Low SNR multimirror Fabry–Perot pressure sensor optic spectrum signal analysis and demodulation via SVM-KNN regressors

Yiguang Yang; Yiguang Yang; Dahe Geng; Hao Chen; Xujin Li; Weihong Zhang; Yibo Yuan; Xiangqian Meng; Li Wenhong

doi:10.1364/AO.509671

Applied Optics
Vol. 63,
Issue 6,
pp. A16-A23
(2024)
•https://doi.org/10.1364/AO.509671

Low SNR multimirror Fabry–Perot pressure sensor optic spectrum signal analysis and demodulation via SVM-KNN regressors

Yiguang Yang, Dahe Geng, Hao Chen, Xujin Li, Weihong Zhang, Yibo Yuan, Xiangqian Meng, and Li Wenhong

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Yiguang Yang, Dahe Geng, Hao Chen, Xujin Li, Weihong Zhang, Yibo Yuan, Xiangqian Meng, and Li Wenhong, "Low SNR multimirror Fabry–Perot pressure sensor optic spectrum signal analysis and demodulation via SVM-KNN regressors," Appl. Opt. 63, A16-A23 (2024)

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- Fiber Optics, Fiber Sensors, and Optical Communications
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About this Article
History
- Original Manuscript: October 19, 2023
- Manuscript Accepted: December 20, 2023
- Published: January 17, 2024
Virtual Issues
Applied Optics Radiography, Applied Optics, and Data Science 2023 (2024)

Abstract

We demonstrate an ensemble learning based method to solve the problem of low SNR Fabry–Perot sensor spectrum signal demodulation. Taking the eight-layer approximate coefficients of a multilevel discrete wavelet transform as input features, an ensemble model that combines multiple SVM and KNN learners is trained. Bootstrap and booting techniques are introduced for better modeling performance and stability. It is shown that the performance of the proposed ensemble model based on SVM-KNN regressors is excellent; an accuracy of 0.46%F.S. relative mean error is achieved. This method could provide insight into the construction of a large scale fiber based Fabry–Perot sensor network.

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Corrections

4 March 2024: Corrections were made to the author listing and affiliations.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Fig. 1. Schematic diagram of C-band FPI sensor interrogation system.

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Fig. 2. (a) Photo of FPI sensor MEMS head chip and glass tube. (b) Photo of FPI sensor with metallic packaging. (c) Schematic diagram of the four-cavity structure of the FPI sensor.

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Fig. 3. (a) Simulation result of cascaded four-cavity FPI intensity reflectivity based on MMFPI theory. (b) Measured reflection optical spectrum of FPI pressure sensor.

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Fig. 4. Reflecting optic spectrums of FPI sensor with scanning pressure values applied in the form of (a) colormap and (b) mesh surface plot.

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Fig. 5. Schematic diagram of full-process SVM-KNN regression based ensemble learning demodulation method.

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Fig. 6. Eight-layer wavelet decomposition approximate coefficients. (a) First layer, (b) second layer, (c) third layer, (d) fourth layer, (e) fifth layer, (f) sixth layer, (g) seventh layer, and (h) eighth layer.

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Fig. 7. Normalized eight-layer wavelet approximate coefficients with scanning pressure values applied in the form of (a) colormap and (b) mesh surface plot.

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Fig. 8. Demodulation performance of SVM and KNN algorithms in test set. (a) SVM demodulation results. (b) KNN demodulation results. (c) SVM demodulation errors. (d) KNN demodulation errors.

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Fig. 9. Validation test results. (a) SVM demodulation values. (b) KNN demodulation values. (c) Bagging demodulation values. (d) Comparison of demodulation errors.

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Tables (2)

Table 1. Length Parameters of the Four-Cavity Structure of the FPI Sensor

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Table 2. Demodulation Performance Evaluation Metrics

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E_{i + 1}^{+} = E_{i}^{+} t_{i} e^{- i θ_{i}} + E_{i + 1}^{-} r_{i},

E_{i}^{-} = - r_{i} E_{i}^{+} + t_{i} E_{i + 1}^{-} e^{i θ_{i}} .

E_{i}^{+} = \frac{1}{t_{i}} [e^{- i θ_{i}}, - r_{i} e^{i θ_{i}}] (\begin{matrix} E_{i + 1}^{+} \\ E_{i + 1}^{-} \end{matrix}),

E_{i}^{-} = \frac{1}{t_{i}} [- r_{i} e^{- i θ_{i}}, e^{i θ_{i}}] (\begin{matrix} E_{i + 1}^{+} \\ E_{i + 1}^{-} \end{matrix}) .

(\begin{matrix} E_{i}^{+} \\ E_{i}^{-} \end{matrix}) = \frac{1}{t_{i}} [\begin{matrix} e^{- i θ_{i}} & - r_{i} e^{i θ_{i}} \\ - r_{i} e^{- i θ_{i}} & e^{i θ_{i}} \end{matrix}] (\begin{matrix} E_{i + 1}^{+} \\ E_{i + 1}^{-} \end{matrix}) .

\begin{aligned} (\begin{matrix} E_{1}^{+} \\ E_{1}^{-} \end{matrix}) & = \frac{1}{t_{1} t_{2} \dots t_{N - 1}} [\begin{matrix} e^{- i θ_{1}} & - r_{1} e^{i θ_{1}} \\ - r_{1} e^{- i θ_{1}} & e^{i θ_{1}} \end{matrix}] \times [\begin{matrix} e^{- i θ_{2}} & - r_{1} e^{i θ_{2}} \\ - r_{2} e^{- i θ_{2}} & e^{i θ_{2}} \end{matrix}] \\ \times \dots \times [\begin{matrix} e^{- i θ_{N - 1}} & - r_{N - 1} e^{i θ_{N - 1}} \\ - r_{N - 1} e^{- i θ_{N - 1}} & e^{i θ_{N - 1}} \end{matrix}] (\begin{matrix} E_{N}^{+} \\ E_{N}^{-} \end{matrix}) . \end{aligned}

(\begin{matrix} E_{1}^{+} \\ E_{1}^{-} \end{matrix}) = \frac{1}{t_{1} t_{2} \dots t_{N - 1}} [\begin{matrix} A & B \\ C & D \end{matrix}] (\begin{matrix} E_{N + 1}^{+} \\ E_{N + 1}^{-} \end{matrix}) .

ω (x) = {\begin{array}{l} 0 & x \leq - s \\ 1 + \frac{x}{s} & - s < x \leq 0 \\ - \frac{x}{s} + 1 & 0 < x \leq s \\ 0 & x > s \end{array} .

P = (1 - ω) P_{k n n} + ω P_{s v m} .

E_{mr} = \frac{e_{max}}{f_{s}},

E_{rr} = \frac{e_{r}}{f_{s}} ω .

Symbol	Description	Length
MC1	Thickness of silicon film	300 µm
MC2	Length of pressure sensing cavity	26 µm
MC3	Thickness of Pyrex substrate	500 µm
MC4	Gap between Pyrex substrate and fiber facet	About 1 mm

	$R^{2}$	RMSE (MPa)	MAPE	$E_{mr}$	$E_{rr}$
SVM	0.989	0.515	4.95%	10.7%	2.57%
KNN	0.994	0.384	3.59%	5.00%	1.92%
Bagging	0.999	0.092	0.94%	1.12%	0.46%

Symbol	Description	Length
MC1	Thickness of silicon film	300 µm
MC2	Length of pressure sensing cavity	26 µm
MC3	Thickness of Pyrex substrate	500 µm
MC4	Gap between Pyrex substrate and fiber facet	About 1 mm

	$R^{2}$	RMSE (MPa)	MAPE	$E_{mr}$	$E_{rr}$
SVM	0.989	0.515	4.95%	10.7%	2.57%
KNN	0.994	0.384	3.59%	5.00%	1.92%
Bagging	0.999	0.092	0.94%	1.12%	0.46%

Abstract

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Equations (11)

Applied Optics