# A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
## 2 Ensemble EMD with LR Related Works
### Emd
Industrial vibration analysis: Enhanced EEMD algorithms with multi-sensor fusion and minimum lower-bound frequency selection enable the precise denoising of acoustic signals from high-voltage shunt reactors. This method eliminates environmental noise interference and accurately assesses the health of equipment [35];
3. Financial forecasting [36]: Integrated into hybrid frameworks (e.g., EEMD-SE-GA-GRU), EEMD decomposes nonlinear stock market data (e.g., Dow Jones Index) into multi-scale IMFs. Clustering IMFs by their sample entropy (SE) complexity reduces the input dimensions by 38%, significantly boosting the prediction accuracy of this approach (R\({}^{2}\) = 0.9814);
4. Geophysical signal processing [37]: While newer variants like SVMD dominate marine MT data denoising, EEMD-inspired decomposition principles underpin noise suppression in wave-induced electromagnetic interference, which improves the subsurface electrical structure analysis of this approach;
5. Environmental modeling: Some studies apply EEMD to PM2.5 prediction (e.g., EEMD-SSA-LSTM, EEMD-ALSTM [38]), and the development of an EEMD-CNN-BiLSTM water environmental indicators prediction method [39] highlights the successful application of EEMD in the field of meteorology. In terms of model comparison, this method mainly includes integrated benchmarks in LSTM, SVR, and urban air quality index prediction research (for example, LSTM-SVR hybrid models are superior to individual models [40]), as well as GIS transformer frameworks for irregular time series [41], and so on. These applications highlight EEMD's adaptability in isolating signal components from noise-polluted, non-linear data through adaptive IMF extraction and ensemble averaging. In summary, EEMD enhances the robustness and dependability of signal decomposition through the incorporation of stochastic elements and integration methodologies. This enables it to effectively address challenges like mode mixing and over-decomposition that are prevalent in traditional EMD methods, which renders it a more potent and trustworthy tool for managing diverse signal types. In the process of using EEMD, the initial task involves identifying the characteristics of the random noise and establishing the number of iterations. Afterward, this noise is merged with the initial signal to create numerous unique random experiments. Each experiment involves combining the initial signal with varying random noise to generate multiple versions featuring diverse random disturbances. Subsequently, EMD is utilized on each noisy signal experiment to derive a collection of IMFs. Ultimately, the outcomes from each experiment pertaining to the identical IMF component are averaged to yield resilient IMFs. Below is a concise overview of the procedure for decomposing time series using EEMD. (1) Initialization  
Assume that there is an initial signal \(x(t)\), along with EEMD parameters (such as iteration count, noise standard deviation, etc. ), and that the selection of the type and parameters of the random noise is to be conducted. (2) Generate random experiments  
For each experiment (\(i\) = 1, 2, \(\ldots\), \(n\)), generate random noise sequences \(N_{i}(t)\) of the same length. The random noise can be Gaussian noise or a uniformly distributed random sequence. (3) Add random noise  
Combine each random noise sequence with the initial signal to obtain signal experiments with noise \(y_{i}(t)=x(t)+N_{i}(t)\). (4) Run EMD  
Apply the EMD algorithm to each signal experiment with noise \(y_{i}(t)\), decomposing it into a set of \(IMF_{i}\) (\(i\) = 1, 2, \(\ldots\), \(k\)) as demonstrated in Equation (1). \[y_{i}(t)=\sum_{i=1}^{k}c_{i}(t)+r_{i}(t) \tag{1}\]  
where \(c_{i}(t)\) is the \(i\)-th \(IMF\) in the experiment, and \(r_{i}(t)\) is the residual term. The initial signal \(x(t)\) depicted by the black line in Figure 1 is processed using a cubic spline interpolation approach that identifies the local minimum and maximum values.