Health state assessment is critical for mechanical equipment’s smooth and healthy operation. This paper proposes a novel approach for health state assessment based on acoustic signals during the process of machinery running. It consists of multi-domain feature (MF) extraction and comprehensive health indicator (CHI) construction. MF is extracted from various acoustic features, including time and frequency (TF) features, mel-frequency cepstral coefficients, and gammatone frequency cepstral coefficients. The stacked long short-term memory (LSTM) is used to extract the high-level features of the MF, which are then input to the downstream PCA to obtain the LSTM-PCA health indicator (LP-HI). Parallelly, the MF is fed into the self-organizing mapping (SOM) model to calculate the minimum quantization error (MQE) as SOM-MQE health indicator (SM-HI). These two indicators are fused using weighted fusion and nonlinear mapping to calculate CHI. The experimental results on air compressor dataset show a 25.8% reduction in evaluation error compared with SOTA results in this paper. The proposed nonlinear mapping function furthermore reduces fitting error on HI by 38.9%. These demonstrate the effectiveness and superiority of the proposed method in machinery health state assessment.