FBG Wavelength Demodulation Method Based on Support Vector Regression Optimized by Sparrow Search Algorithm

Fiber Bragg grating (FBG) wavelength demodulation technique based on tunable Fabry-Perot (F-P) filters (FFP-TF) results in a degradation of the accuracy of the demodulation system due to the hysteresis and temperature drift characteristics of piezoelectric ceramics (PZT) inside the FFP-TF. Artificial intelligence machine learning algorithms can reduce the demodulation error of the system without increasing the complexity of the system. Therefore, this article proposes an FBG wavelength demodulation method based on Support Vector Regression (SVR) optimized by Sparrow Search Algorithm (SSA). The main purpose is to establish a nonlinear fitting relationship between F-P tuning voltage and transmission wavelength, replacing wavelength reference hardware. This method can save system costs, improve system demodulation accuracy, and contribute to the integrated development of demodulation systems. First, the reference grating, driving voltage, tuning time and F-P surface temperature are taken as the input features of the model, and the F-P transmission wavelength is taken as the output feature, and the F-P transmission wavelength compensation model is established by SVR. The SSA-optimized hyperparameters C and g are then input into the SVR model for training to obtain the target compensation model. Meanwhile, the training method of combining sliding window with SVR is proposed to improve the model's global optimization-seeking ability by updating the sliding window's size and sliding speed, which avoids the problem of the model's deterioration in generalization ability over time. After the model training, the correlation coefficient (R-2), Mean Square Error (MSE), and Root Mean Square Error (RMSE) are introduced to evaluate the model and obtain the optimal compensation model. Finally, the FBG wavelength demodulation system based on SSA-SVR is built in Labview and the optimal training model is called. Then the real-time compensation ability of the model is checked by the stability experiment and the cooling experiment. The law of the wavelength compensation error in the frequency range of 0.5 similar to 2.5 Hz driving is explored experimentally, and the compensation ability of the SSA-SVR model is compared with PSO-SVR, LSSVR, and KRR models. The experimental results show that in the frequency range of 0.5 similar to 2.5 Hz, the error between the target value output and the real value of the SSA-SVR algorithm model decreases with the decrease of the driving frequency, which indicates that the demodulation system is more accurate under the low-frequency driving. The fitting coefficient R-2 of the SSA-SVR algorithm reaches 0.999 99 in both training and test data, which is an improvement of 0.001 compared to the KRR algorithm, and the wavelength demodulation error is reduced by more than ten times. At 2.5 Hz driving frequency, the Mean Absolute Error (MAE) of SSA model is 38.689 pm, which is reduced by 28.078 pm compared to the PSO algorithm error, similarly, at 0.5 Hz driving frequency, the SSA model has a MAE of 19.83 pm, which is reduced by 48.8% compared to the PSO optimization algorithm error of 39.68 pm. In addition, the SSA model has the smallest error in all of the different drive frequency tests, showing better generalization performance, while the LSSVR model performs better at high frequencies and shows negative optimization in the low-frequency tests, and the KRR model has the largest error in a wide range of frequencies, indicating that this model has the worst fit. In the stability experiment at 25 degrees C , the fluctuation of the demodulation value based on the SSA-SVR model is kept within 15 pm, and the average absolute error between the demodulation value and that of the sm125 demodulator produced by MOI company in the U.S. A. is 7.28 pm, whereas the stability of the traditional polynomial demodulation method of the reference grating is poorer, and the demodulation error of the SSA is reduced by 88.5% compared with it. For the cooling experiments from 40 to 90 degrees C , the detuned MAE of the SVR compensated model is 7.44 pm, which is 27.6% lower relative to the 5.39 pm of the polynomial fitting method. The experiment proved through error analysis that this method is superior to the reference grating polynomial demodulation method in terms of real-time demodulation and stability, and the error between it and the sm125 demodulator remains within a small range. Compared with the traditional method, this method models the wavelength drift during the natural temperature change process of FFP-TF, realizes the nonlinear fitting between the F-P driving voltage and the transmitted wavelength over a wide range, and verifies that the fiber grating demodulation system can effectively reduce the grating wavelength demodulation error without the help of hardware reference.