# Research on an Ultraviolet Spectral Denoising Algorithm Based on the Improved SVD Method

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## Abstract

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_{2}), followed by noise reduction procedures. It is shown that the improved SVD noise reduction algorithm proposed in this paper enhances the signal-to-noise ratio (SNR) by 18.02% and 16.86%, and reduces the root-mean-square error (RMSE) by 15.13% and 14.92%, respectively, compared with the singular value difference spectrum (SVDS) denoising method and wavelet transform denoising method under the condition of low SNR. Furthermore, there exists a linear relationship between the concentration of SO

_{2}samples and the eigenvalues of the UV spectra, demonstrating a higher linear goodness with a coefficient of 0.99735. The denoising method proposed in this paper does not require the manual setting of various types of parameters, and has a better ability to deal with the noise of UV spectral signals in engineering sites with complex environments.

## 1. Introduction

_{6}) gas employed in GIS demonstrates robust electrical insulation properties and excels in arc extinguishing performance. However, insulation defects that may arise during GIS manufacturing and operational processes can lead to partial discharges, resulting in SF

_{6}decomposition and the formation of various derivative compounds. Among the most prevalent characteristic decomposition components of SF

_{6}gas, the concentration of SO

_{2}serves as a pivotal indicator for assessing GIS insulation conditions. The detection of these characteristic SF

_{6}decomposition components in GIS is typically achieved through a variety of methods, including gas chromatography [4,5], infrared absorption spectrometry [6,7,8], and photoacoustic spectrometry [9].Gas chromatography offers high accuracy in gas detection but is plagued by extended detection periods. Photoacoustic spectrometry boasts high detection sensitivity, albeit susceptible to interference from environmental noise. Infrared absorption spectrometry permits simultaneous detection of multiple gases, but encounters challenges associated with the mutual interference of absorption peaks from each gas and high equipment costs [10].Within the wavelength range of 290 nm to 310 nm, SO

_{2}does not exhibit any characteristic absorption overlap with other SF

_{6}derivatives [11,12]. Consequently, UV absorption spectroscopy presents notable advantages in SO

_{2}detection. These advantages encompass shorter detection periods, reduced equipment costs, and minimized gas consumption.

_{2}within the GIS, it is imperative to undergo a denoising process of the ultraviolet spectral signal. Conventional methods for spectral data noise reduction encompass Fourier transform, wavelet transform, Savitzky–Golay filtering, and empirical mode decomposition (EMD). Fourier transform excels in analyzing signals in the frequency domain, particularly periodic ones, but falls short in extracting features from localized signals. Conversely, wavelet transform and the Savitzky–Golay filter necessitates the manual selection of various filtering parameters, rendering them less suitable for on-site inspections. Furthermore, EMD is an iterative algorithm that demands repeated signal decomposition, potentially leading to modal overlap issues and yielding unstable decomposition results.

- A passive, built-in optical sensor has been engineered, featuring a high-reflectivity concave mirror seamlessly integrated into the flange. This sensor is designed for direct mounting onto the GIS, enabling real-time online monitoring.
- Our innovative approach involves the reconstruction of singular values from noise-inclusive signals into distinct component signals. These component signals are then integrated with the fast Fourier transform (FFT) algorithm, introducing FFT peaks as metrics to characterize the signals. These metrics are subsequently ranked through a decremental process. The singular value corresponding to the first FFT peak surpassing a predefined threshold is chosen as the effective order for denoising.
- Detection experiments involving various concentration gradients were carried out using the SO
_{2}ultraviolet spectroscopy detection platform. The denoising performance of the proposed method was then compared to that of the conventional approach. The results clearly indicate that the method presented in this study outperforms the conventional approach in terms of denoising accuracy, making it a promising option for practical applications.

## 2. Related Work

## 3. Theoretical Method

#### 3.1. Principle of SVD Denoising

_{1}, x

_{2}, x

_{3}, …, x

_{N}), a noise signal S = (s

_{1}, s

_{2}, s

_{3}, …, s

_{N}), and a noisy signal Y = (y

_{1}, y

_{2}, y

_{3}, …, y

_{N}), where N represents the length of the signal, the relationship among the three signals can be expressed as follows:

_{m×n}(m ≤ n):

#### 3.2. Determining the Optimal SVD Decomposition Order

_{i}is preserved, while the remaining singular values are set to zero. This process generates a collection of singular value vectors ${\Delta}_{i}^{\prime}=\mathrm{diag}(0,\cdots ,{\lambda}_{i},\cdots ,0)$, along with the singular value matrix and Hankel matrix, which can be represented in the following form:

_{i}in ${\Delta}_{i}^{\prime}$ is transformed into a matrix of singular values. The matrix is then inverted using singular value decomposition, resulting in the transformation matrix ${H}_{i}^{\prime}$, as depicted in Equations (5) and (6) provided earlier. Subsequently, the Hankel matrix is reduced to yield the component signals Y

_{i}, which correspond to the original signal Y. These component signals are utilized to reconstruct the spectral signal.

## 4. Experimentation and Evaluation

#### 4.1. Denoising of SO_{2} UV Spectral Signal Simulation

_{2}gas within the wavelength range of 290 nm to 310 nm. The data had a sampling interval of 0.11 nm and a signal length of 203. We also used simulated signals with added noise at a SNR of 5 dB, as show in Figure 1 and Figure 2.

_{2}, we assess the denoising performance of the UV-difference spectrum of SO

_{2}using the proposed denoising algorithm, the SVDS method, and the wavelet denoising method. For the wavelet denoising method, we choose the “sym14” wavelet basis function and set the number of decomposition layers to five [20]. The simulation dataset comprises a total of 30 samples. To gauge the denoising effectiveness, we employ the SNR and RMSE metrics. The denoising results are presented in Figure 6 and Figure 7.

#### 4.2. Denoising Experiments for Each Concentration Gradient of SO_{2}

_{2}detection platform was established. This platform was equipped with a setup designed for SO

_{2}analysis. We meticulously prepared five sets of SO

_{2}test samples, each with concentrations of 1, 2, 5, 10, and 20 µL/L. A schematic of the experimental testing platform is depicted in Figure 8.

_{2}gas before being directed to the spectrometer via the focusing mirror. The spectrometer was connected to a computer, which further analyzed and processed the acquired spectral data. The high-reflectivity concave mirrors used in the experiments were integrated into the back of the flange, and the microspectrometer, xenon lamp, single-mode fiber optic, and PC processing terminal were integrated into the portable toolbox, as illustrated in Figure 9.

_{2}at five different concentrations were subjected to noise reduction using three distinct methods: the algorithm proposed in this paper, wavelet transform, and SVDS. Following the Beer–Lambert law, absorbance is directly proportional to gas concentration, taking into account the absorption coefficient and optical path length. Similarly, in the frequency domain, attributes such as the maximum magnitude following FFT are also proportionate to gas concentration. Figure 10 illustrates that the UV absorption spectra of SO

_{2}at varying concentrations, after processing with the algorithm presented in this paper, display a well-defined distribution of absorption peaks and consistent frequency domain characteristics.

_{2}gas concentration after various denoising methods were fitted, as illustrated in Figure 11.

## 5. Conclusions

- (1)
- This study introduces the novel application of the SVD method for denoising SO
_{2}ultraviolet spectral signals. It also proposes an optimized method for selecting the effective order of singular value denoising. This method involves reconstructing each singular value of the original spectral signal into a one-dimensional signal, analyzing it in the frequency domain, and using the frequency value with the highest amplitude as an index to characterize each singular value component. - (2)
- The denoising algorithm’s effectiveness is maximized by selecting the singular value order corresponding to the first significantly changed frequency value as the algorithm’s effective order.
- (3)
- In low SNR conditions, our study reveals that the improved SVD noise reduction algorithm presented in this paper leads to substantial improvements. It boosts the SNR by 18.02% and 16.86%, as compared to the SVDS method and the wavelet transform denoising algorithm, respectively. Additionally, the RMSE diminishes by 15.13% and 14.92%, respectively. Furthermore, the linear relationship between the concentration of SO
_{2}samples and the characteristic value of the UV spectra achieves a remarkable coefficient of 0.99735. The denoising method proposed in this paper does not require manual setting of various types of parameters, and has a better ability to deal with the noise of UV spectral signals in engineering sites with complex environments.

_{2}UV spectra. In future research endeavors, it would be worthwhile to explore whether this method can be extended to the spectra of other characteristic decomposition component gases of SF

_{6}.

## Author Contributions

## Funding

## Institution Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Singular Value Component Signals with Noise, SNR: 5 dB. (

**a**) 1st to 4th singular value component signals; (

**b**) 5th to 8th singular value component signals.

**Figure 9.**Hardware equipment used in the experiment. (

**a**) Gas absorption cells and portable spectral data acquisition box; (

**b**) Highly reflective concave mirrors; (

**c**) Internal optical pathway schematic.

**Figure 11.**Goodness of the linear regression fits. (

**a**) Original signal: 0.936; (

**b**) Improved SVD: 0.997; (

**c**) Wavelet transform: 0.995; (

**d**) SVDS: 0.956.

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**MDPI and ACS Style**

Qin, Z.; Wang, Z.; Wang, R.
Research on an Ultraviolet Spectral Denoising Algorithm Based on the Improved SVD Method. *Appl. Sci.* **2023**, *13*, 12301.
https://doi.org/10.3390/app132212301

**AMA Style**

Qin Z, Wang Z, Wang R.
Research on an Ultraviolet Spectral Denoising Algorithm Based on the Improved SVD Method. *Applied Sciences*. 2023; 13(22):12301.
https://doi.org/10.3390/app132212301

**Chicago/Turabian Style**

Qin, Zhaoyu, Zhaofan Wang, and Ruxing Wang.
2023. "Research on an Ultraviolet Spectral Denoising Algorithm Based on the Improved SVD Method" *Applied Sciences* 13, no. 22: 12301.
https://doi.org/10.3390/app132212301