Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low level SVR approach (HL-SVR) is proposed for data modeling of input parameters of unequal sample sizes in this paper. The proposed approach consists of low-level SVR models for the input parameters of larger sample sizes and high-level SVR model for the input parameters of smaller sample sizes. For each training point of the input parameters of smaller sample sizes, one low-level SVR model is built based on its corresponding input parameters of larger sample sizes and their responses of interest. The high-level SVR model is built based on the obtained responses from the low-level SVR models and the input parameters of smaller sample sizes. A number of numerical examples are used to validate the performance of HL-SVR. The experimental results indicate that HL-SVR can produce more accurate prediction results than SVR. The proposed approach is applied to the stress analysis of dental implant, in which the structural parameters have massive samples but the material of implant can only be selected from Ti and its alloys. The obtained prediction results of the HL-SVR approach are much better than SVR. The proposed approach can be used for the design, optimization, and analysis of engineering systems with input parameters of unequal sample sizes.
APPROPRIATE CRITICAL VALUES FOR PAIRWISE COMPARISONS OF MULTIPLE COMPARISON PROCEDURES FOR NORMAL VARIANCES WHEN SAMPLE SIZES ARE UNBALANCED
