The monitoring data of the complex electromechanical system has obvious high-dimensional nonlinear and complex distribution characteristics. In order to meet the requirements of complex system anomaly identification which are difficult to be satisfied by the traditional method, a kind of Laplacian eigenmaps-support vector domain description method (LE-SVDD) is proposed. On account of the fact that the points which are close in the high-dimensional feature space should also be close after being projected to the low-dimensional feature space, the improved LE method uses a weighted undirected graph to describe a popularity and find the low-dimensional embedment with an embedded method, thereby status popular structures can be found in the high-dimensional data. In the simulation experiments based on the standard Tennessee-Eastman process (TE process) test and training data, the accurate results of nonlinear feature extraction and anomaly identification at different time are given. Respectively, the average false negative rate and false alarm rate are 6.063, 6 and 5.625, 3.125, which are relatively low. It shows that LE-SVDD method has excellent non-linearity and high-dimensional data processing capability in condition monitoring, which is suitable for the monitoring and diagnosis of engineering system.