**Chapter 5**

[54] Zhao H. Slope reliability analysis using a support vector machine. Computers and Geotechnics. 2008;**35**:

*Reliability and Maintenance - An Overview of Cases*

[63] Fang H, Rais-Rohani M, Liu Z, Horstemeyer MF. A comparative study of surrogate modeling methods for multi-objective crashworthiness optimization. Computers & Structures.

2005;**83**(25–26):2121-2136

Technology. 2016;**56**:45-53

[65] Fang H, Horstemeyer MF. Global response approximation with radial basis functions. Engineering

Optimization. 2006;**38**(04):407-424

accuracy at design points for radial basis

[66] Fang H, Wang Q. On the effectiveness of assessing model

functions. Communications in Numerical Methods in Engineering.

[67] Wu Z. Compactly supported positive definite radial function. Advances in Computational Mathematics. 1995;**4**:283-292

[68] Montgomery DC. Design and Analysis of Experiments. New York: John Wiley & Sons, Inc.; 2001

[69] Taguchi G. Taguchi Method-Design of Experiments, Quality Engineering Series. Vol. 4. Tokyo: ASI Press; 1993

[70] Zhou J, Nowak AS. Integration formulas to evaluate functions of random variables. Structural Safety.

1988;**5**(4):267-284

2008;**24**(3):219-235

[64] Wang Q, Fang H, Shen L. Reliability analysis of tunnels using a meta-modeling technique based on augmented radial basis functions. Tunnelling and Underground Space

[55] Hurtado JE. Filtered importance sampling with support vector margin: A

[56] Bourinet J-M, Deheeger F, Lemaire M. Assessing small failure probabilities by combined subset simulation and support vector machines. Structural

[57] Tan XH, Bi WH, Hou XL, Wang W. Reliability analysis using radial basis function networks and support vector machines. Computers and Geotechnics.

[58] Krishnamurthy T. Response Surface Approximation with Augmented and Compactly Supported Radial Basis Functions. Technical Report AIAA-2003-1748. Reston, VA: AIAA; 2003

[59] Goel T, Haftka RT, Shyy W, Queipo NV. Ensemble of surrogates. Structural and Multidisciplinary Optimization.

[60] Acar E, Rais-Rohani M. Ensemble of metamodels with optimized weight factors. Structural and Multidisciplinary Optimization. 2009;**37**(3):279-294

[61] Yin H, Fang H, Wen G, Gutowski M, Xiao Y. On the ensemble of metamodels with multiple regional optimized weight factors. Structural and Multidisciplinary Optimization. 2018;

[62] Ye P, Pan G, Dong Z. Ensemble of surrogate based global optimization methods using hierarchical design space

Multidisciplinary Optimization. 2018;

reduction. Structural and

powerful method for structural reliability analysis. Structural Safety.

Safety. 2011;**33**(6):343-353

2011;**38**(2):178-186

2007;**33**(3):199-216

**58**:245-263

**58**:537-554

**88**

459-467

2007;**29**(1):2-15
