基于隐Markov树故障诊断的确定退火设计

Deterministic annealing design of hidden Markov tree based fault diagnosis

隐Markov树(HMT)模型故障诊断作为一种模式识别问题,其目标是得到最小分类误差。由于误分类率函数为分段线性常数,存在许多局部极小值,因此难以直接最小化。提出使用确定退火(DA)方法来最小化误分类率函数,通过在设计过程中随机化分类决策,并使用Shannon熵限制其随机程度,得到一个光滑的误分类率函数,它在熵为0时收敛到原来的误分类率函数。给出了优化过程中梯度计算的上行-下行算法和基于梯度下降的参数重估公式。提出的基于DA的优化方法用于减速器故障诊断,结果表明使用DA较ML估计可以得到更高的识别率。

As one kind of pattern recognition question, the ultimate objective of hidden Markov tree （HMT） based fault diagnosis is to minimize misclassification rate. The misclassification rate is difficult to optimize directly because the cost surface is riddled with shallow local minima. The deterministic annealing （DA） design methods which minimize the misclassification cost are proposed. In the DA approach, the classifier＇s decision is randomized during design and the level of randomness is controlled via a constraint on the Shannon entropy. The cost function is smooth and converges to the MCE cost at the limit of zero entropy. This algorithm is implemented by a low complexity upward-downward procedure and the parameter restimation is implemented by gradient descent. The application of the presented DA methods to a gearbox fault diagnosis shows that the DA modeling can effectively improve fault identification rate over ML modeling.