Sensitivity and Hessian matrix analysis of structural reliability for uniformly modulated random seismic response

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

This study presents an innovative method to estimate the reliability sensitivity based on the low-discrepancy sampling which is a new technique for structural reliability analysis. Two advantages are contributed to the method: one is that, by developing a general importance sampling procedure for reliability sensitivity analysis, the partial derivative of the failure probability with respect to the distribution parameter can be directly obtained with typically insignificant additional computations on the basis of structural reliability analysis; and the other is that, by combining various low-discrepancy sequences with the above importance sampling procedure, the proposed method is far more efficient than that based on the classical Monte Carlo method in estimating reliability sensitivity, especially for problems of small failure probability or problems that require a large number of costly finite element analyses. Examples involving both numerical and structural problems illustrate the application and effectiveness of the method developed, which indicate that the proposed method can provide accurate and computationally efficient estimates of reliability sensitivity.

During the service of the missile suspension structure, the unexpected fatigue failure is emerged because of the dimension dispersibility resulting from machining deviation and design tolerance. In order to get the main factor of failure, based on the moment method of structural reliability assessment and PCL (Patran Command Language) redevelopment technology of finite element parameter analysis, an effective method is proposed to perform the missile suspension structure fatigue life reliability and parameter sensitivity analysis. Using proposed method, the result of reliability and parameter sensitivity analysis can be got readily with only 81 samples of finite element analysis. Compared with Monte-Carlo, proposed method in this paper is more effective with deducing the number of samples, especially fit for some structural reliability and parameter sensitivity analysis under implicit limit state equation.

Systems with random variables and random excitations exist widely in various engineering problems. Extending the traditional global reliability sensitivity to this double-stochastic system has important guiding significance for its design optimization. However, because there is a certain coupling between the randomness of variables and the randomness of excitation, this coupling mechanism is difficult to determine in practical projects. Therefore, it is difficult to extend the traditional reliability sensitivity analysis method to this double-stochastic system. In this research, it is assumed that there is no correlation between variables and excitations. Then, combining the first-passage method–based dynamic strength formula and the variance-based sensitivity analysis method, an approximate global reliability sensitivity analysis method for this double-stochastic system is proposed. In order to improve the computational efficiency, a nested loop method based on seven-point estimation is proposed for reliability sensitivity analysis. In order to verify the accuracy and efficiency of the proposed method, a Monte Carlo simulation is given as a reference. Three examples are studied and discussed to illustrate the practicality and feasibility of the proposed method.

Reliability sensitivity analysis for water hammer-induced stress failure of fluid-conveying pipe

Variance-based reliability sensitivity with dependent inputs using failure samples

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

Reliability sensitivity analysis (SA) is a method to identify the relationship between the change in reliability and the change in the characteristics of uncertain variables. Very few methods can be applied for the reliability SA for long-term degeneracy mechanism, especially when the time-dependent limit state function regarding the interested performance is implicit. This paper proposes a new method to compute the reliability sensitivity measures. First, a surrogate model called time-dependent polynomial chaos expansion (PCE) is employed to approximate the uncertain output of the model and the extensive probabilistic collocation method (PCM) and moving least squares (MLS) method-based algorithm is proposed to compute the coefficients of the time-dependent PCE. Then, the explicit time-dependent limit state function can be obtained and the reliability sensitivity measures can be calculated straightforwardly. Finally, this approach is applied to an engineering case and the time-dependent reliability sensitivity measures are obtained for the long-term degeneracy mechanism model.

This paper proposes a new corner detection method based on the Hessian matrix. The proposed method can detect features of a pattern or input image using eigenvalue and eigenvector of images. The Hessian matrix has information of ellipse with intensity variance, and corner can be detected by using the eigen-value and eigen-vector analysis and decided weight value. In order to evaluate the proposed algorithm, experiments are performed in many type images. As the result of the test image, it shows the better performance than that of conventional Harris, SUSAN, and symmetric corner detectors.

Dynamic Model-based Saddle-point Approximation for Reliability and Reliability-based Sensitivity Analysis

Sensitivity analysis is used to find the key variables which have significant effect on system reliability. For a product in early design stage, it is impossible to collect sufficient samples. Thus, the probabilistic-based reliability sensitivity analysis methods are difficult to use due to the requirement of probability distribution. As an alternative, interval can be used because it only requires few samples. In this study, an effective global non-probabilistic sensitivity analysis based on adaptive Kriging model is proposed. The global accuracy Kriging model is constructed to reduce overall computational cost. Subsequently, the global non-probabilistic sensitivity analysis method is developed. Compared to existing non-probabilistic sensitivity analysis methods, the proposed method is a global non-probabilistic reliability sensitivity analysis method. The proposed method is easy to use and does not require probability distribution of the input variables. The applicability of proposed method is demonstrated via two examples.

Sensitivity distribution optimization method for planar array capacitive imaging

Microcalcification cluster detection using multiscale products based Hessian matrix via the Tsallis thresholding scheme

In Electrical Impedance Tomography, conductivity images can be reconstructed using a back-projection algorithm which is very similar to the ones used in other imaging modalities. In this study, the basic assumptions underlying the back-projection algorithm are investigated. Under these assumptions, a sensitivity matrix is derived relating the conductivity variation to the variation in gradients. A new image reconstruction method is suggested based on a minimization procedure which is equivalent to the solution of the sensitivity matrix equation in a generalized sense.