System Reliability Method Research Articles

Structural reliability analysis using non-probabilistic convex model

By using the convex model approach, the bounds of the uncertain parameters are only required rather than their precise probability distributions, based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information. In this paper, a non-probabilistic reliability model is given for structures with convex model uncertainty, which is defined as a ratio of the multidimensional volume falling into the reliability domain to the one of the whole convex model. A Monte Carlo simulation is then formulated for the reliability model to obtain a reference solution. A first order approximation method (FOAM) is proposed to solve the reliability model based on a linear approximation of the failure surface. A second order approximation method (SOAM) is further formulated to improve the reliability analysis precision for limit-state functions with relatively strong nonlinearity. By introducing the suggested reliability model, a convex-model-based system reliability method is also formulated. Eight numerical examples are provided to demonstrate the effectiveness of the present methods.

Statistical tolerance analysis of a hyperstatic mechanism, using system reliability methods

The quality level of a mechanism can be evaluated a posteriori after several months by following the number of warranty returns. However, it is more interesting to evaluate a predicted quality level in the design stage: this is one of the aims of statistical tolerance analysis. A possible method consists of computing the defect probability (PD) expressed in ppm. It represents the probability that a functional requirement will not be satisfied in mass production. For assembly reasons, many hyperstatic mechanisms require gaps, which their functional requirements depend on. The defect probability assessment of such mechanisms is not straightforward, and requires advanced numerical methods. This problem particularly interests the VALEO W.S. company, which experiences problems with an assembly containing gaps. This paper proposes an innovative methodology to formulate and compute the defect probability of hyperstatic mechanisms with gaps in two steps. First, a complex feasibility problem is converted into a simpler problem. Then the defect probability is efficiently computed thanks to system reliability methods and the m-dimensional multivariate normal distribution Φm. Finally, a sensitivity analysis is provided to improve the original design. The whole approach is illustrated with an industrial case study, but can be adapted to other similar problems.

Power system: a reliability assessment using FTA

The Fault Tree Analysis (FTA) serves as a powerful tool for system risk analysis and reliability assessment. FTA is a top-down approach to failure analysis, starting with a potential undesirable event and then determining Base event (BE). The undesired state of the system is represented by the Top Event (TE). TE and BE are integrated through electronic logic gates (AND gate, OR gate). The fault tree is a tool to identify and assess the combinations of the undesired events in the control of system operation and its environment that can lead to the undesired state of the system. It is recognized worldwide as an important tool for evaluating safety and reliability in system design, development and operation. In this work, an efficient methodology is utilized to find out reliability assessment of critical and/or complex system. The main features and application of this technique for a power system are discussed. Minimal cut sets are developed by means of Boolean equation method. For main substation all CCF are considered at an average temperature of 35 °C. The objective of this work is to develop a method for power system reliability using the FTA approach. The methodology adopted in this investigation is to generate fault trees for each load point of the power system. This fault trees are related to disruption of energy delivery from generators to the specific load points. Quantitative evaluation of the fault trees represents a standpoint for assessment of reliability of power delivery and enables identification of the most important elements in the power system. The power system reliability is assessed and the main contributors to power system reliability are identified, both qualitatively and quantitatively.

New Linear Programming-Based Bound Method for Structural System Reliability

New Linear Programming-Based Bound Method for Structural System Reliability

Development Composite Customer Damage Function Using the Customer Survey Based Method for Power System Reliability Planning

The optimization in reliability cost-benefit analysis for distribution investment planning has been more attended on energy delivery services in Thailand. In this research, the reliability costs for the customer point of views represented as the interruption costs are presented. The data for analysis is provided from customer survey-based method during 2008-2009. Due to the direct and indirect impacts for electric customer in each category are different, the concept and methodology for data collecting based on customer survey is described. According to interruption costs are different for each sector, the customer survey results are classified into four customer sectors. In each sector, the individual customer damage function derived from survey is aggregated to develop sector customer damage function. The composite customer damage function utilized in regional reliability investment planning is also presented. In addition, the reliability cost evaluation in term of interrupted energy assessment rate for the selected industrial estate is determined in order to investigate industrial customer impact at the level of microeconomics scale. Application areas of reliability cost indices to enhance the effectiveness planning and operation of power distribution system are also recommended.

Single-loop system reliability-based topology optimization considering statistical dependence between limit-states

This paper presents a single-loop algorithm for system reliability-based topology optimization (SRBTO) that can account for statistical dependence between multiple limit-states, and its applications to computationally demanding topology optimization (TO) problems. A single-loop reliability-based design optimization (RBDO) algorithm replaces the inner-loop iterations to evaluate probabilistic constraints by a non-iterative approximation. The proposed single-loop SRBTO algorithm accounts for the statistical dependence between the limit-states by using the matrix-based system reliability (MSR) method to compute the system failure probability and its parameter sensitivities. The SRBTO/MSR approach is applicable to general system events including series, parallel, cut-set and link-set systems and provides the gradients of the system failure probability to facilitate gradient-based optimization. In most RBTO applications, probabilistic constraints are evaluated by use of the first-order reliability method for efficiency. In order to improve the accuracy of the reliability calculations for RBDO or RBTO problems with high nonlinearity, we introduce a new single-loop RBDO scheme utilizing the second-order reliability method and implement it to the proposed SRBTO algorithm. Moreover, in order to overcome challenges in applying the proposed algorithm to computationally demanding topology optimization problems, we utilize the multiresolution topology optimization (MTOP) method, which achieves computational efficiency in topology optimization by assigning different levels of resolutions to three meshes representing finite element analysis, design variables and material density distribution respectively. The paper provides numerical examples of two- and three-dimensional topology optimization problems to demonstrate the proposed SRBTO algorithm and its applications. The optimal topologies from deterministic, component and system RBTOs are compared with one another to investigate the impact of optimization schemes on final topologies. Monte Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach.

Post-hazard flow capacity of bridge transportation network considering structural deterioration of bridges

The flow capacity of a transportation network can be reduced significantly if its constituent bridges are damaged by natural or man-made hazards. For rapid risk-informed decision making on hazard mitigation and response, it is therefore essential to have a capability to predict the post-hazard flow capacity of the network efficiently and accurately. However, this is a challenging task due to the uncertainty in hazards and structural damage, and the complex nature of the network flow analysis. Moreover, the bridge structures may experience significant deterioration over their life cycle, which requires time-varying network reliability analysis. This paper proposes a new non-sampling-based approach to estimate the time-varying post-hazard flow capacity of a bridge transportation network considering structural deterioration of bridges. The proposed approach evaluates the probabilities of structural damage scenarios efficiently using the matrix-based system reliability method and rapidly computes the corresponding flow capacities using a maximum flow capacity analysis algorithm. The matrix-based framework facilitates the integration of these results to obtain the probabilistic distributions and statistical moments of the network flow capacity. It also enables computing various measures useful for risk-informed decision making, such as the conditional mean and standard deviation of flow capacity given observed structural damage, and component importance measures. In the proposed approach, probability calculation and network flow analysis are performed separately, which renders time-varying post-hazard flow capacity analysis efficient. The proposed approach is demonstrated by a numerical example based on the Sioux Falls network under multiple bridge-deterioration scenarios simulating the progress of deterioration.

Seismic Reliability Assessment of Bridges with User-Defined System Failure Events

Bridge-level failure event definitions per limit state have evolved from failure of one key bridge component as representative of the whole bridge system to failure of at least one of multiple components. However, an entire set of bridge failure event possibilities exists between these two extremes in the same limit state, such as failure of any two, any three, or any desired subset of bridge components. This paper proposes a closed-form combinatorial method to evaluate all possible ways in which bridge components can fail within and across limit states. It also highlights bridge component importance measures as key by-products of the closed-form solution. Calculations are illustrated with a particular yet illustrative system failure event, called the augmented event, which incorporates failures of at least one component in a given limit state and joint failures of multiple important components in a previous limit state. Bridges in as-built and retrofitted conditions are used to illustrate the augmentation calculation under seismic loads and the application of the proposed system reliability method. The results reveal an increase in median system fragility at the moderate limit states in the range of 4–20% relative to traditional approaches that neglect augmentation. This methodology to connect bridge components to bridge system reliability can readily support infrastructure stakeholder decision making and risk management through an efficient approach that can adapt to evolving system failure event definitions.

Fatigue system reliability analysis of riveted railway bridge connections

A system-based model for fatigue assessment of riveted railway bridge connections, comprising a number of basic components, is presented in this article. Probabilistic fatigue load spectra are developed through Monte Carlo simulation of train passages over a finite element model of a typical, short-span bridge. Uncertainties arising from loading, resistance and modelling sources are taken into account. The riveted connection is treated through a set of generic sub-systems that capture potential damage in identifiable hot-spots, such as rivets, holes and angle fillets. The fatigue reliability over time is evaluated through system reliability methods by treating these hot-spots as the elements of a structural system. The results show that the probability of failure of the connection depends significantly on the form of the system adopted for the analysis and the rivet clamping force. Damage scenarios accounting for the potential loss of rivet clamping force are investigated, and it is shown that, in some cases, they can affect connection reliability considerably.

A Probabilistic Framework for Gas Turbine Engine Materials With Multiple Types of Anomalies

Some rotor-grade gas turbine engine materials may contain multiple types of anomalies such as voids and inclusions that can be introduced during the manufacturing process. The number and size of anomalies can be very different for the various anomaly types, each of which may lead to premature fracture. The probability of failure of a component with multiple anomaly types can be predicted using established system reliability methods provided that the failure probabilities associated with individual anomaly types are known. Unfortunately, these failure probabilities are often difficult to obtain in practice. In this paper, an approach is presented that provides treatment for engine materials with multiple anomalies of multiple types. It is based on a previous work that has been extended to address the overlap among anomaly type failure modes using the method of Kaplan–Meier and is illustrated for risk prediction of a nickel-based superalloy. The results can be used to predict the risk of general materials with multiple types of anomalies.

Further development of matrix-based system reliability method and applications to structural systems

In efforts to estimate the risk and reliability of a complex structure or infrastructure network, it is often required to evaluate the probability of a ‘system’ event, i.e. a logical function of multiple component events. Its sensitivities with respect to design parameters are also useful in decision-making processes for more reliable systems and in reliability-based design optimisation. The recently developed, matrix-based system reliability (MSR) method can compute the probabilities of general system events including series, parallel, cut-set and link-set systems, and their parameter sensitivities, by use of efficient matrix-based procedures. When the component events are statistically dependent, the method transforms the problem into an integral in the space of random variables which cause the statistical dependence, termed as the common source random variables (CSRVs). One can identify CSRVs by fitting a generalised Dunnett-Sobel (DS) model to a given correlation coefficient matrix. This article introduces two further developments of the MSR method: First, for efficient evaluation, it is proposed that the integral in the CSRV space can be performed using the first- or second-order reliability methods. Second, a new matrix-based procedure is developed to compute the sensitivity of the system failure probability with respect to the parameters that affect the correlation coefficients between the components. In addition, an extensive parametric study is performed to investigate the effect of the error in fitted generalised DS model on the accuracy of the estimates by the MSR method. The further developed MSR method is demonstrated by two examples: system reliability analysis of a three-storey Daniels system structure, and finite element reliability analysis of a bridge pylon system.

Posfust reliability of a unified fuzzy Markov model

Reliability modelling is the most important discipline of reliability engineering. A new method for finding fuzzy system reliability using posfust reliability theory is demonstrated, where the system is modelled as a unified fuzzy Markov model, which consists of fuzzy Markov models assigned in order together with fuzzy transition possibilities between them. The proposed method can model and examine the fuzzy reliability of a system in a more flexible way and as a consequence the fuzzy reliability is expressed as a triangular fuzzy number.

Review on Calculation Methods of Structural System Reliability

In order to find a way to study the structure reliability further, the basic system of structural and the methods of analyzing were introduced. For the series system and parallel system, the calculation can be categorized into Point estimated method and interval estimated method. The point estimated method includes Stevenson-Moses method, Probability Network Evaluation Technique, Conditional Probability Method and Integrated Correlation Coefficient Method. The interval estimated method includes General boundaries of range and the narrow boundaries of range. The principle of method and the calculation steps methods were depicted in detail. This study has significance in theory and practice for the study of structural reliability.

Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications

This paper proposes a single-loop system reliability-based design optimization (SRBDO) approach using the recently developed matrix-based system reliability (MSR) method. A single-loop method was employed to eliminate the inner-loop of SRBDO that evaluates probabilistic constraints. The MSR method enables us to compute the system failure probability and its parameter sensitivities efficiently and accurately through convenient matrix calculations. The SRBDO/MSR approach proposed in this paper is applicable to general systems including series, parallel, cut-set, and link-set system events. After a brief overview on SRBDO algorithms and the MSR method, the SRBDO/MSR approach is introduced and demonstrated by three numerical examples. The first example deals with the optimal design of a combustion engine, in which the failure is described as a series system event. In the second example, the cross-sectional areas of the members of a statically indeterminate truss structure are determined for minimum total weight with a constraint on the probability of collapse. In the third example, the redistribution of the loads caused by member failures is considered for the truss system in the second example. The results based on different optimization approaches are compared for further investigation. Monte Carlo simulation is performed in each example to confirm the accuracy of the system failure probability computed by the MSR method.

Multi‐scale system reliability analysis of lifeline networks under earthquake hazards

AbstractRecent earthquake events evidenced that damage of structural components in a lifeline network may cause prolonged disruption of lifeline services, which eventually results in significant socio‐economic losses in the affected area. Despite recent advances in network reliability analysis, the complexity of the problem and various uncertainties still make it a challenging task to evaluate the post‐hazard performance and connectivity of lifeline networks efficiently and accurately. In order to overcome such challenges and take advantage of merits of multi‐scale analysis, this paper develops a multi‐scale system reliability analysis method by integrating a network decomposition approach with the matrix‐based system reliability (MSR) method. In addition to facilitating system reliability analysis of large‐size networks, the multi‐scale approach enables optimizing the level of computational effort on subsystems; identifying the relative importance of components and subsystems at multiple scales; and providing a collaborative risk management framework. The MSR method is uniformly applied for system reliability analyses at both the lower‐scale (for link failure) and the higher‐scale (for system connectivity) to obtain the probability of general system events, various conditional probabilities, component importance measures, statistical correlation between subsystem failures and parameter sensitivities. The proposed multi‐scale analysis method is demonstrated by its application to a gas distribution network in Shelby County of Tennessee. A parametric study is performed to determine the number of segments during the lower‐scale MSR analysis of each pipeline based on the strength of the spatial correlation of seismic intensity. It is shown that the spatial correlation should be considered at both scales for accurate reliability evaluation. The proposed multi‐scale analysis approach provides an effective framework of risk assessment and decision support for lifeline networks under earthquake hazards. Copyright © 2009 John Wiley & Sons, Ltd.

A computational method of system reliability of a successful product based on a simulated test

PurposeThe purpose of this paper is to put forward a method which uses a computer to make a large number of simulated tests and determine the reference value of a system reliability index according to a unit reliability index.Design/methodology/approachAt the beginning of conducting an index demonstration and development on a new system, its unit reliability index can already reflect the unit reliability level accurately. Based on this characteristic, this index is used as the confidence lower limit of single side estimated in the unit reliability interval to find the failure distribution law of the unit. On this basis, a great number of simulated tests are made by a computer to calculate the unit failure number and reliability point estimated value every test.FindingsThe confidence lower limit of single side estimated in the system reliability interval is found by counting up the simulated test data of these units.Research limitations/implicationsAvailability of data is the main limitation regarding which model will be applied.Practical implicationsA useful advice for system reliability analysis and calculation.Originality/valueThis paper presents a new approach of system reliability analysis.

System reliability and sensitivity under statistical dependence by matrix-based system reliability method

A matrix-based system reliability (MSR) method has been recently proposed to compute the probabilities of general system events efficiently by simple matrix operations. The proposed matrix-based framework describes both a system event and the likelihood of its component events by vectors that are obtained by efficient matrix-based procedures. The probability of the system event is computed by the inner product of the two vectors. Therefore, the method is uniformly applicable to any type of system events including series, parallel, cut-set and link-set systems. In the case when one has incomplete information on component probabilities and/or on the statistical dependence between components, the matrix-based framework enables us to obtain the narrowest bounds on the system probability by linear programming. Various importance measures and conditional probabilities are also efficiently estimated by the proposed method. This paper presents the MSR method and further develops it in terms of statistical dependence and parameter sensitivity of system reliability. First, a method is developed to use the MSR method for systems with statistically dependent components. The correlation coefficients between the basic random variables or the component safety margins are represented by a Dunnett–Sobel class correlation matrix to identify the source of the statistical dependence and to make use of the matrix-based procedure developed for independent components. Second, a new matrix-based procedure is proposed to calculate the sensitivities of system reliability with respect to parameters. This paper demonstrates the MSR method and these further developments by two numerical examples of structural systems. First, the system fragility of a bridge structure is computed based on the analytical fragility models of the bridge components and the correlation coefficients between the seismic demands at different components. In the second example, the MSR method is used to estimate the probability of the collapse of a statically indeterminate structure subjected to an abnormal load. The sensitivities of the probability with respect to the means and standard deviations of uncertain member capacities are estimated for an optimal upgrade of the structural system.

Matrix-based system reliability method and applications to bridge networks

Using a matrix-based system reliability (MSR) method, one can estimate the probabilities of complex system events by simple matrix calculations. Unlike existing system reliability methods whose complexity depends highly on that of the system event, the MSR method describes any general system event in a simple matrix form and therefore provides a more convenient way of handling the system event and estimating its probability. Even in the case where one has incomplete information on the component probabilities and/or the statistical dependence thereof, the matrix-based framework enables us to estimate the narrowest bounds on the system failure probability by linear programming. This paper presents the MSR method and applies it to a transportation network consisting of bridge structures. The seismic failure probabilities of bridges are estimated by use of the predictive fragility curves developed by a Bayesian methodology based on experimental data and existing deterministic models of the seismic capacity and demand. Using the MSR method, the probability of disconnection between each city/county and a critical facility is estimated. The probability mass function of the number of failed bridges is computed as well. In order to quantify the relative importance of bridges, the MSR method is used to compute the conditional probabilities of bridge failures given that there is at least one city disconnected from the critical facility. The bounds on the probability of disconnection are also obtained for cases with incomplete information.

Reliability Assessment of 2400 MWth Gas-Cooled Fast Reactor Natural Circulation Decay Heat Removal in Pressurized Situations

As the 2400 MWth gas-cooled fast reactor concept makes use of passive safety features in combination with active safety systems, the question of natural circulation decay heat removal (NCDHR) reliability and performance assessment into the ongoing probabilistic safety assessment in support to the reactor design, named “probabilistic engineering assessment” (PEA), constitutes a challenge. Within the 5th Framework Program for Research and Development (FPRD) of the European Community, a methodology has been developed to evaluate the reliability of passive systems characterized by a moving fluid and whose operation is based on physical principles, such as the natural circulation. This reliability method for passive systems (RMPSs) is based on uncertainties propagation into thermal-hydraulic (T-H) calculations. The aim of this exercise is finally to determine the performance reliability of the DHR system operating in a “passive” mode, taking into account the uncertainties of parameters retained for thermal-hydraulical calculations performed with the CATHARE 2 code. According to the PEA preliminary results, exhibiting the weight of pressurized scenarios (i.e., with intact primary circuit boundary) for the core damage frequency (CDF), the RMPS exercise is first focusing on the NCDHR performance at these T-H conditions.

Time-Variant Reliability Analysis of Ship Structure Subjected to Fatigue and Corrosion

Based on the characteristics of loading condition of ship structure in service and the degeneration of the strength under fatigue and corrosion, the random time-variant model of ship hull section modulus was set up using the theory of random process. Then the time-variant reliability was analyzed with the method of up-crossing analysis and parallel system reliability. This method could not only present successive decrease of reliability of the ship structure under fatigue and corrosion, but also avoid the complicated numerical integration. It could be seen that this method was easy to achieve. Furthermore, the time-variant reliability was compared with the annual instantaneous reliability through an example, which indicated that this method was more precise, and could provide some references to the decision-making of the reliability, maintenance and safeguard.