## 3 Model Validation and Engineering Examples
### Results of the Decomposition of the Settlement Data for Sections 1-17  
EMD adaptively decomposes settlement data to obtain six components without preset parameters; CEEMDAN adopts the same decomposition parameters as EMD and ultimately obtains five components. The decomposition parameters of VMD are obtained via the optimization algorithm. The decomposition layer is set to six and the secondary penalty factor is set to 500. WPT performs three-layer decomposition to obtain four frequency components. The data from cross-sections 1-17 were decomposed via various methods. Table 3 shows the reconstruction errors for each algorithm, expressed as the mean absolute error (MAE). Although VMD effectively reduces mode mixing, it does not fully preserve settlement integrity. In comparison, EMD has negligible reconstruction error, whereas CEEMDAN improves upon EEMD, achieving nearly zero reconstruction error. Decomposition methods based on the wavelet function (WPT) also demonstrate good integrity after reconstruction. The MAEs for the different algorithms are shown in Table 3.  
The results of the data decomposition at points YG1-17 are shown in Figure 10 below. The vibration frequencies of _IMF_1 to _IMF_5 gradually decrease, which satisfies the requirements of the _IMF_ regarding the crossing of the zero point and the local extreme value point. EMD realizes a frequency decrease function of the components, but it can be seen from _IMF_1 to _IMF_4 that the frequency regularity of each intrinsic mode component is not consistent. In the late stabilization stage, the original measured data form a relatively stable straight line, which becomes nonlinear after EMD and is unfavorable to the learning of the neural network, as the components decomposed through EMD are set to conform to the intrinsic mode components in the entire time domain; this corresponds to the \"endpoint effect\". The data during the later stabilization phase must also align with the variations in the earlier data and cannot be linearly transformed. The principal component (_IMF_6) is consistent with the definitions of simple functions. The decomposition method of CEEMDAN is similar to that of EMD, and owing to the addition of white noise, the decomposed components are smoother and can avoid the endpoint effect well. As shown in Figure 10, the wavelet decomposition method, owing to its excellent time-frequency localization properties, yields better results in signal decomposition and can effectively extract the features of each component so that it presents strong regularity. However, the wavelet decomposition method also has certain limitations. On the one hand, its computational complexity is high, especially when dealing with large-scale data or high-frequency signals, and the computational efficiency has difficulty meeting the demands of real-time applications. On the other hand, wavelet decomposition suffers from the problem of frequency-time nonlocality, which leads to the fact that in some complex signals, the principal components are not sufficiently decomposed and still contain large fluctuations. This limitation may adversely affect the accuracy of the decomposition results and the reliability of subsequent modeling. In contrast, the VMD method provides an effective alternative for signal decomposition because of its adaptive decomposition capability and strong noise immunity. Although VMD may introduce certain signal reconstruction errors after decomposition, it is able to eliminate noise to a certain extent through an iterative optimization mechanism, which significantly improves the smoothness of the signal and the independence of the components. In practical applications, VMD is able to effectively decompose the raw data into two parts, namely trend data and random data, in which the trend data can clearly reflect the basic characteristics of macroscopic changes, such as surface subsidence, whereas the random data show a high degree of regularity, which provides a better basis for further excavating the intrinsic structure of the signal.