic model, combining the clutching effect, the flywheel inertia, and the rotational damping, is formulated to analyze the system with RID (RIDS). Currently, an analysis of the hysteretic behaviors of RID is carried out. To facilitate the design and evaluation of the performance of RIDS, an equivalent linearization method is proposed for RIDS. The feasibility of this simplified method is validated under harmonic excitation. Additionally, the study examines the performance of equivalent linear systems (ELSs) and RIDS under natural ground motions and stochastic stationary excitation in peak and variance responses levels, respectively. Comparison of RID with traditional inerter shows that RID can achieve a more pronounced control with less force transferred to the structure and with the potential to recover vibration energy, highlighting its unique advantages.

Buffeting reliability of high-rise bridge tower in mountain area based on CNN-BiLSTM

In recent years, the wind-induced vibration of structures has received a great deal of scholarly attention due to the increasing scale of large structures. In this study, an algorithm that combines a stochastic pseudo excitation method (SPEM), a convolutional neural network (CNN) and a bidirectional long short-term memory network (BiLSTM), named as SPEM-CNN-BiLSTM (SCBL), is proposed. The SCBL is a surrogate model consisting of three different computational modules, in which the SPEM can provide training samples for CNN-BiLSTM (CBL) network architecture, a convolutional layer extracts features of stochastic parameters and a BiLSTM handles time histories of bridge response. The accuracy of the SCBL prediction results is ensured by the set error threshold. The model also accounts for structural uncertainty in the inputs and is adapted during the training step to be more suitable for reliability analysis. According to the output qualified prediction data, the dynamic reliability based on the 99 % threshold is calculated by obtaining its probability density function, and the wind-induced vibration responses of uncertain bridge towers are studied. Firstly, the wind environment of the bridge tower was analyzed, and the average wind speed of 20 m/s among the bridge area was obtained by field measurements, and Computational Fluid Dynamics (CFD). Secondly, the proposed artificial neural network algorithm is applied to bridge jitter reliability analysis and compared with the traditionally recognized methods: the Monte Carlo method (MCM) and the stochastic pseudo excitation method (SPEM). The results of SCBL calculations are closer to the results of MCM than those of other methods. Additionally, the computational efficiency of the method is improved by 40 times over MCM and 2 times over SPEM. Finally, the data generated by the SCBL method will be used for reliability analysis. Uncertainties in structure, wind speed, and yaw angle all contribute to the uncertainty and dispersion of the stochastic response prediction. Among them, the uncertainty in wind speed has the greatest impact on the reliability.

A novel stochastic approach to investigate the probabilistic characteristics of the ship roll system with sinusoidal restoring force

A novel constrained optimization-oriented exponential–polynomial–closure (CO-EPC) method is developed to investigate the ship roll-motion with non-smooth damping and sinusoidal restoring moments under stochastic wave excitations. The ’non-smooth damping’ and ’sinusoidal restoring moments’ refer to the damping force and restoring force of the system, respectively, which are mathematically expressed using non-smooth and sinusoidal functions. The propagation of uncertainty in the system is governed by the Fokker–Plank–Kolmogorov (FPK) equation, as the presence of stochastic wave excitation induces Markovian behavior in the system responses. The solution of FPK must meet the non-negativity, normalization, and limitation attributes. To fulfill these essential requirements, a novel method has been developed. By deriving the moment functions of the non-smooth terms (for the damping moment part) and the sine terms (for the restoring moment part), the complicated FPK equation is solved. Through two case studies, it is found that the CO-EPC approach demonstrates superior efficiency compared to Monte Carlo simulation and produces more accurate solutions in contrast to the Gaussian closure method. These findings support the effectiveness of CO-EPC in studying the ship roll motion problem under stochastic wave excitations.

Stochastic response of chain-like hysteretic MDOF systems endowed with fractional derivative elements and subjected to combined stochastic and periodic excitation

Stochastic response of chain-like hysteretic MDOF systems endowed with fractional derivative elements and subjected to combined stochastic and periodic excitation

Research on Power Angle Characteristics of One-Machine Infinite-Bus Power Systems of Mixed Gauss and Poisson Stochastic Excitation

Background: A high percentage of renewable energy and a high percentage of power electronic devices are connected to the power system, which leads to the diversification and complexity of stochastic excitation, and the traditional single-excitation stochastic model is no longer applicable. Objective: The study aimed to solve the problem that the high proportion of renewable energy and the high proportion of power electronic equipment are connected to the power system, which leads to the diversification and complexity of stochastic excitation and makes the traditional stochastic model of single excitation no longer applicable. Methods: Firstly, stochastic differential equations for power systems have been modelled with mixed Gaussian white noise and Poisson white noise excitation. Secondly, the Milstein-Euler predictor-corrector method has been developed to solve the stochastic differential equation model of the power system. Finally, the influence of Gauss white noise and Poisson white noise on the power system stability under different excitation intensities has been analyzed. The rationality and correctness of the model have been verified by the simulation of a one-machine infinitebus (OMIB) system. Results: The stochastic differential equation model of a power system with Gauss white noise and Poisson white noise excitation has been established and its angle stability has been analyzed. Increasing the Gaussian white noise and Poisson white noise excitation intensity can lead to an increase in the fluctuation of the power angle curve, as well as an increase in the standard deviation and expected value of the power angle mean curve, which may decrease the stability of the power system. Conclusion: This study provides a reference for stochastic power systems modeling and efficient simulation, and has important application value for power system stability assessment and safety evaluation as well as related patent applications.

Multiscale stochastic optimal control of hysteretic structures based on wavelet transform and probability density evolution method

PurposeContemporary stochastic optimal control by synergy of the probability density evolution method (PDEM) and conventional optimal controller exhibits less capability to guarantee economical energy consumption versus control efficacy when non-stationary stochastic excitations drive hysteretic structures. In this regard, a novel multiscale stochastic optimal controller is invented based on the wavelet transform and the PDEM.Design/methodology/approachFor a representative point, a conventional control law is decomposed into sub-control laws by deploying the multiresolution analysis. Then, the sub-control laws are classified into two generic control laws using resonant and non-resonant bands. Both frequency bands are established by employing actual natural frequency(ies) of structure, making computed efforts depend on actual structural properties and time-frequency effect of non-stationary stochastic excitations. Gain matrices in both bands are then acquired by a probabilistic criterion pertaining to system second-order statistics assessment. A multi-degree-of-freedom hysteretic structure driven by non-stationary and non-Gaussian stochastic ground accelerations is numerically studied, in which three distortion scenarios describing uncertainties in structural properties are considered.FindingsTime-frequency-dependent gain matrices sophisticatedly address non-stationary stochastic excitations, providing efficient ways to independently suppress vibrations between resonant and non-resonant bands. Wavelet level, natural frequency(ies), and ratio of control forces in both bands influence the scheme’s outcomes. Presented approach outperforms existing approach in ensuring trade-off under uncertainty and randomness in system and excitations.Originality/valuePresented control law generates control efforts relying upon resonant and non-resonant bands, and deploys actual structural properties. Cost-function weights and probabilistic criterion are promisingly developed, achieving cost-effectiveness of energy demand versus controlled structural performance.

Efficient reliability analysis of stochastic dynamic first-passage problems by probability density evolution analysis with subset supported point selection

This study introduces a novel point selection procedure for the Probability Density Evolution Method (PDEM) to estimate time-dependent reliability and failure probabilities in dynamic systems under first-passage failure conditions. The method integrates and modifies features of the Subset simulation procedure to adaptively generate dependent sample sets suitable for a reliability analysis by a direct probability integration approach levering PDEM. Performance function assessments are used as weighting factors in the Subset supported Point Selection (S-PS), enhancing the ultimate failure probability estimation accuracy. The presented approach effectively identifies samples in the failure region, particularly benefiting for dynamic systems under stochastic excitation, tested with random dimensions up to 60. It also offers a computationally efficient structural reliability estimation procedure by analyzing full time–history responses. The proposed method provides deeper insights into rare failure events and mechanisms through the visualization of intermediate results. This research presents an advanced framework for estimating structural reliability and understanding critical events in dynamic systems.

Data-driven discovery of interpretable Lagrangian of stochastically excited dynamical systems

Exploring the intersection of deterministic and stochastic dynamics, this paper delves into Lagrangian discovery for conservative and non-conservative systems under stochastic excitation. Traditional Lagrangian frameworks, adept at capturing deterministic behavior, are extended to incorporate stochastic excitation. The study critically evaluates recent computational methodologies for learning Lagrangians from observed data, highlighting the limitations in interpretability and the exclusion of stochastic excitation. To address these gaps, an automated data-driven framework is proposed for the simultaneous discovery of Lagrange densities and diffusion coefficients of stochastically excited dynamical systems by leveraging sparse regression. This novel framework offers several advantages over existing approaches. Firstly, it provides an interpretable description of the underlying Lagrange density, allowing for a deeper understanding of system dynamics under stochastic excitations. Secondly, it identifies the interpretable form of the diffusion coefficient of generalized stochastic force, addressing the limitations of existing deterministic approaches. Additionally, the framework demonstrates robustness and versatility through numerical case studies encompassing both stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs), with results showing almost exact approximations to true system behavior and minimal relative error in derived equations of motion.

Soliton solutions of nonlinear stochastic Fitz-Hugh Nagumo equation

This study deals with the stochastic Fitz-Hugh Nagumo (FHN) equation and its multiple soliton solutions. The underlying model has numerous applications in neuroscience that express the pulse behavior of neurons. In general, different kinds of noise affect neurons, e.g., oscillations in the opening and closing of ion stations within cell membranes and the fluctuations of the different conductivities in the system. This fluctuation creates a sequence of stochastic excitation. Various applications are branching Brownian motion process, flame propagation, nuclear reactor theory, autocatalytic chemical reaction, mobility in neurons, population growth in the open environment, and liquid environment. So, need of the hour to consider the FHN equation under the impact of noise. The ϕ6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^6$$\\end{document}-model expansion method is used to extract the analytical solutions that give a dynamic attitude of the transmission for the nerve impulses of a nervous system. The different constraint conditions for the existence of these solutions are also discussed. The solutions of this model are represented in hyperbolic, trigonometric, and rational forms. The 2 and 3-dimensional behavior of these solutions are depicted by choosing the different values of parameters. The impact of noise on the physical system is analyzed and its real-world applications are discussed. The spikes in the solutions are controlled through the Borel function. These important results will open a new horizon of research for the young researchers.

Phantom Attractors in a Single-Degree-of-Freedom Smooth System Under Additive Stochastic Excitation

Phantom attractors in nonlinear systems under additive stochastic excitation have been recently discovered. This paper uncovers the existence of phantom attractors in a single-degree-of-freedom smooth nonlinear equation, which characterizes the vibration of an inextensible beam subjected to lateral stochastic excitation. It also elucidates that the stochastic averaging method, in this context, may lead to qualitatively erroneous probability density functions, identified as one of the reasons why these attractors were previously overlooked. The study then proceeds to analyze the formation process of the phantom attractor and the critical noise intensity associated with it. Subsequently, the key nonlinear term related to the emergence of phantom attractors is identified by observing whether the system still exhibits phantom attractors after the corresponding nonlinear terms are removed. It is revealed that in this system, the presence of phantom attractors is closely linked to the inertia nonlinearity of the hardening type. The system investigated in this paper is simpler compared to previously identified systems capable of generating phantom attractors. This simplicity aids in facilitating research focused on unraveling the general principles behind the formation of phantom attractors.

3D hydrodynamic simulations of massive main-sequence stars – II. Convective excitation and spectra of internal gravity waves

ABSTRACT Recent photometric observations of massive stars have identified a low-frequency power excess which appears as stochastic low-frequency variability in light-curve observations. We present the oscillation properties of high-resolution hydrodynamic simulations of a $25\,\,{\rm{M}_\odot }$ star performed with the PPMstar code. The model star has a convective core mass of $\approx 12\,\,{\rm{M}_\odot }$ and approximately half of the envelope simulated. From this simulation, we extract light curves from several directions, average them over each hemisphere, and process them as if they were real photometric observations. We show how core convection excites waves with a similar frequency as the convective time-scale in addition to significant power across a forest of low and high angular degree l modes. We find that the coherence of these modes is relatively low as a result of their stochastic excitation by core convection, with lifetimes of the order of 10s of days. Thanks to the still significant power at higher l and this relatively low coherence, we find that integrating over a hemisphere produces a power spectrum that still contains measurable power up to the Brunt–Väisälä frequency. These power spectra extracted from the stable envelope are qualitatively similar to observations, with the same order of magnitude yet lower characteristic frequency. This work further shows the potential of long-duration, high-resolution hydrodynamic simulations for connecting asteroseismic observations to the structure and dynamics of core convection and the convective boundary.

Fractional-Order PIλDμ Control to Enhance the Driving Smoothness of Active Vehicle Suspension in Electric Vehicles

The suspension system is a crucial part of an electric vehicle, which directly affects its handling performance, driving comfort, and driving safety. The dynamics of the 8-DoF full-vehicle suspension with seat active control are established based on rigid-body dynamics, and the time-domain stochastic excitation model of four tires is constructed by the filtered white noise method. The suspension dynamics model and road surface model are constructed on the Matlab/Simulink simulation software platform, and the simulation study of the dynamic characteristics of active suspension based on the fractional-order PIλDμ control strategy is carried out. The three performance indicators of acceleration, suspension dynamic deflection, and tire dynamic displacement are selected to construct the fitness function of the genetic algorithm, and the structural parameters of the fractional-order PIλDμ controller are optimized using the genetic algorithm. The control effect of the optimized fractional-order PIλDμ controller based on the genetic algorithm is analyzed by comparing the integer-order PID control suspension and passive suspension. The simulation results show that for optimized fractional-order PID control suspension, compared with passive suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions reaches over 25%, the average optimization of suspension dynamic deflection exceeds 30%, and the average optimization of tire dynamic displacement is 5%. However, compared to the integer-order PID control suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions decreased by 5%, the average optimization of suspension dynamic deflection increased by 3%, and the average optimization of tire dynamic displacement increased by 2%.

The Long-term Photometric Behavior of 39 Semiregular Variable Stars

Photometric measurements of the light and color variations of 39 semiregular variable stars over a 30 yr time interval have been used to explore the systematics of these variations. These results show the complex nature of the frequency compositions of the light curves of these stars. The frequencies present in the light curves tend to be harmonic in nature, suggesting that both modes of pulsation and shape effects may be involved and the nature of the variations indicates that stochastic excitation is involved.

Structural reliability analysis under stochastic seismic excitations and multidimensional limit state based on gamma mixture model and copula function

A novel method for analyzing the reliability of structures under non-stationary stochastic seismic excitations, considering the combined effect of multiple structural demand extreme values, is proposed. The spectral representation method is employed to establish a non-stationary stochastic seismic excitation model, and based on the theory of first-passage probability, multiple integral formulas for seismic reliability under multidimensional limit states are derived. The extreme value distribution is established using the Gamma mixture model (GMM). The equations for estimating the model parameters are derived based on both fractional moments and moment-generating functions, while the determination of the number of gamma distribution components is guided by the probability distribution and statistical characteristics of the samples. The joint probability density function (JPDF) for multiple demand extreme values is established by incorporating copula functions to account for correlation, and the fitting accuracy of different copula functions is assessed. The proposed method is illustrated using reinforced concrete (RC) frame structures. The results demonstrate that the fitting accuracy of extreme value distribution can be enhanced by adjusting the number of gamma distribution components in the GMM, which exhibits high accuracy in fitting both the main and tail regions. The presence of correlation can induce variations in the JPDF, thereby exerting an influence on the failure probability. Consequently, disregarding correlation is not conducive to reliability analysis.

Active learning-based optimization of structures under stochastic excitations with first-passage probability constraints

In various efforts to manage the risk of structural failures caused by stochastic excitations such as wind and earthquake loads, the first-passage probability often needs to be calculated as a reliability constraint. Estimating the first-passage probability with low computational costs is essential, especially in structural optimization requiring iterative reliability calculations for design alternatives. This paper presents a new active learning-based framework for reliability-based design optimization (RBDO) of structures under stochastic excitations. A mixture-distribution-based formulation of the first-passage probability is utilized to handle the high-dimensional sequences of stochastic excitations during the optimization. The design parameter sensitivity of the first-passage probability is introduced to use a gradient-based optimizer in the RBDO iterations. These procedures employ heteroscedastic Gaussian process-based surrogates of the logarithmic responses. An active-learning scheme identifies the best training point to reduce the computational costs in the first-passage probability calculations and optimization. The numerical examples dealing with the optimal design of an eight-story building system and a tower structure subjected to stochastic wind loads demonstrate the accuracy and efficiency of the proposed method.

The higher-order analysis of response for linear structure under non-Gaussian stochastic excitations with known statistical moments and power spectral density

The frequency-domain analysis method is a fundamental component of the random vibration analysis, in which the corresponding moment spectrum of excitations are the prerequisite. Nevertheless, the determination of the higher-order moment spectra for non-Gaussian stochastic excitations continues to pose a significant challenge in the existing research works. This paper introduces an accurate and efficient computational approach for determining higher-order moment spectra of non-Gaussian stochastic excitations with known statistical moments and power spectral density (PSD). Firstly, following the idea of the simulation method of non-Gaussian stochastic processes, the transformation model between the stationary non-Gaussian stochastic process and underlying Gaussian stochastic process is determined based on the known statistical moments, the PSD of the underlying Gaussian stochastic process is determined using the transformation model. Secondly, the approximate higher-order moment spectra models of stationary non-Gaussian stochastic processes are presented by the PSD of the underlying Gaussian process. Subsequently, the higher-order moment spectra models of non-Gaussian excitations are utilized to compute the higher-order moment spectra of response for the linear structure via the auxiliary harmonic excitation generalized method. Finally, three numerical examples are examined to assess the efficiency and accuracy of the proposed approximate models for the higher-order moment spectra of non-Gaussian stochastic processes.

Dynamic response of a guy line of a guyed tower to stochastic wind excitation: 3D non-linear small-sag cable model

Dynamic response of a guy line of a guyed tower to stochastic wind excitation: 3D non-linear small-sag cable model

Adaptive optimal fault-tolerant vibration control and sensitivity analysis of semi-active suspension based on a self-powered magneto-rheological damper

To reuse the energy dissipated by vehicle suspension, a semi-active suspension with a self-powered magneto-rheological damper is proposed. An electromechanical coupling model of self-powered semi-active suspension is established. The energy conversion efficiency is defined and investigated by changing the electrical parameters. By considering unmodeled dynamics and perturbation values, an adaptive optimal fault-tolerant control algorithm is proposed to ensure the vibration-isolation performance. The robust index of the adaptive optimal fault-tolerant control algorithm is constructed using the Lyapunov equation and evaluated by changing the key parameters. The sensitivity of the key parameters to the damping force is investigated using a grey relation analysis approach. Furthermore, multi-objective optimization between the vibration-isolation capability and energy harvesting is conducted. Via analysis, the proposed suspension can harvest more energy near the second resonance range. Compared to passive control and self-powered mode, the adaptive optimal control algorithm mitigates vibration more significantly in the time and frequency domains, respectively, under stochastic excitation. The robust index is most sensitive to inductance and the diameter of the magnetism cylinder. The length of the damping channel and the diameter of the magnetism cylinder influence the sensitivity of key parameters to the damping force most obviously.