Optimum Safety Factor Research Articles

Reverse optimum safety factor approaches as effective tools for reliability-based topology optimization with application to cementless hollow stems used in total hip replacement

Reverse optimum safety factor approaches as effective tools for reliability-based topology optimization with application to cementless hollow stems used in total hip replacement

Reverse Versus Inverse Optimum Safety Factor Approaches for Reliability-based Topology Optimization

Reverse Versus Inverse Optimum Safety Factor Approaches for Reliability-based Topology Optimization

Probabilistic stability analysis of failed and stable cases of coal pillars

The conventional design criterion of the safety factor for pillar stability is a deterministic approach characterised by non-random and exact values of its input parameters i.e. strength and stress. The integrity of pillars often jeopardized when some fluctuations or deviations occur in their strength and stress due to uncertainties in field conditions. To counter these unknown fluctuations or deviations, the coal pillars are designed with safety factors greater than unity and their exact values are selected based on local geomining factors. This practice does not guarantee stability against the geomining uncertainties and consequently lock-up the coal in the bigger size of the pillars. Therefore, to assess the variability in the input parameters in pillar design, this paper presents a probabilistic approach to analyse the stability of coal pillars considering the cases of stable and failed pillars in Indian coalfields. The databases of input design parameters are collected for stable and failed coal pillars from different Indian coal mines. The probabilistic distribution fittings of strengths, stresses and safety factors of stable flat, stable inclined, failed flat and failed inclined pillar cases are derived to know their means and standard deviations. The Monte Carlo Simulation and the First Order Reliability Method have been implemented to solve the limit state functions. The failure probabilities estimated for stable flat, stable inclined, failed flat and failed inclined cases are 0.29, 0.28, 0.56, and 0.99 respectively. The analysis recommends the safety factors of corresponding threshold failure probabilities of stable flat pillars as 1.61 and for stable inclined pillars as 1.41 in Indian mines with the ranges of design parameters considered in their databases. Therefore, the probabilistic stability analysis can provide an additional design criterion to select the optimum safety factor of pillars for improved recovery rates in coal mines.

A Reliability optimization of a coupled soil structure interaction applied to an offshore wind turbine.

In this paper, a dynamic analysis of an offshore wind turbine (OWT) considering soil structure interaction (SSI) is performed. The design of these highly expensive structures tends to find the best compromise between cost and safety. To do so, a coupling between reliability-based design optimization and the numerical model of the OWT is required. An extension of some RBDO methods such as the Optimum Safety Factor (OSF), Hybrid Method (HM) in the case of an OWT considering SSI is then proposed. Based on the efficiency of these methods, the Robust Hybrid Method (RHM) is then applied to overcome the drawbacks of the current methods. By comparing it results to the classical ones, the advantages and the efficiency of the RHM is then presented. The effects of the SSI on the optimal configuration is then discussed. Finally, the RHM is applied to an improoved wind turbine model containig 18 design variables to determine the optimal structural configuration of a 2 MW OWT.

Reliability-based topology optimization as effective strategy for additive manufacturing: Influence study of geometry uncertainty on resulting layouts

The effectiveness of Additive Manufacturing (AM) is to fabricate very complex configurations that can be resulting layouts from topology optimization. The topology optimization can be classified into two models: Deterministic Topology Optimization (DTO) and Reliability-Based Topology Optimization (RBTO). The DTO may lead to unrealistic designs since it provides a single solution for a given design space. However, the RBTO is considered as a topology generator which provides several layouts. This way the designer can overcome the manufacturing constraint problems such as overhang, minimum feature size, anisotropy …, that may lead to a failure during the production process. Two RBTO strategies based on the Inverse Optimum Safety Factor (IOSF) are presented in this work: Objective-Based IOSF Approach and Performance-Based IOSF Approach. These approaches can be efficiently used as a topology regularization procedure. In addition, to consider the geometry uncertainty, different layouts can be obtained when increasing the reliability index values in order to provide more choices for designers. The geometry uncertainty is applied here in a manner to not affect the boundary conditions which can lead to change the structure’s functioning. The resulting RBTO layouts in this work, are too organic which leads to manufacturability problems. To use the conventional manufacturing procedures, classic CAD primitives must be used to simplify the geometry, that may lead to lose the optimality. Because of this manufacturability difficulty, AM is then obligatory. The RBTO being a good design tool for AM, paves the way to the next developments to overcome other fabrication constraints considering the reliability index values as a topology regulator.

An efficient reliability-based design optimization study for PCM-based heat-sink used for cooling electronic devices

Nowadays, development of new technologies requires efficient mechatronic components which needs more sophisticated cooling systems. Furthermore, phase change material (PCM) based heat sinks presents an appropriate technique for electronic devices. Then, the aim of this work is to propose an efficient methodology that determines an optimal design of such a PCM-based cooling system. Despite of the satisfaction of the optimal solution founded by the deterministic design optimization (DDO), the reliability level is not controlled. For this reason, reliability-based design optimization (RBDO) studies were performed. In fact, RBDO approaches aim to find the best compromise between safety and cost by taking into consideration uncertainties for the studied model. Therefore, several methods are studied, such as the optimum safety factor approach and the hybrid method. Yet, the application of these methods is limited only to linear materials. Hence, this study presents an extension in the case of nonlinear materials. In addition, to overcome problems of the classical hybrid approach, a Robust Hybrid Method (RHM) is proposed. A numerical application is used to study the different DDO and RBDO methods. Then, the efficiency of the RHM method for PCM-based heat sinks is verified.

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

Introduction. The Deterministic Topology Optimization model provides a single solution for a given design space, while the Reliability-Based Topology Optimization model provides several reliability-based topology layouts with high-performance levels. The objective of this work is to develop two strategies that can provide the designer with two categories of resulting topologies. Materials and Methods. Two alternative approaches based on the Inverse Optimum Safety Factor are developed: the first one is called the Objective-Based IOSF Approach and the second one is called Performance-Based IOSF Approach. When dealing with bridge structures, the uncertainty on the input parameters (boundary conditions, material properties, geometry, etc.) and also output parameters (compliance, etc.) should not be ignored. The sensitivity analysis is the fundamental idea of both developed approaches, identifies the role of each parameter on the structural performance. In addition, the optimization domain choice is important when eliminating material that should not affect the structure functioning. Results. Two numerical examples on a 2D bridge structure are presented to demonstrate the efficiency of the developed approaches. When considering a certain reliability level, the Reliability-Based Topology Optimization leads to two different configurations relative to the Deterministic Topology Optimization one. When increasing the reliability levels, the quantity of materials decreases that leads to an increase in the number of holes in the structures. Discussion and Conclusion. In addition to their simplified implementation, the developed alternative approaches can be considered as two generative tools to produce two different categories (families) of solutions where an alternative choice between two functions (objective/performance) is presented.

Reliability-based topology optimization using inverse optimum safety factor approaches

The Deterministic Topology Optimization (DTO) model generates a single solution for a given design space, while the Reliability-Based Topology Optimization (RBTO) model provides several reliability-based topology layouts with high performance levels. The objective of this work is to develop two approaches, which can lead to two new topology categories. The two alternative approaches; namely Objective-Based Inverse Optimum Safety Factor (IOSF) and Performance-Based IOSF, are developed based on the IOSF. When designing a structure, the uncertainty in the input parameters influences the output parameters and thus a sensitivity analysis was carried out for the developed approaches. The analysis shows the influence of each parameter on the structure performance. Two numerical applications are presented to show the effectiveness of the developed approaches. When considering a certain reliability level, unlike the DTO, the RBTO results in different configurations. Unlike the results of the previous studies, the consideration of the geometry uncertainty reveals that the structural volume increases as the reliability level increases. Additionally, the developed approaches can be considered as two generative tools that can produce two different categories/families of solutions.

A modified hybrid method for a reliability-based design optimization applied to an offshore wind turbine

In this article, a dynamic analysis of an offshore wind turbine (OWT) considering soil structure interaction (SSI) is performed. The design of these highly expensive structures tends to find the best compromise between cost and safety. To do so, a coupling between reliability-based design optimization and the numerical model of the OWT is required. An extension of some RBDO methods such as the optimum safety factor, hybrid method, and the robust hybrid method in the case of an OWT considering SSI is then proposed. Results show that these techniques lead to an optimal configuration in the unsafe zone. For this, a modified hybrid method (MHM) is developed in order to overcome the drawback of the other methods. By comparing it results to the classical ones, the advantages and the efficiency of the MHM is then presented.

Reliability-based design optimization for heat flux analysis of composite modular walls using inverse reliability assessment method

Abstract Modular composite walls are widely used in many industrial applications such as thermal applications, different kinds of heat exchangers … etc. These structures allow to rapidly and economically divide spaces and to create separate areas. Different size and shape of a wall can be combined and connected to build permanent or temporary walls that meet a space's specific needs. The integration of reliability and optimization concepts into the modular composite wall design seeks to provide structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the classical coupling between the numerical modeling, the reliability analyses and the optimization methods leads to a high computational cost and weak convergence stability. To overcome these difficulties, several developments have been carried out during the last three decades. Some of these approaches treat the convergence stability such the hybrid approaches and the others treat the computing time problem such optimum safety factor approaches. In this paper, a new method called Inverse Reliability Assessment Method (IRAM) is proposed to deal with a single type of variables for the studied optimization problem. It consists of performing the optimization process to find the Failure Point (FP) and next an inverse assessment of the reliability level is carried out to find the RBDO solution. A numerical application on the heat flux analysis is carried out using two computational procedures on two different cases of a composite modular walls. The first procedure is to assess the reliability level of the given point and the second one is to improve the resulting values, through the RBDO using the proposed method (IRAM).

Efficient optimum safety factor approach for system reliability-based design optimization with application to composite yarns

Introduction. The integration of reliability and optimization concepts seeks to design structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to very high computational cost and weak convergence stability. Materials andMethods. Several methods have been developed to overcome these difficulties. The methods called Reliability Index Approach (RIA) and Performance Measure Approach (PMA) are two alternative methods. RIA describes the probabilistic constraint as a reliability index while PMA was proposed by converting the probability measure to a performance measure. An Optimum Safety Factor (OSF) method is proposed to compute safety factors satisfying a required reliability level without demanding additional computing cost for the reliability evaluation. The OSF equations are formulated considering RIA and PMA and extended to multiple failure case.Research Results. Several linear and nonlinear distribution laws are applied to composite yarns studies and then extended to multiple failure modes. It has been shown that the idea of the OSF method is to avoid the reliability constraint evaluation with a particular optimization process.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of decoupling the optimization and the reliability analyses. It provides designers with efficient solutions that should be economic satisfying a required reliability level. It is demonstrated that the RBDO compared to OSF has several advantages: small number of optimization variables, good convergence stability, small computing time, satisfaction of the required reliability levels.

An approach for the reliability-based design optimization of shape memory alloy structure

The reliability-based design optimization looks for the best compromise between safety and cost taking into account uncertainties in the structure. This methodology does not only provide an improved design but also a high level of confidence. As a result, the reliability analysis is integrated in the optimization loop in order to improve the performance of the structure while maintaining the assumed reliability level. For that reason, several formulations, such as optimum safety factor method and hybrid method (HM) are developed to reach this purpose. These methods have been applied only to linear materials. However, nowadays, there are increasing interests in the use of nonlinear materials such as shape memory alloy. In this context, this article proposes an extension of these approaches in the case of nonlinear material in order to study their efficiency. A method called robust hybrid method is proposed to overcome the problem of classical hybrid one. A numerical application is then used in order to present the advantages of the modified HM for treating the problem of structures with nonlinear material.

Inverse Optimum Safety Factor Method for Reliability-Based Topology Optimization Applied to Free Vibrated Structures

Introduction. The classical topology optimization leads to a prediction of the structural type and overall layout, and gives a rough description of the shape of the outer as well as inner boundaries of the structure. However, the probabilistic topology optimization (or reliability-based topology optimization) model leads to several reliability-based topologies with high performance levels. The objective of this work is to provide an efficient tool to integrate the reliability-based topology optimization model into free vibrated structure. Materials and Methods. The developed tool is called inverse optimum safety method. When dealing with modal analysis, the choice of optimization domain is highly important in order to be able to eliminate material taking account of the constraints of fabrication and without affecting the structure function. This way the randomness can be applied on certain boundary parameters. Results. Numerical applications on free vibrated structures are presented to show the efficiency of the developed strategy. When considering a required reliability level, the resulting topology represents a different topology relative to the deterministic resulting one. Discussion and Conclusion. In addition to its simplified implementation, the developed inverse optimum safety factor strategy can be considered as a generative tool to provide the designer with several solutions for free vibrated structures with different performance levels.

An efficient optimization based on the robust hybrid method for the coupled acoustic–structural system

In this article, an analytical formulation of the response of the coupled acoustic–structural system were performed. The reliability-based design optimization (RBDO) aims to find the best compromise between cost and safety. We present here an extension of the Hybrid Method and the Optimum Safety Factor method in case of coupled acoustic-structural problems. The Robust Hybrid Method (RHM) is then applied in order to overcome the difficulties of the other methods. Numerical examples showed the effectiveness and efficiency of the RHM on acoustic–structural systems. Results showed that the optimal solution obtained by the RHM is more reliable than the other methods.

RELIABILITY-BASED DESIGN OPTIMIZATION USING OPTIMUM SAFETY FACTORS FOR LARGE-SCALE PROBLEMS

Introduction. Reliability-Based Design Optimization (RBDO) model reduces the structural weight in uncritical regions, does not only provide an improved design but also a higher level of confidence in the design.Materials and Methods. The classical RBDO approach can be carried out in two separate spaces: the physical space and the normalized space. Since very many repeated researches are needed in the above two spaces, the computational time for such an optimization is a big problem. An efficient method called Optimum Safety Factor (OSF) method is developed and successfully put to use in several engineering applications. Research Results. A numerical application on a large scale problem under fatigue loading shows the efficiency of the developed RBDO method relative to the Deterministic Design Optimization (DDO). The efficiency of the OSF method is also extended to multiple failure modes to control several out-put parameters, such as structural volume and damage criterion.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of a single optimization problem to evaluate the design point, and a direct evaluation of the optimum solution considering OSF formulations. It provides designers with efficient solutions that should be economic, satisfying a required reliability level with a reduced computing time.

Reliability based design optimization of coupled acoustic-structure system using generalized polynomial chaos

In this work, an analytical formulation and numerical implementation of the response of the coupled structure-acoustic system were performed. The acoustic pressure inside the cavity as well as the plate displacement are analyzed. This study is combined with a probabilistic analysis to account for variability of different parameters, considered as random variables, which are material properties. A reliability based design optimization (RBDO) using the generalized polynomial chaos (gPC) is addressed. In order to reduce the computational cost of the classical approach of RBDO problem, the optimum safety factor (OSF) method coupled with the gPC procedure is applied to the coupled acoustic-structure systems. Numerical examples showed the effectiveness and efficiency of the OSF based on gPC for the reliability optimization of the structural-acoustic system with probabilistic random variables.

Reliability Based Design Optimization for Multiaxial Fatigue Damage Analysis Using Robust Hybrid Method

AbstractThe purpose of the Reliability-Based Design Optimization (RBDO) is to find the best compromise between safety and cost. Therefore, several methods, such as the Hybrid Method (HM) and the Optimum Safety Factor (OSF) method, are developed to achieve this purpose. However, these methods have been applied only on static cases and some special dynamic ones. But, in real mechanical applications, structures are subject to random vibrations and these vibrations can cause a fatigue damage. So, in this paper, we propose an extension of these methods in the case of structures under random vibrations and then demonstrate their efficiency. Also, a Robust Hybrid Method (RHM) is then developed to overcome the difficulties of the classical one. A numerical application is then used to present the advantages of the modified hybrid method for treating problem of structures subject to random vibration considering fatigue damage.

Reliability-based design optimization of shank chisel plough using optimum safety factor strategy

Reliability integration into tillage machine design process is a new strategy to overcome the drawbacks of classical design approaches and to achieve designs with a required reliability level. Furthermore, design optimization of soil tillage equipments under uncertainty seeks to design structures which should be both economic and reliable. The originality of this research is to develop an efficient methodology that controls the reliability levels for complex statistical distribution cases of random tillage forces. This developed strategy is based on design sensitivity concepts in order to determine the influence of each random parameter. The application of this method consists in taking into account the uncertainties on the soil tillage forces. The tillage forces are calculated in accordance with analytical model of McKyes and Ali with some modifications to include the effect of both soil–metal adhesion and tool speed. The different developments and applications show the importance of the developed method to improve the performance of the soil tillage equipments considering both random geometry and loading parameters. The developed method so-called OSF (Optimum Safety Factor) can satisfy a required reliability level without additional computing time relative to the deterministic design optimization study. Since the agricultural equipment parameters are extremely nonlinear, we extended the OSF approach to several nonlinear probabilistic distributions such as lognormal, uniform, Weibull and Gumbel probabilistic distribution laws.

Reliability-based design optimization for fatigue damage analysis

The objective of reliability-based design optimization (RBDO) is to design structures which should be both economic and reliable. The existing methods lead to very high computational cost, local optima, and weak convergence stability. In this paper, we present a new methodology of RBDO, leading to global solutions without additional computing cost for the reliability evaluation. The safety factor formulation for linear and nonlinear cases has been used to reduce efficiently the computational time. This technique is fundamentally based on a study of the sensitivity of the limit state function with respect to the design variables. In order to demonstrate analytically the efficiency of this methodology, the optimality conditions are then used. The presented application on fatigue damage analysis shows the advantages of the optimum safety factor (OSF) for treating complex structural problems.

Extension of optimum safety factor method to nonlinear reliability-based design optimization

In the reliability-based design optimization (RBDO) model, the mean values of uncertain system variables are usually applied as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical programming problem. Therefore, a RBDO solution that reduces the structural weight in uncritical regions does not only provide an improved design but also a higher level of confidence in the design. In this paper, we present recent developments for the RBDO model relative to two points of view: reliability and optimization. Next, we develop several distributions for the hybrid method and the optimum safety factor methods (linear and nonlinear RBDO). Finally, we demonstrate the efficiency of our safety factor approach extended to nonlinear RBDO with application to a tri-material structure.