## 1 Introduction
In consequence, this situation might cause an inaccurate or low steady-state separation performance for the targeted source even if the computing or tracking process is sufficiently long [11]. Instead, the implementation of neural networks or artificial intelligence algorithms in BSS could avoid this deficiency and have the advantage that the objective function and optimization algorithm are independently assigned. In this way, the optimization algorithm can be flexibly combined with different criteria such as batch processing and variable step-size learning, according to the actual demand [12]. In addition, finding network computing and computational intelligence implementations of BSS is of great necessity for it could increase the robustness of the separation algorithms in contrast with a linear separation method such as ICA, eliminating the uncertainties and ambiguities in the real-world sources. For instance, [PERSON] et al. advanced a shallow neural network-based separation method, which is updated by the error-gated Hebbian rule and suitable for multi-context blind source separation simultaneously [13]. [PERSON] designed a biased dense neural network on the basis of a maximum likelihood estimation criterion in order to obtain a better steady-state separating performance [14]. Particularly, in light of temporal convolutional encoder and weighting masks, a convolutional time-domain audio separation network (Conv-TaskNet) was proposed by [PERSON] and [PERSON] for single-channel or underdetermined speech separation tasks [15]. Conv-TaskNet sufficiently exploited the time-frequency spec trogram for speech signals and output the probabilistic masking, but it cannot perfectly reconstruct the source signals when they have obvious frequency overlapping. [PERSON] proposed a LSTM variant single target speaker extraction method, composed of a speaker embedder and separator networks [16]. [PERSON] employed an end-to-end W-shaped network to extract a fetal ECG signal, but it is a dual-path structure and can only be utilized in two channels [17]. Although the neural network-based BSS methods endorse the overall separating performance under different application scenarios, when applied in actual railway environments, the BSS technology still confronts the specific non-stationary and time-varied spectral characteristics of complicated noisy signals. Due to this, accurately extracting the target signal in the actual railway, such as with a rail defect signal, remains an intractable challenge. In this case, the time-frequency analysis (TFA) plays a pivotal role in characterizing the non-stationary signal attributes across time and frequency domains [18]. There are two primary approaches to incorporate TFA into blind source separations. Firstly, in an undetermined BSS scenario, discrete TFA techniques can be employed to decompose the insufficient observations into a set of resolved signals. For instance, [PERSON] compared variational mode decomposition (VMD) and discrete wavelet transform (DWT) in decomposing the single-channel signal when combined with ICA and found that VMD demonstrated slightly higher effectiveness [19]. Secondly, given that BSS techniques can be utilized in both image and signal separation, continuous TFA or spectrograms can serve as direct inputs for estimating the separation weights. Such TFA approaches provide a comprehensive understanding of signal dynamics that surpasses conventional BSS techniques focusing solely on temporal or spectral domains. [PERSON] et al. combined a short-time Fourier transform (STFT) with convolutive BSS to calculate more reliable unmixing filters [20]. But, according to [PERSON]'s uncertainty principle, the STFT suffers from the limited TF resolution and information loss caused by linear TF conversion and the fixed window functions. In this regard, a continuous wavelet transform (CWT) can be used in BSS to give a higher resolution representation with scalable windows.