High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

Abstract

High dimensional reliability analysis is unavoidable if a structural system involving stochastic process because Karhunen–Loève (K‐L) expansion is commonly used. Reliability analysis for structural systems with computationally intensive numerical models and high dimensions is challenging. In this study, an effective high dimensional reliability analysis method is proposed based on principal components and active subspace (PCAS) and active Kriging, and is termed as PCAS‐AK. The proposed method can address two shortcomings existing in PCAS: the latter select training samples randomly and cannot deal with parallel processing. The proposed method, however, selects training samples adaptively, subsequently, the training samples that have high contribution to probability of failure are selected, which can improve computational efficiency. To reduce overall computational time and allow parallelization, K‐weighted‐means combined with learning function are used to select multiple samples at each iteration. After the dimension reduction of both input and output spaces, the samples selected by adaptive method are used to construct Kriging model in the latent low‐dimensional space. Three examples are used to demonstrate the applicability and accuracy of the proposed method. Results show that the proposed method can deal with parallel processing and is, generally, more effective than PCAS for high dimensional reliability problems.

Positioning failure error identification of industrial robots based on particle swarm optimization and Kriging surrogate modeling

“…In manufacturing processes, existing a certain deviation between the machined and ideal surfaces, and the surface characteristics can be described by the normal direction and points on that surface. [32][33] In this paper, the SDT 34 is used to describe the accumulation of errors in three-dimensional entities, and the variables on a product's surfaces are decomposed into three translation vectors and three rotation vectors, which are called small displacement screws, as shown in Formulae (3) and (4).…”

AOK‐ES: Adaptive optimized Kriging combining efficient sampling for structural reliability analysis

“…19 Under this case, the surrogate model-based approaches have been developed by using a mathematic model to replace the time-consuming simulation calculation, which dramatically elevates the calculating efficiency while achieving an acceptable accuracy. Classical surrogate models include response surface, 20,21 neural network, 22,23 support vector machine, 24,25 Kriging model, 26,27 etc. This paper focuses on the Kriging model because of its superior approximation ability 28 and unique variance prediction ability.…”

Kriging‐based reliability analysis for a multi‐output structural system with multiple response Gaussian process

“…Under this circumstance, although the classic structural reliability methods can be applied, including first-order reliability method (FORM), 4 second-order reliability method (SORM), 5 first-order saddle point approximation (FOSPA) based reliability method, 6 moment-based reliability method, 7 etc., however these methods cannot effectively balance the computational accuracy and efficiency. In terms of this issue, several surrogate model-based reliability methods have been reported, which include the response surface method (RSM), 8 neural networks, 9 the Kriging model, 10 support vector machine (SVM), 11 etc. Due to the ability to describe the uncertainty of predicted value, 12,13 the Kriging model has been widely introduced into structural reliability analysis.…”