中文摘要：

针对支持向量机（Support vector machine, SVM）的惩罚系数难以确定、核函数必须满足Mercer定理等问题，相关向量机（Relevance vector machine, RVM）应运而生以解决上述问题，并在趋势预测等领域得到一定的应用。核函数是决定RVM预测精度的关键因素之一，目前的研究通常是人为选择单一核函数，因此增加了对参数的依赖性并降低了RVM预测的鲁棒性。为了解决以上问题，提出一种新的自适应多核组合RVM预测方法。该方法首先选择多个核函数，利用粒子滤波产生核函数权重，建立多核组合RVM集，然后经过不断地迭代预测、权值更新和重采样，自适应获取最优多核组合RVM，从而自适应融合多个核函数的特性，克服基于单一核函数RVM的局限，提高预测精度和鲁棒性。利用仿真对提出方法进行了验证，并将其应用于机械设备的剩余寿命预测，取得了比基于单一核函数RVM更好的预测效果。

英文摘要：

In view of some shortcomings of support vector machine, for instance, it is difficult to select the regularization parameter and the kernel function must satisfy Mercer＇s condition, relevance vector machine （RVM） is developed and applied to the field of trend prediction. The performance of RVM, to a large extent, depends on the kernel function. However, a single kernel function is generally selected artificially and subjectively in current studies on RVM, which increases its dependency of the RVM to parameters and decreases the robustness in prediction process. To solve the problem, a new adaptive multi-kernel RVM is proposed for prediction. In the method, multiple kernel functions are selected originally and their weights are generated by the particle filter （PF） algorithm to construct multi-kernel RVM models. Then the optimal multi-kernel RVM model is obtained by iterative processes, i.e., predicting, weights updating and resampling. The effectiveness of the proposed method is validated by a simulation study and a ease study of remaining useful life prediction of machinery. The results demonstrate that the proposed method obtains higher prediction accuracies compared with the single kernel RVM models.