Efficient reliability analysis based on adaptive sequential sampling design and cross-validation

Jeong

Computational Intelligence

2019

An approximate model called metamodel or surrogate model is a mathematical model that numerically approximates response of a system during an engineering simulation process or test. The introduction of a metamodel makes it possible to express response defined in the design problem as a simple mathematical function of design variables. A metamodel can be built with response surface method (RSM), kriging, neural network, radial basis function, and so on. Each method has its advantages and disadvantages. A combined metamodel called hybrid model, ensemble model, or multiple surrogates has been developed to maximize each metamodel's strength. The hybrid model of this research includes RSM and kriging. Besides, a strategy to refine the hybrid metamodel is implemented by reducing design space. In this process, information related to Hessian is utilized for an unconstrained optimization problem, on the contrary feasibility for a constrained optimization problem. This research presents a new hybrid metamodel‐based optimization strategy called refined hybrid metamodel. Five mathematical test problems, two‐bar design, spring design, and propeller shaft design problems are solved with the suggested method, verifying its usefulness. Most of the optimal results with the proposed method are closer to exact solutions with smaller function evaluations than existing methods.

“…Weights of RS and kriging models in the hybrid model are calculated based on CV error in this study. The CV of the metamodel is represented as

{CV}_{j} = \frac{1}{m} \sum_{i = 1}^{m} {(y_{i} - {\overset{y}{true}}_{j - i})}^{2}, j = K ((), kriging), R ((), RS),

where

{\overset{true^}{y}}_{j - i}

means the generated metamodel except for the i th design point among m sample points. Equation requires no additional design point to evaluate the metamodel with existing sample points.…”

Section: The Suggested Rhmm Algorithmmentioning

confidence: 99%

“…20,21 Weights of RS and kriging models in the hybrid model are calculated based on CV error in this study. The CV of the metamodel is represented as 10,29…”

Section: Hybrid Modelmentioning

confidence: 99%

An approximate optimization strategy using refined hybrid metamodel

Jeong

Computational Intelligence

2019

Applied Mathematical Modelling

“…In this section, the comparison between the proposed method and the Monte Carlo simulation method is carried out. In this paper, the exact system reliability cannot be assessed analytically, so the system reliability is compared by the Monte Carlo simulation method with N max = 10 8 realizations are used as a 'true' value [36] for the comparisons.…”

Section: Accuracy and Computation Efficiency Validationmentioning

confidence: 99%

Reliability assessment of multi-state phased mission system with non-repairable multi-state components

Li¹,

Huang²,

Li³

et al. 2018

Phased mission systems (PMSs) like satellites and spacecraft perform their functions over non-overlapping mission periods, called phases. One of the challenges in assessing reliability of PMSs comes from considering the s-dependence among phases, and the consideration on the multi-state behavior of components and systems makes the reliability analysis even more difficult. To effectively address this problem, a multi-state multivalued decision diagram algorithm for PMS and a multi-state multi-valued decision diagram model for phased mission system (PMS-MMDD) method is developed for the reliability modelling of non-repairable multi-state components. Based on the Semi-Markov process, a Markov renewal equation-based method is developed to deal with non-exponential multistate components and a numerical method, the trapezoidal integration method, is used to compute the complex integrals in the path probability evaluation. A case study of a multistate attitude and orbit control system in a spacecraft is analyzed to illustrate the proposed PMS-MMDD model and the Markov renewal equation-based evaluation method. The accuracy and computation efficiency of the proposed method are verified by the Monte Carlo simulation method.

Numerical Meth Engineering

“…In the past 10 years, Kriging‐based active learning algorithms have drawn the most attention for reliability analysis and reliability‐based optimization . The common idea shared in these methods is to start from an initial design of experiment (DoE), and enrich it sequentially by adding new points based on the predefined learning function.…”

Section: Introductionmentioning

confidence: 99%

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Cheng

Lü

2020

Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis.This learning function is developed under the framework of the variance-bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.