An optimization method for brake instability reduction with fuzzy-boundary interval variables

Data interpolation is critical in the analysis of geophysical data when some data are missing or inaccessible. We interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters — the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We find that the first parameter must be carefully chosen to balance between the accuracy and numerical stability when data contain noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. Our approach is first illustrated by a synthetic gravity data set from a single survey line, and then it is generalized to the case over a survey grid. In both numerical experiments, the TSE method demonstrates an improved interpolation accuracy in comparison with the minimum curvature method. Finally, we apply the TSE method to a ground gravity data set from the Abitibi Greenstone Belt, Canada, and an airborne gravity gradient data set from the Vinton Dome, Louisiana, USA.

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 computational cost of reliability analysis and optimization of medium/large structural systems is prohibitively high. One of the reasons for this situation is the use of inefficient methods, such as finite differences, for design sensitivity analysis. A significant increase in the efficiency of reliability computations is expected from the integration of reliability methods with the discrete and continuum methods of design sensitivity analysis. So far, only the discrete method has been used in the so-called stochastic finite element method. Integration of reliability computations with the continuum method of design sensitivity analysis is proposed in this paper as a new, powerful approach to the probabilistic design of large structural systems. Basic formulations and solution methods of reliability analysis, design sensitivity analysis of reliability indices, reliability-based optimization, and multiobjective reliability-based optimization are reviewed with focus on the sensitivity informatio...

Structural reliability analysis with fuzzy random variables using error principle

Analysis of common cause failure effect on system reliability in seismic PSA

A reliability model is proposed to solve the problem of hybrid uncertainty with both random and interval variables in slope engineering. A hybrid uncertainty model based on the dimension reduction method and Taylor expansion is constructed to approximate the limit state function. Using the polynomial theorem and variable transformation method, the origin and center moments’ interval of the limit state function are calculated. Moment information is applied to the expansion of a three-parameter Weibull distribution, and the cumulative distribution function and probability density function of limit state function are determined. As a result, the failure probability interval of the slope is calculated. The interval uncertainty problem is transformed into an interval certainty problem using Taylor expansion without solving for the statistical moment of limit state function using multiple integrals and iteratively searching for the most probable failure points. The numerical results from two slopes show that the proposed method is effective and feasible.

For structural reliability problems simultaneously involving random variables, interval variables and fuzzy variables, an iteration algorithm is proposed to deal with the propagation of uncertainties. Corresponding to assumed membership value in the membership level interval [0,1], the membership interval of fuzzy variables can be obtained. After the fuzzy variables and the interval variables’ effects on the extreme value of performance function are alternately and iteratively analyzed with the random variables’ effects on statistical properties of the performance function, converged design point can be calculated, and the reliability can be as well calculated by the fourth moment algorithm based on the point estimate method. Finally the membership function of the reliability can be solved. Owing to the faster convergence of the iteration algorithm, the efficiency of the proposed algorithm is highly improved compared to the conventional numerical simulation method. And the adoption of fourth moment method proves much better in accuracy than only applying first order reliability method in the iteration algorithm. After the basic concept and process of the proposed algorithm is detailed, several numerical and engineering examples are studied to demonstrate its advantage both in efficiency and accuracy.

SummaryA new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd.

A sensitivity analysis estimates the effect of the change in the uncertain variable parameter on the probability of the structural failure. A novel fuzzy random reliability sensitivity measure of the failure probability is proposed to consider the effect of the epistemic and aleatory uncertainties. The uncertainties of the engineering variables are modeled as fuzzy random variables. Fuzzy quantities are treated using the y-cut approach. In fact, the fuzzy variables are transformed into the interval variables using the y-cut approach. Genetic approach considers different possible combinations within the search domain (y-cut) and calculates the parameter sensitivities for each of the combinations.

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.

Estimating the seismic response of nonlinear structures equipped with nonlinear viscous damper subjected to pulse-like ground records

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);

威布尔分布是可靠性科学和工程中常用的随机变量分布之一。将具有威布尔分布的非线性可靠度函数对数线性化，可方便威布尔参数的求解，但却降低了参数估计的精度。针对这个问题，提出了应用泰勒级数展开结合最小二乘法提高威布尔分布的拟合精度。通过数值模拟和实例计算，对比分析了泰勒级数展开–最小二乘法与普通最小二乘法及其加权处理的拟合效果。结果表明，该方法可以有效降低威布尔曲线拟合的误差，为可靠性试验提供参考。 Weibull distribution is one of the common random variable distributions in reliability science and engineering. Despite the fact that log-linearizing the nonlinear reliability function with Weibull distribution contributes to solving the Weibull parameters, the precision of parameter estimation is reduced. Thus, a method by combining Taylor series expansion and least square method is pro-posed to improve fitting precision of the Weibull distribution. Contrastive analyses on Taylor series expansion-least square method, common least square method and weighted least square method are conducted to access the fitting effects via numerical simulation and calculation. The results show that the proposed method can reduce the Weibull curve fitting error effectively and thus can be reference for reliability test.

In many engineering applications, both random and interval variables may exist. The mixture of both types of variables has been dealt with in robust design for single disciplinary systems. This work focuses on robustness assessment for general multidisciplinary systems with the presence of both random and interval variables. To alleviate the intensive computational demand, we propose a semi-second-order Taylor expansion method to estimate robustness. A performance function is approximated linearly in terms of random variables, but the interaction terms between random and interval variables are kept. Robustness is measured by the standard deviation of a system performance. The maximum and minimum standard deviations over the interval variables are identified. With proposed method, the impact of both random and interval variables on the system performance can be found efficiently.

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.