The functional time series signals generated during the operation of electromechanical systems contain fault characteristic information. This study proposes a fault identification method for electromechanical systems based on functional data feature engineering and multi-layer kernel extreme learning machine (MLKELM) optimized by sparrow search algorithm (SSA). First, multiple time series signals under different fault conditions are functionalized under the B-spline basis function system, and the feature reduction space is constructed by functional principal component analysis (FPCA) and principal differential analysis (PDA) to extract fault features. Second, the minimum redundancy and maximum relevance (mRMR) method is performed on the initial feature set for feature selection. In addition, the size of the optimal feature subset is determined by the class separability of feature subset (CSFS) criterion. Finally, deep feature learning and fault identification are implemented by MLKELM and the pre-defined parameters are optimized based on the SSA in this process to improve its performance. The experimental results show that the proposed method can effectively extract the fault features of function time series signals, and then accurately identify the faults of electromechanical systems.