# Study on Denoising Method of Photoionization Detector Based on Wavelet Packet Transform

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## Abstract

**:**

## 1. Introduction

_{2}/RGO nanocomposites to prepare MOS sensors, which can monitor 1–1000 ppm of ethanol. MOS sensors made of reduced GO/carbon monoxide nanocomposites can monitor 1 ppb of xylene. The response time of the sensor was shortened by LaCoO

_{3}modified ZnO, and the optimum temperature of four alcohol homologous gases monitored by a ZnO sensor was studied. However, MOS gas sensors have poor selectivity.

## 2. VOC Monitoring Device

#### 2.1. PID Module

#### 2.2. Single-Machine Serial Port Transmission Module

#### 2.3. Design of the Upper Machine Module

#### 2.4. VOCs Online Detection Device and Method

^{5}Pa. The standard gas used in this article was derived from Jining Xieli Specialty Co. Ltd., Jining, China. A standard gas bottle capacity is 8 L, the concentration of the standard gas is 2000 ppm benzene gas, and the gas is filled with nitrogen. A quality flowmeter was used to control the amount of the standard gas to calculate the content of the standard gas. The unit of the quality flowmeter is in L/min. Through Equation (1), the concentration of the standard gas can be calculated and its unit can be converted to mg/L to facilitate the calculation of the gas content in the gas cylinder. Among them, C is the mass concentration (mg/m

^{3}) of benzene gas, X is the volume concentration 2000 ppm, and M is the molar mass of benzene.

## 3. PID Sensor Signal Denoising Method Based on Wavelet Analysis

#### 3.1. Selection of a Wavelet Decomposition Level

_{k}and g

_{k}are the conjugation filters; q

_{k}is the low-pass filter coefficient; g

_{k}is the high-pass filter coefficient.

_{0}= $\phi (x)$, μ

_{1}= $\psi (x)$, at this time:

_{n}(x), ${V}_{j}^{2n}$ is the closure space of μ

_{2n}(x), ${V}_{j}^{2n+1}$ is the closure space of μ

_{2n+1}(x), then ${V}_{j}^{n}$ can be decomposed as:

_{i}in MSE is the original signal; ${\widehat{Y}}_{i}$ is the signal after noise.

#### 3.2. Selection of the Wavelet Packet Base

_{0}+ a

_{1}cos (aw) + b

_{1}sin (aw) + a

_{2}cos (2aw) + b

_{2}sin (2aw) + a

_{3}cos (3aw) + b

_{3}sin (3aw) + a

_{4}cos (4aw) + b

_{4}sin (4aw) + a

_{5}cos (5aw) + b

_{5}sin (5aw)

^{2}of this polynomial fitting was 0.9826 degrees to meet the minimal value requirements of the MSE of the db wavelet packet base. The minimal value of the MSE of the db wavelet packet base $\mathrm{f}\left(\mathrm{a}\right)min$ was 1.3213

_{0}+ a

_{1}cos (bw) + b

_{1}sin (bw) + a

_{2}cos (2bw) + b

_{2}sin (2bw) + a

_{3}cos (3bw) + b

_{3}sin (3bw) + a

_{4}cos (4bw) + b

_{4}sin (4bw) + a

_{5}cos (5bw) + b

_{5}sin(5bw)

^{2}of this polynomial fit was 0.9844, and the fitting accuracy met the requirements of the maximum value of the SNR of the db wavelet packet base. The db wavelet packet base SNR value $f\left(b\right)max$ was 36.8389.

_{0}+ a

_{1}cos (xw) + b

_{1}sin (xw) + a

_{2}cos (2xw) + b

_{2}sin (2xw) + a

_{3}cos (3xw) + b

_{3}sin (3xw) + a

_{4}cos (4xw) + b

_{4}sin (4xw) + a

_{5}cos (5xw) + b

_{5}sin (5xw)

^{2}of the polynomial fit was 0.9996, and the fitting accuracy met the extremely small value of the MSE of the sym wavelet packet base. The minor value of the MSE of the sym wavelet packet base $f\left(c\right)min$ was 1.3213.

_{0}+ a

_{1}cos (xw) + b

_{1}sin (xw) + a

_{2}cos (2xw) + b

_{2}sin (2xw) + a

_{3}cos (3xw) + b

_{3}sin (3xw) + a

_{4}cos (4xw) + b

_{4}sin (4xw) + a

_{5}cos (5xw) + b

_{5}sin (5xw)

^{2}of the polynomial fit was 0.9996, and the fitting accuracy met the requirements of the great value of the SNR of the sym wavelet packet base. The maximum value of the SNR of the sym wavelets $f\left(x\right)max$ was 36.8389.

#### 3.3. Self-Adaptive Weight Threshold Denoise Method Based on a Wavelet Decomposition Node Energy

_{i,j}can be calculated by Equation (2), S is the weight of the energy of the wavelet decomposition node.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Bior1.3 wavelet packet 3−layer decomposition of 5.57 ppm benzene gas PID with the noise signal.

**Figure 11.**Comparison of the denoising effect between the traditional wavelet packet and threshold weight wavelet packet.

Evaluation Indicator | 2-Layer Decomposition | 3-Layer Decomposition | 4-Layer Decomposition |
---|---|---|---|

SNR | 33.0418 | 36.6291 | 6.0453 |

MSE | 3.1490 | 1.3867 | 6.3679 |

Wavelet Packet Base | MSE | SNR | Wavelet Packet Base | MSE | SNR |
---|---|---|---|---|---|

db2 | 1.3541 | 36.7320 | sym2 | 1.3541 | 36.7320 |

db3 | 1.3213 | 36.8389 | sym3 | 1.3213 | 36.8389 |

db4 | 1.3892 | 36.6203 | sym4 | 1.3995 | 36.5880 |

db5 | 1.3719 | 36.6747 | sym5 | 1.4136 | 36.5441 |

db6 | 1.3722 | 36.6734 | sym6 | 1.3415 | 36.7721 |

db7 | 1.4312 | 36.4900 | sym7 | 1.3853 | 36.6322 |

db8 | 1.4004 | 36.5848 | sym8 | 1.4062 | 36.5668 |

db9 | 1.3803 | 36.6479 | sym9 | 1.4184 | 36.5291 |

db10 | 1.3886 | 36.6219 | sym10 | 1.4133 | 36.5446 |

db11 | 1.4221 | 36.5177 | sym11 | 1.3713 | 36.6761 |

db12 | 1.3832 | 36.6383 | sym12 | 1.4075 | 36.5627 |

db13 | 1.4323 | 36.4864 | sym13 | 1.4272 | 36.5022 |

**Table 3.**The db series wavelet packet base corresponded to the parameter value of the MSE fitting function.

a_{0} = 1.4 | a_{1} = 0.0148 | b_{1} = −0.02251 | a_{2} = 0.02968 |

b_{2} = −0.02415 | a_{3} = 0.02019 | b_{3} = −0.01056 | a_{4} = 0.03571 |

b_{4} = −0.01956 | a_{5} = 0.01173 | b_{5} = −0.0007733 | w = 0.471 |

**Table 4.**The db series wavelet packet base corresponded to the parameter values of the SNR fitting function.

a_{0} = 36.59 | a_{1} = 0.04017 | b_{1} = 0.06998 | a_{2} = −0.08918 |

b_{2} = 0.0732 | a_{3} = −0.06034 | b_{3} = 0.03041 | a_{4} = −0.1132 |

b_{4} = 0.05443 | a_{5} = −0.03743 | b_{5} = −0.0002794 | w = 0.4731 |

**Table 5.**The sym series wavelet packet base corresponded to the parameter value of the MSE fitting function.

a_{0} = 1.389 | a_{1} = −0.003555 | b_{1} = −0.02018 | a_{2} = 0.0003253 |

b_{2} = −0.005518 | a_{3} = 0.02447 | b_{3} = −0.02445 | a_{4} = 0.01532 |

b_{4} = 0.003341 | a_{5} = −0.01182 | b_{5} = 0.0009305 | w = 0.5068 |

**Table 6.**The sym series wavelet packet base corresponded to the parameter values of the SNR fit function.

a_{0} = 36.62 | a_{1} = 0.01159 | b_{1} = 0.06443 | a_{2} = −0.0009322 |

b_{2} = 0.0179 | a_{3} = −0.07799 | b_{3} = 0.07653 | a_{4} = −0.04938 |

b_{4} = −0.01174 | a_{5} = 0.03721 | b_{5} = −0.002947 | w = 0.5074 |

Wavelet Packet Base | MSE | SNR | Wavelet Packet Base | MSE | SNR |
---|---|---|---|---|---|

haar | 1.3867 | 36.6291 | rbio 1.3 | 1.4672 | 36.3840 |

dmey | 1.4553 | 36.4168 | rbio 1.5 | 1.6119 | 35.9748 |

bior 1.3 | 1.3166 | 36.8543 | rbio 2.2 | 1.4232 | 36.5151 |

bior 1.5 | 1.4407 | 36.4621 | rbio 2.4 | 1.3220 | 36.8363 |

bior 2.2 | 1.6239 | 35.9424 | rbio 2.6 | 1.3933 | 36.6075 |

bior 2.4 | 1.3496 | 36.7465 | rbio 2.8 | 1.3866 | 36.6285 |

bior 2.6 | 1.3824 | 36.6414 | rbio 3.1 | 2.2907 | 34.4489 |

bior 2.8 | 1.3646 | 36.6978 | rbio 3.3 | 1.4753 | 36.3598 |

bior 3.1 | 6.4503 | 29.9554 | rbio 3.5 | 1.4547 | 36.4198 |

bior 3.3 | 1.9288 | 35.1958 | rbio 3.7 | 1.3718 | 36.6752 |

bior 3.5 | 1.5646 | 36.1035 | rbio 3.9 | 1.3718 | 36.6750 |

bior 3.7 | 1.4093 | 36.5579 | fk 4 | 1.3307 | 36.8085 |

coif 1 | 1.4168 | 36.5348 | fk 6 | 1.3724 | 36.6733 |

coif 2 | 1.3994 | 36.5879 | fk 8 | 1.3713 | 36.6767 |

coif 3 | 1.4208 | 36.5218 | fk 14 | 1.3773 | 36.6571 |

coif 4 | 1.4008 | 36.5836 | fk 18 | 1.4258 | 36.5062 |

coif 5 | 1.4443 | 36.4499 | fk 22 | 1.4485 | 36.4374 |

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**MDPI and ACS Style**

Liu, Z.; Feng, X.; Dong, C.; Jiao, M.
Study on Denoising Method of Photoionization Detector Based on Wavelet Packet Transform. *Chemosensors* **2023**, *11*, 146.
https://doi.org/10.3390/chemosensors11020146

**AMA Style**

Liu Z, Feng X, Dong C, Jiao M.
Study on Denoising Method of Photoionization Detector Based on Wavelet Packet Transform. *Chemosensors*. 2023; 11(2):146.
https://doi.org/10.3390/chemosensors11020146

**Chicago/Turabian Style**

Liu, Zengyuan, Xiujuan Feng, Chengliang Dong, and Mingzhi Jiao.
2023. "Study on Denoising Method of Photoionization Detector Based on Wavelet Packet Transform" *Chemosensors* 11, no. 2: 146.
https://doi.org/10.3390/chemosensors11020146