## 1 Introduction
Variational modal decomposition (VMD) stands out as a cutting-edge technique for decomposing nonlinear signals into multiple frequency bands, distinguishing itself from conventional spatial frequency and subspace signal processing methods. Notably, it eliminates the need for computationally intensive calculations for both recursive and non-recursive signals. This breakthrough allows for the comprehensive construction and resolution of variational problems, achieving the separation of signal frequency bands [32; 33]. This innovative time-frequency analysis method accomplishes signal decomposition by constructing and solving constrained variational problems. It transforms the original signal into a specified number of intrinsic mode functions (IMFs), a capability that is highly effective in handling nonlinear and non-smooth signals. In the realm of structural damage identification, highly sensitive time series sample parameters are found at critical structural points, categorizable into the time domain, frequency domain, and time-frequency domain based on signal types [34]. Utilizing VMD to preprocess vibration signals from structural damage points, followed by smoothing and noise reduction, proves to be a viable approach. Currently, numerous scholars have delved into the efficacy of VMD in processing vibration signals related to structural damage. [PERSON] et al. [35] introduced a structural damage identification method leveraging VMD and Chirplet transform, successfully achieving precise location and quantification of structural damage, both in single and multi-point damage scenarios. [PERSON] [36] furthered exploration of VMD's capabilities by integrating it with deep learning models like CNN, LSTM, and BiLSTM. This integration was tested using the IASC-ASCE SHM benchmark model, yielding impressive accuracy in damage identification. This underscores the promising potential of VMD in the field of structural damage identification. Self-attention mechanisms represent a variant of attention mechanisms, adept at capturing internal correlations within data or features themselves [37]. The self-attention mechanism facilitates the model in capturing long-range dependencies between different positions within an input sequence. These mechanisms enable the model to comprehend data representation across various locations and subspaces, facilitating the learning of relevant information in different representation subspaces. Consequently, this empowers the model to discern correlations between distinct parts of the entire input information [38]. In time series data, there are correlations between data sequences from the same measurement point at different time steps. However, the efficacy of signal decomposition or feature extraction techniques is often constrained in capturing these correlations. By incorporating the self-attention mechanism, the model can be trained on extensive data to learn the inherent dependencies and assign weighted importance to different values. This application enhances the model's capability to discern similar response waveform patterns to a certain degree, thereby improving its overall discriminative power. At the heart of the convolutional self-attention neural network (CSANN) lies the self-attention mechanism layer and the convolutional layer. The self-attention layer is crucial for correlating features at different nodes of the time series data with the model output, thereby determining the representation of the time series. Meanwhile, the convolutional layer focuses on extracting local feature information within the temporal neighborhood, performing essential feature transformations [39]. Drawing inspiration from multivariate decomposition and smoothing processes applied to time series signals through variational mode decomposition in various fields [40; 41], this paper introduces a damage identification model that combines VMD and CSANN.