Reliability Analysis of Structure for Fuzzy Safety State

Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.

Model uncertainty in structural reliability

In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of perturbation principle. First, the fuzzy characteristic parameters of the structural fuzzy random variables are expressed as the sums of their true values and fuzzy perturbations. At the same time, the perturbations are equivalently selected. Second, the probability density function and the performance function are decomposed into a series of intervals under different level cut sets, and the Taylor series is expanded on the upper and lower limits of the intervals. Finally, according to the definition of structural reliability, based on the direct integration method, the sigmoid function is introduced into the reliability function to approximate the step function, and the fuzzy reliability is obtained. The simulation results show the effectiveness and accuracy of the proposed method, and it provides a feasible way for structural reliability analysis with fuzzy variables or fuzzy random variables.

The accelerated lifetime test is a widely used and effective approach in reliability analysis because of its shorter testing duration. In this study, product lifetimes are assumed to follow the Gompertz distribution. This article primarily focuses on performance comparisons between the linear model and the inverse power-law model, both of which are utilized to characterize the relationship between the shape parameter and stress levels. To test model robustness, we also generate data from the Sine-Modified Power Gompertz distribution, a more flexible alternative. We conduct Monte Carlo simulations using four estimation methods: the maximum likelihood method, the least squares method, the maximum product of spacing method, and the Cramér-von Mises method, for small, medium, and large sample sizes. The comparison of mean squared error serves as a critical indicator for evaluating the performance of different methods and models. Additionally, the shape parameter and reliability function are obtained based on the estimation results. Finally, a real dataset is analyzed to demonstrate the most suitable accelerated life model, and the Akaike Information Criterion is used to further assess model fit. Furthermore, we employ leave-one-out cross-validation (LOOCV) to prove this model’s generalizability.

A general formal approach for fuzzy reliability analysis in the possibility context

: The Aircraft Structural Reliability and Risk Handbook provides: a) A reference on basic statistics, probability, and reliability techniques required for conducting structural risk and reliability analyses, and b) Illustrative examples of how to apply these techniques to problems involving the nucleation and growth of fatigue cracks in metallic airframe structure. This particular volume describes the fundamentals of probabilistic analysis and structural reliability analysis for the next flight.

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.

The study and analysis of repairable systems is an important topic in reliability. Analytical techniques become very complicated and unrealistic especially for modern complex systems. There have been attempts in the literature to evolve more realistic techniques using simulation approach for reliability analysis of systems. The purpose of this paper is to develop a novel Markov system dynamics (MSD) simulation framework for the reliability modeling and analysis of a repairable system. This paper proposes a hybrid approach called as MSD approach which combines the Markov approach with system dynamics simulation approach for reliability modeling. This approach will have the advantages of both Markov as well as system dynamics methodologies. The proposed framework is illustrated for a repairable two component system. The results of the simulation obtained in this work when compared with that obtained by traditional Markov analysis clearly validate that this novel MSD approach is an alternative approach for reliability modeling and analysis.

Smart transmitters are increasingly being deployed in safety critical systems. Although the processing and diagnostic features provided by digital systems are advantageous, it introduces additional complexity in reliability modelling of systems. The conventional Fault Tree Analysis (FTA) method for system reliability analysis has its shortcomings in modelling digital systems, to incorporate its dynamic system interaction and failure modes in detail. This is because some of the failure modes may arise due to the dynamic interactions between the modules of the system. Dynamic Flowgraph Methodology (DFM) was identified as one of the optimistic approaches to handle these interactions. DFM approach combines multi‐valued logic modelling and analysis capabilities to handle systems consisting of components that have multiple degraded states and exhibit dynamic behaviour. However, only few DFM tools have been developed and some of them are not available in public domain. The DFM approach relies heavily on development and implementation of its decision tables. The logic information present within the decision tables can be meticulously implemented using Petri Nets. Also, there are plenty of free Petri Nets tools available online. Thus, the idea of DFM was used in this work to capture the dynamic interactions by developing decision tables. The decision tables were transformed into the Petri Net models to perform the analysis. The paper demonstrates the potential of the hybrid DFM – Petri Net approach for dynamic reliability analysis of smart transmitter.

Fuzzy reliability modeling of gracefully degradable computing systems

This paper focuses on a reliability analysis of an offshore wind turbine support structure which is part of an assessment and monitoring framework for wind turbines in operation. The reliability analysis builds upon structural, loading, limit state and uncertainty models comprising design, production and erection data. This model basis facilitates the reliability analysis of the ultimate, the fatigue and the serviceability limit states utilizing stochastic finite elements. The complexity of the individual models dictates an efficient solution scheme for the reliability analysis. Such an algorithm is developed in the present paper consisting of an adaptive response surface algorithm and an importance sampling Monte-Carlo algorithm. The response surface algorithm is based on predetermined experimental designs and facilitates the adjustment of design parameters for an optimized prediction variance in the design point region. Approaches for the consideration of multiple design points and the augmentation of the design for reduction of the prediction variance are introduced. In this paper, a reliability analysis for a tripod support structure of a Multibrid M5000 wind turbine is performed. A comparison with the target reliabilities specified in DIN EN 1990 (2002) shows that the requirements are fully met. However, the consideration of system reliability leads to the conclusion that at the end of the service life there is a significant probability of fatigue damages. The quantification of the reliability for the individual structural components for all limit states facilitates an identification of sensitive components. The results of this study can support the targeted application of monitoring systems, the optimization of the support structures and additionally highlight the need for criteria to the systems reliability.

This study presents a methodology for determining the optimal target reliability of a civil structure using the life-cycle cost (LCC) concept. The relationship between the reliability index and the estimated LCC is analyzed in order to find optimal target reliability. As a simple explanation of the method, the study uses steel bridges as an example. The analysis reveals that the LCC of steel bridges has great influence on target reliability, especially when the bridges have many lanes and long spans. It is also ascertained that higher target reliability is required to minimize the LCC when the number of lanes or average daily traffic (ADT) increases. Reliability analyses considering various traffic conditions were also conducted to observe changes in structural reliability with regard to such conditions. After the optimal target reliability is determined, target reliability adjustment can be performed. The analysis results show that the target reliability index can be adjusted consistently within the appropriate ranges by modifying the resistance factor in a limit state equation. In the last part of the study, an example bridge case study was performed to confirm the possibility of practical application of the presented method.

The paper presents a hybrid active-learning approach for structural reliability analysis via adaptive Kriging surrogate models. The quasi first-order reliability method is first proposed for characteristic truncation point of a structural performance function. This is used to define a truncation boundary via the joint probability distribution function of input random variables. To reduce simulation time for new training samples, a U-function based criterion is further implemented to refine the candidate sample set. Since the reliability-based expected improvement function and U functions are combined together to evaluate new training samples, it finalizes a hybrid active-learning Kriging (HALK) to develop adaptive surrogate models for the structural reliability analysis. Several numerical examples are presented to demonstrate potential applications of the proposed HALK algorithm. Compared to benchmark results provided by the brutal force Monte-Carlo simulation method, the effectiveness of the HALK approach has been justified by dealing with various structural reliability problems.

Structural reliability analysis based on improved wolf pack algorithm AK-SS

A stress-strength interference model in its interval form, with uncertain quantities of structures described by interval numbers, is used for reliability analysis. Such structural reliability analysis problem is called structural interval reliability analysis. A discrete possibility degree method for structural interval reliability is proposed. By comparing equally-spaced-points of structural interval stress value and structural interval strength value, a partition for comparison relations (big, equal or small) between interval stress and interval strength is built. Based on this partition, new concepts for interval reliability analysis are defined, such as structural safety possibility degree and structural failure possibility degree, etc. By one simple example, the feasibility and effectiveness of discrete possibility degree method for structural interval reliability are demonstrated.