A response surface method based on weighted regression for structural reliability analysis

Approximation methods such as the response surface method (RSM) are widely used to alleviate the computational burden of engineering analyses. For reliability analysis, the common approach in the RSM is to use regression methods based on least square methods. However, for structural reliability problems, RSMs should approximate the performance function around the design point where its value is close to zero. Therefore, in this study, a new response surface called ADAPRES is proposed, in which a weighted regression method is applied in place of normal regression. The experimental points are also selected from the region where the design point is most likely to exist. Examples are given to demonstrate the benefit of the proposed method for both numerical and implicit performance functions.     

An optimization method for learning statistical classifiers in structural reliability

Monte Carlo simulation is a general and robust method for structural reliability analysis, affected by the serious efficiency problem consisting in the need of computing the limit state function a very large number of times. In order to reduce this computational effort the use of several kinds of solver surrogates has been proposed in the recent past. Proposals include the Response Surface Method (RSM), Neural Networks (NN), Support Vector Machines (SVM) and several other methods developed in the burgeoning field of Statistical Learning (SL). Many of these techniques can be employed either for function approximation (regression approach) or for pattern recognition (classification approach). This paper concerns the use of these devices for discriminating samples into safe and failure classes using the classification approach, because it constitutes the core of Monte Carlo simulation as applied to reliability analysis as such. Due to the flexibility of most SL methods, a critical step in their use is the generation of the learning population, as it affects the generalization capacity of the surrogate. To this end it is first demonstrated that the optimal population from the information viewpoint lies around in the vicinity of the limit state function. Next, an optimization method assuring a small as well as highly informative learning population is proposed on this basis. It consists in generating a small initial quasi-random population using Sobol sequence for triggering a Particle Swarm Optimization (PSO) performed over an iteration-dependent cost function defined in terms of the limit state function. The method is evaluated using SVM classifiers, but it can be readily applied also to other statistical classification techniques because the distinctive feature of the SVM, i.e. the margin band, is not actively used in the algorithm. The results show that the method yields results for the probability of failure that are in very close agreement with Monte Carlo simulation performed on the original limit state function and requiring a small number of learning samples.     

An adaptive directional importance sampling method for structural reliability

In this paper, an adaptive directional importance sampling (ADIS) method is presented. The algorithm is based on a directional simulation scheme in which the most important directions are sampled exact and the others by means of a response surface approach. These most important directions are determined by a β-sphere enclosing the most important part(s) of the limit state. The β-sphere and response surface are constantly updated during sampling with information that becomes available from the exact evaluations making the scheme adaptive.Various widely used test problems, representing a broad range of complex limit states that can occur in practice, of which several that pose potential problems to stochastic methods in general, demonstrate the high efficiency, accuracy and robustness of the method. As such, the ADIS method is of particular interest in applications with a low probability of failure and medium number (up to about 40) of stochastic variables, for instance in aircraft and nuclear industry.     

Optimal planning of structural performance monitoring based on reliability importance assessment

Recently, the effective use of information from structural health monitoring (SHM) has been considered as a significant tool for rational maintenance planning of deteriorating structures. Since a realistic maintenance plan for civil infrastructure has to include uncertainty, reliable information from SHM should be used systematically. Continuous monitoring over a long-term period can increase the reliability of the assessment and prediction of structural performance. However, due to limited financial resources, cost-effective SHM should be considered. This paper provides an approach for cost-effective monitoring planning of a structural system, based on a time-dependent normalized reliability importance factor (NRIF) of structural components. The reliability of the system and the NRIFs of individual components are assessed and predicted based on monitored data. The total monitoring cost for the structural system is allocated to individual components according to the NRIF. These allocated monitoring costs of individual components are used in Pareto optimization to determine the monitoring schedules (i.e., monitoring duration and prediction duration).     

一种基于改进MCMC算法的模型修正方法

标准马尔可夫链蒙特卡罗(MCMC)算法不易收敛、拒绝率高,使其应用受到限制。在贝叶斯方法中引入最大熵值法来估计参数的后验概率密度函数最大值,进而将布谷鸟算法中新鸟巢更新的思想融入Metropolis-Hasting(MH)抽样算法得到改进的MH抽样算法,同时使用支持向量机(SVM)建立待修正参数与有限元模型输出之间的代理模型,以提高模型修正的计算效率。分别使用三自由度线性系统和平面桁架模型来验证本文方法的有效性,结果表明:修正后样本的马尔可夫链混合性能好,停滞概率低,修正后参数相对误差均小于2%。     

An efficient response surface method using moving least squares approximation for structural reliability analysis

The response surface method (RSM) is widely adopted for structural reliability analysis because of its numerical efficiency. However, the RSM is time consuming for large-scale applications and sometimes shows large errors in the calculation of the sensitivity of the reliability index with respect to random variables. In order to overcome these problems, this study proposes an efficient RSM applying a moving least squares (MLS) approximation instead of the traditional least squares approximation generally used in the RSM. The MLS approximation gives higher weight to the experimental points closer to the most probable failure point (MPFP), which allows the response surface function (RSF) to be closer to the limit state function at the MPFP. In the proposed method, a linear RSF is constructed at first and a quadratic RSF is formed using the axial experimental points selected from the reduced region where the MPFP is likely to exist. The RSF is updated successively by adding one new experimental point to the previous set of experimental points. Numerical examples are presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the conventional RSM.     

A new artificial neural network-based response surface method for structural reliability analysis

This paper presents a new artificial neural network-(ANN)based response surface method in conjunction with the uniform design method for predicting failure probability of structures. The method involves the selection of training datasets for establishing an ANN model by the uniform design method, approximation of the limit state function by the trained ANN model and estimation of the failure probability using first-order reliability method (FORM). In the proposed method, the use of the uniform design method can improve the quality of the selected training datasets, leading to a better performance of the ANN model. As a result, the ANN dramatically reduces the number of required trained datasets, and shows a good ability to approximate the limit state function and then provides a less rigorous formulation in the context of FORM. Results of three numerical examples involving both structural and non-structural problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Compared with the conventional ANN-based response surface method, the proposed method is much more economical to achieve reasonable accuracy when dealing with problems where closed-form failure functions are not available or the estimated failure probability is extremely small. Finally, several important parameters in the proposed method are discussed.     

基于改进SCAM算法的结构物理参数识别贝叶斯方法

针对贝叶斯估计中逐分量自适应Metropolis(single component adaptive Metropolis,SCAM)算法易生成重复性样本,导致抽样效率低、结果误差大等问题,重新定义了提议分布方差的表达式,提出了改进的SCAM算法,使得抽样样本序列构成的马尔可夫链相对稳定.进而将贝叶斯理论与改进的SCA...     

基于随机无网格伽辽金法和蚂蚁算法的结构可靠性分析

 用摄动随机无网格伽辽金法(PSEFGM)求解随机结构的响应,然后采用蚂蚁算法对结构可靠性进行了分析。摄动随机无网格伽辽金法具有不需要划分单元和精度高等特点。蚂蚁算法是一种智能型随机搜素优化算法,对目标函数没有任何可微甚至连续的要求,可有效克服经典算法易于陷入局部最优解的常见弊病。数值实例表明,在随机结构可靠性分析方面,随机无网格迦辽金法与蚂蚁算法比经典算法具有明显的优势。     

粒子滤波参数估计方法在齿轮箱剩余寿命预测中的应用研究

针对非线性非高斯系统的剩余寿命（RUL）预测问题,本文提出了一种基于粒子滤波（PF）理论的设备剩余寿命预测方法。首先建立设备的非线性状态空间模型（含有未知的时变参数）,然后通过粒子滤波算法估计出设备状态的概率密度函数（PDF）,从而根据该PDF计算出设备的RUL。此外,计算设备RUL的期望值和95%置信区间,并对模型的预测效果进行评估,验证预测的有效性和准确性。最后通过齿轮箱的全寿命实验,对本文所提方法的有效性进行实例验证,将实验结果和传统的比例风险模型（PHM）预测结果对比分析,结果表明本文提出的剩余寿命预测方法要优于传统的PHM预测方法。     

A semi-analytical simulation method for reliability assessments of structural systems

A semi-analytical simulation method is proposed in this paper to assess system reliability of structures. Monte Carlo simulation with variance-reduction techniques, systematic and antithetic sampling, is employed to obtain the samples of the structural resistance in this method. Variance-reduction techniques make it possible to sufficiently simulate the structural resistance with less runs of structural analysis. When resistance samples and its moments determined, exponential polynomial method (EPM) is used to fit the probability density function of the structural resistance. EPM can provide the approximate distribution and statistical characteristic of the structural resistance and then the first-order second-moment method can be carried out to calculate the structural failure probability. Numerical examples are provided for a structural component and two ductile frames, which illustrate the method proposed facilitates the evaluation of system reliability in assessments of structural safety.     

An orthogonal normal transformation of correlated non-normal random variables for structural reliability

In this paper, an efficient and explicit technique is proposed for transforming correlated non-normal random variables into independent standard normal variables based on the three-parameter (3P) lognormal distribution. In contrast with the classic Nataf transformation, the derived equivalent correlation coefficient in non-orthogonal standard normal space of the proposed transformation is expressed as an explicit formula, thereby avoiding tedious iteration algorithm or multifarious empirical formulas. Meanwhile, the applicable range of the original correlation coefficient is determined based on fundamental properties of the proposed expression of correlation distortion and the definition of correlation coefficient. The proposed transformation requires only the first three moments (i.e., mean, standard deviation, and skewness) of basic random variables, as well as their correlation matrix. Therefore, the proposed transformation can also be applied even when the joint distribution or marginal distributions of the basic random variables are unknown. Several numerical examples are presented to demonstrate the user-friendliness, efficiency, and accuracy of the proposed transformation applied in structural reliability analysis involving correlated non-normal random variables.     

A reliability allocation method for agricultural machinery based on AHP-IFM

In the product design phase, the available product failure data are limited, and the weight allocation method is often used to assign reliability targets to each unit. The integrated factors method (IFM) can calculate the reliability allocation weights considering multiple influencing factors simultaneously, but it cannot reflect the difference in the importance of each factor and each unit. The analytic hierarchy process (AHP) can calculate the relative importance weights of each factor and each unit. Combining the AHP with the IFM can make the IFM more adaptable to the system and more accurate for reliability allocation. However, the current combination method can cause two problems: the invalidation of the influencing factor weights and the imbalance of the unit weights. To address these two shortcomings, the AHP-IFM proposed in this paper introduces a weight weakening factor and exponentially corrects the unit weights for units, which can better apply the relative importance weights of each influencing factor and each unit to the reliability allocation. The effectiveness of the AHP-IFM is verified by comparison with existing methods and data. Finally, an AHP-IFM applicable to agricultural machinery is proposed, and the reliability allocation of a no-till seeder is used as a case to verify the feasibility of the AHP-IFM.     

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.     

基于可靠性试验的飞机振动数据归纳方法研究

运用疲劳累积损伤等效理论，提出一种新的基于可靠性试验的飞机振动环境数据归纳方法，较好地满足了基于可靠性试验的飞机振动数据归纳要求，经某型飞机实测振动数据检验，此归纳方法具有可操作性和工程实用价值。     

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.     

An improved sieve point method for the reliability analysis of structures

The efficiency of existing stochastic analysis method depends on the discretization of the random variables domain. The number theoretical method has been proposed to discretize the random variable space and solve the generalized density evolution equation via sampling strategy. This method traditionally involves hyper-ball sieving (HS) algorithm to sample the representative point set. However, the sieving radius of the hyper-ball is determined subjectively, and the efficiency and accuracy of the analysis depend on the selected radius. To avoid this subjective selection, an equal volume hyper-ball sieving method is presented in this paper. By transforming the hypercube spatial volume of random variables into that of an equivalent hyper-ball, the radius of the equal volume hyper-ball is obtained analytically. This radius is further optimized with a minimum star discrepancy in the representative point set. The performance and accuracy of the proposed method are checked in four numerical examples, and the representative point set such obtained is more uniform with smaller NRP leading to more accurate and efficient subsequent stochastic analysis than the HS method.     

Research on fatigue reliability prediction model and structural improvement of welded drive axle housing based on master S-N Curve method

Fatigue reliability prediction of welded structures is mainly based on nominal stress or hot spot stress method, but there are some problems such as grid sensitivity and joint geometry dependence. The Master S-N curve method can solve these problems well, but the corresponding reliability model needs to be studied. In this paper, the fatigue reliability model of welded structures based on the Master S-N curve method is studied. Considering the randomness of life and the correlation of failure, a reliability model is proposed, which reduces the computational burden by establishing a median damage-random threshold rule. Taking the welded drive axle housing as an object, the system reliability is analyzed under the bench test condition, and verified by the experimental data. After the verification, this method is used to predict the reliability of the axle housing under variable amplitude loading collected in the test field, and the results are verified by Monte Carlo (MC) method. When the P-S-N curves are parallel, the model is accurate, which is the characteristic of the Master S-N curve method. This method only needs to input the median damage value of the weak part, which is easy to be applied. This method can speed up the reliability prediction cycle of welded structures, which is beneficial to product innovation and optimal design. Finally, an improved design scheme is proposed for the weak parts of welding, and the effects of welding leg width, welding depth, and closed weld on fatigue life are revealed.