Nonstationary Excitation Research Articles

Three modes of the nonstationary holographic current excitation in a gallium oxide crystal

We report the nonstationary holographic current excitation in a β-Ga2O3 crystal at light wavelength . The material demonstrates insulating properties and high transparency for visible light, but this, however, does not prevent the dynamic space-charge grating formation and the holographic current observation for various external electric fields —zero, dc and ac ones. The signal amplitude is measured and analyzed vs. the frequency of phase modulation, spatial frequency and electric field value. The main photoelectric parameters such as specific photoconductivity, sensor responsivity and diffusion length of carriers are determined for the blue region of spectrum.

Series System Reliability of Uncertain Linear Structures under Gaussian Excitation by Cross Entropy–Based Importance Sampling

We present an adaptive importance sampling (IS) method to estimate the reliability of linear structures with parameter uncertainties that are subjected to Gaussian process excitation. Structural failure is defined as a union of multiple first-passage failure events. The main contribution is the introduction of an efficient IS density for the uncertain structural parameters. This density is determined by minimizing the cross-entropy (CE) between the theoretically optimal IS density of the structural parameters and a chosen parametric family of probability distributions. The CE minimization procedure requires evaluation of the system failure probability conditional on fixed values of the uncertain parameters. A closed-form analytical approximation of this conditional failure probability was derived based on an upper bound on the out-crossing rate. Finally, a joint IS density of the random excitation and the uncertain structural parameters was introduced to estimate the series system failure probability involving parameter uncertainties. The accuracy and efficiency of the proposed method was demonstrated by means of two examples: a Gaussian white noise–excited two-story linear shear frame; and a six-story, three-bay moment-resisting steel frame subjected to a filtered nonstationary Gaussian excitation.

Feasibility of using self‐sensing component and response prediction model for rotation monitoring of shear wall structures

SummaryThis study presents a designed framework of structural monitoring for coupled shear wall structures by integrating a theoretical response estimation model and a prototype micro‐voltage sensing module. Inspired by the deformation mode of coupled shear walls, a supplemental self‐sensing component is proposed for predicting the target flexural deformation. The self‐sensing component is designed to include permanent magnets and cross wires and installed parallel to the coupling beam. The relative velocity between the two attached walls is obtained using electromagnetic (EM) induction and measured micro‐voltages. Accordingly, the theoretical principle of the self‐sensing prediction model is then derived, and the calculation flowchart is presented. Illustratively, a detailed finite element model was performed in ABAQUS to investigate the feasibility and robustness of the proposed self‐sensing model under different excitation scenarios, and a parametric study is performed. Then, the nonstationary excitation is adopted to further investigate the performance of the self‐sensing model. Furthermore, an EM‐based sensing module for low‐level velocity measurement is developed and the prototype is tested by utilizing a shaking table test with satisfactory performance.

Spectral decomposition-based explicit integration method for fully non-stationary seismic responses of large-scale structures

This paper presents a spectral decomposition-based explicit integration method for random vibration analysis of large-scale linear structures subjected to fully non-stationary seismic excitations. In this method, the seismic excitation process is decomposed using the spectral representation method, leading to a discrete representation of the excitation process in terms of an orthogonal random vector. Next, an explicit expression for the state response vector of structures with respect to the orthogonal random vector is derived by direct discretization and integration of the structural state equation, in which the time-dependent coefficient matrix can be obtained in a recursive manner. Since the state response vector contains only the displacement and velocity responses of structures, the finite-difference formulas are further used to obtain the explicit expression for the structural acceleration responses. These explicit expressions can be used not only to directly calculate the correlation matrix and evolutionary power spectral density of stochastic responses of structures, but also to efficiently evaluate the response samples required in the Monte Carlo simulation. For demonstration purposes, the proposed method is applied to the random vibration analysis of a coupled building system and a large-scale space-frame structure excited by two kinds of fully non-stationary seismic inputs; other existing methods are employed to illustrate the high accuracy and efficiency of the proposed method.

Experimental Study on Dynamic Interaction between Large U-Shape Aqueduct and Water

Hydrodynamic interaction between water and structure plays an important role in the evaluation of seismic response of aqueducts in area of high seismicity. This interaction differs in axial, lateral and vertical direction of aqueduct. Both impulsive and convective effects of water exist in lateral direction. In presented study, shaking table tests were conducted with a 1/10 model of U-shape aqueduct, of 30 m long, to study the hydrodynamic interaction. With the analyses of aqueduct and water responses to stationary White Noise excitations as well as non-stationary excitations, impulsive and convective effects of water were deduced quantitatively. Characteristic frequencies and corresponding modes of aqueduct were identified with the transfer functions of acceleration, sloshing frequencies in lateral direction were recognized with the transfer functions of seat force. Impulsive mass was deduced from the alteration in fundamental frequency and the corresponding modal seat forces of the aqueduct with and without water. Convective mass was obtained from the wave height of sloshing and lateral seat forces recorded, or the lateral modal seat force and damping ratio. Comparison was made with those given in simplified methods for rigid structure. Observed hydrodynamic pressure on the structure in the test was smaller than that based on the rigid assumption.

Parameters uncertainty in pareto optimization of nonlinear inerter-based suspension system under nonstationary random road excitation

Ignoring the possible impacts of uncertainties in vehicle components during the design phase can undermine the safety of passengers and the vehicle performance. The main function of a suspension system is to provide satisfactory ride comfort and road-holding with a sufficiently low probability of rollover. Despite many studies on the design of new suspension systems with inerters, the effect of uncertainties in vehicle weight and tire stiffness on the design of suspension with inerters has not received much attentions. This paper presents a new type of suspension with inerters and asymmetric dampers and investigates the dynamic behavior of a vehicle under variable vehicle speed. Moreover, the effect of uncertainties on the choice of acceptable values of inerters is evaluated. For this investigation, the authors developed a 9-DOF full vehicle model with roll and yaw motions under non-stationary random road excitations in the time and frequency domains and studied its dynamic response with different suspension models. The optimal design was performed using a multi-objective optimization algorithm called MOEA/D. The best model was then used to determine the effect of uncertainties on the choice of inerters. The optimization results show that using the optimized suspension with inerters and nonlinear dampers instead of conventional design improves the ride comfort by 0.16%, the vehicle road-holding by 3.54%, and the rollover probability by 44.73%. In the proposed model, by changing the values of vehicle parameters with uncertainty, the choice of inerters to have an acceptable performance would be variable.

Autoregressive spectrum-guided variational mode decomposition for time-varying modal identification under nonstationary conditions

Modal identification is an important research subject in structural health monitoring. It is a mature subject for modal identification of time-invariant and stationary conditions. Because time-varying properties are valuable for damage detection and time-varying system identification, and because the environmental loads do not always satisfy the assumption of stationarity, it is necessary to develop accurate identification methods for time-varying structures, structures under nonstationary excitations, or the coupling of the two conditions. The variational mode decomposition (VMD) method, which adaptively decomposes the signal into narrow-band intrinsic modes, shows the potential for time-varying and nonstationary conditions. However, parameter selection greatly affects the accuracy of mode decomposition. In this study, a new modal identification method based on an autoregressive spectrum-guided variational mode decomposition method is proposed for the application of time-varying and nonstationary conditions. First, the determination of the initial center frequencies for VMD is proposed using an autoregressive spectrum-guided method to greatly improve the accuracy. Second, a method to select the optimal balancing factor is developed to improve the decomposition accuracy by controlling the proper bandwidth. Subsequently, an instantaneous frequency identification method is presented by detecting the ridge of the time–frequency distribution. Finally, studies of numerical and actual structures demonstrate the capacity of the proposed method for practical applications of time-varying cases and nonstationary conditions.

Feedback-driven error-corrected single-sensor analytics for real-time condition monitoring

In this paper, a single-sensor based output-only algorithm is proposed for real-time condition monitoring of mechanical vibrating systems. Four key aspects of real-time condition monitoring and maintenance are presented through Recursive singular spectrum analysis (RSSA): (a) Filtering, (b) Enhancification, (c) Fault detection, and (d) Modal identification. Recent prominence of eigen perturbation (EP) solutions for condition monitoring has led to the development of RSSA as the go-to real-time algorithm for single-sensor diagnosis. As single-sensor econometrics has been long sought as a viable option for cases involving instrumentation redundancies, non-optimal sensor placement, and cost considerations, RSSA provides replication, scalability, and transferability for real-time fault detection studies. With the output vibration signals streaming in real-time, the Hankel covariance matrix is formed which filters out the noise subspace in the grouping stage. Online enhancification becomes particularly useful when the signal statistics are masked by time-varying non-stationary excitation. Application examples involving AM–FM signals and operational noise in structural systems demonstrates the versatility of RSSA towards spatio-temporal fault detection in real-time. The efficacy of the proposed algorithm is further validated by experimental investigations of real-time complete modal identification from partial sensor information. With applications extending to real-time passive control and aligned to current infrastructure monitoring demands worldwide, RSSA demonstrates potential to establish as a benchmark algorithm for online condition monitoring.

Inelastic Response of Base-Isolated Tall Buildings under Nonstationary Winds: Response History Analysis and Statistical Linearization Approach

AbstractThis study investigated uncoupled crosswind and alongwind responses of base-isolated tall buildings under nonstationary wind excitations. The base isolation system has hysteretic restoring ...

Non-stationary approximate response of non-linear multi-degree-of-freedom systems subjected to combined periodic and stochastic excitation

An approximate method is presented for determining the non-stationary response of multi-degree-of-freedom non-linear systems subjected to combined periodic and stochastic excitation. Specifically, first, decomposing the system response as a combination of a periodic and of a zero-mean stochastic component, transfers the equation of motion into two sets of equivalent coupled differential sub-equations, governing the deterministic and the stochastic component, respectively. Next, the derived stochastic sub-equations under non-stationary stochastic excitation are cast into equivalent linear equations by resorting to the non-stationary statistical linearization method. Further, the related Lyapunov differential equations governing the second moment of the linear stochastic response, and the deterministic sub-equations governing the periodic response, are solved simultaneously using standard numerical algorithms. Pertinent Monte Carlo simulation demonstrates the applicability and accuracy of the proposed semi-analytical method.

Sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations based on adjoint variable method

Sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations based on adjoint variable method

Structural damage identification under nonstationary excitations through recurrence plot and multi-label convolutional neural network

Civil engineering structures inevitably suffer from nonstationary ambient excitations in practice, which make conventional damage identification methods relying on the stationary assumption ineffective. This study presents a novel method based on unthresholded assembled recurrence distance matrix (UARDM) and multi-label convolutional neural network (CNN) for structural damage identification under nonstationary excitations. UARDM is a new type of recurrence plot (RP) that is proposed to integrate information of multiple channels and dispense with the artificially selected threshold. It reveals intrinsic dynamic characteristics of the structure using its vibration responses from the perspective of global probabilistic autocorrelation. After that, CNN is applied to automatically extract damage-sensitive features of UARDMs and classify them for the identification of damage cases. Instead of the traditional single-label CNN model that labels each combination of damage location and level as an objective class, the multi-label CNN model is developed to decouple the identification processes of damage locations and levels in order to improve the identification accuracy and computational efficiency. It evaluates the damage level at each location through a sub-branch with an independent set of labels and detects the damage locations by fusing information of all the sub-branches. A comprehensive comparison was conducted among single-label and multi-label CNN models input with raw accelerations, unthresholded multivariate recurrence plots (UMRPs), unthresholded recurrence plots (URPs) and UARDMs through numerical simulation and experimental test. It was demonstrated that the proposed structural damage identification method based on UARDM and multi-label CNN was able to identify multiple damage locations and levels under various stationary and nonstationary excitations with higher accuracy, efficiency and robustness, and even able to detect multiple-damage cases that were not measured beforehand and involved in the training dataset.

Research on the transmission law of kurtosis of SDOF system under nonstationary and non-Gaussian random excitations

Vibration fatigue failure of structures under complex random excitations is a common problem in the field of engineering, and it seriously endangers the reliability and safety of major equipments and structures. It is particularly important to accurately predict the vibration fatigue life of structures under random excitations. Generally, it is assumed that the vibration excitation of engineering structures follows a stationary Gaussian distribution, but the actual excitation usually follows a nonstationary and non-Gaussian distribution, especially under harsh or variable working conditions. The vibration fatigue life of structures is closely related to the structural dynamic response characteristics, and the kurtosis of the structural response has a particularly obvious influence on the vibration fatigue life. In this paper, taking the single-degree-of-freedom system as an example and by decomposing complex random excitations in frequency segments, the dynamic response law of the system under nonstationary and non-Gaussian random excitations is studied in depth, and a mathematical model describing the transmission law of the kurtosis between the decomposed signal of excitation and response signal is established. The results show that there is a close linear relationship between the kurtosis of the structural dynamic response and the kurtosis of the decomposed signal obtained by frequency decomposition of the excitation signal by 3.2 times the half power bandwidth at the damped natural frequency of the structure. It is possible to quantitatively estimate the kurtosis of the structural response according to this relationship, which lays the foundation for accurately predicting the vibration fatigue life of structures under nonstationary and non-Gaussian random excitations.

Ride comfort and energy dissipation of vehicle suspension system under non-stationary random road excitation

Response of vehicle suspension system has traditionally been studied under the assumption of stationary road excitation. However, road excitation becomes a non-stationary random input in the time domain when the vehicle travels at a varying speed. In this paper, we investigate the non-stationary response of vehicle suspension under random road excitation. Despite its importance and relevant applications, this problem has not been well addressed in the literature. The non-stationary random road excitations in the time domain are computed using a high precision Gaussian-Legendre integration method. The evolutionary spectral theory is then applied to evaluate the response in the time-frequency domain. Numerical results for a quarter-car model are presented and effects of vehicle acceleration and road roughness on the ride comfort, energy dissipation from the suspension, and time-variant half-power frequency band for the constant speed and various constant acceleration cases are examined. The consideration of energy dissipation provides new insights on the relationships between ride comfort and fuel consumption, which is important for designs of optimized energy-ride comfort suspension systems under non-stationary road excitations.

Exact benchmark solutions of random vibration responses for thin-walled orthotropic cylindrical shells

The exact solutions of random vibration responses of orthotropic thin cylindrical shells are imperative for verifying numerical approaches. This study proposes the discrete analytical method (DAM) and achieves the exact benchmark responses of thin-walled orthotropic cylindrical shells under stationary and nonstationary random excitations for the first time. Firstly, by revisiting the governing motion equations of elastic orthotropic shells based on the Flügge shell theory, the closed-form modal shape functions of orthotropic cylindrical shell with shear diaphragm boundary condition are introduced into stationary and nonstationary random vibration analyses. The power spectral density functions and root mean squares (RMSs) for stochastic responses of thin shell subjected to various random excitations, including the point, surface, base acceleration and moving excitations, are analytically derived by using the pseudo excitation method. Moreover, DAM is proposed to enhance the computational efficiency by implementing the discretization of the modal coordinates, frequency and temporal domains. Finally, the exact benchmark solutions of stationary and nonstationary stochastic responses are achieved, and the results indicate high accuracy and efficiency of proposed DAM. The excitation bandwidth and spatial distribution have significantly different effects on various types of responses, and maximum response RMS declines with increasing of acceleration of moving load.

Reliability-based stochastic optimal control of frame building under near-fault ground motions

Most of stochastic optimal control methods were developed on the basis of Itô stochastic differential equation, which assumes that the external excitation is white Gaussian noise or filtered white Gaussian noise. However, this assumption is far from the real excitations, which hinders the applications of stochastic optimal control theory. In this paper, the reliability-based stochastic optimal control via direct probability integral method (DPIM) for building structure is proposed, which is applicable to performance-based design of general control systems of linear structures under non-stationary and non-white random excitations. Firstly, the DPIM is utilized to accurately and efficiently compute dynamic reliability of the controlled system. Then, the reliability-based objective function is suggested to optimize the parameters of the placed control devices of building structure, and reliability-based maximum story controllability index is established to determine the optimal placement of control devices, thus fulfilling the stochastic optimal control of structure. Finally, a 10-story shear frame building controlled by active tendons under random excitations of near-fault earthquake ground motions verifies the effectiveness of the proposed optimal control method. Moreover, the optimal control schemes of frame structure under near-fault non-pulse and impulsive ground motions are compared, indicating that the velocity pulses of near-fault ground motions impose significant effect on structural responses, and the more control energy is needed for guaranteeing structural safety.

Efficient reliability analysis based on deep learning-enhanced surrogate modelling and probability density evolution method

An improved method, termed as the AL-DLGPR-PDEM, is presented to address high-dimensional reliability problems. The novelty of this work lies in developing a complete framework for combining the deep learning (DL) architectures, serving as the utility of dimension reduction, and the Gaussian process regression (GPR), resulting in the so-called DLGPR model. First, the parameters of both the DL and the GPR are inferred using a joint-optimization scheme, rather than the traditional two-step, separate-training scheme. Second, the network configuration of the DLGPR is optimally determined by using a grid-search procedure involving cross-validation, instead of an empirical setting manner. On this basis, the DLGPR is adaptively refined via an active learning (AL)-based sampling strategy, so as to gain the desired DLGPR using as fewer training samples as possible. Eventually, the finalized DLGPR is evaluated at the whole representative point set, thereby the probability density evolution method (PDEM) is conducted accordingly. Two numerical examples are investigated. The first one tackles with the static reliability analysis of a planner steel frame, where the case of small failure probabilities is also considered; the second one addresses the dynamic reliability analysis of the steel frame under fully non-stationary stochastic seismic excitation. Comparisons against other existing reliability methods are conducted as well. Results demonstrate that the proposed AL-DLGPR-PDEM achieves a fair tradeoff between accuracy and efficiency for dealing with high-dimensional reliability problems in both static and dynamic analysis examples.

Hybrid coupled damper for the mitigation of torsional vibrations and rotational irregularities in an automotive crankshaft: Concept and design subtleties

This paper presents a new configuration to tackle a twofold problem affecting a crankshaft: the torsional vibrations and the oscillation of the speed at the back end of the shaft due to the torque ripples created by the cylinders. These two phenomena already have industrial solutions, but the requirement levels increase and impose constant improvements. Moreover, the common vibration dampers rely on energy dissipation as heat, which in a context of waste reduction could be avoided. This concept relies on the association of an optimal passive mechanical damper, an electric circuit and electromechanical converters, without any external power supply, in order to ensure a safe operation. From a more fundamental point of view, these elements link a time-periodic correction and a nonstationary cyclic excitation. The core idea of the concept is to enable a redistribution of the energy within this coupled electromechanical circuit, where each element can behave as a power consumer or supplier, so that the oscillations of the mechanical elements can be decreased. In this paper, the authors describe and model this new concept in order to investigate the resulting dynamic behavior and the key design parameters that affect the damping performance.

A stochastic analysis method of transient responses using harmonic wavelets, Part 1: Time-invariant structural systems

The transient response components have significant impacts on the stochastic response analysis of structural systems subjected to nonstationary stochastic excitations. However, available stochastic analysis methods focus on the steady-state response components. This paper proposes a novel stochastic analysis method of the transient responses for multi-degree-of-freedom (MDOF) structural systems subjected to nonstationary stochastic excitations based on periodic generalized harmonic wavelets (GHW). Firstly, the importance of transient response components on structural systems is discussed in detail. The equations of motion of the MDOF structural systems are established by using the periodic GHW with considering the rigid displacement components. The linear algebraic equations with respect to the wavelet coefficients of responses and excitations are established, respectively. Then the connection equations of wavelet coefficients in all scales are established to include the transient components in the responses. A stochastic analysis method of transient responses for structural systems is proposed based on the periodic GHW, and the time-varying power spectral density functions of the structural responses are obtained in a semi-analytical form. The proposed method is validated by two numerical examples, which illustrate the high efficiency and high accuracy of the novel method.

Нестационарное запаздывание установления нелинейных колебаний в системе двух связанных осцилляторов. Часть 1. Общие положения. Формирование упрощенной системы.

Нестационарное запаздывание установления нелинейных колебаний в системе двух связанных осцилляторов. Часть 1. Общие положения. Формирование упрощенной системы.