In hybrid random vibration analysis under multi-point excitations, the structural response generally exhibits non-Gaussian characteristics, and higher-order statistical information of the excitations is necessary for higher-order analysis of the response. However, no theoretical model currently exists for multi-point correlated excitations, and naturally the higher-order analysis of the response is also unavailable. To address these challenges, a new method integrating vector decomposition, conditional expectation, the pseudo excitation method (PEM), and the mixed-degree cubature formula (MDCF) is proposed. First, the vector of multi-point correlated excitations is decomposed into multiple independent excitation vectors. Second, based on the power spectral density (PSD) of Gaussian excitation and the superposition principle, formulas for the PSD and higher-order spectra of the response of the deterministic structure are derived. Third, the PEM is employed to establish a more efficient and practical formula for the higher-order spectra. Fourth, by introducing the concept of conditional expectation, the hybrid random vibration analysis is transformed into a series of conventional random vibration analyses for deterministic structures. The MDCF is then introduced to evaluate the integral of the conditional expectation, yielding the PSD and higher-order spectra of the response. Finally, two examples are provided to verify the accuracy and efficiency of the proposed method and to demonstrate the necessity of hybrid random vibration analysis.

The translation process-based spectral representation method is widely used to simulate the non-stationary non-Gaussian stochastic ground motions. However, the computation of the underlying evolutionary power spectral density matrix and its decomposition require substantial computational effort at discrete time-frequency points. To address this problem, this paper proposes an adaptive interpolation strategy for selecting the time-frequency interpolation points to improve the simulation efficiency. Firstly, the correlation function equations between non-Gaussian stochastic processes and the underlying Gaussian stochastic processes are constructed using Mehler's formula. A fast calculation method for the evolutionary power spectral density of the underlying Gaussian processes is introduced based on the interpolation technique. Secondly, the discrete time-frequency interpolation points are determined based on the amplitude information of the evolutionary power spectral density of the underlying Gaussian stochastic processes. The evolutionary power spectral density matrix is decomposed at these time-frequency interpolation points. The decomposed spectrum is then expressed as a sum of products of various time and frequency components. Spline interpolation is applied to these components at the discrete time-frequency points to approximate the matrix decomposition required by the spectral representation method, improving the efficiency of the decomposition. Additionally, the Fast Fourier Transform further accelerates simulation efficiency. Finally, the accuracy and efficiency of the proposed method for simulating non-stationary non-Gaussian stochastic ground motions are verified by considering the real ground motion record, stochastic vector processes, different probability distribution types, different power spectrum density types, and the number of variates.

The spatial variability of structural parameters has a significant impact on the stochastic response and reliability analysis of engineering structures. In traditional methods, structural parameters are often simplified into random variables, and the spatial correlations among them are frequently neglected. Representing the spatial variability of structural parameters using random fields provides a more realistic and effective alternative. Although the traditional Monte Carlo simulation method can still maintain high accuracy in handling the reliability problems of structures with spatial variability, it becomes a great impediment when the computational cost of obtaining structural responses is expensive. In this paper, an integrated structural reliability analysis method that is easy to implement, efficient, and accurate is proposed by integrating a general random field simulation approach and an improved reliability analysis method. First, using the random field simulation method based on active learning kriging, 1D random field simulation of spatially variable parameters is realized with a small number of random variables. Correspondingly, the reliability problem of a 1D structure with spatially variable parameters can be transformed into a reliability problem that only contains random variables. Subsequently, within the active learning kriging Monte Carlo simulation framework, a new learning function that fully accounts for the impact of sample point signs, the error of the predicted failure probability, the probability density function values, and the U-values is proposed, and it is named SEFU. Finally, the accuracy and effectiveness of the proposed method were verified through three engineering examples, which analyzed the effects of the number of meshed elements, the scales of fluctuation, and the coefficient of variation on the structural reliability index. The results indicate that the novel proposed method significantly improves the computational efficiency of reliability analysis with high estimating accuracy of the failure probability. Further, the new learning function exhibits higher computational efficiency compared with the classical U and expected feasibility functions.

Conventional research on vortex-induced vibration (VIV) fatigue of elastic cylinders often neglects the inherent randomness of system parameters and the impact of connection joints, potentially overestimating the structural reliability. This paper presents a unified probabilistic framework for assessing the VIV fatigue reliability of elastic cylinders with semi-rigid connection joints. First, a VIV fatigue analysis method is developed by integrating the wake oscillator model (WOM) with a multi-scale finite element model (FEM). The boundary condition employed in the WOM is calibrated against the FEM-derived natural frequency to capture the effects of semi-rigid constraints on VIV dynamics. The resulting VIV response is then used to reconstruct hot-spot stresses at connection joints via the multi-scale FEM, yielding a physically consistent VIV fatigue assessment. On this basis, a global performance function is formulated to capture the coupled failure modes of both the cylinder and connection joints, and the structural failure probability is evaluated via a sparse grid-based maximum entropy method that accounts for various uncertain system parameters as well as the joint probability of wind speed and direction. The effectiveness of the proposed framework is verified through a case study involving a transmission tower steel tube with insert-plate connection joints. The results demonstrate that the proposed framework achieves promising accuracy and efficiency by comparing it with the Monte Carlo simulation and existing moment-based methods. Moreover, it is revealed that the connection joints and the joint probability distribution of wind speed and direction have significant effects on VIV fatigue reliability.

Fatigue damage assessment under complex non-stationary non-Gaussian (NS-NG) random loadings remains a challenging problem in structural engineering, as existing time- and frequency-domain fatigue analysis methods suffer from inherent limitations in accuracy and applicability. This study develops a generalized, high-efficiency time-domain random fatigue analysis method for structures under NS-NG excitations. The Johnson transformation model and a sample-interpolation-based technique are introduced to realize accurate and fast generation of NS-NG random excitations. Inspired by the explicit time-domain method (ETDM), an explicit time-domain expression of hotspot stress for linear time-invariant structures is derived, and an efficient equation-solving strategy is proposed to conveniently determine the unknown coefficient matrices. Based on the obtained stress responses, structural fatigue damage is evaluated using the rainflow counting algorithm and cumulative damage criteria, and the statistical characteristics of fatigue damage can be determined by the Monte Carlo simulation. Numerical comparisons with different time- and frequency-domain methods demonstrate that the proposed method provides an accurate, efficient and broadly applicable solution for fatigue analysis under complex random loadings.

Owing to the absence of robust analytical and theoretical analysis methods, the elastic–plastic ultimate bearing capacity of angle steel section components in transmission towers is usually addressed by finite element simulation and experiments. In this work, the elastic stiffness matrix that accounts for the deformation of the element was derived using a fifth-order interpolation function. The dual nonlinear static analysis method was proposed by combining the material nonlinear plastic stiffness matrix and geometrical nonlinear stiffness matrix. The material nonlinear plastic stiffness matrix of the beam element with angle section was derived through the yield surface and the concentrated plastic hinge models, and the geometrical nonlinear stiffness matrix of the angle section was derived by the rigid-body criterion. The accuracy and effectiveness of the analysis method proposed in this work were verified through various examples, and the research results can provide theoretical references for the analysis and calibration of the mechanical properties of transmission towers.

Frequency domain analysis is the important component in the random vibration analysis. However, frequency domain analysis for the non-classically damped linear structure under non-Gaussian random excitations remains a challenge. Thus, this paper establishes a unified computational framework of higher-order moment spectra of response, and performs reliability assessment based on moment spectra of response. Firstly, the theoretical expressions of the higher-order moment spectra of response are deduced by the complex mode superposition method and the generalized impulse response function. Secondly, the expressions of the higher-order moment spectra of response are reconstructed with the help of responses for the harmonic excitation. Subsequently, the dynamic reliability is estimated based on the approximation joint probability density function which is constructed through the unified Hermite polynomial model and Gaussian Copula function. Finally, two numerical examples are investigated to verify the accuracy and efficiency of the calculation method of response the higher-order moment spectra and the dynamic reliability.

Recently, the reliability analysis methods combining active learning Kriging strategies and Monte Carlo simulation (AK-MCS) are increasingly popular. Among them, active learning strategies based on the error analysis of the predicted failure probability are relatively efficient. However, most of the strategies fail to comprehensively consider the effect of updating the Kriging model on the overall prediction error. In this paper, a new active learning Kriging method, which is based on the quantitative analysis of the prediction error, is proposed for structural reliability. First, based on the statistical properties of the Kriging model, the rigorous error analysis of AK-MCS for predicting the failure probability is derived; then, the effect of updating the Kriging model with new training samples on the error of the predicted failure probability is analyzed. To effectively reduce the prediction error of the failure probability, a learning function combined with the pseudo Kriging strategy is proposed. Additionally, an error-based stopping criterion matching the learning function is developed. By combining the error-based learning function and convergence criterion, a new active learning Kriging method for structural reliability is proposed. Finally, four examples are used to verify the effectiveness of the proposed method. The results demonstrate the high efficiency of the proposed method in assessing structural reliability.

The moments method is an attractive non-intrusive method, where estimating statistical moments and reconstructing the probability density function (PDF) are crucial to this approach. However, existing methods for estimating statistical moments face challenges in balancing efficiency and accuracy. Furthermore, the flexible distributions used to construct the PDF may have limited applicability for certain performance functions. In this paper, a full-domain moment method, which is based on a new point estimate method (PEM), monotonic transformation, and the normal inverse Gaussian (NIG) distribution, is proposed. First, an equivalent performance function is constructed through a properly designed monotonic transformation, which maintains the same failure probability as the original performance function but shifts the statistical moments into the applicable domain of the NIG distribution. Then, a new PEM, which combines the bivariate adaptive hybrid dimension reduction method (B-AH-DRM) and the Kriging surrogate model, is employed to estimate the first four central moments of the equivalent performance function. Based on the estimated first four central moments and the NIG distribution, the PDF of the equivalent performance function is constructed, and the failure probability is then calculated. Finally, several examples are used to validate the effectiveness of the proposed method in structural reliability analysis.

For large-span structures, the non-uniform effects of random ground excitations cannot be ignored. Some methods for the random vibration analysis of structures under non-uniform ground excitations were developed, among which the methods based on the explicit time-domain method (ETDM) received widespread attention due to their efficiency. However, the methods based on the ETDM face challenges in determining coefficient matrices conveniently due to the difficulty of separating response effects from non-uniform ground acceleration, velocity, and displacement excitations. In this paper, an ETDM is proposed to determine the responses of structures under non-uniform ground excitations, and an efficient Monte Carlo simulation (MCS) method based on the proposed ETDM and a random process simulation approach is proposed for the random vibration analysis of structures. First, a linear expression of the structural responses, which contains some undetermined coefficients, is derived from the dynamic equilibrium equation of the displacement input method (DIM). Second, an equation-solving method is used to obtain the undetermined coefficients conveniently according to some finite element analysis results. Third, the samples of non-stationary ground excitations are generated by a random process simulation method, the corresponding response samples are determined based on the response expression form the proposed ETDM, and the statistical information of these response samples can be obtained by the MCS method. Finally, a bridge under different non-uniform ground excitations is taken as an example to illustrate the applicability, accuracy and efficiency of the proposed random vibration analysis method.

For estimating structural fatigue damage or fatigue lives under random loads, time-domain methods are accurate and able to combine with nonlinear damage evolution models but too inefficient. Spectral methods, in contrast, are highly efficient but mostly based on Miner’s linear damage accumulation rule, which cannot reflect the nonlinear process of real fatigue damage. In this paper, by combining the block cycle jump technique which is frequently used in time-domain methods, with Dirlik’s spectral method for fatigue life estimation, a new spectral method for fatigue damage estimation that can be based on nonlinear damage models is proposed. Based on experimental data and numerical simulations, the ability of estimation nonlinear fatigue damage and computational accuracy and efficiency of this method is verified. Results show that this method inherits the advantage of high efficiency of classical spectral methods while its accuracy is also sufficiently high.

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.

The first-order reliability method (FORM) is simple and efficient for solving structural reliability problems but may have large errors and converge slowly or even result in divergence when dealing with strongly nonlinear performance functions. For this case, the existing second-order reliability method (SORM) achieves higher computational accuracy but with a consequent decrease in efficiency. To achieve a better balance between accuracy and efficiency, this paper proposes an improved FORM and an improved SORM. First, an improved modified symmetric rank 1 (IMSR1) algorithm, in which the line search strategy for step length is unnecessary, is proposed for iterations of the FORM, and an adaptive Kriging model with a rational update criterion is presented to improve the efficiency of the FORM. Then, an improved FORM with high efficiency and good convergence is proposed. Second, due to the good precision of the adaptive Kriging model at the final design point, the Hessian matrix is available easily without additional computational effort, and an improved SORM with the same efficiency as the improved FORM is presented naturally. Finally, the accuracy, efficiency, and convergence of the proposed methods are verified by numerical and engineering examples.

From the perspective of accuracy, efficiency and versatility, calculating statistical moments for different forms of performance functions in a unified way remains a challenge, and their accuracy also considerably affects the results of subsequent reliability analysis. In this article, a new dimension-reduction model, termed as adaptive hybrid dimension-reduction model (AH-DRM), is derived to approximate the performance functions with different characteristics relatively accurately. Based on the AH-DRM, a highly flexible point estimation method (PEM), which has good versatility for the various forms of performance function, is developed for statistical moments estimation of stochastic systems. Subsequently, to illustrate the performance of the proposed method for different performance function forms, three examples, including weakly, moderately and strongly nonlinear benchmark examples, are investigated. The results indicate that the proposed method is versatile for each example and can receive desirable accuracy for evaluating the first-four central moments of the performance functions with high efficiency. Finally, the developed PEM is applied to reconstruct the probability density function of the performance function and calculate the reliability of structures with the aid of the saddle-point approximation (SPA) method, and two practical engineering examples are used to verify the applicability of the proposed method in structural reliability analysis.

A novel approach for the probabilistic assessment of seismic earth pressure against nonlinear backfills is introduced in this study. To implement reliability-based design for the retaining structures under seismic loading condition, nonlinear upper bound analysis is adopted to obtain the seismic earth pressure through optimization procedure. Firstly, rigorous analytical function is formulated to reveal the normal-shear stress information along the failure surface in soil with nonlinear failure criterion. Subsequently, a kinematic equation is put forward to estimate the seismic earth pressures by balancing the external work rate and the internal energy dissipation rate. The solutions are verified by the Discontinuity Layout Optimization numerical modellings based on the derived stress data from the proposed method. To consider the probability analysis of nonlinear backfill properties, the moment method is presented by combining the adaptive dimension decomposition with the direct integral method. According to the estimated first four statistical moments, the approximated probability density function of the performance function is determined contently. Finally, the failure probability of seismic earth pressure is calculated based on the proposed moment method. Two numerical examples demonstrate that the moment method can be adapted to the characteristics of nonlinear backfills and further improve the accuracy of reliability estimation by introducing higher-order moments analytically.

The system reliability analysis of complex engineering structures remains a challenge in the field of reliability. In this work, a high-order moment method using generalized factorized dimensional reduction method (GF-DRM) and iterative maximum entropy method (IMEM) is proposed for structural system reliability assessment. Firstly, the performance functions are described uniformly by equivalent description methods for various system reliability problems. Secondly, a novel point estimation method (PEM) based on GF-DRM is proposed for the high-order moments estimation of the equivalent performance function. Thirdly, the system failure probability of the structures is accurately determined by using the IMEM, which can automatically determine the order of moments. Finally, four examples, including numerical and engineering cases, are investigated to demonstrate the accuracy and efficiency of the proposed method, in which results obtained from the proposed method are compared with some other existing moment methods and Monte Carlo simulation (MCS) method. The results of the examples show the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and system reliability analysis.

The identification of a suitable transformation model and the calculation of correlation coefficients constitute essential steps in the simulation a nonstationary and non-Gaussian stochastic process. For stochastic ground motion, its nonstationary and non-Gaussian properties are well-known. In this paper, an easy-to-implement simulation method of a nonstationary and non-Gaussian stochastic process with known time-varying statistical moments is proposed. The approximate transformation model between the nonstationary and non-Gaussian stochastic process and the underlying Gaussian process, which contains the wider range of applicability and the availability of explicit expressions for determining the distribution parameters, is determined. The time-varying correlation coefficient of the underlying Gaussian process is calculated through the proposed interpolation method. Furthermore, the effectiveness of the proposed simulation method of the nonstationary and non-Gaussian stochastic ground motion is verified by numerical examples.

Random fields are widely used to represent the uncertainty of some parameters in engineering, and numerous simulation approaches have been developed for Gaussian and non-Gaussian random fields. However, the unified methods among them suffer from low computational accuracy and efficiency or discontinuities in the simulated random fields. Therefore, an easy-to-implement general simulation method based on the active learning Kriging model is proposed for a one dimensional(1D) Gaussian or non-Gaussian random field in this paper. In the proposed method, there are two stages. One stage, called the inner loop, is to construct the Kriging approximation of a random field sample with enough accuracy by some samples of the random variables at some discretized locations, in which an active learning strategy based on the error estimation for the Kriging model is introduced to select adaptively the added locations, and a fast sampling method is presented to determine efficiently the samples at the added locations. In the other stage, called the outer loop, some random field samples are represented accurately by their corresponding Kriging approximations through training iteratively. Furthermore, several numerical examples are presented to show the accuracy, effectiveness and generality of the proposed method for 1D Gaussian and non-Gaussian random fields by comparing with the Karhunen–Loève(KL) expansion method. Meanwhile, the effects of the types of correlation function and the scales of fluctuation on the simulation results are analyzed.

为研究特高压输电塔所用Q420B结构钢在酸雨环境下的腐蚀疲劳裂纹扩展行为,开展了Q420B的CT试样在人工酸雨喷雾腐蚀环境下的腐蚀疲劳试验.试验采用背面应变法监测裂纹长度,研究喷雾方式、pH值、应力比对裂纹扩展速率的影响.试验现象及断口分析表明,CT试样的断裂类型主要为穿晶疲劳断裂,腐蚀疲劳机制主要为阳极溶解机制.对于各工况,基于Paris模型推导了考虑模型参数随机性及da/dN数据波动性的腐蚀疲劳裂纹扩展速率P-da/dN-ΔK模型.结果表明,腐蚀疲劳裂纹扩展速率的离散性随应力强度因子幅的增大呈先减小后增大的趋势,该现象与Paris模型参数的线性相关性有关;相较于浸泡腐蚀,喷雾腐蚀下的裂纹扩展阶段存在明显的裂纹闭合效应,导致在ΔK较低阶段喷雾工况裂纹扩展速率均低于纯疲劳工况;腐蚀液pH值越低,裂纹扩展速率曲线斜率越大,但其初始速率也越低;应力比方面,增大应力比能明显缓解裂纹闭合效应,且裂纹扩展速率随应力比的升高而升高.

In the frequency-domain analysis of structures under non-Gaussian excitations, the determination of high-order moment spectra of excitations remains a substantial challenge due to the complexity and inaccuracy of the existing estimation method. This paper proposes the practical calculation method of the high-order moment spectra models for quadratic Gaussian stochastic processes. Firstly, the expressions of the first four moment spectra of quadratic Gaussian stochastic processes are derived based on the relation between the high-order cumulant function of Gaussian stochastic processes and high-order moment function. Secondly, a practical calculation method of the high-order moment spectra is presented by the ratio of the corresponding component moment functions. Finally, two numerical examples are investigated to validate the efficiency and accuracy of the practical calculation method of the high-order moment spectra for quadratic Gaussian stochastic processes.