# Prediction of Structural Damage Trends Based on the Integration of LSTM and SVR
## 1 Introduction  
Large-scale equipment and structures are increasingly common among individual lives and in production processes. Issues, including corrosion aging, deformation, and damage, occur when such structures are subject to environmental erosion and various loads over long service periods. These problems affect the health of the structures to varying extents. In serious cases, such issues can lead to the fracture and collapse of the structure, threatening the safety of lives and property as well as destabilizing the development of the social economy [1, 2]. It is thus necessary to implement maintenance measures at an early stage of damage instead of dealing with an accident after the damage occurs. The prediction of structural damage is one of the key measures to achieve early damage diagnosis and prediction [3, 4]. However, the vibration signals of most engineering structures are relatively complex and exhibit characteristics such as nonlinearity and nonstationarity [5]. Using appropriate signal processing techniques to extract damage information when structural damage occurs is a key issue that needs to be addressed in structural health state prediction [6]. Although the wavelet transform proposed in the literature [7] has the characteristic of multi-resolution, it requires artificial selection of wavelet bases and lacks self-adaptability. Although empirical mode decomposition (EMD) in the literature [8] solves the problem of wavelet transform's lack of self-adaptability, it still has some problems, such as modal aliasing, significant endpoint effects, and lack of a complete theoretical basis. Variationalmode decomposition (VMD) [9] has a mature theoretical foundation. By decomposing signals into fixed-scale component signals, it can effectively solve the problem of modal aliasing with relatively weak endpoint effects. [PERSON] used VMD to decompose the power load series into subsequences with limited bandwidth, improving the prediction accuracy of power load [10]. [PERSON] et al. used VMD to decompose the wind speed into several IMF components that fluctuate around the central frequency, helping to restore its fluctuation characteristics during the prediction process [11]. The prediction of early structural damages requires appropriate time-series prediction methods. At present, there are many time-series prediction methods, such as the least squares support vector machine [12], auto-regressive integral moving average model (ARIMA) [13], artificial neural network [14; 15], and deep learning model [16; 17]. However, many current models have certain limitations in prediction research. For example, the traditional BP neural network is difficult to deal with long-term and complex problems, and its generalization ability is weak; the ARMA prediction model is easier to deal with stationary time series than non-stationary time series. Although the improved ARIMA model based on ARMA is suitable for the prediction of non-stationary time series, it is difficult to select the lag order in the model training period, and it is difficult to obtain the optimal value of the lag order. In the training process of the echo state network, the problem of local extremum is easy to appear, which affects the prediction effect of the model. Long short-term memory (LSTM) networks have become a popular research model in the framework of the recurrent neural network (RNN) and even deep learning and have received extensive attention [18]. To date, LSTM has been widely used in machine health monitoring [19], the prediction of bearing life [20], remaining useful life [21], watershed pollutant flux [22], short-term wind power [23], temperature [24], car suspension health, lithium battery, and other fields. [PERSON] et al. [25] implemented a loss function to iteratively refine and enhance the accuracy and robustness of traffic flow prediction based on \(\Delta_{\textit{free}}\)-LSTM; a large number of experiments on four benchmark datasets show that \(\Delta_{\textit{free}}\)-LSTM is superior to both canonical and nonparametric models.