scholarly journals Probabilistic Optimum Design of Aircraft Structures

2000 ◽  
Author(s):  
Landon Onyebueke ◽  
Ikechukwu Nnamani
Keyword(s):  
Optimum Design ◽  
Limit State ◽  
Simulation Method ◽  
Sensitivity Analyses ◽  
State Function ◽  
Limit State Function ◽  
Approximate Methods ◽  
Aircraft Structures ◽  
Stochastic Data ◽  
Search Approach

Abstract This paper discusses the application of probabilistic design methodology for the optimum design of aircraft structures. Material properties and loads are considered as stochastic data in formulating the optimization model for the design. The procedure accommodates various types of sensitivity analyses. Attention is focused on studies in which both the aerodynamic and structural designs are optimized simultaneously. Tradeoffs between drag and structural weight for aircraft wings are affected by two aerodynamic-structural interactions. First, structural weight affects the required lift and, thus drag. Second, structural deformations change the aerodynamic shape. Design results obtained using the Monte Carlo simulation method, and the limit state function approach, are presented. The limit state function method applies the Most Probable Point (MPP) search approach. Some of the approximate methods that have been applied for the search are FORM, AMV, AIS, etc.

scholarly journals Heuristic Operator for Reliability Assessment of Frame Structures

2021 ◽  
Author(s):  
Ali Kaveh ◽  
Seyed Rohollah Hoseini Vaez ◽  
Pedram Hosseini ◽  
Mohammad Ali Fathali
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Simulation Method ◽  
Frame Structures ◽  
State Function ◽  
Limit State Function ◽  
Cross Sectional ◽  
Story Drift ◽  
Steel Frame Structures ◽  
External Loads

In structural design of steel frames, in order to achieve proper safety, the effect of uncertainties in the design and loading parameters of the structure must be considered. This approach is obtained by defining a reliability index. In this study, the Modified Dolphin Monitoring (MDM) operator was used to evaluate the reliability index of three well-known steel frame structures based on the Hasofer-Lind method. The reliability index was evaluated using the EVPS and VPS algorithms and with considering the MDM operator on them. The constraint of the last story drift is considered as limit state function. The random variables consist of external loads, modulus of elasticity, moment of inertia and cross-sectional areas. According to the number of evaluations of the limit state function, the results show the efficiency of this method in comparison to the Monte Carlo simulation method. Also, the values of the most probable point (MPP) are examined.

Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

2021 ◽  
pp. 1045389X2110263
Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Sensitivity Analyses ◽  
State Function ◽  
Reliability Indices ◽  
Buckling Restrained Brace ◽  
Polynomial Response Surface ◽  
Nonlinear Dynamic Analyses ◽  
High Computational Cost

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

An Efficient Response Surface Method Using Givens Transformation for Structural Reliability Analysis

2012 ◽  
Vol 532-533 ◽  
pp. 408-411
Author(s):  
Wei Tao Zhao ◽  
Yi Yang ◽  
Tian Jun Yu
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Mathematical Techniques ◽  
Input Variables ◽  
Improved Accuracy

The response surface method was proposed as a collection of statistical and mathematical techniques that are useful for modeling and analyzing a system which is influenced by several input variables. This method gives an explicit approximation of the implicit limit state function of the structure through a number of deterministic structural analyses. However, the position of the experimental points is very important to improve the accuracy of the evaluation of failure probability. In the paper, the experimental points are obtained by using Givens transformation in such way these experimental points nearly close to limit state function. A Numerical example is presented to demonstrate the improved accuracy and computational efficiency of the proposed method compared to the classical response surface method. As seen from the result of the example, the proposed method leads to a better approximation of the limit state function over a large region of the design space, and the number of experimental points using the proposed method is less than that of classical response surface method.

Development of Ultimate Strength Evaluation Method for Piping Subjected to Seismic Loads

2013 ◽  
Author(s):  
Hideo Machida ◽  
Hiromasa Chitose ◽  
Tatsuhiro Yamazaki
Keyword(s):  
Power Plants ◽  
Evaluation Method ◽  
Failure Modes ◽  
Limit State ◽  
Seismic Loading ◽  
Earthquake Resistance ◽  
State Function ◽  
Limit State Function ◽  
Input Acceleration ◽  
Resistance Tests

This paper reports the results of the study on the failure modes and limit loads of piping in nuclear power plants subjected to cyclic seismic loading. By investigating the past fracture tests and earthquake resistance tests, it became clear that dominant failure mode of piping was fatigue, and the effect of ratchet strain was negligible. Until now, the stress generated with the acceleration of an earthquake was classified into the primary stress. However, the relationship between the input acceleration and the seismic response displacement of the pipe observed from earthquake resistance tests is non-linear, and increasing rate of displacement is lower than that of input acceleration in elastic-plastic stress condition. Therefore, the seismic loading can be treated as displacement controlled loading. To evaluate the reliability-based critical acceleration, a limit state function was defined taking the variations in the fatigue strength or some parameters into consideration. By using the limit state function, the reliability was evaluated for the typical piping of boiling water reactor (BWR) plants subjected to cyclic seismic loading, and a partial safety factors were calculated. Based on these results, a fatigue curve corresponding to the target reliability was proposed.

A New Reliability Evaluation Algorithm Using Response Surface Methodology Combined With Space Mapping Technique

2006 ◽  
Author(s):  
Lixin Zhang ◽  
Zhijun Jian ◽  
Zhaohui Xu
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Limit State ◽  
Space Mapping ◽  
Mapping Technique ◽  
State Function ◽  
Limit State Function ◽  
New Approach ◽  
Successive Response ◽  
Evaluation Algorithm

A new method is proposed to tackle the huge computation cost involved in Successive Response Surface Methodology applied to the reliability analysis, in which Space Mapping technique is combined with Response Surface Methodology. While the new approach is performed, the limit state function is only fitted at the first iteration; at other iterations Space Mapping technique is employed to map the original limit state function into the new ones. Experimental design, corresponding model evaluations and response surface fitting of the limit state function are not done repetitively as what we do while SRSM is used, which leads to the great cutting down of computational efforts.

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Probabilistic Optimum Design of Composite Laminates

1998 ◽  
Vol 32 (1) ◽  
pp. 68-82 ◽  
Author(s):  
S. Mahadevan ◽  
X. Liu
Keyword(s):  
Objective Function ◽  
Optimum Design ◽  
Composite Laminates ◽  
Plate Theory ◽  
Limit State ◽  
Strength Criterion ◽  
System Level ◽  
State Function ◽  
Practical Procedure ◽  
Reliability Method

This paper proposes a procedure for the optimum design of composite laminates under probabilistic considerations. The problem is formulated to consider the minimization of laminate weight as the objective function and the reliability requirements as the constraints. Both system-level and element-level reliabilities are considered. The first-order reliability method (FORM) is used to estimate the reliability of each ply group, and system reliability is computed based on series or parallel system assumptions. The Tsai-Wu strength criterion is adopted to derive the limit state function of individual ply groups in the laminate. The gradient and sensitivity information of the objective function and the constraints with respect to the design variables are obtained by using sensitivity analysis based on the composite plate theory. Thus the proposed procedure brings together modern concepts of reliability analysis, composite laminate behavior and nonlinear optimization to develop a rational and practical procedure for the optimum design of composite laminates. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

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