Cyclic spectral coherence (CSCoh) is an effective tool to reveal the cyclostationarity of the fault-induced components (FICs). Integrating CSCoh over the domain of the spectral frequency or decomposing CSCoh by matrix factorization methods can provide an enhanced diagnosis spectrum. However, for compound faults, the integration-based strategy or the factorization-based method will fail once the features of different faults are coupled with each other in the informative frequency band. In light of this, we present a novel harmonic sparse structured nonnegative matrix factorization (HSSNMF) framework, enabling us to learn a part-based representation of CSCoh with the desired harmonic sparse structures (HSSs) of FICs. Specifically, the proposed method is formulated as an optimization problem with explicit HSS constraints in the objective function, where an iterative solving algorithm and an initialization way for the optimization problem are provided. Moreover, the convergence and complexity of HSSNMF are analyzed theoretically and empirically. Extensive comparisons in both the synthetic and experimental data are conducted to verify the advantages. The qualitative results show that HSSNMF not only can isolate the FICs from the noisy data but can also separate the different FICs from each other, and the quantitative results demonstrate that the performance of the proposed algorithm is improved by at least 10%.