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This book offers unique insight on structural safety and reliability by combining computational methods that address multiphysics problems, involving multiple equations describing different physical phenomena and multiscale problems, involving discrete sub-problems that together describe important aspects of a system at multiple scales. The book examines a range of engineering domains and problems using dynamic analysis, nonlinear methods, error estimation, finite element analysis and other computational techniques.

This book also:

· Introduces novel numerical methods

· Illustrates new practical applications

· Examines recent engineering applications

· Presents up-to-date theoretical results

· Offers perspective relevant to a wide audience, including teaching faculty/graduate students, researchers and practicing engineers.



Reliability Education


Mechanical System Lifetime

We present, in three parts, the approaches for the random loading analysis in order to complete methods of lifetime calculation.
First part is about the analysis methods. Second part considers modeling of random loadings. A loading, or the combination of several loadings, is known as the leading cause of the dwindling of the mechanical component strength. Third part will deal with the methods taking into account the consequences of a random loading on lifetime of a mechanical component.
The motivations of the present document are based on the observation that operating too many simplifications on a random loading lost much of its content and, therefore, may lose the right information from the actual conditions of use. The analysis of a random loading occurs in several ways and in several approaches, with the aim of later evaluate the uncertain nature of the lifetime of a mechanical component.
Statistical analysis and frequency analysis are two complementary approaches. Statistical analyses have the advantage of leading to probabilistic models (Demoulin B (1990a) Processus aléatoires [R 210]. Base documentaire « Mesures. Généralités ». (*)) provide opportunities for modeling the natural dispersion of studied loadings and their consequences (cracking, fatigue, damage, lifetime, etc.). The disadvantage of these statistical analyses is that they ignore the history of events.
On the other hand, the frequency analyses try to remedy this drawback, using connections between, firstly, the frequencies contained in the loading under consideration and, secondly, whether the measured average amplitudes (studied with the Fourier transform, FT) or their dispersions (studied with the power spectral density, PSD) (Kunt M (1981) Traitement numérique des signaux. Éditions Dunod; Demoulin B (1990b) Fonctions aléatoires [R 220]. Base documentaire « Mesures. Généralités ». (*)). The disadvantage of frequency analyses is the need to issue a lot of assumptions and simplifications for use in models of lifetime calculation (e.g., limited to a system with one degree of freedom using probabilistic models simplified for the envelope of the loading).
A combination of the two analyses is possible and allows a good fit between the two approaches. This combination requires a visual interpretation of the appearance frequency. Thus, a random loading is considered a random process to be studied at the level of the amplitude of the signal, its speed, and its acceleration.
Raed Kouta, Sophie Collong, Daniel Play

Uncertainty Quantification and Uncertainty Propagation Analysis


Likelihood-Based Approach for Uncertainty Quantification in Multi-Physics Systems

This chapter presents a computational methodology for uncertainty quantification in multi-physics systems that require iterative analysis between models corresponding to each discipline of physics. This methodology is based on computing the probability of satisfying the inter-disciplinary compatibility equations, conditioned on specific values of the coupling (or feedback) variables, and this information is used to estimate the probability distributions of the coupling variables. The estimation of the coupling variables is analogous to likelihood-based parameter estimation in statistics and thus leads to the likelihood approach for multi-disciplinary analysis (LAMDA). Using the distributions of the feedback variables, the coupling can be removed in any one direction without loss of generality, while still preserving the mathematical relationship between the coupling variables. The calculation of the probability distributions of the coupling variables is theoretically exact and does not require a fully coupled system analysis. The LAMDA methodology is first illustrated using a mathematical example and then applied to the analysis of a fire detection satellite.
Shankar Sankararaman, Sankaran Mahadevan

Bayesian Methodology for Uncertainty Quantification in Complex Engineering Systems

This chapter presents a Bayesian methodology for system-level uncertainty quantification and test resource allocation in complex engineering systems. The various component, subsystem, and system-level models, the corresponding parameters, and the model errors are connected efficiently using a Bayesian network. This provides a unified framework for uncertainty analysis where test data can be integrated along with computational models across the entire hierarchy of the overall engineering system. The Bayesian network is useful in two ways: (1) in a forward problem where the various sources of uncertainty are propagated through multiple levels of modeling to predict the overall uncertainty in the system-level response; and (2) in an inverse problem where the model parameters of multiple subsystems are calibrated simultaneously using test data. Test data available at multiple data are first used to infer model parameters, and then, this information is propagated through the Bayesian network to compute the overall uncertainty in the system-level prediction. Then, the Bayesian network is used for test resource allocation where an optimization-based procedure is used to identify tests that can effectively reduce the overall uncertainty in the system-level prediction. Finally, the overall Bayesian methodology for uncertainty quantification and test resource allocation is illustrated using three different numerical examples. While the first example is mathematical, the second and third examples deal with practical applications in the domain of structural mechanics.
Shankar Sankararaman, Sankaran Mahadevan

The Stimulus-Driven Theory of Probabilistic Dynamics

Probabilistic Safety Assessments (PSA) are widely used to evaluate the safety of installations or systems. Nevertheless, classical PSA methods—as fault trees or event trees—have difficulties dealing with time dependencies, competition between events and uncertainties. The Stimulus-Driven Theory of Probabilistic Dynamics (or SDTPD) copes with these dynamics aspects. It is a general theory based on dynamic reliability, supplemented by the notion of stimulus. Hence, each event is divided into two phases: the stimulus activation (as soon as all the conditions for the event occurrence are met) and a delay (before the actual occurrence of the event), with a possible stimulus deactivation if the conditions are no more met. It allows modeling in an accurate way the competitions between events. This chapter presents the theory of the SDTPD as well as the solving of a simple example, using the MoSt computer code.
Agnès Peeters

The Pavement Performance Modeling: Deterministic vs. Stochastic Approaches

The pavement performance modeling is an essential part of pavement management system (PMS). It estimates the long-range investment requirement and the consequences of budget allocation for maintenance treatments of a particular road segment on the future pavement condition. The performance models are also applied for life-cycle economic evaluation and for the prioritization of pavement maintenance treatments. This chapter discusses various deterministic and stochastic approaches for calculating the pavement performance curves. The deterministic models include primary response, structural performance, functional performance, and damage models. The deterministic models may predict inappropriate pavement deterioration curves because of uncertain pavement behavior under fluctuating traffic loads and measurement errors. The stochastic performance models assume the steady-state probabilities and cannot consider the condition and budget constraints simultaneously for the PMS. This study discusses the Backpropagation Artificial Neural Network (BPN) method with generalized delta rule (GDR) learning algorithm to offset the statistical error of the pavement performance modeling. This study also argues for the application of reliability analyses dealing with the randomness of pavement condition and traffic data.
Md. Shohel Reza Amin

Probabilistic Considerations in the Damage Analysis of Ship Collisions

Ship collision events are often analyzed by following the approach of internal mechanics and external dynamics. The uncertainties in collision scenario parameters, which are used in the calculation of external dynamics, are usually quantified during ship collision analysis. However, uncertainties in the material and geometric properties are often overlooked during the analysis of internal mechanics. Consequently, it may lead to overestimation or underestimation of ship structural design capacity, which could impact on system performance.
This study aims to show a framework for assessing the reliability of ship hull structures during collision events. Finite element analysis using ABAQUS software and simplified analytical methods have been utilized to model the resistance of ship hull plates against the impact from the bulbous bow of a striking ship. The particulars of a general cargo vessel involved in a real-life collision have been used in the study to determine the external force required for the considered hull plate to resist. Based on Monte Carlo simulation, reliability analysis has been carried out to model the uncertainties of hull plate displacement. Two thousand design sets of the geometric and material properties were propagated through the simplified analytical model to obtain the resulting displacement data. These data were subsequently analyzed to obtain a probabilistic model for hull plate displacement, along with the variable sensitivity.
Abayomi Obisesan, Srinivas Sriramula, John Harrigan

An Advanced Point Estimate Method for Uncertainty and Sensitivity Analysis Using Nataf Transformation and Dimension-Reduction Integration

This article presents an advanced point estimate method (APEM) with the purposes of estimating the moments of model outputs and identifying the sensitivities of inputs variables. The APEM consists of four ingredients, i.e. (1) Nataf transformation, (2) a generalized dimension-reduction method, (3) the Gauss–Hermite integration (GHI), and (4) a global sensitivity index. Nataf transformation enables the APEM to deal with the practical engineering problems generally involving the random variables often given the marginal distributions and correlations. The generalized dimension-reduction method with the univariate and the bivariate formulas is adopted to decompose a high-dimension function into several one- and two-dimension functions, respectively. Consequently, the moments of the high-dimension function are approximated by that of the decomposed low-dimension functions, which are further calculated by the GHI. As a complement to the APEM, a global sensitivity index is additionally proposed. Through three numerical examples and two applications, the APEM shows good performance at estimating the moments of random functions, and the global sensitivity index is validated for defining the influence of a variable’s variation in standard normal space on model responses.
Xiaohui H. Yu, Dagang G. Lu

Reliability and Risk Analysis


Risk Assessment of Slope Instability Related Geohazards

The paramount importance of slope instability hazards assessment and management is by and large recognized. The general mechanisms of slope instability processes are now fairly well understood but there remains the problem of establishing the risks to lives and property. This is being tackled by relating the local ground conditions to the regional geological surveys and integrating this with site-specific information to produce a hazard potential estimate.
Herein lies the guiding principle of the current chapter, i.e., to describe slope instability related geohazards and methods to estimate the associated risks in an appropriate and effective way. A case study is presented to illustrate the need and tools of a probabilistic framework for slope instability analysis and emphasize that deterministic and probabilistic approaches can often be regarded as complementary.
Mihail E. Popescu, Aurelian C. Trandafir, Antonio Federico

Advances in System Reliability Analysis Under Uncertainty

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.
Chao Hu, Pingfeng Wang, Byeng D. Youn

Reliability of Base-Isolated Liquid Storage Tanks under Horizontal Base Excitation

Reliability of base-isolated liquid storage tanks is evaluated under random base excitation in horizontal direction considering uncertainty in the isolator parameters. Generalized polynomial chaos (gPC) expansion technique is used to determine the response statistics, and reliability index is evaluated using first order second moment (FOSM) theory. The probability of failure (p f) computed from the reliability index, using the FOSM theory, is then compared with the probability of failure (p f) obtained using Monte Carlo (MC) simulation. It is concluded that the reliability of broad tank, in terms of failure probability, is more than the slender tank. It is observed that base shear predominantly governs the failure of liquid storage tanks; however, failure due to overturning moment is also observed in the slender tank. The effect of uncertainties in the isolator parameters and the base excitation on the failure probability of base-isolated liquid storage tanks is studied. It is observed that the uncertainties in the isolation parameters and the base excitation significantly affect the failure probability of base-isolated liquid storage tank.
S. K. Saha, V. A. Matsagar

Robust Design of Accelerated Life Testing and Reliability Optimization: Response Surface Methodology Approach

Due to cost and time savings and improving reliability, accelerated life tests are commonly used; in which some external stresses are conducted on items at higher levels than normal. Estimation and optimization of the reliability measure in the presence of several controllable and uncontrollable factors becomes more difficult especially when the stresses interact. The main idea of this chapter is employing different phases of response surface methodology to obtain a robust design of accelerated life testing. Since uncontrollable variables are an important part of accelerated life tests, stochastic covariates are involved in the model. By doing so, a precise estimation of reliability measure can be obtained. Considering the covariates as well as response surface methodology simultaneously are not addressed in the literature of accelerated life test. This methodology can be used on the conditions that a broad spectrum of variables is involved in the accelerated life test and the failed units have a massive cost for producers. Though considering covariates in the experiments, the optimization of reliability can generate more realistic results in comparison with noncovariates model. For the first step of this study, experimental points using D-optimal approach are designed to decrease the number of experiments as well as the prediction variance. The reliability measure is estimated under right censoring scheme by Maximum likelihood estimator (MLE) assuming that lifetime data have an exponential distribution with parameter, λ, depending on the design and stress variables as well as covariates. In order to find the best factor setting that leads to the most reliable design, response surface methodology is applied to construct the final mathematical program. Finally, a numerical example is analyzed by the proposed approach and sensitivity analyses are performed on variables.
Taha-Hossein Hejazi, Mirmehdi Seyyed-Esfahani, Iman Soleiman-Meigooni

Reliability Measures Analysis of a Computer System Incorporating Two Types of Repair Under Copula Approach

In this chapter, the authors have studied the reliability characteristics of a home or office based computer system constructed with hardware connectivity. The system contains multi possible stages that can be repaired. The designed system is studied by using the Markov process, supplementary variable technique, Laplace transformation, and Gumbel–Hougaard family of copula to obtain the various reliability measures such as transition state probabilities, availability, reliability, cost analysis, and sensitivity.
Nupur Goyal, Mangey Ram, Ankush Mittal

Reliability of Profiled Blast Wall Structures

Stainless steel profiled walls have been used increasingly in the oil and gas industry to protect people and personnel against hydrocarbon explosions. Understanding the reliability of these blast walls greatly assists in improving the safety of offshore plant facilities. However, the presence of various uncertainties combined with a complex loading scenario makes the reliability assessment process very challenging. Therefore, a parametric model developed using ANSYS APDL is presented in this chapter. The significant uncertainties are combined with an advanced analysis model to investigate the influence of loading, material and geometric uncertainties on the response of these structures under realistic boundary conditions. To review and assess the effects of the dynamics and nonlinearities, four types of analyses including linear static, nonlinear static, linear transient dynamic, and nonlinear transient dynamic are carried out. The corresponding reliability of these structures is evaluated with a Monte Carlo simulation (MCS) method, implementing the Latin hypercube sampling (LHS) approach. The uncertainties related to dynamic blast loading, material properties, and geometry are represented in terms of probability distributions and the associated parameters. Dynamic, static, linear, and nonlinear responses of the structure are reviewed. Stochastic probabilistic analysis results are discussed in terms of the probability of occurrence, the cumulative distribution functions (CDFs), and the corresponding variable sensitivities. It is observed that using the approach taken in this study can help identify the important variables and parameters to optimize the design of profiled blast walls, to perform risk assessments, or to carry out performance-based design for these structures.
Mohammad H. Hedayati, Srinivas Sriramula, Richard D. Neilson

Reliability Assessment of a Multi-Redundant Repairable Mechatronic System

The reliability modelling of redundant systems is an important step to estimate the ability of a system to meet the required specifications. Markov chains have characteristics making it very simple the graphic representation of this type of model. They however have the disadvantage of being quickly unworkable because of the size of the matrices to be manipulated when systems become complex in terms of number of components or states. This issue, known as of combinatorial explosion is discussed in this chapter. Two methods are proposed. The first one uses the concept of decoupling between phenomena driven by different dynamics. The second is based on a principle of iteration after cutting the model into classes of membership. Both are based on the principles of approximating the exact result by reducing the scale of the problem to be solved. A case study is eventually carried out, dealing with the reliability modelling and assessing of a mechatronic subsystem used for an Unmanned Aerial Vehicle flight control with a triple modular redundancy. Results are discussed.
Carmen Martin, Vicente Gonzalez-Prida, François Pérès

Infrastructure Vulnerability Assessment Toward Extreme Meteorological Events Using Satellite Data

In the chapter is discussed some aspects of the theoretical and methodological basis for using of remote sensing data of snow cover for hazards assessment related to meteorological, climatic, hydrological, and hydrogeological risks over urban areas. Main focus is on the urban infrastructure risk assessment toward extreme snowstorms using satellite data. A method for determining the snow cover parameters on remote sensing data base (in particular MOD10A1 and SWE products, normalized index of snow depth (NDSI), and local meteorological observations) has been proposed. A method for data integrating from various sources on the basis of the modified Ensemble Transform Kalman Filter (ETKF) and Kernel Principal Component Analysis (KPCA) of data distributions has been proposed. It is shown that the proposed approach has quite high relative accuracy in comparison with existing methods, algorithms, and products (if MOD10A1 and SWE products have been used separately) with application for urban agglomeration. As an example, the approach have been used for analysis of extreme snowfall in Kiev (March 21–23, 2013). Quantitative assessments of risk indicators and vulnerability parameters of municipal infrastructure under emergency effects have been proposed.
Yuriy V. Kostyuchenko

Geostatistics and Remote Sensing for Extremes Forecasting and Disaster Risk Multiscale Analysis

The method of analysis of multisource data statistics is proposed for extreme forecasting and meteorological disaster risk analysis. This method is based on nonlinear kernel-based principal component algorithm (KPCA) modified according to specific of data: socioeconomic, disaster statistics, climatic, ecological, infrastructure distribution. Using this method the set of long-term regional statistics of disasters distributions and variations of economic activity has been analyzed. On these examples the method of obtaining of the spatially and temporally normalized and regularized distributions of the parameters investigated has been demonstrated. Method of extreme distribution assessment based on analysis of meteorological measurements should be described. Analysis of regional climatic parameters distribution allows to estimate the probability of extremes (both on seasonal and annual scales) toward mean climatic values change. The way to coherent risk measures assessment based on coupled analysis of multidimensional multivariate distributions should be described. Using the method of assessment of complex risk measures on the base of coupled analysis of multidimensional multivariate distributions of data the regional risk of climatic, meteorological, and hydrological disasters were estimated basing on kernel copula semi-parametric algorithm.
Yuriy V. Kostyuchenko

Time-Dependent Reliability Analysis of Corrosion Affected Structures

Incorporating the effect of corrosion into the reliability analysis of a structure is of paramount importance. Since deterioration due to corrosion is uncertain over time, it should ideally be represented as a time-dependent probabilistic (i.e. stochastic) process. For a more accurate reliability analysis and failure assessment, the multi-failure mode analysis of structures is explained in this chapter.
Sensitivity analysis is also discussed as a key part of reliability analysis from which the effect of different variables on service life of the structure can be investigated.
Worked examples of some structures such as cast iron water mains, concrete sewers and post-tension concrete bridges will also be presented and the results are discussed.
Mojtaba Mahmoodian, Amir Alani

Multicut-High Dimensional Model Representation for Reliability Bounds Estimation

The structural reliability analysis in presence of mixed uncertain variables demands more computation as the entire configuration of fuzzy variables needs to be explored. The existence of multiple design points plays an important role in the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this chapter, a method for estimating the reliability bounds of structural systems involving multiple design points in presence of mixed uncertain variables is presented. The proposed method involves weight function to identify multiple design points, multicut-high dimensional model representation for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables and fast Fourier transform for solving the convolution integral.
A. S. Balu, B. N. Rao

Approximate Probability Density Function Solution of Multi-Degree-of-Freedom Coupled Systems Under Poisson Impulses

A solution procedure is proposed to approximate the probability density function (PDF) solution of high-dimensional non-linear systems under Poisson impulses. The PDF solution yields the generalized Fokker–Planck–Kolmogorov (FPK) equation. First a state-space-split method is proposed to reduce the high-dimensional generalized FPK equation to a low dimensional equation. After that, the exponential–polynomial closure method is further adopted to solve the reduced FPK equation for the PDF solution. In order to show the effectiveness of the proposed solution procedure, a two-degree-of-freedom coupled pitch–roll ship motion system and a 10-degree-of-freedom mass–spring–damper system are investigated, respectively. Compared to the simulated results, the proposed solution procedure is effective to obtain the PDF solution, especially in the tail region which is very important for reliability analysis.
H. T. Zhu

Evaluate Reliability of Morgenstern–Price Method in Vertical Excavations

Considering force and moment equilibrium equations simultaneously, Morgenstern–Price’s method is more well mannered than other computational algorithms in slope stability field. On the other hand, because of its simplification, Rankine’s theory has its particular fans in handy calculations and pre-estimations of safe depth in vertical self-stable excavations, classically and academically. To have a comparison of abovementioned methods’ results, in this study, a variety of analyses have been performed using the Morgenstern–Price’s algorithm with SLIDE software in which the cohesion factor of soil changes over a range between 5 and 95 kPa and the inner friction angle is applied less than 40°. The analyses results including self-stable excavation depths between 1 and 8 m and related factors of safety (1–3) are derived and collected in a 90° slope. Moreover, using Rankine’s formula in the same geometry, the determination of safe vertical self-stable excavation depth is performed in various factors of safety. Finally, a relation between two methods is presented as a correlation as well as a reliability evaluation.
Shaham Atashband

Probabilistic Approach of Safety Factor from Failure Assessment Diagram

Global and partial deterministic safety factors are defined through a failure assessment diagram to evaluate the failure risk of a structure or a component.
The use of a failure assessment diagram is extended to evaluate the safety factor and the security factor of a conventional probability of failure. The safety factor is defined from the failure assessment curve which has a probability of failure equal to unity. The security factor is defined from an isoprobability failure curve. Three examples of this method are described concerning gas and water pipes and boiler tubes.
Guy Pluvinage, Christian Schmitt

Assessing the Complex Interaction and Variations in Human Performance Using Nonmetrical Scaling Methods

Human reliability and human performance in safety-critical systems is driven by various influences of complex interactions with the situational conditions under which the human needs to operate. Human reliability assessment methods (HRA methods) often do only consider these interrelations insufficiently, because they are missing a clear mathematical treatment of such interactions. Only simplified mathematical calculations like addition of the effects or simple dependency models are used to represent such interrelations. Better treatment of such interrelationships would require a multidimensional approach which also meets the mathematical constraints of data available for human reliability assessment. Typical constraints are for instance: adaptive change of weights and parameters relevant for human interactions in the course of a safety-critical interaction, multi actor environments, or individual styles of decision making.
At the department of human and organizational engineering and systemic design of the University Kassel/Germany, a method is being developed to overcome the constraints of HRA and herewith make human reliability assessment a key for the success of a resilient system. The method is built on the approach of the mathematical algorithm of NMDS (nonmetrical multidimensional scaling) and is applied to HRA issues in various industries such as nuclear, rail, aviation, or air traffic management. The section will outline the use of the method to enhance HRA for resilience engineering and will show examples of application in the industrial settings. It will conclude with an outline towards better inclusion of human contributions into reliability and safety.
Oliver Straeter, Marcus Arenius

Markov Modeling for Reliability Analysis Using Hypoexponential Distribution

Reliability is the probability that the system will perform its intended function under specified working condition for a specified period of time. It is the analysis of failures, their causes and consequences. Reliability analysis is the most important characteristic of product quality as things have to be working satisfactorily before considering other quality attributes. Usually, specific performance measures can be embedded into reliability analysis by the fact that if the performance is below a certain level, a failure can be said to have occurred. Markov model is widely used technique in reliability analysis. The hypoexponential distribution is used in modeling multiple exponential stages in series. This distribution can be used in many domains of application. In this chapter we find a modified and simple form of the probability density function for the general case of the hypoexponential distribution. The new form obtained is used in an application of Markovian systems to find its reliability.
Therrar Kadri, Khaled Smaili, Seifedine Kadry

Decision Making Under Uncertainty


Reliability-Based Design Optimization and Its Applications to Interaction Fluid Structure Problems

The objectives of this work are to quantify the influence of material and operational uncertainties on the performance of structures coupled with fluid, and to develop a reliability-based design and optimization (RBDO) methodology for this type of the structures. Such a problem requires a very high computation cost, which is mainly due to the calculation of gradients, especially when a finite element model is used. To simplify the optimization problem and to find at least a local optimum solution, two new methods based on semi-numerical solution are proposed in this chapter. The results demonstrate the viability of the proposed reliability-based design and optimization methodology relative to the classical methods, and demonstrate that a probabilistic approach is more appropriate than a deterministic approach for the design and optimization of structures coupled with fluid.
Abderahman Makhloufi, Abdelkhalak El Hami

Improved Planning In-Service Inspections of Fatigued Aircraft Structures Under Parametric Uncertainty of Underlying Lifetime Models

Certain fatigued structures must be inspected in order to detect fatigue damages that would otherwise not be apparent. A technique for obtaining optimal inspection strategies is proposed for situations where it is difficult to quantify the costs associated with inspections and undetected failure. For fatigued structures for which fatigue damages are only detected at the time of inspection, it is important to be able to determine the optimal times of inspection. Fewer inspections will lead to lower fatigue reliability of the structure upon demand, and frequent inspection will lead to higher cost. When there is a fatigue reliability requirement, the problem is usually to develop an inspection strategy that meets the reliability requirements. It is assumed that only the functional form of the underlying invariant distribution of time to crack detection is specified, but some or all of its parameters are unspecified. The invariant embedding technique proposed in this paper allows one to construct an optimal inspection strategy under parametric uncertainty. Under fatigue crack growth, the damage tolerance approach is considered. The new technique proposed for planning in-service inspections of fatigued structures under crack propagation requires a quantile of the t-distribution and is conceptually simple and easy to use. The numerical examples are given.
Nicholas A. Nechval, Konstantin N. Nechval

Diffuse Response Surface Model Based on Advancing Latin Hypercube Patterns for Reliability-Based Design Optimization

Since variances in the input parameters of engineering systems cause subsequent variations in the product performance, Reliability-Based Design Optimization (RBDO) is getting a lot of attention recently. However, RBDO is computationally expensive. Therefore, the Response Surface Methodology (RSM) is often used to improve the computational efficiency in the solution of problems in RBDO. In this chapter, the Diffuse Approximation (DA), a variant of the well-known Moving Least Squares (MLS) approximation based on a progressive sampling pattern is used within a variant of the First Order Reliability Method (FORM). The proposed method simultaneously uses points in the standard normal space (U-space) as well as the physical space (X-space). At last, we investigate the optimization of the process parameters for Numerical Control (NC) milling of ultrahigh strength steel. The objective functions are tool life and material removal rate. The results show that the method proposed can decrease the number of `exact' function calculations needed and reduce the computation time. It is also helpful to adopt this new method for other engineering applications.
Peipei Zhang, Piotr Breitkopf, Catherine Knopf-Lenoir-Vayssade

The Stochastic Modeling of the Turning Decision by Left-Turning Vehicles at a Signalized Intersection in a University Campus

The turning decision of a vehicle, at a signalized intersection, depends on the characteristics of the road users (e.g., vehicle, pedestrians, bicycles) and the intersection. The objective of this chapter is to estimate the turning decision of left-turning vehicles at a signalized intersection in a university campus. The signalized intersection, at the crossing of Boulevard de Maisonneuve Ouest and Rue MacKay within the Sir George Williams campus of the Concordia University (Montreal, Canada), is considered as a case study. The traffic video data were collected from 10 a.m. to 5 p.m. during the period of July–October in the year 2010. Vehicles turn at the intersection based on the gap between those and the crossing traffic, and complete the turning maneuver accepting the adequate gap (time or distance). The mean value of accepting the gap is known as the critical gap acceptance (CGA). The stochastic modeling of the left-turning decision is implemented at two stages—the estimation of the CGA by using probabilistic approaches; and the determination of the factors’ contribution by applying backpropagation neural network (BPN). The stochastic distribution functions estimate the CGA for passenger cars and other vehicles (e.g., buses, trucks, and vans) as 14.3 s and 16.5 s, respectively. The BPN models determine the bicycle distance from conflict point, platoon bicycles, existence of bicycle at conflict zone, bicycles’ speed, vehicles’ speed, pedestrians’ speed, number of vehicles passed, and vehicle moving at conflict zone are the predominant factors of left-turning decision.
Md. Shohel Reza Amin, Ciprian Alecsandru

Decision Making Behavior of Earthquake Evacuees: An Application of Discrete Choice Models

Destination choice modeling, after an earthquake, is challenging for the moderate seismic zones due to the shortage of evacuation data. Destination choice decisions are important for emergency planners to ensure the safety of evacuees, and to estimate the demand and specify the capacity of shelters. This study proposes a model for the behavior of evacuees in the aftermath of an earthquake using households as the unit of analysis. This study also considers heterogeneous mixtures of population in terms of income and ethnicity from different parts of the city. The Stated Preference (SP) method, using various hypothetical scenarios of shelter choice game in the event of a large earthquake, is applied to collect information on destination choices. Data were collected by e-mail back surveys, door-to-door surveys, and surveys in public places (e.g., at shopping malls, public parks, and student dormitories). This study proposes an error component model and a random coefficient model. The random coefficient models capture the heterogeneous responses of respondent while the error component model counts for correlations between destination choices. The results from the proposed disaggregate method are more comprehensive than those from the HAZUS method since it accounts for factors that impact decisions on destination choices.
Umma Tamima, Luc Chouinard

Preventive Maintenance and Replacement Scheduling in Multi-component Systems

Maintenance and replacement schedule is one of the most important issues in industrial-production systems to ensure that the system is sufficient. This chapter presents a multi-objective model to schedule preventive maintenance activities for a series system of several standby subsystems where each component has an increasing rate of occurrence of failure (ROCOF). The planning horizon divided into the same length and discrete intervals that in each period three different maintenance actions such as maintenance, replacement, and do nothing can be performed. The objectives of this model are maximizing the system reliability and minimizing the total system cost. Because of nonlinear and complex structure of the mathematical model, non-dominated sorting genetic algorithm (NSGA-II) is used to solve this model. Finally, a numerical example is illustrated to show the model’s effectiveness.
Seyed Ahmad Ayatollahi, Mirmehdi Seyyed-Esfahani, Taha-Hossein Hejazi


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