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Failure credibility is popular in measuring safety degree of structure under fuzzy uncertainty, but the heavy computational cost is still a challenge in estimating the failure credibility. To alleviate this issue, an iterative method combining adaptive Kriging and fuzzy simulation (AK-FS) has been developed by Ling et al. However, for the problem with complex performance function, a large candidate sampling pool is needed in the AK-FS, which makes the training process of the Kriging model fairly time consuming. In order to improve the estimation efficiency of failure credibility through reducing the size of candidate sampling pool in AK-FS, an efficient sample reduction strategy based on adaptive Kriging (SR-AK) is proposed in this paper. In the SR-AK, the estimation of failure credibility is transformed into searching two active points in candidate sampling pool. After updating the Kriging model in each circle, current active points can be easily identified. Then, according to the properties of the active points and the prediction characteristics of Kriging model, the samples in current candidate sampling pool can be divided into two sets, i.e., the samples affect the estimation of active points and the samples have no effect on it. Obviously, the samples in the latter set can be deleted from current candidate sampling pool to reduce its size. By using this sample reduction strategy, the process for training Kriging model is accelerated circle by circle, which is very helpful to save the analysis time and improve the computational efficiency in estimating failure credibility. Four examples are employed to demonstrate the performance of the proposed SR-AK in fuzzy safety degree analysis. [ABSTRACT FROM AUTHOR]

Most of the existing methods for estimating time-dependent failure credibility (TDFC) are based on optimization algorithms, which may result in a heavy burden on the computational cost and accuracy issue related to the local optimization. In order to achieve the best compromise between computational accuracy and cost, an efficient method is proposed in this work by embedding a single-loop adaptive Kriging model (S-AK) into the dichotomy searching algorithm (S-AK-DSA). The proposed S-AK-DSA can be regarded as a double-loop procedure. In the inner loop, the Kriging model of the real time-dependent performance function (TD-PF) is updated iteratively to accurately predict the signs of the upper/lower boundary of the TD-PF minimum with respect to the time variable at the given membership level. Based on the inner loop, the outer loop searches TDFC by continuously dichotomizing the searching interval of the TDFC. The advantages of S-AK-DSA are mainly manifested in two aspects. Firstly, S-AK-DSA converts the problem of optimizing the exact value of the upper/lower boundary into the problem of accurately identifying their signs, which can avoid the use of optimization algorithms. Secondly, at different membership levels, the S-AK-DSA method chooses the candidate sample pool and continuously updates the current Kriging model of TD-PF, and the adaptive learning function as well as appropriate stopping criterion can effectively reduce the cost of predicting the signs of the upper/lower boundary and improve the computational accuracy. Four case studies are introduced to demonstrate the feasibility and superiority of the proposed S-AK-DSA approach. [ABSTRACT FROM AUTHOR]

Time-dependent failure credibility (TDFC) in a given service time of interest can reasonably quantify the safety of the structure with fuzzy inputs. However, the estimation of TDFC requires high computational cost because it involves multi-layer optimization, especially for problems with the implicit performance functions in engineering. In order to improve the efficiency of estimating TDFC under satisfied precision, this paper proposes an efficient dichotomy searching algorithm (DSA) combined with double-loop adaptive Kriging (D-AK) model (shorten as D-AK-DSA). In the proposed D-AK-DSA, a double-loop adaptive Kriging model is constructed to provide the directions for the dichotomy searching TDFC. In the inner loop, the AK model is constructed to surrogate the relation of the performance function and time variable at the given fuzzy input realization so as to obtain the minimum performance function with respect to the time for the outer loop, and in the outer loop, the AK model is constructed to identify the sign of the upper/lower boundary of the minimum performance function with the fuzzy inputs at a given membership interval so as to provide the dichotomy searching direction for TDFC. By the proposed dichotomy searching strategy, accurately solving the values of the upper/lower boundaries in evaluating TDFC is innovatively replaced by identifying the signs of them, which greatly reduces the difficulty of constructing the outer AK model. At the same time, the proposed method enhances the convergence of the outer AK surrogate model by establishing a reasonably improved learning function. Three examples verify the accuracy and efficiency of the proposed D-AK-DSA method. [ABSTRACT FROM AUTHOR]

Failure credibility is popular in measuring safety degree of structure under fuzzy uncertainty due to its excellent property of self-duality. Existing methods for estimating failure credibility can be mainly divided into two categories, i.e., the simulation-based methods and the optimization-based methods. The simulation-based methods are universal and robust, but time-consuming in dealing with high-dimensional problems. The optimization-based methods are efficient and flexible, but the precision of the failure credibility estimate will be impacted by the local optimum solution resulted from some optimization techniques. Thus, in order to overcome the disadvantages of existing methods, an efficient method by combining genetic algorithm and active learning Kriging (AK-GA) is proposed to estimate failure credibility in this paper. Firstly, by use of the fuzzy simulation, the estimation of failure credibility is transformed into finding for the failure/safety sample that processes the maximum joint membership function (MF) from the fuzzy simulation pool, which makes the credibility estimation less difficult to be computed. Secondly, the genetic algorithm is used to find the failure/safety sample with maximum joint MF. Thirdly, to drastically improve the computational efficiency of the proposed method, active learning Kriging is embedded to accurately and efficiently distinguish the failure and safety sample in computing the fitness function of genetic algorithm. Four mathematical and engineering test examples are used to demonstrate the accuracy and efficiency of the proposed AK-GA for estimating failure credibility. [ABSTRACT FROM AUTHOR]

The failure credibility can be used to measure the safety level of the structure under the fuzzy inputs, but the computational efficiency for estimating the failure credibility is still a challenge. A novel method by combining the adaptive Kriging with fuzzy simulation (AK-FS) is proposed to efficiently estimate the failure credibility. The proposed method firstly employs the FS to transform the estimation of failure credibility into a classification problem, which can be viewed as a bi-level strategy. In the inner loop, a Kriging model for the actual complicated performance function is actively trained by U-learning function in the sample pool generated by FS until the convergent condition is satisfied, on which the samples are divided into failure group and safety group by the well-trained Kriging model instead of the actual performance function in the outer loop. Finally, the failure credibility is obtained by respectively searching the maximum joint membership degrees of the samples in these two groups. The proposed AK-FS method only evaluates the actual performance function in the process for constructing the Kriging model. Since the U-learning function can iteratively construct a sufficiently accurate Kriging model with model evaluations as little as possible, thus the failure credibility can be efficiently and accurately estimated by the proposed AK-FS method. The advantages of the proposed AK-FS method are demonstrated by several examples. [ABSTRACT FROM AUTHOR]

How to accurately and efficiently estimate the failure credibility is widely concerned in safety analysis under fuzzy uncertainty. To solve this issue, an iterative method combining the adaptive Kriging with fuzzy simulation (AK-FS) was put forward by Ling et al. But for the problem with multidimensional fuzzy inputs and/or high safety degree, AK-FS is inefficient. In order to improve the computational efficiency of AK-FS, a novel hypercube-based fuzzy simulation (HBFS) combined with adaptive Kriging (shorten as AK-HBFS) is proposed in this paper. The first key technique of the proposed method is to develop the HBFS for constructing the candidate sampling pool. In the HBFS, the active point is defined at first. Then, the estimation of the failure credibility is transformed into seeking for the active point. By using an adaptive hypercube shrinkage strategy, the active point can be quickly searched from the samples whose joint membership functions (JMFs) are smaller than the JMF of the active point. Thus, the size of the candidate sampling pool in the AK-HBFS is smaller than that of the original AK-FS, and it helps save the training time of the Kriging model in the AK-HBFS compared to the AK-FS. The second key technique of the proposed method is that the process for finding the active point is efficiently realized by the U-learning function based AK model, rather than calling the true performance function directly. The merits of the proposed AK-HBFS are demonstrated by four test cases. [ABSTRACT FROM AUTHOR]

Since failure credibility has some perfect properties such as the self-duality, it is developed to be a popular failure measure indicator under the fuzzy uncertainty. In order to globally measure the contribution of fuzzy input to the failure credibility, the failure-credibility-based importance measure (FC-IM) is proposed in this paper. It is defined by the fuzzy average difference between unconditional failure credibility and conditional one on fixing the fuzzy input over its entire fuzzy input distribution range, and the mathematical properties of the proposed FC-IM are also discussed. Additionally, an efficient method by combining adaptive Kriging and double-loop fuzzy simulation is developed to estimate FC-IM. Finally, three examples are presented to illustrate the rationality of the proposed FC-IM and the feasibility of the proposed estimation method for FC-IM. [ABSTRACT FROM AUTHOR]