Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Henry Arenbeck ◽  
Samy Missoum ◽  
Anirban Basudhar ◽  
Parviz Nikravesh
Keyword(s):  
Multibody Systems ◽  
Adaptive Sampling ◽  
Design Space ◽  
Limit State ◽  
Uniform Design ◽  
Probability Of Failure ◽  
Support Vector ◽  
State Function ◽  
Nominal System ◽  
Truncated Normal

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

Reliability Analysis Method Based on Support Vector Machines Classification and Adaptive Sampling Strategy

2012 ◽  
Vol 544 ◽  
pp. 212-217 ◽  
Author(s):  
Hong Yan Hao ◽  
Hao Bo Qiu ◽  
Zhen Zhong Chen ◽  
Hua Di Xiong
Keyword(s):  
Reliability Analysis ◽  
Adaptive Sampling ◽  
Limit State ◽  
Computational Cost ◽  
Sampling Strategy ◽  
Support Vector ◽  
State Function ◽  
Analysis Method ◽  
Design Problems ◽  
Vector Machines

For probabilistic design problems with implicit limit state functions encountered in practical application, it is difficult to perform reliability analysis due to the expensive computational cost. In this paper, a new reliability analysis method which applies support vector machine classification(SVM-C) and adaptive sampling strategy is proposed to improve the efficiency. The SVM-C constructs a model defining the boundary of failure regions which classifies samples as safe or failed using SVM-C, then this model is used to replace the true limit state function,thus reducing the computational cost. The adaptive sampling strategy is applied to select samples along the constraint boundaries. It can also improves the efficiency of the proposed method. In the end, a probability analysis example is presented to prove the feasible and efficient of the proposed method.

Reliability Analysis of Foundation Pit by Improved Response Surface Method

2011 ◽  
Vol 147 ◽  
pp. 197-202 ◽  
Author(s):  
Jiang Zhou ◽  
Jing Cao ◽  
Yu He ◽  
Jie Song
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Lateral Displacement ◽  
Limit State ◽  
Uniform Design ◽  
Design Parameters ◽  
State Function ◽  
Foundation Pit ◽  
Improved Response Surface Method

Lacking of explicit limit state function (LSF) will result large quantities of computational efforts for a FEAM based structural reliability analysis. An improved response surface (RS) method is proposed to analyze the failure probability of foundation pit through combining uniform design (UD) and non-parametric regression (NPR). Deferent levels of design parameters are first delicately selected according to UD and then FEAM is used to analysis corresponding pit response parameters including maximum lateral displacement of wall, settlement of ground, safety factor of overall stability, safety factors of against overturning, heave and piping. The RS relationship is then established through NPR based on inputs and responses. At last, a direct Mont Carlo Simulation is carried out to obtain the probability density function of response parameters.

Iterative Algorithm for Structure Reliability Analysis Based on Support Vector Classification Method

2007 ◽  
Vol 353-358 ◽  
pp. 1009-1012
Author(s):  
Chao Ma ◽  
Zhen Zhou Lu
Keyword(s):  
Reliability Analysis ◽  
Iterative Algorithm ◽  
Limit State ◽  
Sampling Procedure ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Structure Reliability ◽  
Important Region ◽  
Actual Limit

For reliability analysis of structure with implicit limit state function, an iterative algorithm is presented on the basis of support vector classification machine. In the present method, the support vector classification machine is employed to construct surrogate of the implicit limit state function. By use of the proposed rational iteration and sampling procedure, the constructed support vector classification machine can converge to the actual limit state function at the important region, which contributes to the failure probability significantly. Then the precision of the reliability analysis is improved. The implementation of the presented method is given in detail, and the feasibility and the efficiency are demonstrated by the illustrations.

Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Dimitrios I. Papadimitriou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Topology Optimization ◽  
Limit State ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Probability Of Failure ◽  
Mean Value ◽  
Second Order ◽  
State Function ◽  
Sensitivity Derivatives ◽  
Reliability Method

A reliability-based topology optimization (RBTO) approach is presented using a new mean-value second-order saddlepoint approximation (MVSOSA) method to calculate the probability of failure. The topology optimizer uses a discrete adjoint formulation. MVSOSA is based on a second-order Taylor expansion of the limit state function at the mean values of the random variables. The first- and second-order sensitivity derivatives of the limit state cumulant generating function (CGF), with respect to the random variables in MVSOSA, are computed using direct-differentiation of the structural equations. Third-order sensitivity derivatives, including the sensitivities of the saddlepoint, are calculated using the adjoint approach. The accuracy of the proposed MVSOSA reliability method is demonstrated using a nonlinear mathematical example. Comparison with Monte Carlo simulation (MCS) shows that MVSOSA is more accurate than mean-value first-order saddlepoint approximation (MVFOSA) and more accurate than mean-value second-order second-moment (MVSOSM) method. Finally, the proposed RBTO-MVSOSA method for minimizing a compliance-based probability of failure is demonstrated using two two-dimensional beam structures under random loading. The density-based topology optimization based on the solid isotropic material with penalization (SIMP) method is utilized.

Failure Assessment and Reliability Analysis of CFRP Composite Pressure Vessel

2007 ◽  
Vol 348-349 ◽  
pp. 225-228
Author(s):  
Jun Shen ◽  
M.L. Zhang ◽  
D.Y. Hou
Keyword(s):  
Reliability Analysis ◽  
Pressure Vessel ◽  
Progressive Failure ◽  
Limit State ◽  
Probability Of Failure ◽  
Fiber Direction ◽  
State Function ◽  
Design Variables ◽  
Composite Pressure Vessel ◽  
Cfrp Composite

A new approach for progressive failure and reliability analysis of carbon fiber reinforced polymeric (CFRP) composite pressure vessel with many base random variables is developed in the paper. The elastic constants of CFRP lamina and geometric parameters of the vessel are selected as the base design variables. CFRP lamina specimen and pressure vessel were manufactured and tested in order to obtain statistics of design variables. The limit state function for progressive failure analysis was set up. Then the progressive failure and reliability analysis of the vessel were performed according to the stiffness degradation model based on Monte Carlo simulation procedure using MATLAB. The distributions of failure loads and the probability of failure of the vessel were obtained. The feasibility and accuracy of the proposed method is validated by good agreement between the simulation and experimental results. Further analysis indicates that the lamina tensile strength in the fiber direction and hoop layer thickness of the vessel have significant influence on the probability of failure of composite pressure vessel.

Safety and Reliability Analysis of Composites Under Low Velocity Impact

2016 ◽  
Author(s):  
Shivdayal Patel ◽  
Suhail Ahmad ◽  
Manander Singh
Keyword(s):  
Material Properties ◽  
Limit State ◽  
Composite Plates ◽  
Probability Of Failure ◽  
Matrix Cracking ◽  
Low Velocity Impact ◽  
State Function ◽  
Random Parameters ◽  
Low Velocity ◽  
Velocity Impact

Low velocity impact on composite plates is studied taking material properties and initial velocity as random parameters. Graphite fiber reinforced composite plates are susceptible to damage due to impact by foreign objects and in plane loading. In order to assess the safe load carrying capacity and the probability of failure under impact, dynamic analysis of composite plate subjected to low velocity impact is carried out. Finite element method is used to study impact. During impact, the in-plane damage modes such as matrix cracking, fiber failure and shear cracking are modeled using a failure criterion. The out of plane de-lamination is modeled using cohesive surfaces. The uncertainties associated with the system properties due to the inherent scatter in the geometric and material properties and input loads are modeled in a probabilistic fashion. Random parameters represent various characteristics appearing in the limit state function. The probabilistic analysis and reliability prediction of the system is carried out using Gaussian response surface method and validity of method for the present problem is establish using Monte Carlo simulation (MCS) procedure. Sensitivity analysis of the probability of failure with respect to random parameters considered is an important study for design optimization. The safety level qualification is achieved in terms of reliability level targeted. The mean and standard deviations of random variables show an appreciable influence on the probabilistic failure. Systematic changes in the input parameters are governed by the probabilistic sensitivity tools to achieve target reliability.

Markov Description of Corrosion Defects Growth and Its Application to Reliability Based Inspection and Maintenance of Pipelines

2008 ◽  
Author(s):  
S. A. Timashev ◽  
M. G. Malyukova ◽  
L. V. Poluian ◽  
A. V. Bushinskaya
Keyword(s):  
Markov Model ◽  
Conditional Probability ◽  
Limit State ◽  
Simulation Method ◽  
Probability Of Failure ◽  
State Function ◽  
Main Concern ◽  
Defect Parameter ◽  
Pipeline Failure ◽  
Pressurized Pipelines

The paper describes a Markov model of corrosion growth of pipe wall defects and its implementation for assessing the conditional probability of pipeline failure and optimizing pipeline repair and maintenance. This pure growth Markov model is of the continuous time, discrete states type. This model is used in conjunction with the geometrical limit state function (LSF) to assess the conditional probability of failure of pressurized pipelines when the main concern is loss of containment. It is shown how to build an empirical Markov model for the length, depth and width of defects, using field data gathered by In-line inspection (ILI) or direct assessment (DA) or by using a combination of a differential equation (DE) that describes defect parameter growth with the Monte Carlo simulation method. As a result of implementation of this approach the probability for the defect parameters being in a given state (analog of a histogram) and the transition intensities (from state to state) are easily derived for any given moment of time. This approach automatically gives an assessment of the probability of failure of a pipeline segment, as it is derived using the data from a specific pipeline length. This model also allows accounting for the pipeline failure pressure LSF. On the basis of this model an algorithm is constructed for optimizing the time of the next inspection/repair. This methodology is implemented to a specific operating pipeline which was several times inspected by a MFL inspection tool. The expected number and volume of repairs depend on the value of the ultimate permissible pipeline failure probability. Sensitivity of pipeline conditional failure rate and optimal repair time to actual growth rate is investigated. A brief description of the software that implements the described above technology is given.

Sampling-Based RBDO Using Probabilistic Sensitivity Analysis and Virtual Support Vector Machine

2012 ◽  
Author(s):  
Hyeongjin Song ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
Liang Zhao ◽  
David Lamb
Keyword(s):  
Sensitivity Analysis ◽  
Support Vector Machine ◽  
Probabilistic Sensitivity Analysis ◽  
Limit State ◽  
Computational Cost ◽  
Classification Method ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Virtual Samples

In this paper, a sampling-based RBDO method using a classification method is presented. The probabilistic sensitivity analysis is used to compute sensitivities of probabilistic constraints with respect to random variables. Since the probabilistic sensitivity analysis requires only the limit state function, and not the response surface or sensitivity of the response, an efficient classification method can be used for a sampling-based RBDO. The proposed virtual support vector machine (VSVM), which is a classification method, is a support vector machine (SVM) with virtual samples. By introducing virtual samples, VSVM overcomes the deficiency in existing SVM that uses only classification information as their input. In this paper, the universal Kriging method is used to obtain locations of virtual samples to improve the accuracy of the limit state function for highly nonlinear problems. A sequential sampling strategy effectively inserts new samples near the limit state function. In sampling-based RBDO, Monte Carlo simulation (MCS) is used for the reliability analysis and probabilistic sensitivity analysis. Since SVM is an explicit classification method, unlike implicit methods, computational cost for evaluating a large number of MCS samples can be significantly reduced. Several efficiency strategies, such as the hyper-spherical local window for generation of the limit state function and the Transformations/Gibbs sampling method to generate uniform samples in the hyper-sphere, are also applied. Examples show that the proposed sampling-based RBDO using VSVM yields better efficiency in terms of the number of required samples and the computational cost for evaluating MCS samples while maintaining accuracy similar to that of sampling-based RBDO using the implicit dynamic Kriging (D-Kriging) method.

Application of Partial Safety Factors for Fitness-for-Service Assessment of Pressure Equipment With Local Metal Loss

2017 ◽  
Author(s):  
Takuyo Kaida ◽  
Shinsuke Sakai
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Probability Of Failure ◽  
Pressure Vessels ◽  
Metal Loss ◽  
State Function ◽  
Safety Factors ◽  
Loss Assessment ◽  
Reliability Method ◽  
Partial Safety Factors

Reliability analysis considering data uncertainties can be used to make a rational decision as to whether to run or repair a pressure equipment that contains a flaw. Especially, partial safety factors (PSF) method is one of the most useful reliability analysis procedure and considered in a Level 3 assessment of a crack-like flaw in API 579-1/ASME FFS-1:2016. High Pressure Institute of Japan (HPI) formed a committee to develop a HPI FFS standard including PSF method. To apply the PSF method effectively, the safety factors for each dominant variable should be prepared before the assessment. In this paper, PSF for metal loss assessment of typical pressure vessels are derived based on first order reliability method (FORM). First, a limit state function and stochastic properties of random variables are defined. The properties of a typical pressure vessel are based on actual data of towers in petroleum and petrochemical plants. Second, probability of failure in several cases are studied by Hasofer-Lind method. Finally, PSF’s in each target probability of failure are proposed. HPI published a new technical report, HPIS Z 109 TR:2016, that provide metal loss assessment procedures based on FORM and the proposed PSF’s described in this paper.

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