A Novel ESN-DeepONet and Kriging Double Layer Model for Time-dependent Reliability Analysis with Random Process

Time-dependent structural system reliability analysis model and its efficiency solution

An accurate method for the analysis of remaining life for pressure vessels already in service would certainly help operation managers facing the question of when to replace mayor pieces of processing equipment. Operating companies would also realize the consequent savings derived from knowing in advance the probability of failure, or from safely extend the operating life of facilities. In this paper the first steps are undertaken towards a probabilistic analysis model for predicting the reliability of cracked pressure vessels as a function of applied operating loads using fracture mechanics. The analysis takes into account the variability in material properties, uncertainty in operating loads, continuing degradation of structural residual strength due to crack initiation and propagation and the combined effect of existing crack and newly initiating crack. The information gathered from inspections and non-destructive tests can be incorporated, together with the stresses caused by the operating loads, into the calculations. A numerical example is provided to demonstrate the methodology. Introduction The development of cracks due to fatigue is one of the main causes of interruption of service for pressure vessels. Cracked pressure vessels would generally be out of service and receive appropriate repair. However, sometimes the vessels need to continue to service until the maintenance or repair condition becomes available. In addition, leaving the cracked pressure vessel in service, provided that it maintains acceptable reliability and safety level, has great economical benefit. Because of these reasons, analysis and assessment of the reliability and safety of cracked pressure vessels becomes an increasingly interesting topic for the petroleum and gas industries. Traditional analysis for the reliability of cracked pressure vessels are based on classical fracture mechanics methods, such as the application of Paris-Erdogan formulation[1,2], and focus generally on single crack initiation and propagation using deterministic analysis. This deterministic technique does not take into consideration the variability and uncertainty of material properties and working loads that, as measurements show, demonstrate significant variation. In this paper a new reliability analysis model is proposed for cracked pressure vessels based on probabilistic fracture mechanics technique. This new model takes into account an extended set of variables such as:variability in material properties;uncertainty in working loads;continuing degradation of structural residual strength due to crack initiation and propagation andthe combined effect of existing and newly initiating cracks. Compared to traditional analysis models based on deterministic analysis techniques, the probabilistic model it is expected to provide a more accurate prediction for the reliability and the safety of cracked pressure vessels. This increased accuracy will improve the decision making process and should translate into significant savings in inspection, repair and replacement expenses for cracked pressure vessels. Reliability Analysis Model The basic procedure for calculation of reliability of cracked pressure vessels in the proposed analysis model is as follows: 1) identify the probability of fracture failure at loading cycle N due to the crack initiating at loading cycle Nd (Nd < N);

This paper examines multi-platform phased missions, which involves a number of platforms working together to achieve a common objective. A simulation model for multi-platform phased mission system reliability analysis is proposed. The model simulates the fault processes of various platforms within mission life by using a modularized multi-platform phased mission system model. With the Monte Carlo method together, the reliability of entire mission and mission phases can be analyzed. A hypothetical example system is used to show the application of this simulation model and the result exhibits that the reliability conditions of system within the mission and each mission phase can be evaluated and controlled effectively.

The capabilities of smart meters and the potential vulnerabilities they introduce make the Advanced Metering Infrastructure (AMI) a critical components of the Smart Grid. A virus propagating among meters and massively issuing remote disconnect commands could have catastrophic consequences. To understand and assess the risk posed by a given set of meter devices getting compromised, we introduce a novel modeling approach based on fuzzy Markov chain. Markov modeling is one of the main approaches used to analyze the reliability of critical systems. Markov models are usually analyzed using mathematical approaches or Monte-Carlo Simulation. For large and complex systems, traditional Markov models suffer from the state explosion problem and quickly become intractable. The key idea of our approach to solve this issue in the context of the smart grid is to leverage the hierarchical topology of AMI to build a high-level model where components represent Neighborhood Area Networks (NAN) instead of individual meters. The fuzzy Markov formalism enables our solution to take into account gradual component degradation. We propose a Fuzzy Markov Model (FMM) for reliability analysis of a Smart Grid. The reliability of each NAN is represented by a number in [0, 1] which denotes the state of that component in the FMM.We define the transition probabilities between states of the fuzzy Markov model based on the fuzzy time-to-failure value for each NAN. We utilize the Fuzzy Monte Carlo Simulation (FMCS) approach to calculate the fuzzy time-to-failure value of each NAN. Our proposed method enables us to assess the reliability of the entire AMI at the meter level while keeping the model manageable.

Due to multiple implicit limit state functions needed to be surrogated, adaptive Kriging model for system reliability analysis with multiple failure modes meets a big challenge in accuracy and efficiency. In order to improve the accuracy of adaptive Kriging meta-model in system reliability analysis, this paper mainly proposes an improved AK-SYS by using a refined U learning function. The improved AK-SYS updates the Kriging meta-model from the most easily identifiable failure mode among the multiple failure modes, and this strategy can avoid identifying the minimum mode or the maximum mode by the initial and the in-process Kriging meta-models and eliminate the corresponding inaccuracy propagating to the final result. By analyzing three case studies, the effectiveness and the accuracy of the proposed refined U learning function are verified.

This paper is devoted to the use of a proportional hazards model (PHM) for reliability analysis of solder joints through two case studies: a drop-impact test and a vibration test. The lifetime data collected under various load conditions can be integrated in establishing a PHM for reliability analysis of solder joints. PHM has the capability of evaluating the influence of load conditions (e.g. drop height, power spectrum density in random vibration) on the life span of solder joints. Using this capability, this paper focuses on the implementation of PHM for estimating the reliability characteristics (MTTF and probability density function (p.d.f.) of failure) of solder joints whose load conditions are not contained in the training dataset of the PHM. In comparison with the naive use of lifetime data by simply ignoring the effect of load conditions, the two case studies verify the effectiveness of PHM in providing consistent reasonable estimation of the reliability characteristics of solder joints. The perspectives and the procedures of the use of PHM in this paper are generic and can be directly adopted for other systems/products.

In some special engineering circumstances, it is likely that all parameters of an uncertain automotive structure can only be treated as interval variables due to limited knowledge, but meanwhile their lower and upper bounds can just be modeled as fuzzy variables rather than as deterministic values due to ambiguous information. To handle this dual uncertainties case, a reliability-based optimization method with fuzzy-boundary interval variables is developed in this study, and it is further extended to carry out squeal instability analysis and reduction of brake involving both limited and vague information. In the proposed method, fuzzy-boundary interval variables are utilized to cope with the above dual uncertainties of structure parameters and help to build up the structure response analysis model. First, the structure responses are derived on the basis of α-cut strategy, Taylor series expansion, subinterval analysis, and central difference method. Then, with the aid of fuzzy possibility theory, a reliability analysis model of structure response is developed, which can make use of extra reliability information and thus quantify the reliability more accurately. Next, a reliability-based optimization model involving fuzzy-boundary interval variables is established by integrating the uncertain response analysis model and the reliability analysis model. Finally, the proposed method is extended to carry out automotive brake squeal instability analysis and optimization. The numerical investigations demonstrate the applicability and effectiveness of the proposed method.

Multi-state homogeneous Markov models in reliability analysis

Fault trees are a key model in reliability analysis. Classical static fault trees (SFT) can best be analysed using binary decision diagrams (BDD). State-based techniques are favorable for the more expressive dynamic fault trees (DFT). This paper combines the best of both worlds by following Dugan’s approach: dynamic sub-trees are analysed via model checking Markov models and replaced by basic events capturing the obtained failure probabilities. The resulting SFT is then analysed via BDDs. We implemented this approach in the Storm model checker. Extensive experiments (a) compare our pure BDD-based analysis of SFTs to various existing SFT analysis tools, (b) indicate the benefits of our efficient calculations for multiple time points and the assessment of the mean-time-to-failure, and (c) show that our implementation of Dugan’s approach significantly outperforms pure Markovian analysis of DFTs. Our implementation Storm-dft is currently the only tool supporting efficient analysis for both SFTs and DFTs.

Uncertainty exists widely in the engineering field, and the reliability of products has time-dependent characteristics due to the accumulation of product use time and material performance degradation. Traditional time-dependent reliability solutions such as span rate and Monte Carlo are difficult to be applied in engineering practice due to their complex principles and low computational efficiency. Therefore, this paper proposes a time-dependent reliability analysis method based on neural network response surface learned form the idea of limit value. This method uses inverse reliability sampling and establishes a response surface model between the design variables and the limit value of the limit state function to convert the time-dependent reliability into time-invariant reliability. Then, the traditional method is used to solve the time-dependent reliability, which improves calculation efficiency and accuracy of time-dependent reliability analysis. Finally, two examples are used to verify the effectiveness of the method.

O-rings are commonly used due to their simple structure and excellent performance. However, the time-dependent creep behavior of rubber during usage can significantly impact the working performance and service life of the O-ring. The phenomenological creep constitutive model establishes a relationship between the deformation of rubber materials under creep conditions and time, by incorporating a creep function that considers the significance of damage. Based on the phenomenological creep constitutive model, we establish a simulation model for the contact pressure of an engine O-ring. This model characterizes the time-dependent degradation process of the O-ring’s sealing performance by tracking the variation of contact pressure and contact surface width over time. To account for the randomness of rubber material model parameters and compression amount, we develop a time-dependent reliability analysis model for the O-ring using the first-order second-moment (FOSM) method. The research findings can establish a theoretical foundation for the assessment, analysis, and evaluation of O-ring sealing’s time-dependent reliability.

To effectively perform the reliability analysis of the flap deflection angle, the reliability analysis framework is developed by introducing fault logic and a data-driven model. Herein, the fault logic analysis is used to study the fault mechanism and filter out the characteristic fault parameters that can be used to collect input data for data-driven modelling; the data-driven modelling is employed to establish a reliability analysis model with a small amount of input data. Under this proposed framework, the improved dung beetle optimization algorithm for back propagation (IDBO-BP) method is developed to perform the reliability modelling of the flap deflection angle. To validate the effectiveness of the proposed framework, we study the fault logic of flap symmetry and establish a surrogate model of flap deflection based on the fault parameters and the IDBO-BP algorithm. According to the predicted results of the flap deflection angle, the reliability model based on the fault mechanism can reflect the actual flap motion. At the same time, the proposed IDBO-BP algorithm has excellent modelling and simulation property by comparing with other optimization algorithms. Thus, the efforts of this study provide a new solution to the problem of reliable analysis with uncertain fault parameters. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

ABSTRACTIn the present study, reliability analysis of near surface disposal facility is performed, by assessing the probability of sequential failure of the multi barrier system using the contaminant transport model. The concentration and dose rate of the radionuclide evolve with time hence there is a need for time dependent reliability analysis. Due to the low values of expected probabilities of failure, an enhanced Monte Carlo (EMC) method and Subset simulation is employed. The Result of the analysis show that, the EMC method is useful to evaluate the probability of failure associated with the barrier system which has low probability of failure.

A primary concern in practical engineering design is ensuring high system reliability throughout a product life-cycle subject to time-variant operating conditions and component deteriorations. Thus, the capability to deal with time-dependent probabilistic constraints in reliability-based design optimization is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. The NERS employs kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization technique is integrated with the NER S to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation mechanism is developed based on mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis and existing advanced reliability analysis and design methods can be used. The NERS is integrated with RBDO for the design of engineered systems with time-dependent performance deterioration. A design case study is used to demonstrate the efficacy of the proposed NERS approach.

Modular multi‐level converter (MMC) with press‐packing IGBT devices is the popular and key equipment of VSC‐HVDC system, its reliability is directly related to the equipment safe operation. However, it is difficult to analyse the reliability using the failure statistical approach due to less fault data. In order to improve the reliability analyses accuracy, it is necessary to use the physical failure method by considering the main components fatigue failure mode. The reliability analysis models are presented for the MMC sub‐module with the press‐packing IGBT device and metallised film capacitors. First, based on the MMC‐HVDC simulation model, the losses and the junction temperatures of the IGBT devices were derived by the temperature field model, which the failure rates can be calculated. Furthermore, based the corrosion failure mode, the failure rate calculation of the metallised film capacitor was investigated using the voltage stress and thermal stress, the reliability calculation of the MMC sub‐module was presented by combining the main components failure rates. Finally, the reliability of the VSC‐HVDC based MMC was also presented with the different operation mode. The achievement is helpful to assess and improve the reliability of the VSC‐HVDC.