In order to make a good compromise of cost and safety with small data in the early structural design stage, a practical decoupled credibility-based design optimization method is developed in the ...presence of fuzzy uncertainty. In the proposed approach, failure credibility is constructed as optimization constraints estimated by fuzzy advanced first-order second-moment method. By approximating the fuzzy credibility constraint by the adaptive Kriging surrogate model, a fuzzy credibility-based design is decoupled to a common deterministic optimization so that various existing optimization algorithms can be easily applied. Compared to the traditional double-loop approach, the newly proposed method is more efficient and strongly practical for complicated engineering problems. Design results of three structural engineering examples also show advantages in accuracy and computation speed of the proposed method over the traditional double-loop approach.
Nanoscale S‐type NbOx locally active memristors (LAMs) open up new opportunities in the brain‐inspired neuromorphic computing. Simple yet accurate models for these memristors can provide benefits for ...designing related circuits and systems. Considering that the DC voltage–current plot of the NbOx LAM under current sweeping is composed of three regions, that is, high resistance region, negative differential resistance region, and low resistance region, a three‐segment piecewise‐linear method is applied to fit these three regions. Based on this developed relation of the voltage and current at DC, a simple model for the NbOx LAM is proposed. The parameters of the proposed model can be easily identified in terms of the quasi‐static and dynamic electrical characteristics. A series of numerical simulations corroborate that the proposed model can accurately emulate the quasi‐static voltage–current characteristics and oscillating behaviours of the NbOx LAM.
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.
Local reliability sensitivity (RS) and global RS can provide useful information in reliability-based design optimization, but the algorithm for solving them is still a challenge, especially in case ...of small failure probability and high dimensionality. In this paper, a novel method by combining Monte Carlo simulation (MCS) with line sampling (LS), an efficient method for estimating small failure probability in case of the high dimensionality, is proposed to evaluate local RS and global RS simultaneously. Since the proposed method employs LS samples to approximately screen out the failure samples from the MCS sample set, the proposed method possesses both the efficiency of the LS and the accuracy of the MCS. One numerical example and two engineering examples illustrate the accuracy and the efficiency of the proposed method.
Failure possibility (FP) is widely used to measure safety degree of structure in the presence of fuzzy uncertainty, but how to quantify the effect of fuzzy distribution parameter on FP is seldom ...investigated. For searching the important parameter to FP and guiding the FP-based design optimization, the local sensitivity of FP (LS-FP) is firstly defined by the partial derivative of FP with respect to the fuzzy distribution parameter in this paper. Then, the analytical solution is derived for the LS-FP in special cases; a universal algorithm is proposed to solve LS-FP by use of the fuzzy simulation. The proposed universal algorithm includes three creative steps. The first is explicitly expressing FP as the joint membership function of the fuzzy inputs at the fuzzy most possible failure point (F-MPP) by use of the fuzzy simulation, on which LS-FP can be equivalently transformed as the partial derivative of F-MPP with respect to the fuzzy distribution parameter. The second is using the characteristic of F-MPP to derive the analytical solution of the partial derivative of F-MPP. The third is establishing an efficient method to estimate F-MPP for completing LS-FP, where new learning function and stopping criterion are proposed to improve the computational efficiency. The proposed algorithm has no limitation on the nonlinearity of performance function and can be applied in any fuzzy membership distribution form of the fuzzy input. Several examples are used to validate the wide applicability, the accuracy, and the efficiency of the proposed algorithm to solve LS-FP.
Based on two procedures for efficiently generating conditional samples, i.e. Markov chain Monte Carlo (MCMC) simulation and importance sampling (IS), two reliability sensitivity (RS) algorithms are ...presented. On the basis of reliability analysis of Subset simulation (Subsim), the RS of the failure probability with respect to the distribution parameter of the basic variable is transformed as a set of RS of conditional failure probabilities with respect to the distribution parameter of the basic variable. By use of the conditional samples generated by MCMC simulation and IS, procedures are established to estimate the RS of the conditional failure probabilities. The formulae of the RS estimator, its variance and its coefficient of variation are derived in detail. The results of the illustrations show high efficiency and high precision of the presented algorithms, and it is suitable for highly nonlinear limit state equation and structural system with single and multiple failure modes.
Reliability measures the ability that the structure finishes its intended function without failures by taking uncertainties into account. Reliability sensitivity commonly is defined as the partial ...derivative of the failure probability with respect to the distribution parameter, which is often of great importance for the reliability-based design optimization. In this paper, two improvements and one extension of the subdomain sampling (SS) method are researched. The first improvement is the criterion for adaptively determining the number of subdomains. The second improvement is that based on the first improvement, adaptive Kriging (AK) model is embedded into the modified SS (MSS) method to substitute the actual limit state function to identify the limit states of the samples generated in the MSS method. Through adaptively partitioning the distribution region, the size of candidate sampling pool in each circle of updating process of Kriging model is decreased compared with that in the method with the candidate samples being directly sampled in the whole uncertain distribution region, which improves the efficiency of each circle’s updating process. Then, the MSS-based adaptive Kriging (AK-MSS) method is extended to the reliability sensitivity analysis where no extra model evaluations are needed after the failure probability is assessed by the AK-MSS method. That is to say, the reliability and the reliability sensitivity can be simultaneously estimated by the AK-MSS method. Results of case studies in this paper demonstrate the effectiveness of the AK-MSS method.
The system failure possibility of multi-mode structural system (referred to as system) under fuzzy uncertainty is the joint membership function of input vector at the system fuzzy design point, and ...it can reasonably measure the safety degree of the system. The system fuzzy simulation (S-FS) can be combined with adaptive Kriging model (AK-S-FS) to solve the system failure possibility. In the current AK-S-FS method, the system fuzzy design point is searched in the maximum value region of the fuzzy input vector corresponding to the 0 membership level, and its computational efficiency still needs to be improved. Thus, a hierarchical system fuzzy simulation combined with adaptive Kriging model (AK-HS-FS) method is proposed to improve the efficiency of searching the system fuzzy design point in this paper. The efficiency of the proposed AK-HS-FS method comes from the innovative strategies of three aspects. The first is the strategy of the hierarchical system fuzzy simulation (HS-FS). Compared with the S-FS with the system fuzzy design point searched roughly in the maximum possible value region, the strategy of the HS-FS is to exploratively expand the search region by transferring from a larger membership level to a smaller one. The overall search region of the system fuzzy design point can be reduced without losing the search accuracy in the HS-FS. The second is the strategy of the hierarchical training. Compared with training the system Kriging model in the combined candidate sample pool (CSP) of all layers, it is more time-saving to train the system Kriging model layer by layer in the hierarchical CSP. The third is the strategy of iteratively reducing the CSP. According to the properties of the system fuzzy design point and the probability properties of the Kriging prediction, the required time of training the system Kriging model can be further reduced by iteratively reducing the CSP, and the reduction of the CSP can ensure the accuracy without introducing any computational cost and complexity. The results of case studies fully verify that the AK-HS-FS is much more efficient than the AK-S-FS under satisfying the computational accuracy.
An efficient methodology is presented to perform the reliability-based optimization (RBO). It is based on an efficient weighted approach for constructing an approximation of the failure probability ...as an explicit function of the design variables which is referred to as the ‘failure probability function (FPF)’. It expresses the FPF as a weighted sum of sample values obtained in the simulation-based reliability analysis. The required computational effort for decoupling in each iteration is just single reliability analysis. After the approximation of the FPF is established, the target RBO problem can be decoupled into a deterministic one. Meanwhile, the proposed weighted approach is combined with a decoupling approach and a sequential approximate optimization framework. Engineering examples are given to demonstrate the efficiency and accuracy of the presented methodology.
In this paper, a novel combined fatigue life reliability analysis model is constructed from the perspective of inverse analysis of Manson-Coffin equation. By the derived equivalent threshold of low ...cycle fatigue life, the failure event that the combined fatigue life is less than or equal to the presupposed threshold is equivalently transformed into the event that the actual strain range in the low cycle fatigue mode is larger than or equal to the inverse strain range threshold. The inverse strain range threshold corresponds to the equivalent threshold of low cycle fatigue life derived by the presupposed threshold of combined fatigue life. Then, the inverse strain range-based limit state function is constructed to analyze the fatigue life reliability, where solution of the exponential Manson-Coffin equation which is used to determine the low cycle fatigue life is avoided. A combination of the inverse strain range-based limit state function and adaptive Kriging (AK) model is constructed first to estimate the combined fatigue life reliability where the AK model directly surrogates the inverse strain range-based limit state function, and this algorithm is defined as a full-surrogate algorithm. The inverse strain range-based limit state function consists of two nested parts. The first part is the structural analysis which is usually an implicit function and the second part is the life analysis which is usually an explicit function. In this regard, another combination of the inverse strain range-based limit state function and AK model is constructed to estimate the combined fatigue life reliability, where the AK model only surrogates a part of inverse strain range-based limit state function, i.e., the implicit structural analysis part, and this algorithm is regarded as a semi-surrogate algorithm. Two aero-engine structures are analyzed to validate the effectiveness of the proposed method.
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