Abstract: According to the low on-line efficiency of the shift invariant sparse coding, a fast shift invariant sparse coding algorithm which has high on-line efficiency is proposed in this paper. Then the on-line faults recognition can be realized combining the sparse representation classification. The algorithm transforms the shift invariant optimization problem from the time domain to the frequency domain firstly. The sparse coefficient and classification dictionary are solved quickly using the feature sign and Lagrange dual method, which can reduce the computational time complexity without the loss of classification accuracy. And the real-time performance for fault recognition will be promoted. The experimental results of engine show that, while the engine works in the idle and 1500~2000?r/min conditions, the novelty algorithm gets the average recognition accuracy of five kinds of common faults are respectively 92.35% and 91.44%, which are approximately equal to other algorithms. But the average online fault recognition speed are 13.91?ms and 14.5?ms respectively, the dictionary training time are 1.43?s and 1.47?s, which are obviously faster than those of other recognition algorithms.

Key words: shift invariant, sparse representation classification, feature sign, Lagrange dual method, real-time performance, gasoline engine, on-line fault recognition

摘要： 针对移不变稀疏编码算法在线运行时效率不高的问题，提出一种能够明显提高移不变稀疏编码效率的快速算法，并结合稀疏分类实现对汽油发动机故障的在线识别。该算法首先把移不变问题从时域转换到频域上，然后采用特征标记法和拉格朗日对偶法对稀疏系数和分类字典进行求解，在保证稀疏识别精度的同时大幅降低了问题求解的时间复杂度，从而有效改善了发动机故障在线识别系统的实时性。在发动机上的实验结果表明，该算法在怠速和1?500~2?000?r/min工况下对五种常见机械故障的平均识别精度分别为92.35%和91.44%，和其他识别算法大致持平。但其平均在线分类时间仅为13.91?ms和14.5?ms，且分类字典的平均训练速度同样仅为1.43?s和1.47?s，均明显快于其他识别算法。

关键词: 移不变, 稀疏分类, 特征标记, 拉格朗日对偶, 实时性, 汽油发动机, 在线故障识别