## 2 Methodology
### Noise Reduction Method Based on Empirical Mode Decomposition  
After the differential analysis of residents, we can obtain the typical residential electricity consumption data. However, the data for each type of residential electricity consumption are strong and noisy. To reduce the noise and further improve the prediction accuracy, we use the empirical mode decomposition method to decompose the complex original signal. This method can decompose complex and unstable load signal into a relatively stable Intrinsic Mode Function (IMF), which is reconstructed into a more stable time series. By using the empirical mode decomposition method, the IMF component is selectively input into the subsequent prediction model to reduce noise and further improve prediction accuracy. The specific process is shown in Figure 2.  
Empirical mode decomposition (EMD) is a time-frequency analytical method of signal proposed in 1998, where the signal refers to a time series signal [35]. Common time series signal processing methods can be divided into three categories: time domain, frequency domain, and time-frequency domain [36]. Time-domain analytical features include meaning, variance, kurtosis, peak-to-peak value, etc. Frequency-domain features include frequency, energy, etc. Time-frequency domain analysis includes wavelet transform, etc.  
The EMD theory holds that all signals are composed of a finite number of Intrinsic Mode Functions. The IMF component contains local characteristic signals of different time scales of the original signal. The empirical mode decomposition method can make the non-stationary data smooth, and then it performs the Hilbert transform to obtain the time spectrum diagram and the frequency with physical meaning [37]. EMD decomposes the input signal into several eigenmode functions and a residual, which is composed of the following formula:  
\[I(n)=\sum\limits_{m=1}^{M}IMF_{m}(n)+Res_{M}(n)I(n) \tag{10}\]  
where I(n) represents the input signal, \(IMF_{m}(n)\) represents the intrinsic mode function of \(M_{th}\), and \(Res_{M}\) (\(n\)) represents the residual. Where in the process of extracting IMF is called screening, and the process of screening is as follows.  
First, we mark the local extreme points. Then, we connect the maximum points to form the upper envelope through a cubic spline line and connect the minimum points to form the lower envelope. After that, we find the mean value \(m_{1}\) of the upper and lower envelope. Finally, we subtract the mean value \(m_{1}\) of the upper and lower envelopes from the input signal \(X(t)\).  
\[I(n)-m_{1}=h_{1}I(n)-m_{1} \tag{11}\]  
One iteration of the above process cannot guarantee that \(h_{1}\) is an IMF, and the above process needs to be repeated until \(h_{1}\) is an IMF. The iterative stopping criterion produces the number of executions of an intrinsic modulus function screening process, and the stopping criterion standard deviation (SD) used in this method is shown in Equation (12):  
\[\mathrm{SD_{k}}=\sum_{n=0}^{T}\frac{\left|h_{k-1}(n)-h_{k}(n)^{2}\right|}{h_{ k-1}^{2}(n)} \tag{12}\]  
In summary, EMD is atime-frequency domain signal processing method that can decompose signals based on the time-scale characteristics of the data without presetting any basic functions. EMD has obvious advantages in dealing with non-stationary and nonlinear data. It is suitable for analyzing nonlinear and non-stationary signal sequences.  
This is because the basis functions of EMD are derived from the signal itself. Therefore, this analysis is adaptive compared to traditional methods where the basis functions are fixed. EMD is based on the sequential extraction of energy associated with various intrinsic time scales of the signal, starting from finer time scales (high-frequency modes) to coarser time scales (low-frequency modes). The sum of IMFs is well-matched to the signal, thus reducing noise while maintaining integrity.