To reduce the runtime and ensure enough computation accuracy, this paper proposes a structural reliability assessment method by the use of sensitivity analysis (SA) and support vector machine (SVM). The sensitivity analysis is firstly applied to assess the effect of random variables on the values of performance function, while the smallinfluence variables are rejected as input vectors of SVM. Then, the trained SVM is used to classify the input vectors, which are produced by sampling the residual variables based on their distributions. Finally, the reliability assessment is implemented with the aid of reliability theory. A 10bar planar truss is used to validate the feasibility and efficiency of the proposed method, and a performance comparison is made with other existing methods. The results show that the proposed method can largely save the runtime with less reduction of the accuracy; furthermore, the accuracy using the proposed method is the highest among the methods employed.
In recent years, a number of structural reliability assessment methods, including firstorder reliability method (FORM) [
To overcome the lowfidelity of RSM and low computing efficiency of MCSM, several researchers have attempted to construct the limit state function based on the intellectual techniques, such as artificial neural networks [
The input vectors of SVM model are the variables influencing the structural reliability assessment. For a largescale civil structure, its reliability is affected by a number of variables due to the complex service environment and loading situations. If all of influencing variables are taken into consideration with no regard to their importance in the process of reliability assessment, it will increase the sample size of input variables, complicate the SVM model, and enlarge the data storage memory demands while decreasing the classification accuracy (CA) of SVM model. In fact, some input variables have slight effect on the reliability assessment results. Therefore, it is necessary to eliminate the smallinfluencing variables before assessing the structure reliability. Recently, a series of SA techniques have been developed and studied for the purpose of quantifying the importance of input variables. These SA techniques are divided into two classes: global SA methods and local SA methods [
In order to reduce the dimension of input samples, simplifying the SVM model in the case of ensuring computation accuracy, this paper presents a novelty reliability analysis method based on SA and SVM. The smallinfluence variables in the limit state function are extracted in virtue of Sobol’s SA method and are rejected as input vectors of SVM model. The SVM model is trained and tested by samples of residual variables. The reliability assessment is implemented with the aid of reliability theory. To validate the applicability and efficiency of the proposed method, the reliability assessment of a 10bar planar truss is employed. In addition, some comparisons are also carried out.
Sobol’s method is a variancebased global SA technique that has been applied to assess the relative importance of input variables on the output. It is able to decompose the variance of the output into terms due to individual input variables and terms due to the interactions between input variables.
Consider a square integrable function,
If the following condition
Therefore, the partial variances,
The relative importance of input variables is quantified by a set of indices, namely, firstorder
In order to investigate the total sensitivity index
The variances in (
Usually, the input variables whose total sensitivity indices are less than 0.3 are considered to be slight of contribution on the output of
SVM is an emerging machine learning technique that has been successfully applied to pattern classification and regression analysis. It is based on the VapnikChervonenkis dimension of statistical learning theory and the principle of structural risk minimization; thus it has a better generalization capability than the conventional classification methods. This is based on the principle of empirical risk minimization.
Suppose a set of training examples
Among these separating hyperplanes, the one socalled optimal separating hyperplane (OSH) separates all vectors without error and the distance between the closest vectors to the hyperplane is maximal. The OSH is found by minimizing
The Lagrange multipliers,
In the case of linearly nonseparable training data, by introducing slack variables,
Similarly, the corresponding dual problem is expressed as
With the OSH found, the decision function can be written as
The reliability assessment based on SA and SVM can be implemented as follows.
Calculate the total sensitivity indices of each input variable in the limit state function,
The samples used for the SA in Step
Produce the test samples of residual variables according to their distributions. The number of test samples is
Count the number of samples located in class I. Consequently, the failure probability,
A numerical 10bar planar truss has been adopted to validate the proposed reliability assessment method. The young’s modulus of each bar is
Distribution types of random variables.
Variables 





(m^{2})  (MN)  (MN)  (MN)  
Mean value  0.0001  −160  160  −160 
Coefficient of variation  0.15  0.5  0.5  0.5 
Distribution types  Normal  Normal  Normal  Normal 
10bar planar truss.
The ultimate strength of this material is assumed to be 480 MPa. Consequently, the limit state function,
The Sobol’s method was employed to analyze the contribution of each variable on the output variance of limit state function. Firstly, the Latin hypercube sampling technique [
Sensitivity indices of each variable.
It is noted that a total number of
A total number of 20000 test samples are constructed and input into the trained SVM model. The classification results of test samples are shown in Table
Classification results.
Method  Samples  Class  Number of samples  Classification number for different classes  CA (%)  Total CA (%)  

I  II  
SA and SVM  Train  I  60  43  17  71.67  96.29 
II  640  9  631  98.59  
Test  I  1396  1007  389  72.13  96.06  
II  18604  399  18205  97.86  


SVM  Train  I  60  44  16  73.33  96.14 
II  640  11  629  98.28  
Test  I  1396  902  494  64.61  95.28  
II  18604  451  18153  97.58 
It is observed in Table
In order to validate the applicability, other three structure reliability assessment methods (i.e., RSM, MCSM, and SVM) are employed to evaluate the structural failure probability. The failure probabilities evaluated by these four methods are listed in Table
Failure probabilities evaluated by different methods.
Method  MCSM  RSM  SVM  SA and SVM 

Failure probability (%)  6.98  10.29  6.77  7.03 
Error (%)  —  47.42  3.01  0.72 
Amount of FEA  20000  27  700  700 
The classification result of SVM model is also listed in Table
The amount of FEA required by each method is also listed in Table
In this study, a novelty reliability assessment method based on SA and SVM has been developed and successfully applied for reliability assessment of a 10bar planar truss. The results show that the proposed method not only reduces data storage memory requirements with enough computation accuracy, but also has a better assessment capability in comparison with other methods.
The proposed assessment method integrating both SA and SVM is proved to be a successful example. However, it should be noted as well that our success in the proposed method was only achieved through numerical simulations, and more field tests should be done to testify its feasibility and efficiency in practice.
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
The work is supported by the National Natural Science Foundation of China (nos. 51278127 and 50878057), the Ph.D. Programs Foundation of Ministry of Education (no. 20093514110005), and the National 12th FiveYear Research Program of China (no. 2012BAJ14B05), China.