# Noise Cancellation Method Based on TVF-EMD with Bayesian Parameter Optimization
## 5 Conclusions  
An optimized TVF-EMD model based on a Bayesian algorithm was adopted to develop a noise cancellation model for denoising the CO\({}_{2}\) concentration signal of a building. The Bayesian algorithm was used to optimally estimate the TVF-EMD parameters, namely the bandwidth threshold \(\xi\) and B-spline order \(n\), and the adaptive matching of the given CO\({}_{2}\) concentration signal. The main conclusions can be summarized as follows:  
In parameter optimization, a synthetic measurement index consisting of CCKur was used as the objective function of TVF-EMD. This function could identify anomalous signals while preserving the signal profile and avoided excessive noise reduction. In the proposed noise cancellation model, a thresholding parameter \(H_{thr}=0.5\), based on the Hurst exponent, was introduced as a measurement index for selecting the relevant IMFs for signal reconstruction.  
The hyperparameter \(\xi\) was more important for decomposition results. The efficacy of the synthetic measurement index was verified against five optimization indices: CC, Kur, MI, EE, and EEMI on decomposed IMFs. The results demonstrated that the proposed CCKur index was sensitive to \(\xi\), and the selection of CCKur as a synthetic measurement index and \(\max\{CCKur\}\) as an objective function were reasonable and effective.  
The noise reduction effect between different signal-denoising models, that is, TVF-EMD with default values, EMD, moving average method, and exponential smoothing method, was compared in terms of SNR, MSE, RSE, and NRMSE. The proposed noise cancellation model yielded the largest absolute value of SNR and the smallest MSE, RSE, and NRMSE, demonstrating the high noise reduction capability of the proposed model for CO\({}_{2}\) concentration signals.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & **Proposed** & **TVF-EMD with** & \multirow{2}{*}{**EMD**} & **Moving Average** & **Exponential** \\  & **TVF-EMD** & **Default Values** & & **(Window = 40)** & **Smoothing** \\  & **(\(\xi\) = 0.015,\(n\) = 4)** & **(\(\xi\) = 0.1,\(n\) = 26)** & & **(\(\mu\)s = 0.5)** \\ \hline SNRabs & 71.376 & 71.296 & 71.141 & 71.251 & 71.239 \\ _MSE_ & 7.877 & 95.976 & 3217.423 & 154.281 & 21.473 \\ _RSE_ & 0.000276 & 0.00336 & 0.112 & 0.00540 & 0.000752 \\ _NRMSE_ & 0.0166 & 0.0581 & 0.3614 & 0.0736 & 0.0274 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the noise reduction effect under different signal-denoising models.  
**Author Contributions:** Data curation, M.Y. and K.L.; Formal analysis, M.Y.; Funding acquisition, H.Y.; Investigation, H.Y.; Methodology, M.Y. and H.Y.; Project administration, H.Y.; Resources, H.Y.; Software, M.Y. and L.D.; Validation, L.D.; Visualization, H.Y.; Writing--original draft, M.Y.; Writing--review & editing, K.L. and L.D. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Project funded by the China Postdoctoral Science Foundation, grant number No. 2022M721845.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.