The fiber Fabry-Perot (F-P) filter plays a critical role in fiber Bragg grating (FBG) wavelength demodulation systems. However, the continuous drift in the transmission wavelength and driving voltage curve of the F-P filter due to changes in the ambient temperature can significantly decrease the wavelength demodulation accuracy. To correct the drift error, researchers have proposed several wavelength correction methods, such as the F-P etalon, FBG reference grating, and gas absorption line reference methods. Despite high accuracy, these methods can increase the system's cost and complexity. Recently, with the increased applications of artificial intelligence, machine learning methods have emerged as a novel and highly portable option for correcting temperature drift errors in F-P filter at a relatively low cost. Currently, the most commonly employed technique for temperature drift correction is support vector machine (SVM), which does not take into account the high temporal correlation among samples before and after temperature drift data. To this end, we propose an Attention-LSTM network-based temperature drift correction method for F-P filters. The temperature drift data for the F-P filter is a typical time series with dynamic characteristics, indicating that the current drift depends both on the present input and the past input. We adopt the LSTM model for feature extraction and apply the attention mechanism to assign different weights to various input features. The combination of short-term and long-term memory, along with the attention mechanism, enhances the demodulation accuracy of the F-P filter.

We select FBG0 as the reference grating and the other three FBGs as sensing gratings. The input features employed in the model include temperature, temperature change rate, and the spectral position of FBG0. The output of the model is the absolute wavelength drift of sensing FBG3. Due to the strong temporal correlation in the temperature drift data of the F-P filter, a fixed length of time series samples is first selected, and then a multi-temporal training dataset is obtained by sliding it successively in a backward direction. By adopting the LSTM algorithm, the hidden states are generated for each time step by learning the input information of the current and past times and are then integrated into a context vector that serves as the input for the attention layer. The attention layer processes the data further by assigning weights to give significant information larger values, highlights important information, and filters out useless information, thus improving the model's prediction accuracy. The ReLU layer is employed after the attention layer to enhance the model's non-linear fitting abilities. Finally, a linear layer is adopted for dimensionality reduction to obtain the temperature drift prediction results of the F-P filter. The proposed model's effectiveness is validated by comparing it to the traditional LSTM model in the same temperature environment.

In a heating-cooling-heating temperature variation environment, the proposed model is compared to a traditional LSTM model in error correction results of temperature drift for the three sensing gratings (Table 2). Experimental results show that the maximum temperature drift correction error of the traditional LSTM model is 16.64 pm, while the Attention-LSTM model reduces the maximum temperature drift correction error to 6.75 pm. Additionally, the proposed model is compared to common temperature drift models such as LSSVM, RNN, and LSTM in a slowly changing monotonous cooling environment (Table 3). Experimental results indicate that the performance of the Attention-LSTM model is superior to other temperature drift models. The above experimental results demonstrate that the proposed model integrates the attention mechanism with traditional LSTM models for time series modeling. This model adopts LSTM to extract long-term and short-term data sample information over time and the attention mechanism to assign different weights to the sample features. As a result, important feature information is highlighted, and the demodulation accuracy and stability are improved.

We thoroughly consider the time correlation between temperature drift data samples and the dynamic drift law. We not only take into account the influence of current inputs on the drift amount but also capture the effect of past inputs on the demodulation results. The LSTM model is employed for feature extraction and an attention mechanism is introduced to propose an F-P filter temperature drift error correction method based on the Attention-LSTM network. The attention mechanism assigns different weights to different features in the model to improve the modeling accuracy of the LSTM model. We conduct temperature drift error correction experiments in two temperature variation environments and compare the Attention-LSTM model with traditional LSTM model, RNN model, and LSSVM model. Experimental results demonstrate that the performance of the Attention-LSTM model in temperature drift error correction is significantly better than that of other models, with a MAXE of only 5.39 pm and MAE and RMSE of just 2.07 pm and 2.62 pm respectively. Meanwhile, compared to traditional hardware methods, the proposed error correction method based on the attention mechanism and LSTM network is low-cost with high portability, as it does not require any hardware equipment. This approach provides a new perspective for temperature drift error correction of tunable F-P filters.