PRA-MFCS: Performance reliability analysis based on multi-fidelity simulation and clustering surrogate model under multiple failure modes

Kriging surrogate model has extracted extensive attention in reliability evaluation, owing to its excellent applicability and operability nowadays, which confronts with difficulties in balancing the efficiency and accuracy for complicated mechanical assets with multiple failure modes. Consequently, this paper devises a multi-performance reliability analysis approach within the surrogate model framework, particularly innovative in its use of cluster mixing weight. Specifically, high-value test points are selected to fit the surrogate model after sorting the samples referring to the corresponding values; then, a cluster-based active learning strategy is employed to accomplish rapid convergence, and the particle swarm algorithm is utilized to optimize relevant parameters. Afterwards, the mixing weight for every performance referring to the contributions to the final reliability is determined, and the failure probability is subsequently predicted. Furthermore, the superiority of the proposed approach with the clustering surrogate model and mixing weight, compared with traditional sampling as well as other surrogate models, has been verified via case studies, contributing to overcoming the multi-performance reliability analysis oriented to complicated mechanical assets.

Time-dependent reliability analysis of structural systems based on parallel active learning Kriging model

Active learning-based structural reliability evaluation Kriging model and sequential importance sampling

As composite structures play a key role in aircraft structure design, assessing probability of failure (PF) of the composite structures has become important to ensuring safety of the aircraft design. To assess the PF of the design, computational models are frequently used to estimate probability of the composite structures but the computational models have uncertainty in predicting failures due to lacking knowledge of composite structure failures. Structural tests can provide additional knowledge of the failures to effectively reduce the uncertainty in the computational model. The presence of multiple failure modes due to variabilities is the other concern because correlated failure modes causes difficulty to estimate PF and it brings significant error for use of the effective reliability analysis methods, such as FORM or SORM. Undetected failure mode is the other issue relevant to the multiple failure modes. A single test can detect one failure mode, each failure modes has different probability of occurrence. Hence, a existing failure mode may not be detected and neglected. Possibly we have significantly under estimated PF. In the study, we make an uncertainty quantification model to estimate PF for correlated failure modes. Also the probability of failure occurrence of each failure modes is also estimated with the model. The model is demonstrated through a simple example and PF estimation of a curved composite panel with a hole is made. From the numerical study, it is observed that performing a single failure test can significantly reduce conservativeness on estimating PF. Test for a given probability of failure allows lighter design.

Multi-state systems have received considerable attention recently with regards to reliability and maintenance. Since most mechanical equipment operates under some sort of stress or load, it tends to deteriorate or degrade over time, thus possibly resulting in discrete degradation states (damage degrees), ranging from perfect functioning to complete failure. This multi-state deterioration is the motivation for using condition monitoring tools for the purpose of modeling, diagnosis, prognosis, and condition-based maintenance. Most mechanical equipment is subject to multiple independent failure modes and degradation processes. Rather than independently diagnosing and prognosing the health condition of the equipment for a single failure mode, it is important to investigate how multi-dimensional condition monitoring information can be used for recognition purposes of the state of the health of equipment with multiple independent failure modes. This paper focuses on a non-repairable piece of equipment with multiple independent failure modes, in which the state of the equipment for each single failure mode is not directly observable and only incomplete information is available through condition monitoring. The main objective of this paper is to develop a method to obtain an observation probability matrix which can be used as the main tool for damage degree classification of each failure mode. An observation probability matrix represents the statistical relationship between the actual health state (damage degree and failure mode) of the equipment and the condition monitoring information. This observation probability matrix is an input for such methods, as hidden Markov models, hidden Semi-Markov models, and Naïve Bayes classifiers. We modify the Naïve Bayes classifier to use this observation probability matrix for classification. The result of this paper is applied for damage degree classification of a planetary gearbox, which is subject to multiple failure modes.

CSP-free adaptive Kriging surrogate model method for reliability analysis with small failure probability

Compared with the methods solving failure probability of the structural system with multiple failure modes, those solving failure probability of a single failure mode are simpler and more well-developed, thus in order to employ the latter to establish the former, the addition laws of the failure probability are derived mathematically by use of the basic principles of probability theory. In the derived addition laws, the failure probability of the structural system with n failure modes is expressed as a combination of the failure probabilities of 2 n−1 single failure modes. Therefore, the failure probability of the structural system with multiple failure modes can be solved by the well-developed methods for the failure probability of a single failure mode. After reviewing the boundary theories, such as the second-order boundary, the third-order boundary, and the linear programming based boundary for analyzing the failure probability of the structural system with multiple failure modes, the derived addition laws are applied to evaluate several former order joint failure probability involved in those boundary theories. Additionally, a new small-scale linear programming based boundary theory which can sufficiently reduce the scale of the linear programming model involved is proposed. Two numerical examples, including a series and a parallel structural system, are employed to demonstrate the accuracy and efficiency of proposed techniques.

Uncertainty exists widely in engineering practice. An engineering system may have multiple failure criteria. In the current paper, system reliability analysis with multiple failure modes under both epistemic and aleatory uncertainties is presented. Epistemic uncertainty is modelled using p-boxes, while aleatory uncertainty is modelled using probability distributions. A first-order reliability method is developed and non-linear performance functions are linearized by the sampling method instead of the commonly used Taylor’s expansion at the most probable point. Furthermore, multiple failure modes in a system are often correlated because they depend on the same uncertain variables. In order to consider these correlated failure modes, the methods proposed by Feng and Frank are extended in this paper in order to calculate the joint probability of failure for two arbitrary failure modes under both aleatory and epistemic uncertainties. The Pearson correlation coefficient of two arbitrary failure modes is determined by the sampling method. Since two types of uncertainty exist in the system, the probability of system failure is an interval rather than a point value. The probability of failure of the system can be obtained by the combination of the extension ‘narrow’ bound method and the interval arithmetic. A numerical example is presented to demonstrate the applicability of the proposed method.

The failure modes of complex systems are often highly dependent. Aiming at the reliability analysis of engineering systems with multiple failure modes, an efficient surrogate model for system reliability with multiple failure modes is proposed, namely, the Copula Adaptive Kriging surrogate model (CAKSM). First, the initial Kriging model is established based on the initial samples. In order to select more effective added samples to update the Kriging model, a new learning function, namely, Copula Unites with Expected Improvement Function (CUEIF), is established. The function can make a reasonable sample selection by considering the failure correlation. Then, based on the optimal Copula function, the reliability data of each failure mode are coupled and analyzed. In order to adapt to various computing scales, regularization is introduced to improve the prediction speed of the surrogate model, and the probability density function of each performance function is obtained by introducing nonparametric kernel density estimation. Finally, the effectiveness of the CAKSM method and the learning function CUEIF is verified through four examples.

Reliability analysis of corrosion affected underground steel pipes considering multiple failure modes and their stochastic correlations

Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables

A multi-mode failure boundary exploration and exploitation framework using adaptive kriging model for system reliability assessment

Equipment failures in large-scale manufacturing systems are triggered by diverse stresses or factors. If failures of all types are jumbled together without clear analysis and classification, technicians misjudge strategies, incurring unnecessary costs. Therefore, systematically categorizing failures and prescribing corresponding maintenance actions are critical for optimal maintenance decision-making. By aggregating numerous failure modes into three representative categories based on the damage amount, frequency and probability of failure, and maintenance actions, this study firstly investigates a repairable system subject to multiple random failure modes. Secondly, a system reliability model is developed and an optimal maintenance strategy is derived to minimize the expected system cost. Thirdly, a four-dimensional decision model is proposed, and then the analytical expressions of system reliability and steady-state availability are deduced. The expected long-term operating cost of the system is formulated by using the theory of renewal process and geometric process. Finally, A numerical study of an energy system consisting of two series-connected equipment shows the validity and feasibility of the proposed policy.

The purpose of this paper is to study the reliability life calculation model of aerial rolling bearing considered the correlation of failure model. By mean of collecting relevant experiment data of vibration signal and temperature signal in the life test of the aerial rolling bearings, and analyse time domain and frequency domain, we can analyse the main failure modes and mechanism (e.g. wear, fatigue). The characteristic parameters that characterize the healthy state of aerial rolling bearings obviously are extracted further. Considering that the bearings expose multiple failure modes in the working process in most case, bearing fault diagnosis method is based on fuzzy theory. It is used to clarify the failure mechanism of different failure modes and the degradation rule of performance characteristic parameters. It’s very essential that establish the clear relationships between performance degradation and symptomatic set. According to the fault diagnosis results, each of failure modes is established the performance degradation model respectively. Considering the correlation between multiple different failure modes, Copula theory is introduced to analyse the correlation between multiple failure modes. Base on Copula theory, it’s obtained the life distribution model of aerial bearing based on multiple failure modes. Life distribution model are verified by subsequent experiments, which show that life distribution model of aerial rolling bearing in this paper, is feasible and necessary.

The reliability assessment of structures with multiple failure modes and small failure probability is challenging due to the time-consuming simulations required. Active learning Kriging methods for structural reliability with multiple failure modes have shown high computational efficiency and accuracy. However, selecting the appropriate sample and its failure mode to update the Kriging models remains a key problem. In this paper, we propose a new learning function and stopping criterion to further improve the efficiency of structural system reliability analysis. Firstly, we propose a new learning function that combines the expected improvement function and the U learning function. This function selects the most suitable samples, balancing the degree of expected improvement of samples to the limit state surface and the degree of misclassification probability of samples. Secondly, we propose a new stopping criterion that considers both the accurate construction of limit state surfaces and the probability of accurately predicting the signs of samples. This criterion avoids premature or late termination of the active learning process. Thirdly, the sequential MCS simulation method is employed in the active learning process to efficiently evaluate small failure probability problems. By analyzing four examples, we verify the accuracy and efficiency of the proposed structural reliability analysis method.