In the real-time damage monitoring of structures under complex conditions, the damage source is easily affected by various external dynamic factors, and the monitoring information processing needs to continuously and accurately analyze the damage source signals containing a lot of noise information. The monitoring signal of acoustic emission technology is a typical non-stationary dynamic data set, and the received signal and the source signal are typically time-varying unstable. This study proposes a time-varying convolution BSS algorithm for non-stationary signals that may separate dynamic time-varying convolution mixed signals. Firstly, with the use of the variable Decibel Bayesian (VB) inference approach based on the Gaussian process (GP) prior, the non-stationary source is isolated from the time-varying convolution signal frame by frame. Secondly, VB learning is used to retrieve the source signal and mixed matrix that contains parameter information. To facilitate VB inference, the acquired parameters and hyperparameters are propagated to multiple frames as prior information, and the posterior distribution is obtained by combining the likelihood function. Lastly, an estimate of the source signal is established. The acoustic emission damage signal modeling experiment verifies the algorithm's effectiveness. This study provides a new theoretical approach to real-time continuous damage signal analysis in complex environments.