Reliability analysis method of mechanical system with correlated failures

Efficient system reliability analysis illustrated for a retaining wall and a soil slope

A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis

Introduction:Reliability analysis is a good tool to deal with the uncertainty and has been widely used in the engineering system. The first order reliability method (FORM) is generally used to calculate the reliability index but FORM is time-consuming and requires derivative computing.Methods:Artificial Bee Colony (ABC) algorithm is a very simple, robust and population-based stochastic optimization algorithm. In this study, an ABC-based reliability analysis was proposed to calculate the reliability index of engineering system through combining Artificial Bee Colony (ABC) algorithm with FORM. FORM was adopted to calculate the reliability index and design point. ABC is used to solve the constrained optimization about FORM. The procedure of ABC-based reliability analysis was presented in detail.Results and Conclusion:The proposed method was verified by two classic examples and then applied to geotechnical engineering. The results show that the ABC algorithm can effectively solve the global optimization problem in FORM. Results demonstrate that ABC-based reliability analysis is a good approach to obtain the reliability index and design point with a good accuracy so that it can be applied to analyze the reliability of a complex engineering system.

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.

Reliability analysis of corroded pipelines: Novel adaptive conjugate first order reliability method

The optimal design of multidisciplinary systems under uncertainty involves three types of iterative analyses- multidisciplinary analyses, reliability analyses, and optimization. If these processes are carried out in a nested manner in reliability based multidisciplinary design optimization (RBMDO), the computational expense can be enormous. Computationally efficient simultaneous analysis and design (SAND) or All-AtOnce methods have been developed earlier for deterministic MDO. Single loop RBDO methods have also been developed to integrate reliability analysis and optimization in a single loop. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints. The formulation allows for solution with a single design optimization loop by using the KKT optimality conditions of the first-order reliability method (FORM) as constraints in the design optimization along with disciplinary consistency constraints. Alternative solution processes which remove the FORM MPP’s from the decision space and many constraints from the problem are developed. The alternative solution methods are more efficient and more robust than using nonlinear programming to solve the single loop formulation. A numerical example is solved with the two proposed solution algorithms. I. Introduction In the design of multidisciplinary systems it is often necessary to make decisions under uncertainty. This requires that multidisciplinary systems modeling be integrated with uncertainty analysis and optimization. A common example of such an engineering design application would be the design of an aircraft wing under uncertain aerodynamic loading conditions, with multiple structural components with uncertain capacities, such that the entire structural system achieves a prescribed level of reliability. The problem has coupled physics, in that the pressure distribution is dependent upon the deflection, and the deflection is dependent on the pressure distribution. Such designs have been performed using multidisciplinary optimization (MDO). Other examples where MDO may be applied include electronics packaging, in which the disciplines of heat transfer and circuit analysis are coupled, the design of new types of aircraft and integrating them into an existing fleet of aircraft, and even the management of interconnected homeland infrastructures. While MDO has matured with the development of different types of algorithms for various types of problems and design organizations, there has been little work to incorporate reliability analysis into MDO. However, system and component reliabilities are often a major concern in the design of multidisciplinary systems. MDO can be computationally expensive due to the need to achieve consistency across multiple disciplinary analysis codes; each disciplinary analysis code may be computationally expensive to run. Further, the optimal design of multidisciplinary systems under uncertainty involves three types of iterative procedures- multidisciplinary analyses, reliability analyses, and optimization. The integration of these three procedures is referred to in this paper as reliability based multidisciplinary design optimization (RBMDO). If these processes are carried out simultaneously, the computational expense can be enormous. Computational savings can often be achieved with simultaneous analysis and design (SAND) or All-At-Once methods, which allow for the solution of the multidisciplinary analyses and the optimization in one single loop. Single loop RBDO methods allow for the integration of reliability analysis and optimization in a single loop. Applying SAND and single-loop RBDO together may allow for large computational savings when applied to problems in RBMDO. This paper develops a novel formulation of RBMDO problems with both system and component level reliability constraints based on the SAND method for MDO and by use of the KKT conditions of the first order reliability method (FORM). The resulting formulation may be solved as a standard nonlinear programming problem. While the single loop formulation presented in this paper is a solution of the RBMDO problem, robustness and efficiency are improved through two improved algorithms which can remove the MPP’s from the decision space, thereby significantly reducing the optimizer’s workload.

In order to ensure high reliability of complex engineered systems against deterioration or natural and man-made hazards, it is essential to have an efficient and accurate method for estimating the probability of system failure regardless of different system configurations (series, parallel, and mixed systems). Since system reliability prediction is of great importance in civil, aerospace, mechanical, and electrical engineering fields, its technical development will have an immediate and major impact on engineered system designs. To this end, this chapter presents a comprehensive review of advanced numerical methods for system reliability analysis under uncertainty. Offering excellent in-depth knowledge for readers, the chapter provides insights on the application of system reliability analysis methods to engineered systems and gives guidance on how we can predict system reliability for series, parallel, and mixed systems. Written for the professionals and researchers, the chapter is designed to awaken readers to the need and usefulness of advanced numerical methods for system reliability analysis.

An investigation was performed to study the effect of uncertainty in applied loads, helix angles, and failure stresses on the probability of failure of composite cylinders. Also, the effect of the factor of safety on the probability of failure of the cylinder was studied. The probability of failure for a composite cylinder subject to axisymmetric loading was obtained using the First Order Reliability method (FORM). The failure of the cylinder was studied based on first ply failure. Ply failure was predicted using the non-smooth Hashin criterion. Hashin criterion is based on writing a different interaction equation for separate failure modes. Four failure modes are considered associated with matrix or fiber failure, in either tension or compression. The accuracy of FORM as applied to this problem was verified by comparing the FORM results to those obtained by Monte-Carlo Simulation method with importance sampling. i x µ = mean values of the design parameters i x

In this work, a novel framework is proposed for the risk based design optimization of engineering systems by minimizing the demand on the system components’ accuracy (which directly relates to their cost). The fundamental development of this work is an analytical upper bound for calculating the probability of failure. This is in contrast with First Order Reliability Method (FORM), where a lower bound is used in calculating the probability of failure. FORM is one of the most popular methods for reliability analysis of engineering systems. In this paper, we show that FORM results in an optimistic measure of risk, hence potentially catastrophic in engineering design. A more accurate measure of failure is proposed by utilizing an analytical upper bound for the distribution of reliability index (the length of the most probable point vector to origin). This distribution is a function of the eigenvalues of the linearized limit state function in the normal space which results in a better understanding of failure phenomenon. The proposed formulation is computationally efficient and straightforward to solve, since it only involves finding eigenvalues in each iteration. This algorithm is applicable to any linearizable continuous limit state function with any type of distribution for the design variables. The method is applied to two examples and its accuracy is compared with the Monte Carlo simulation and FORM, demonstrating its effectiveness and value.

The relationship between the reliability probabilities of the component and the system is hard to get. If this relationship can be obtained easily, the reliability of the system can be calculated by using the reliability structures of the components. The common method to express this relationship is using the linear correlation index, which only shows the linear correlation between the components failure rather than the relationship between high nonlinear functions. In order to describe this relationship accurately and calculate the system reliability using the component reliability structures, a Uniform Design (UD)-Saddlepoint Approximation (SA)-based system reliability analysis method is proposed. The system reliability analysis method is decomposed to three simple steps: (1) calculating the weight coefficient which represents the contribution rate of each component to system reliability, (2) approximating Cumulant Generation Function (CGF) of each component, (3) calculating CGF of the system and approximating the system reliability with SA method. The weight coefficient of each component is derived from UD method, and a variable interval selection method is developed to decrease the required number of samples and increase the accuracy of the weight coefficients. First-Order Saddlepoint Approximation (FOSA) method or Mean-Value First-Order Saddlepoint Approximation (MVFOSA) method is used to analyze the CGF of a component performance function. Then the CGF of the system can be obtained by the weighted addition law by combining the CGFs of components performance functions with the weight coefficients. Finally, the system reliability can be approximated by SA method. Four examples are employed to demonstrate that the new method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

This work presents reliability analysis of Nano Engineered Reinforced Concrete (NERC) beam designed according to EN1992-1-1(2008) and its reference standard. In the reliability analysis, variability in load, geometric properties, Optimal Nano Engineered Concrete (ONEC) grade and other design variables were considered. The reliability analysis utilized FORM (First Order Reliability Method) with FORTRAN subroutine programs developed for the NERC beam failure modes at ultimate limit state. Results indicated that NERC beam behaves in a similar manner to conventional reinforced concrete beam on strength aspect. At design point, the NERC beam failed to meet the target safety index values provided by EN1990: 2002 (EC0) as a reference standard of EN1992-1-1 (2008) for all the failure modes considered. Furthermore, variations in span and reinforcement ratio have been found to be capable of changing the criticality of failure modes of NERC beam. Also, variation in characteristic yield strength of steel was found to severely affect NERC beam safety. This study recommends that unnecessary variation of span, reinforcement ratio and characteristic yield strength of steel should be avoided in NERC beams at project implementation stage so as to reduce the possibility of unforeseen structural failures. The work suggested that the safety margin provided by EN1992-1-1 (2008) and its reference standards for the design of singly reinforced concrete sections without shear reinforcement be improved. Finally, the study observed the need for incorporation of reliability-based design in Civil Engineering design standards.

A Critical Study on the Haldar and Mahadevan's Reliability Analysis

System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method

This study proposes a system reliability analysis of rack storage facilities subjected to forklift colliding events. The proposed system reliability analysis consists of two steps: the first step is to identify dominant failure modes that most contribute to the failure of the whole rack facilities, and the second step is to evaluate the system failure probability. In the first step, dominant failure modes are identified by using a simulation-based selective searching technique where the contribution of a failure mode to the system failure is roughly estimated based on the distance from the origin in the space of the random variables. In the second step, the multi-scale system reliability method is used to compute the system reliability where the first-order reliability method (FORM) is initially used to evaluate the component failure probability (failure probability of one member), and then the probabilities of the identified failure modes and their statistical dependence are evaluated, which is called as the lower-scale reliability analysis. Since the system failure probability is comprised of the probabilities of the failure modes, a higher-scale reliability analysis is performed again based on the results of the lower-scale analyses, and the system failure probability is finally evaluated. The illustrative example demonstrates the results of the system reliability analysis of the rack storage facilities subjected to forklift impact loadings. The numerical efficiency and accuracy of the approach are compared with the Monte Carlo simulations. The results show that the proposed two-step approach is able to provide accurate reliability assessment as well as significant saving of computational time. The results of the identified failure modes additionally let us know the most-critical members and their failure sequence under the complicated configuration of the member connections.

The international Maritime Organization (IMO) Weather Criterion has proven to be the governing stability criteria regarding minimum metacentric height for e.g., small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessarily representative for current new buildings with large superstructures. Thus, it seems reasonable to investigate the possibility of capsizing in beam sea under the joint action of waves and wind using direct time domain simulations. This has already been done in several studies. Here, it is combined with the first order reliability method (FORM) to define possible combined critical wave and wind scenarios leading to capsize and corresponding probability of capsize. The FORM results for a fictitious vessel are compared with Monte Carlo simulations, and good agreement is found at a much lesser computational effort. Finally, the results for an existing small ferry will be discussed in the light of the current weather criterion. 1. Introduction Recently, the International Maritime Organization (IMO) has initiated a thorough revision of the intact stability rules in the framework of goal-based design, e.g., Peters et al. (2013). Several draft guidelines have been issued, e.g., SDC 1/INF.8 (IMO 2013) discussing in details the requirements for the hydrodynamic software to be applied including qualitative and quantitative assessment procedures. The focus so far has been mostly on failure modes related to the change of righting lever in waves, notably parametric rolling and pure loss of stability, whereas the dead ship behavior in beam sea still is based on the existing Weather Criterion issued by IMO (1985) as Resolution A.562. This criterion is based to a large extent on model tests of older hull forms and does not provide any probability of capsize for a given vessel, just a pass/no pass result. Furthermore, the wave environment is not explicitly specified in the criterion thus leading to the same requirement whether the ship is sailing in restricted areas or not. A very detailed and precise description of the drawbacks in the IMO Weather Criterion, as applied to modern ships, is given in Bulian and Francescutto (2004). In a recent study by Tompuri et al. (2015), a detailed investigation on application of the second generation intact stability criteria has been done. However, the criterion for dead ship condition is excluded from this thorough study because the criterion is thought to be still in the early phase of development.