Reliability-based Structural Design Research Articles

Stochastic Analysis of Water Hammer and Applications in Reliability-Based Structural Design for Hydro Turbine Penstocks

The randomness of transient events, and the variability of its associated dependencies, ensures that water hammer and surges in a pressurized pipe system are inherently stochastic. To improve reliability-based structural design, a stochastic transient model is developed for water conveyance systems in hydropower plants. The statistical characteristics of key factors in boundary conditions, initial states, and hydraulic system parameters are analyzed on the basis of a large record of observed data from hydro plants in China; the probability distributions of annual maximum water hammer pressures are then simulated by using a Monte Carlo method and verified with an analytical probabilistic model for a simplified pipe system. The key loading characteristics (annual occurrence, sustaining period, and probability distribution) are introduced and discussed. By using an example of penstock structural design, it is shown that the total water hammer pressure should be split into two individual random variable loads—the steady/static pressure and the water hammer pressure rise during transients—and that different partial load factors should be applied to individual loads to reflect specific physical and stochastic features. Particularly, the normative load (usually the unfavorable value at a 95-percentage level) for steady/static hydraulic pressure should be taken from the probability distribution of its maximum values over a pipe’s design life, whereas for the water hammer pressure rise, as the second variable load, the probability distribution of its annual maximum values determines its normative load.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

A Method for Materials Selection in Reliability-Based Design Diagram of Structural Components under Creep-Fatigue Damage Mode

A new method for materials selection in reliability-based design was applied to the high temperature structural components under creep-fatigue damage mode. The creep-fatigue interaction law was formulated in terms of creep time fraction (creep damage) and fatigue cycle fraction (fatigue damage) using pure creep and pure fatigue material properties referring NIMS creep and fatigue datasheets for ferritic heat resistant steels such as 1Cr-1Mo-0.25V steel forging, 12Cr-1Mo-1W-0.3V steel bar and 2.25Cr-1Mo steel plate. The statistical distribution under the creep-fatigue damage mode was fitted well with the two-dimensional log-normal distribution function but the scatter bands of creep-fatigue data were considerably larger compared with the cases using pure creep and pure fatigue damage distributions. Once the ratio of creep damage to fatigue damage was fixed, the confidence limit could be restricted within more reasonable range for design application. The diagram was expressed by the relationship between creep stress vs. fatigue strain range for those three materials and the apparent superiority of 12Cr-1Mo-1W-0.3V steel bar to other materials was demonstrated. Thus this diagram was proved to be an effective tool for decision making of materials selection and structural reliability-based design even at the very initial stage of design process, that is, the front-loading design of components.

Reliability-based design and optimization of adaptive marine structures

The objectives of this work are to quantify the influence of material and operational uncertainties on the performance of self-adaptive marine rotors, and to develop a reliability-based design and optimization methodology for adaptive marine structures. Using a previously validated 3D fluid–structure interaction model, performance functions are obtained and used to generate characteristic response surfaces. A first-order reliability method is used to evaluate the influence of uncertainties in material and load parameters and thus optimize the design parameters. The results demonstrate the viability of the proposed reliability-based design and optimization methodology, and demonstrate that a probabilistic approach is more appropriate than a deterministic approach for the design and optimization of adaptive marine structures that rely on fluid–structure interaction for performance improvement.

Performance-Based Design of Residential Wood-Frame Buildings for Flood Based on Manageable Loss

The Structural Engineering Institute of the American Society of Civil Engineers Committee on the Reliability-Based Design of Wood Structures recently completed a special project entitled “The next step for ASCE 16: Performance-based design of wood structures.” This paper presents the methodology and several illustrative examples of the design of residential wood-frame buildings for flood. The control variable of interest is losses in terms of either U.S. dollars or percent of construction costs. To do this, assembly-based vulnerability is coupled with existing durability data for wood and wood-based products; and when not available, logical assumptions were required. A series of illustrative examples are shown with various mitigation strategies applied to investigate the change in loss fragilities, and subsequently, economic risk if the fragility is recoupled with the flood hazard curve. The method is shown to work efficiently and the results are logical, thus it may find application by aiding developers, land-use planners, engineers, and potentially owners of wood-frame buildings in their design and retrofit decisions.

Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications

A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system’s state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to H2 (i.e., minimum variance) controller synthesis is also examined.

Tradeoff of Weight and Inspection Cost in Reliability-Based Structural Optimization

This paper develops a methodology for cost-optimal, reliability-based structural design and inspection planning of aircraft structures subject to fatigue damage growth. An optimization problem is formulated to minimize the expected lifetime cost while maintaining a minimum acceptable reliability level. The effect of structural design and inspection schedule on operational cost and reliability is explored. The optimization parameters are the inspection times, types, and structural thickness. A computational technique using a combination of Monte Carlo simulation to estimate the crack size distribution after inspections and first-order reliability method to calculate failure probability at any time is developed to expedite reliability calculations. The paper shows that the simultaneous design of the structure and inspection regime allows trading the cost of additional structural weight against the inspection cost.

Fuzzy reliability-based optimum design of laminated composites

In conventional reliability-based optimum design of structures, the reliability is computed based on the probability assumption, and the design objective and constraint are considered as deterministic ones. In many cases, however, there exist some fuzzy factors in the design objective and constraint functions. In this paper, the fuzzy reliability and fuzzy constraint are introduced to establish the fuzzy reliability-based optimum model for laminated composites. The examples show that the method developed in this paper can give consideration to both the reliability demand and the economic aspect of a structure. Since the fuzzy reliability-based optimum design is a ‘soft’ design, the present results provide a new methodology for the effective evaluation of structural reliability and bring us an alternative optimum design idea.

Specification of design criteria based on probabilistic measures of design performance

To date, reliability-based structural design standards have been developed using deterministic design procedures that are formulated to achieve target levels of structural reliability (target safety indices) without requiring explicit reliability calculations. Target safety indices have been selected to match typical safety levels in previous design standards. However, the current levels of structural safety are not necessarily the most appropriate, and it has been suggested that explicit risk-based measures of structural performance should be used to optimise the target levels of design performance. Explicit risk-based measures could be used to underpin deterministic design requirements or they could be used directly for explicit risk-based design. The paper discusses the use of risk-based measures in the development and application of design Standards. The paper also discusses broader issues related to the development of design Standards, including the influence of international standardisation.

2117 破損モード間の相関を有する限界状態の標準化空間での評価法

This study deals with the standardized transformation methods for structural reliability-based design and these evaluations by considering the mathematical approaches of reliability index for its design safety. In practice, several design variables are estimated as random variables according to the failure phenomenon. i.e. normal and/or non-normal distributions. In addition, there are correlations between these random variables. Then, we reconsider evaluation spaces as standardized space throughout some transformation methods. And we investigate some characteristics of limit state functions on various design spaces by using simulation.

Some observations on performance-based and reliability-based seismic design of asymmetric building structures

In previous work by the second author and others, a framework for a reliability-based, performance-based seismic design procedure was presented. That framework was based on static pushover analyses of two-dimensional models of building structures. In this paper, some preliminary observations and results are presented from a study in which the framework is extended to be used with three-dimensional analysis models to explicitly account for the torsional behavior of asymmetric building structures.

2204 信頼楕円体を考慮した最適信頼性設計法に関する一考察

This study deals with an optimization for structural reliability-based design and these assessments by considering the statistical uncertainties of reliability index. Although the expected total cost which is composed of the initial cost and the cost for failure of the structural system has been investigated, it is crucial to consider the annual prediction cost during the life duration. It is also important to evaluate the cost not only on structural failure but also on designer's faults according to the statistical uncertainties of reliability index. Furthermore, it is necessary that the cost of the reliability test is taken into accunt in determining the expected total cost because uncertainties of parameters are strongly dependent upon the quality control, material test or random sampling stimulation. In this study, the optimization and its assessment for an extended model which includes the cost mentioned above are suggested by using confidence ellipsoid. In addition, the influence analysis about the statistical uncertainty of reliability index is perfomed by numerical calculation.

A method for reliability-based economic design of building structures

In limit states design codes for building structures, the load and resistance factors are derived based on a ‘;target’ reliability index, which is determined based on a code calibration process. It is not clear whether the target reliability index selected through the code calibration is optimal with respect to the cost, because through calibration the structural safety is achieved quantitatively while the economic aspects are only considered qualitatively. The intention of the present paper is to formulate a basic approach to reliability-based economic design, based on structural reliability theory. The focus of the paper is to derive an analytical solution to optimized reliability index. A parametric study is conducted for sensitivity analysis of the optimal reliability index to different variables. Finally, the application of the solution to design codes, i.e. determining load and resistance factors in design formulae, is outlined. Dans les codes de conception d'états limite se rapportant à la construction des structures de bâtiments, la charge et les facteurs de résistance reposent au départ sur un index de fiabilitié ‘cible’, qui est basé sur un processus de calibrage de code. Il n'est pas possible de savoir si l'index de fiabilitié cible choisi par le calibrage de code est optimal en ce qui concerne le coût parce que lors du calibrage, la sécurité structurelle est évaluée de façon quantitative. L'objectif de cet article est de formuler une appréciation de référence sur la conception reposant sur la fiabilité économique, basée sur la théorie de fiabilité structurelle; le point fort de ce texte est de trouver une solution analytique afin d'optimiser l'index de fiabilité. Une étude paramétrique est conduite pour analyser la sensibilité de la fiabilitié optimale de l'index par rapport aux diffeérentes variables. Au total, est proposée une solution consistant à concevoir des codes, c'est-à-dire la détermination de la charge et des facteurs de résistance sous l'aspect de formules.

An Outer Approximations Approach to Reliability-Based Optimal Design of Structures

We present a new formulation of the problem of minimizing the initial cost of a structure subject to a minimum reliability requirement, expressed in terms of the so-called design points of the first-order reliability theory, i.e., points on limit-state surfaces that are nearest to the origin in a transformed standard normal space, as well as other deterministic constraints. Our formulation makes it possible to use outer approximations algorithms for the solution of such optimal design problems, eliminating some of the major objections associated with treating them as bilevel optimization problems. A numerical example is presented that illustrates the reliability and efficiency of the algorithm.

Code Development for Ship Structures—A Demonstration

A demonstration summary of a reliability-based structural design code for ships is presented for two ship types: a cruiser and a tanker. One reason for the development of such a code is to provide specifications which produce ship structure having a weight savings and/or improvement in reliability relative to structure designed by traditional methods. Another reason is to provide uniform safety margin for ships within each type. For both ship types, code requirements cover four failure modes: hull girder bulkling, unstiffened plate yielding and buckling, stiffened plate buckling, and fatigue of critical detail. Both serviceability and ultimate limit states are considered. Because of limitation on the length, only hull girder modes are presented in this paper. Code requirements for other modes will be presented in future publication. A specific provision of the code will be safety check expression, which, for example, for three bending moments (still water Ms, wave Mw, and dynamic Md), and strength Mu, might have the form, following the partial safety factor format: γsMs+γwMw+γdMd≤φMu γs, γw, γd, and φ are the partial safety factors. The design variables (M’s) are to be taken at their nominal values, typically values in the safe side of the respective distributions. Other safety check expressions for hull girder failure that include load combination factors, as well as consequence of failure factors, are considered. This paper provides a summary of safety check expressions for the hull girder modes.

Reliability-Based Structural Design with Markov Decision Processes

An optimal structural design is defined as the synthesis of a structural initial design and its maintenance/management policy over a design lifetime. Using a Markov decision process (MDP) model and structural reliability theory, a designer at the initial design stage is able to incorporate a reliability-based model of the lifetime process of the structure. The advantage of MDP is that it systematically characterizes the entire process, including decisions, costs, and system performance. It also provides a solution of this dynamic problem through a static method, thus retaining computational tractability. A long-term maintenance policy under the criterion of minimum expected lifetime cost can be found with respect to the chosen initial design, and used to select an optimum initial design to minimize cost and maintain acceptable reliability. For an existing structure, the approach gives a decision maker a future maintenance policy leading to identification of the minimum discounted expected future cost of the structure, based on its present condition, and maintains acceptable reliability.

Reliability-based structural optimal design using the Neumann expansion technique

The reliability-based structural optimization formulated using the advanced first order second moment (AFOSM) method contains a suboptimization process. This corresponds to obtaining the most probable failure point of the failure constraint and requires excessive computational work to solve the random state equation with random parameters in the stiffness matrix. This paper presents a numerically efficient method to reduce the computational effort by using the Neumann expansion technique to deal with the random state equation in the suboptimization process. Several examples of truss and beam structures with uncertainties in design variables and loads, including non-normal distributions, are taken. The results show the method can give accurate solutions and reduce computation time.

Multi-Objective Optimization Of Reliability-based Structural Design

Both reliability-based structural design and multi-objective optimization techniques have received extensive attention. The proposed approach, using multi-objective optimization strategies, aims to deal with reliability-based. structural design optimization problems with multi-pie design goals. Among reliability analysis, a transformation method based on the advanced firsl order second moment (AFOSM) method is used to evaluate the failure probability of single failure mode, and the Cornell’s upper bound is used to estimate system failure probability with multifailure mode. In multi-objective optimization, the promising surrogate worth trade-off method (SWT) is used. Through the numerical solution of two design examples. it is concluded that the multi-objective 0plimization approach, which improvc.~ the decision-making capability of designers or decision makers and it is an effective design tool for engineers in the solution of multi-objective problems with uncertainties.

Continuum Sensitivity Method for Reliability-Based Structural Design and Optimization*

ABSTRACT 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...

System reliability and redundancy in structural design and evaluation

Several reliability-based structural design and evaluation specifications for buildings, bridges, and offshore platforms have been proposed and implemented in North America, Asia, Australia and Europe. Thus far, however, these are largely limited to individual structural component checks and do not generally include requirements of system reliability and redundanry. The main purpose of this paper is to contribute to the development of more rational system reliability-based structural design and evaluation specifications. In this context, effects of material behavior, correlations, variabilities of resistances and loads, resistance sharing, structural damage, and number of members, on both the system reliability and redundancy of a parallel system are investigated, and a framework for including system effects in structural design and evaluation specifications is proposed.