Parallel System Reliability Research Articles

Improved Bayesian model updating of geomaterial parameters for slope reliability assessment considering spatial variability

In engineering practice, Bayesian model updating using field data is often conducted to reduce the substantial inherent epistemic uncertainties in geomaterial properties resulting from complex geological processes. The Bayesian Updating with Subset simulation (BUS) method is commonly employed for this purpose. However, the wealth of field data available for engineers to interpret can lead to challenges associated with the “curse of dimensionality”. Specifically, the value of the likelihood function in the BUS method can become extremely small as the volume of field data increases, potentially falling below the accuracy threshold of computer floating-point operations. This undermines both the computational efficiency and accuracy of Bayesian model updating. To effectively address this technical challenge, this paper proposes an improved BUS method developed based on parallel system reliability analysis. Leveraging the Cholesky decomposition-based midpoint method, the total failure domain in the original BUS method, which involves a low acceptance rate, is subdivided into several sub-failure domains with a high acceptance rate. Facilitated with an improved Metropolis-Hastings algorithm, the improved BUS method enables the consideration of a large volume of field data and spatial variability of geomaterial properties in the probabilistic back analysis. The results of an illustrative soil slope, involving spatially variable undrained shear strength, demonstrate that the improved BUS method is effective in simultaneously incorporating a substantial volume of field measurements and observations in the model updating process. Through a comparison with the original BUS method, the improved BUS method is shown to be useful for Bayesian model updating of high-dimensional spatially variable geomaterial properties and slope reliability assessment.

Series–Parallel System Analysis and Reliability Research of Grid Structures Considering Adaptive Dynamic Bounding Threshold

There are many bars in grid structures, and their topological relationships are complex, so the workload of calculations involved in researching their reliability is large. In this paper, based on the geometric topological relationship within a grid structure, a series–parallel system analysis of the structure is carried out by means of node analysis, constraint grade division, and hierarchical combination analysis, and the series–parallel analysis results for the structure are used to judge the failure of the structure. In order to avoid the problem of missing important components due to unreasonable selection of the bounding threshold when identifying failed components, an adaptive dynamic bounding threshold method with high accuracy is introduced. The failure probability value of the failure path is calculated using the direct numerical integration method, and the reliability of the whole structure is obtained. Finally, the validity of this method is verified using an example of a square pyramid grid structure. The results show that the method is feasible for series–parallel system analysis, structural failure judgment, and reliability analysis of a grid structure.

An innovative adaptive Kriging-based parallel system reliability method under error stopping criterion for efficiently analyzing the global reliability sensitivity index

An innovative adaptive Kriging-based parallel system reliability method under error stopping criterion for efficiently analyzing the global reliability sensitivity index

The reliability analysis based on the generalized intuitionistic fuzzy two-parameter Pareto distribution.

In this paper, the two-parameter Pareto lifetime distribution is considered with vague shape and scale parameters, where parameters are set as generalized intuitionistic fuzzy numbers. A new L-R type intuitionistic fuzzy number is introduced, and cuts of the new fuzzy set are provided. The generalized intuitionistic fuzzy reliability characteristics such as reliability, conditional reliability, hazard rate and mean time to failure functions are defined, along with the special case of the two-parameter Pareto generalized intuitionistic fuzzy reliability analysis. Furthermore, the series and parallel system reliability are evaluated by the generalized intuitionistic fuzzy sets. Finally, for certain cases of the fuzzy shape and scale parameters and cut set values, the generalized intuitionistic fuzzy reliability characteristics are provided and compared through several illustrative plots.

Reliability of arrangement networks in terms of the h-restricted edge connectivity

The h-restricted edge connectivity λh is an important parameter to measure the reliability of massive parallel computing system. The λh of G is the minimum cardinality of a set of edges in G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. The arrangement graph is a generalization of the star graph, but its order is more flexible than that of the star graph. This paper investigates the h-restricted edge connectivity of the (n,k)-arrangement graph An,k, and determines that λ1(An,k)=2k(n−k)−2, λ2(An,k)=3k(n−k)−6 with k≤n−2.

Parametric Plots of Limit-State Surfaces as a Design Tool in Time-Variant System Reliability

The ability to accurately determine the temporal safe region in time-variant reliability analysis is seminal for reliability-based design. When stochastic excitations are present and discrete-time approaches are invoked, the errors can be large when one uses only one past safe event (and one new failure event) at each time-step. Furthermore, when all previous safe events are accumulated and used, the calculations can be time consuming and the accuracy not ensured. In this paper, a minimal, or a so-called extreme limit-state, surface is obtained to identify the system temporal safe region in an economical manner. To do this, the limit-state surface motion for each failure mode is recorded as a parametric polar plot that provides both magnitude and relative angle of the vectors from the origin to the most-likely failure points (MLFPs) in standard normal space. The angle differences provide correlation and the magnitude differences provide importance. At the component-level, a few logical policies that compare correlation and the magnitude ensure that the safe region is sufficiently recognized. At the system-level, the temporal average of correlations and the magnitudes at the component-level, along with series or parallel system designations, foretells which failure modes are needed to form the system extreme limit-state surface. The impact of the work includes an immediate recognition of the important failure modes and reduced computation for methods such as multi-normal integration. Case studies of both series-system reliability and parallel-system reliability are presented using structural beams excited by stochastic loads and plagued with degrading material properties and dimensions. The accuracy of the extreme LSS is demonstrated cogently. The use of the polar plots as a design tool becomes evident.

Estimate the Parallel System Reliability in Stress-Strength Model Based on Exponentiated Inverted Weibull Distribution

In this paper, we employ the maximum likelihood estimator in addition to the shrinkage estimation procedure to estimate the system reliability (Rk ) contain Kth parallel components in the stress-strength model, when the stress and strength are independent and non-identically random variables and they follow two parameters Exponentiated Inverted Weibull Distribution (EIWD). Comparisons among the proposed estimators were presented depend on simulation established on mean squared error (MSE) criteria.

Parallel system reliability analysis with a CECBO algorithm

The existing engineering structural system is featured by complicated limit state functions of high nonlinearity, resulting in the conventional reliability analysis approach that is unable to evaluate these problems accurately or even unavailable. Various analytical methods have been presented by researchers over the past decades. However, these methods have difficulties in striking a balance between accuracy and computational efficiency. This paper proposes a relatively efficient and accurate procedure to estimate the failure probability of the parallel system based on the FORM and a new metaheuristic algorithm, chaotic enhanced colliding bodies optimization algorithm (CECBO). The CECBO has shown robustness, high accuracy, and implementation simplicity for solving optimization problems from previous work. Thus, the CECBO is employed to search the point of maximum likelihood (PML), a point that yields the highest value of the probability density function in the failure domain, through solving an optimization model and then approximates the failure domain of the parallel system to estimate the failure probability accurately. The results of the test examples indicate that the proposed procedure is promising for the estimation of the failure probability of a parallel system in terms of accuracy and efficiency.

Regression Modelling on Reliability Variation of a Parallel Series System of (m, ni) Order with Addition and Removal of Parallel Paths

A regression model is fitted on variation of reliability of parallel series system of (m, ni) order (called initial system) by adding (or removing) the arbitrary number of parallel paths. The initial system is transformed by adding (or removing) the ‘p’ (or ‘k’) parallel paths. A reliability variation method is devised to obtain directly the reliability of the transformed system in terms of reliability of the initial system and reliability of the added (or removed) system. The variation in reliability is evaluated in both cases to see the effect of parallel paths on initial system reliability. Also, the variation in reliability of a particular parallel series system of order (4, 1) is obtained by assuming constant failure rate of the components. The effect of parallel paths and failure rate of the components on variation of reliability of the system is examined by fitting the linear regression model. The values of R2 and adjusted R2 are calculated to see the best fit of the model in order reduce the computing efforts to obtain the reliability of the transformed system. The results are shown numerically and graphically. The application of the study is discussed with justification.

Control Strategy of Parallel Systems with Efficiency Optimisation in Switched Reluctance Generators

Abstract To solve motor heating and life shortening of parallel switched reluctance generator (SRG) induced by uneven output currents due to different external characteristics, we generally adopt current sharing control (CSC) to make each parallel generator undertake large load currents on average to improve the reliability of parallel power generation system. However, the method usually causes additional loss of power because it does not consider the efficiency characteristics of each parallel generator. Therefore, with the efficiency expression for the parallel system of SRG established and analysed, the control strategy based on differential evolution (DE) algorithm is proposed as a mechanism by which to enhance generating capacity and reliability of multi-machine power generation from the perspective of efficiency optimisation. We re-adjust the reference current of each parallel generator to transform the working point of each generator and implement the efficiency optimisation of parallel system. The performance of the proposed control method is evaluated in detail by the simulation and experiment, and comparison with traditional CSC is carried out as well.

Analiza niezawodności systemów równoległych w sytuacji jednocześnie występujących uszkodzeń wywołanych wspólną przyczyną oraz uszkodzeń elementów dzielących obciążenie

For parallel system reliability, the mean time to failure of parallel system under common cause failure (load-sharing failure) is shorter than that of the system without common cause failure (load-sharing failure). The traditional calculation approaches of mean time to failure of parallel systems do not consider the possible effect of common cause and load-sharing failure. However, it may result in the poor accuracy of mean time to failure of parallel system and pose a threat to system reliability. This paper not only considers the effect of common cause failure with stress strength, but also investigates the joint effect of the load-sharing and common cause failures. Besides, the joint failure model of three-dependent-component parallel system are established, and the corresponding properties are analyzed. Finally, a numerical example is used to illustrate the proposed method.

Application of adaptive surrogate models in time-variant fatigue reliability assessment of welded joints with surface cracks

The time-variant fatigue reliability of welded joints subjected to stochastic loading is assessed based on the PHI2 method, which takes the time-variant reliability problem as a two-component parallel system reliability problem. The complex fatigue process that takes place at the weld toe is modeled as a semi-elliptical surface crack growth process. Surrogate models, representing surface crack sizes at a time instant, are applied to solve the reliability problem involving time-consuming fatigue crack growth analyses. Polynomial regression models and Kriging interpolation models are both employed. Their corresponding adaptive procedures are also adopted to improve the reliability results. Some adjustments of the active refinement algorithm based on the Kriging model are proposed to make it more suitable for the present study. The time-variant fatigue reliability assessment of a T-plate welded joint is carried out. Without using the adaptive procedures, the Kriging models can better represent the crack sizes compared with the polynomial models. The outcrossing rate formulated by the PHI2 method is sensitive to the reliability index of the first component of the two-component parallel system. The effectiveness of the adaptive procedures, which improve the reliability results, is demonstrated.

Design, optimisation and reliability allocation for energy systems based on equipment function and operating capacity

Designers of energy systems often face challenges in balancing the trade-off between cost and reliability. In literature, several papers have presented mathematical models for optimizing the reliability and cost of energy systems. However, the previous models only addressed reliability implicitly, i.e., based on availability and maintenance planning. Others focused on allocation of reliability based on individual equipment requirements via non-linear models that require high computational effort. This work proposes a novel mixed-integer linear programming (MILP) model that combines the use of both input-output (I-O) modelling and linearized parallel system reliability expressions. The proposed MILP model can optimize the design and reliability of energy systems based on equipment function and operating capacity. The model allocates equipment with sufficient reliability to meet system functional requirements and determines the required capacity. A simple pedagogical example is presented in this work to illustrate the features of proposed MILP model. The MILP model is then applied to a polygeneration case study consisting of two scenarios. In the first scenario, the polygeneration system was optimized based on specified reliability requirements. The technologies chosen for Scenario 1 were the CHP module, reverse osmosis unit and vapour compression chiller. The total annualized cost (TAC) for Scenario 1 was 53.3 US$ million/year. In the second scenario, the minimum reliability level for heat production was increased. The corresponding results indicated that an additional auxiliary boiler must be operated to meet the new requirements. The resulting TAC for the Scenario 2 was 5.3% higher than in the first scenario.

Fuzzy Reliability-Vulnerability for Evaluation of Water Supply System Performance

The reliability of water supply system is a critical factor in the development and the ongoing capability to succeed in life and people's health. Determining of its, with high certainty, for performance of water supply system is developed to ensure the sustainability of system. Reliability (Re) plays a great role in evaluation of system sustainability. The probability approaches have been used to evaluate the reliability problems of systems. The probability approach is failed to address the problems of reliability evaluation that comes by subjectivity, human inputs and lack of history data. This research proposed two models; I) traditional model: fuzzy reliability measure suggested by Duckstein and Shresthaand then developed by El-Baroudy; and II) developed model: fuzzy reliability-vulnerability model. The two models implemented and evaluation of water supply system by using two hypothetical systems (G and H). System (G) consists of a single pump and System (H) consists of a two parallel pumps. Triangular and trapezoidal membership functions (MFs) are used to investigate of the reliability measure to the form of the membership function. The results agree with expectations that the reliability of parallel component system {ReH (0.53)} is higher than the reliability of single component system {ReG (0.47)}. Moreover, the result by using fuzzy set reduces the effect of subjectively in process of decision-making (DM). The fuzzy reliability vulnerability is able to handle different fuzzy representations and different operation environment of system

Implementation of directional simulation to estimate outcrossing rates in time‐variant reliability analysis of structures

AbstractTime‐dependent reliability analysis of structures by the use of an outcrossing approach normally requires the so‐called outcrossing rate to be estimated. A variety of methods has been recorded in the literature to evaluate this rate both for continues and discrete processes. Despite the availability of these methods, still more general and at the same time less sophisticated approaches are desired. In this paper, attempt is made to use the basic idea of “parallel system reliability formulation” to calculate the outcrossing rate for circumstances where the processes are continuous. These calculations are carried out by directional simulation. It is shown that this approach is simple to implement and may be used for the cases where the problem involves nonstationary processes and also for the cases where several limit state functions may have to be considered.

Reliability analysis of a ship hull structure under combined loads including slamming loading

During the last decades, much attention has been paid to long-term structural reliability analyses applied to design and maintenance planning of ships. However, many extreme loads occur in short time periods in particular severe sea conditions. In this paper, a random process model of the ship hull girder subjected to still-water, wave- and slamming-induced loads is formulated based on the random process theory covering a short time period during extreme seas in the short time duration of slamming. The correlation of the peak value of slamming- and wave-induced loads is considered according to the fact that the wave and the velocity of the ship are the dominating causes of the slamming. Through the analysis of the stochastic process of limit state function, the reliability is evaluated by means of up-crossing analysis and parallel system reliability method. In a numerical example, the influences of the damping ratio, slamming rate and correlation coefficient on the failure probability are analysed, considering different failure modes. The results show that the buckling failure of the deck under compression is the most dangerous case and the damping ratio influences the impact of the slamming load on the reliability.

Applying weakest t-norm based approximate intuitionistic fuzzy arithmetic operations on different types of intuitionistic fuzzy numbers to evaluate reliability of PCBA fault

This research addresses system reliability analysis using weakest t-norm based approximate intuitionistic fuzzy arithmetic operations, where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers. Due to the incomplete, imprecise, vague and conflicting information about the component of system, the present study evaluates the reliability of system in terms of membership function and non-membership function by using weakest t-norm (Tw) based approximate intuitionistic fuzzy arithmetic operations on different types of intuitionistic fuzzy numbers. In general, interval arithmetic (α-cut arithmetic) operations have been used to analyze the fuzzy system reliability. In complicated systems, interval arithmetic operations may occur the accumulating phenomenon of fuzziness. In order to overcome the accumulating phenomenon of fuzziness, this research adopts approximate intuitionistic fuzzy arithmetic operations under the weakest t-norm arithmetic operations (Tw) to analyze fuzzy system reliability. The approximate intuitionistic fuzzy arithmetic operations employ principle of interval arithmetic under the weakest t-norm arithmetic operations. The proposed novel fuzzy arithmetic operations may obtain fitter decision values, which have smaller fuzziness accumulating and successfully analyze the system reliability. Also weakest t-norm arithmetic operations provide more exact fuzzy results and effectively reduce fuzzy spreads (fuzzy intervals). Using proposed approach, fuzzy reliability of series system and parallel system are also constructed. For numerical verification of proposed approach, a malfunction of printed circuit board assembly (PCBA) is presented as a numerical example. The result of the proposed method is compared with the listing approaches of reliability analysis methods.

Gradual reliability analysis of mechanical component systems

Components within a system may be related to one another in two primary ways: in either a serial or a parallel configuration. The other way associated system components is developed on the basis of series and parallel systems. Although some complex systems cannot generate from series and parallel system, the result of this paper is helpful to study more complex gradual system reliability problems. In this paper, a hypothesis is formed that the reliability of the components of the system is variable with time. Then, the reliability of the system is gradual, on condition that the components are combined by some related way. If the system reliability analysis is based on the static analysis, it may be different from the actual value of the reliability because the components of the system would afford stochastic load or generate degradation of performance. The method considering the random resistant degradation may make the result of reliability accurate. In this paper, gamma process is used to simulate the use of the components of the system, as deterioration is generally uncertain and non-decreasing, it can best be regarded as a gamma process. Combining the Edgeworth series method and forth moment technique, the method that calculate the reliability of series and parallel system is deduced. Then, the reliability of different systems and the failure rate of the systems are illustrated with time. The results show that the reliability of the systems will decline in different ways with time.

Impact of translation approach for modelling correlated non-normal variables on parallel system reliability

The adequacy of two approximate methods based on incomplete information, namely method P and method S, for constructing multivariate distributions with given marginal distributions and covariance has not been studied systematically. This article aims to study the errors of the method P and method S. First, the method P and method S as well as the exact method are presented. Second, the performance of the two approximate methods is evaluated based on their abilities to match exact solutions for system probabilities of failure. Finally, an illustrative example of a parallel system is investigated to demonstrate the errors associated with the two methods. The results indicate that the errors in system probabilities of failure for the two methods highly depend on the level of system probability of failure, the performance function underlying the system, and the degree of correlation. Such errors increase greatly with decreasing system probabilities of failure. When the target system probability of failure is larger than 1.0E−03, the system probabilities of failure obtained from the two methods and the exact method are of the same order of magnitude. The maximum error in the system probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.

A Practical Fuzzy Adaptive Control Strategy for Multi-DOF Parallel Robot

Multiple Degrees of Freedom (DOF) parallel robots possess the advantages of being compact structure, great stiffness, stability and high accuracy, so such platforms have been widely used in application areas as diverse as the spacecraft motion simulators, radio telescopes, and medical rehabilitation devices. In this paper, after giving a brief review on the control strategies for parallel robot, a 6-DOF robot system for medical purposes based on simulation as well as real environment is established. In order to improve the position tracking accuracy for such objects with time-varying and nonlinear parameters, a practical fuzzy adaptive controller is designed based on the kinematics of parallel platform, where fuzzy inference units are utilized to modify the PID parameters in real-time by using the position feedback from the robot actuators. Finally, both virtual and actual experiment results demonstrate that the proposed algorithm is able to effectively reduce the position tracking errors compared with the traditional PID controller, and the reliability and feasibility of such parallel robotic system can also be guaranteed.