Reliability-Based Optimum Design of a Simple Offshore Platform Based on Genetic Algorithms

In this paper, the problem of reliability-based optimal design of simple offshore platform is studied, and a nonlinear fatigue damage model based on damage mechanics and genetic algorithms are used in the fatigue reliability optimum design of the structure under stochastic wave load. The fatigue damage model and the yield failure reliability analyzing model are used in the paper. The reliability of the models and the effectiveness of genetic algorithm are shown by the results of optimum design.

Reliability-Based Full-Life Cycle Optimum Design of Offshore Jacket Platform

Based on the consideration of operation environment and structural property, an optimum design model of offshore jacket platform is developed in this paper, namely, the reliability-based full-life cycle optimum design model. In this model, the time-dependent reliability assessment method for structural members is established by combination of the decrease of sectional size and performance deterioration of material. The initial investment, maintenance cost and failure loss cost are assembled into the model. The total cost of the platform structure system in its full service period is chosen as the objective function, and the initial reliabilities of the layer elements partitioned in advance are taken as the design variables. Different models are obtained, depending on whether the system reliability constraint is considered or not. This optimum design model can result in the lowest full-life cost and the optimal initial layer reliability of an offshore jacket platform in the design of marine structures. The feasibility of this model is illustrated with an actual jacket platform in the Liaodong Gulf as an example.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

OPTIMUM DESIGN BASED ON RELIABILITY IN STOCHASTIC STRUCTURE SYSTEMS

The optimum design method based on the reliability is presented to the stochastic structure systems （i. e., the sectional area, length, elastic module and strength of the structural member are random variables ） under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique（PNET） method were obtained. After derivation calculus ,the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.

Ergonomic Reliability Assessment of VDT Systemfor Operation Design Based on Improved BPNN and HCR under Special Circumstances

Ergonomic reliability plays a significant role in the safe operation of devices.With the spread of infectious diseases around the world,in work environments with high loads and high infection rates,medical staff work in a state of high self-protection.The use of visual display terminal(VDT)for medical equipment has undergone fundamental changes,and the traditional medical equipment human-machine interface design needs to be improved.After the completion of design and development,a VDT design enters the experimental testing stage,which has significant limitations for simulating the work of medical staff in the high-load and high-infection environments.The testing cost is high,and subjects face harsh conditions;thus,an ergonomic reliability model that can predict the use of VDT in such special high-infection and high-load circumstances must be established.An ergonomic reliability model based on an improved backpropagation neural network(BPNN)and human cognition reliability(HCR)is proposed for predicting and evaluating operation flows according tomedical equipment VDTs.Firstly,a small data sample can be used to train BPNN to generate a network that can ensure suitable accuracy.To prevent the model from falling into local optimal solutions,the bat algorithm is introduced to improve the BPNN.Compared to a traditional BPNN,the superiority of the improved BPNN is clearly demonstrated.Secondly,the HCR method is used to analyze and highlight changes in the human factor reliability of VDTs for medical equipment in different time processes and operating processes according to BPNN prediction results,to provide a reference for selecting the optimalmethod.Finally,the validity and availability of the proposedmethod are verified through an eye tracker experiment and statistical analysis results.

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

Reliability Design for Longitudinal Slope Length of Expressway

The significance and the strategies of applying the reliability design method of longitudinal slope length in expressway engineering were explored in this study.The objective is to offer insights that can be beneficial for designing longitudinal slope lengths in contemporary expressway projects,with a focus on enhancing their reliability and safety.

Optimum Design for Offshore Platform Structural Reliability

In this paper, the main problems concerning reliability design of offshore platform structure are described and the general steps for the use of Safety Coefficient Method are presented.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

Exponential System Reliability Test Design Based on Information Fusion

By analyzing the shortage of reliability test design and thinking over the producer's risk and consumer's risk, the information fusion technology is used to set up a reliability test design model( RTDM). By analyzing the demands and constraint conditions of the RTDM and with applications of Bayesian approach and Monte Carlo method( MCM),this paper puts forward the exponential distributed subsystems and the information fusion technology among them. According to the posteriori risk criteria,formulas of producer's risk and consumer's risk were also inferred,and with the help of Matlab software,selection of the optimum test plan was solved. Finally,validity of the model had been proved by a test of series parallel system.

Reliability Design of Ice-Maker System Subjected to Repetitive Loading

Parametric Accelerated Life Testing (ALT) was used to improve the reliability of ice-maker system with a fractured helix upper dispenser in field. By using bond graphs and state equations, a variety of mechanical loads in the assembly were analyzed. The acceleration factor was derived from a generalized life-stress failure model with a new load concept. To reproduce the failure modes and mechanisms causing the fracture, new sample size equation was derived. The sample size equation with the acceleration factor also enabled the parametric accelerated life testing to quickly reproduce early failure in field. Consequently, the failure modes and mechanisms found were identical with those of the failed sample. The design of this testing should help an engineer uncover the design parameters affecting the reliability of fractured helix upper dispenser in field. By eliminating the design flaws, gaps and weldline, the B1 life of the redesign of helix upper dispenser is now guaranteed to be over 10 years with a yearly failure rate of 0.1% that is the reliability quantitative test specifications (RQ).

Reliability Design for Impact Vibration of Hydraulic Pressure Pipeline Systems

The research of reliability design for impact vibration of hydraulic pressure pipeline systems is still in the primary stage,and the research of quantitative reliability of hydraulic components and system is still incomplete.On the condition of having obtained the numerical characteristics of basic random parameters,several techniques and methods including the probability statistical theory,hydraulic technique and stochastic perturbation method are employed to carry out the reliability design for impact vibration of the hydraulic pressure system.Considering the instantaneous pressure pulse of hydraulic impact in pipeline,the reliability analysis model of hydraulic pipeline system is established,and the reliability-based optimization design method is presented.The proposed method can reflect the inherent reliability of hydraulic pipe system exactly,and the desired result is obtained.The reliability design of hydraulic pipeline system is achieved by computer programs and the reliability design information of hydraulic pipeline system is obtained.This research proposes a reliability design method,which can solve the problem of the reliability-based optimization design for the hydraulic pressure system with impact vibration practically and effectively,and enhance the quantitative research on the reliability design of hydraulic pipeline system.The proposed method has generality for the reliability optimization design of hydraulic pipeline system.

Impact of Improving Design Factor over 0.72 on the Safety and Reliability of Gas Pipelines and Feasibility Justification

Many years experience of the operation of high stress (>72% specified minimum yield strength, SMYS) gas pipelines and statistical analysis results of pipeline incidents showed that the operating pipelines at stress levels over 72% SMYS have not presented problems in USA and Canada, and design factor does not control incidents or the safety of pipelines. Enhancing pipeline safety management level is most important for decreasing incident rate. The application history of higher design factors in the U.S and Canada was reviewed. And the effect of higher factors to the critical flaw size, puncture resistance, change of reliability with time, risk level and the arrest toughness requirements of pipeline were analyzed here. The comparison of pipeline failure rates and risk levels between two design factors (0.72 and 0.8) has shown that a change in design factor from 0.72 to 0.8 would bring little effect on failure rates and risk levels. On the basis of the analysis result, the application feasibility of design factor of 0.8 in China was discussed and the related suggestions were proposed. When an operator wishes to apply design factor 0.8 to gas pipeline, the following process is recommended: stress level of line pipe hydro test should be up to 100% SMYS, reliability and risk assessment at the design feasibility or conceptual stage should be conducted, Charpy impact energy should meet the need of pipeline crack arrest; and establish and execute risk based integrity management plan. The technology of pipeline steel metallurgy, line pipe fabrication and pipeline construction, and line pipe quality control level in China achieved tremendous progresses, and line pipe product standards and property indexes have come up to international advanced level. Furthermore, pipeline safety management has improved greatly in China. Consequently, the research for the feasibility of application of design factor of 0.8 in China has fundamental basis.

Reliability Simulation and Design Optimization for Mechanical Maintenance

Reliability model of a mechanical product system will be newly reconstructed and maintenance cost will increase because failed parts can be replaced with new components during service, which should be accounted for in system design. In this paper, a reliability model and reliability-based design optimization methodology for maintenance are presented. First, based on the time-to-failure density function of the part of the system, the age distributions of all parts of the system during service are investigated, a reliability model of the mechanical system for maintenance is developed. Then, reliability simulations of the systems with WeibuU probability density functions are performed, the system minimum reliability and steady reliability for maintenance are defined based on reliability simulation during the life cycle of the system. Thirdly, a maintenance cost model is developed based on replacement rates of the parts, a reliability-based design optimization model for maintenance is presented, in which total life cycle cost is considered as design objective and system reliability as design constrain. Finally, the reliability-based design optimization methodology for maintenance is used to design of a link ring for the chain conveyor, which shows that optimal design with the lowest maintenance cost can be obtained, and minimum reliability and steady reliability of the system can satisfy requirement of system reliability during service of the chain conveyor.

RESEARCH PROGRESS ON STRUCTURAL FATIGUE RELIABILITY DESIGN AND ANALYSIS METHODS OF CHINESE RAILWAY VEHICLES

A state-of-art review is given to the new advances on fatigue reliability design and analysis methods of Chinese railway vehicle＇s structures. First, the structures are subject to a complicated random fatigue stressing history and this history should be determined by combining dynamic simulation and on-line inspection. Second, the random fatigue constitutions belong to an intrinsic fatigue phenomenon and a probabilistic model is developed to well describe them with two measurements of survival probability and confidence, similar model is also presented for the random stress-life rela- tions and extrapolated appropriately into Song fatigue life regime. Third, concept of the fatigue limit should be understood as the fatigue strength at a given fatigue life and a so-called local Basquin model method is proposed for measuring the random strengths. In addition, drawing and application methods of the Goodman-Smith diagram for integrally characterizing the random fatigue strengths are established in terms of ten kilometers. Fourth, a reliability stress-based method is constructed with a consideration of the random constitutive relations. These new advances form a new frame work for railway fatigue reliability design and analysis.

Time-Variant Reliability-Based Multi-Objective Fuzzy Design Optimization for Anti-Roll Torsion Bar of EMU

Although various types of anti-roll torsion bars have been developed to inhibit excessive roll angle of the electric multiple unit(EMU)car body,it is critical to ensure the reliability of structural design due to the complexity of the problems involving time and uncertainties.To address this issue,amulti-objective fuzzy design optimization model is constructed considering time-variant stiffness and strength reliability constraints for the anti-roll torsion bar.A hybrid optimization strategy combining the design of experiment(DoE)sampling and non-linear programming by quadratic lagrangian(NLPQL)is presented to deal with the design optimization model.To characterize the effect of time on the structural performance of the torsion bar,the continuous-time model combined with Ito lemma is proposed to establish the time-variant stiffness and strength reliability constraints.Fuzzy mathematics is employed to conduct uncertainty quantification for the design parameters of the torsion bar.A physical programming approach is used to improve the designer’s preference and to make the optimization results more consistent with engineering practices.Moreover,the effectiveness of the proposed method has been validated by comparing with current methods in a practical engineering case.

DYNAMIC RESPONSE OPTIMIZATION DESIGN FOR ENGINEERING STRUCTURES BASED ON RELIABILITY

In many practical structures, physical parameters of material and applied loads have random property.To optimize this kind of structures,an optimum mathematical model was built.This model has reliability constraints on dynamic stress and displacement and upper & lower limits of the design variables. The numerical characteristic of dynamic response and sensitivity of dynamic response based on probability of structure were deduced respectively. By equivalent disposing, the reliability constraints were changed into conventional forms. The SUMT method was used in the optimization process.Two examples illustrate the correctness and practicability of the optimum model and solving approach.

Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization （RBDO） is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a ＂black-box＂ and their gradients are not available or not reliable. On the basis of the reliable design space （RDS） concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing （RSP） approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.