In practical engineering, mechanical structures are affected by time-dependent uncertainties and by correlated failure modes. This study proposes an enhanced time-variant reliability analysis framework by coupling a mixed Archimedean Copula model with an adaptive Kriging model driven by the maximum expected prediction error (MEPE) learning function. The mixed Copula combines Gumbel, Clayton and Frank components, so that upper-tail, lower-tail and nearly symmetric dependence can be represented in one model. The MEPE function combines Kriging prediction variance and leave-one-out cross-validation error through a dynamic balance factor, which guides early global exploration and later refinement near the most probable point trajectory. For the planar three-bar structure, the mixed-Copula failure probability at t = 7 is 0.4078, close to the direct-MCS benchmark 0.4059, with a relative error of 0.47%; the number of original limit-state evaluations decreases from 1.00 × 106 to 326, corresponding to a 99.97% reduction. For the two-rod parallel structure, the mixed-Copula failure probability at T = 2 is 0.0987, close to the direct-MCS benchmark 0.0992, with a relative error of 0.50%; the number of original limit-state evaluations decreases to 284. The calculated upper- and lower-tail dependence coefficients of the mixed Copula are 0.1345 and 0.2985 for the planar three-bar structure and 0.0003 and 0.3709 for the two-rod parallel structure. These quantitative results show that the proposed framework can describe nonlinear failure dependence more flexibly than a single Copula while retaining high computational efficiency.
Due to uncertainties such as loads and material degradation, the reliability of the crane boom changes over time. In this paper, a hybrid interval process and random model is used to characterize the uncertainty of crane boom. Considering that the reliability in actual engineering is often determined by a variety of failure modes, this paper considers three failure modes: strength failure, stiffness failure and stability failure. Because reliability analysis of crane boom involves time-consuming finite element analysis, a hybrid time-variant reliability analysis method based on the Kriging model is proposed to alleviate this issue. To reduce the computational complexity of the hybrid uncertain model, the equivalent uncertainty transformation method is employed. For the transformed model, an active learning method is utilized to construct a high-precision Kriging model, which can further reduce the analysis time. Based on the constructed Kriging model, the time-variant reliability results of the crane boom under multiple failure modes can be obtained by the Monte Carlo analysis. The proposed method is first verified by a cylindrical pressure vessel mathematical example and then applied on the reliability of crane booms.
Kun Zhang, Zihan Zhang, Jian Liu et al.· Proceedings of the Instituti...· 0 citations
Comparative studies across six benchmark cases demonstrate that the Two-Stage AK-MCS method reduces the average number of function evaluations by 2.0% to 10.0% compared to the standard AK-MCS method.
To evaluate the performance distribution of centrifugal pumps under dimensional deviation in design, this paper proposes a novel reliability analysis method combining the Bayesian‐Kriging model and the Copula function. A data‐driven surrogate model is established to rapidly predict the performance responses corresponding to varying design parameters. Both the manufacturing uncertainty of design dimensions and the epistemic uncertainty of the surrogate model are fully considered, and the Bayesian posterior distribution is employed to propagate the epistemic uncertainty of the surrogate model. The Copula function is adopted to construct the joint distribution of two critical pump performance indicators, namely head and efficiency, which effectively reduces the required number of sampling points. The developed Bayesian‐Kriging surrogate model achieves a relative error of less than 1% for all test samples, demonstrating satisfactory prediction accuracy. The joint reliability evaluation results obtained by the Copula‐based method are highly consistent with those calculated via the Monte Carlo sampling (MCS) method. For a single test case, the MCS method requires 10
8
samples, whereas the proposed Copula‐based reliability method only needs 10
3
samplings, which significantly reduces the computational cost. These results verify the outstanding advantages of the proposed method in terms of both calculation accuracy and computational efficiency. Furthermore, performance reliability evaluation of a typical centrifugal pump is conducted using the developed method, yielding a reliability value of 0.99820 with a 95% confidence interval of [0.99806, 0.99833].
Yi Li, Guangzhong Hu, Ping Wang et al.· Quality and Reliability Engi...· 0 citations
To overcome the limitation of deterministic topology optimization (DTO) which ignores uncertainties, this paper proposes a multi-probability-constrained reliability-based topology optimization (MRBTO) model for structures under multiple displacement constraints.
The MRBTO model treats loads and material properties as random variables and uses a series system to represent multiple failure modes. System failure probability is calculated using the first-order reliability method (FORM). An outer loop adaptively adjusts the structural volume to meet a target failure probability, while an inner loop employs a modified SIMP method to optimize the material layout. A two-stage dynamic Gaussian sensitivity filtering (DGSF) method eliminates checkerboards and gray elements. The framework is validated on a 2D MBB beam and a cantilever beam using Monte Carlo simulation.
Compared with DTO, MRBTO reduces the failure probability from approximately 50% to target levels (e.g. 5% or 1%) with high precision. The volume increase is modest – 5% for the cantilever beam even at the strictest target (1%), and about 7% for the MBB beam, which is a slight increase that is acceptable given the large reliability gain. Combined with DGSF, the discreteness rate (grayness ratio) drops from over 30% to nearly 0%, producing crisp boundaries and well-controlled displacements. MRBTO successfully handles multiple independent displacement constraints and different target failure probabilities simultaneously.
A novel volume-controlled MRBTO model that handles system-level multi-failure probabilities is introduced, integrating DGSF to eliminate gray elements and boundary blurring. The dual-loop solution strategy efficiently couples reliability analysis with topology optimization, offering a practical and robust design tool under uncertainties.
Xiaona Yang, Qiliang Zhang, Zongwei Hu et al.· Multidiscipline Modeling in...· 0 citations
This study presents an individualized inverse Gaussian process-based reliability modeling and optimal degradation test design for rubber V-belts, addressing the high cost, long duration, and data scarcity of traditional reliability demonstration testing (RDT). Degradation experiments on five B-type V-belts monitored slip ratio, tension force, and primer crack depth every 12 h, yielding lifetimes between 190 and 209 h (mean: 197 h). A stochastic degradation model incorporating individual heterogeneity was developed, with parameters estimated via Bayesian inference using Markov Chain Monte Carlo. By minimizing the asymptotic variance of the 0.1-quantile lifetime under cost constraints, an optimal RDT scheme was derived. Results show that when the asymptotic variance is below 0.0035, the relative error between estimated and actual lifetimes remained below 1.52%. The optimal plan—four samples, 18 measurements, and a 10-h interval—achieves high evaluation accuracy at a total cost of 7696 CNY. This work advances existing methods by explicitly modeling individual variability, justifying the inverse Gaussian process choice through empirical validation, and offering a practical, cost-efficient RDT framework extensible to other degradation-prone products.
Unknown authors· Proceedings of the Instituti...· 0 citations
Conventional validation methods for multi-output models generally assume probabilistic descriptions of all input variables. In engineering applications, however, sparse data and limited knowledge may permit some inputs to be specified only by intervals, which limits the applicability of existing methods under random and interval mixed uncertainty. This challenge is prevalent in numerical simulation of various aerospace structural systems. A reliability-metric-based validation method for multi-output models under random and interval mixed uncertainty is proposed in this paper. The Mahalanobis distance (MD) is used to account for correlations among multiple responses, and interval analysis is introduced to construct an interval-valued MD. A conservative validation metric is then defined as the probability that the upper bound of the model–experiment MD is smaller than the lower bound of the MD corresponding to the engineering-tolerance vector. The metric therefore quantifies, from a reliability perspective, the probability that model predictions satisfy prescribed engineering tolerances. Because the coupling between random and interval uncertainties prevents a straightforward analytical solution, a baseline numerical procedure based on Monte Carlo simulation (MCS) is developed. Two numerical examples and two engineering examples demonstrate the applicability of the method. The results indicate that the proposed metric accommodates random and interval mixed uncertainty, accounts for correlations among multiple outputs, and provides a probabilistic measure of agreement between model predictions and experimental measurements. The method offers an interpretable basis for assessing the credibility of complex engineering simulation models.
Guijie Li, Yu-Han Yao, Kang Wang· Aerospace· 0 citations
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