1. Introduction

Recent years have seen the rapid growth and development of optical fiber sensors (OFSs) due to their superior features such as immunity to electromagnetic interference, capabilities for remote operation, multiplexing, and distributed sensing [1–3]. Among different configurations, interferometer-based OFSs, arguably one of the simplest optical fiber sensing modalities, have attracted wide research interest and have been extensively demonstrated for measuring a diverse array of quantities [4–6]. A quick search in Google Scholar with the keywords optical fiber interferometer returns about 369,000 results (accessed on March 4^th, 2022). In addition to the structures that are well-known in free-space optics, such as the Fabry-Perot interferometer, the Michelson interferometer, the Mach-Zehnder interferometer, and the Sagnac interferometer, a unique device of OFSs, the multimode interference-based sensor, has emerged owing to its ease of fabrication and high sensitivity [6–8].

An interferometer-based OFS is commonly interrogated using a broadband light source and an optical spectrum analyzer, where the spectral response of the sensor within a certain wavelength window (limited by the bandwidth of the light source) is measured. The characteristic spectrum of the interferometer-based sensor typically includes multiple fringe troughs within the wavelength window with different/similar magnitudes, which are simply manifestations of resonance (and the harmonics) of different pairs of modes supported in the optical fiber. In most of the reported interferometer-based OFSs, a measurand of interest is encoded into a single and/or multiple distinct fringe troughs in the sensor’s whole spectrum, where a variation of the measurand is determined by quantifying the change in the wavelength or the magnitude of the troughs, so-called the dip tracking method [3–8]. The dip tracking approach (especially the single-dip tracking approach) is intuitive and easy to apply and is widely accepted in the community and somewhat used as the gold standard in the process of sensor calibration. As a result, the majority of the research efforts in the past years have been poured into the fabrication of interferometer-based OFSs using different micromachining techniques [5,9] and different types of optical fibers [6,8,10–12], in order to enhance the performance of OFSs.

However, we argue that the commonly used demodulation method, i.e., the dip tracking approach, poses significant limitations on OFSs, especially the interferometer-based, in terms of sensing performance (e.g., reliability, dynamic range, functionality, etc.), which, unfortunately, has not been widely recognized in the community. The fundamental reason for this limiting aspect is that a large portion of information buried in the sensor’s spectral response is lost due to the fact that the dip tracking method only focuses on one or several particular optical features (e.g., fringe troughs) [13,14]. For example, the sensor’s spectrum can get distorted when subject to a large change in the measurand of interest, where the distinct troughs might shift out of the observation wavelength window or disappear, causing ambiguities to identify the sensing troughs. As a result, the sensor’s dynamic range and reliability are compromised. On the other hand, the spectral response of an interferometer-based OFS (e.g., a heterostructure-based) is highly sensitive to the fusion splicing condition in the sensor fabrication process, if fusion splicing is involved, especially for multimode fiber-based sensors [6]. Hence, with slight variations of splicing conditions, devices with characteristic spectra without any dominant peaks or troughs can often result, which cannot be used for sensing based on the conventional dip tracking approach. But, indeed, these devices would be utilized if there were more advanced demodulation techniques for OFSs. Therefore, there is an urgent need for a new approach to optical fiber sensing that can effectively overcome the above-mentioned limitations. For example, is it possible for OFSs to learn to sense, that is to directly learn the relationship between the measured raw data (i.e., the whole spectrum over the observation wavelength window) and the measurand of interest and subsequently predict an unknown measurement based on the completed learning process, regardless of the spectral shape (i.e., with/without dominant fringe troughs)? The answer is YES, as it will be shown later.

Machine learning techniques have been widely used in various fields in recent years, from biology [15], geoscience [16], robotics [17], to quantum physics [18] and photonics [19,20], thanks to their extraordinary strengths in classification, pattern recognition, prediction, and system optimization. Machine learning is especially attractive and proves powerful when there is a lack of an exact model that mathematically describes the relationship between the input and output of a system. Artificial neural networks (ANNs), one of the most popular machine learning models, can learn to identify useful features included in the input dataset and approximate a model that can directly map the input to the output, making them universal functional approximators [21]. Of particular relevance here, ANNs have been used for event identification based on analyzing responses from distributed optical fiber sensors [22–25]. Harnessing the ultra-high sensitivity of OFSs, ANNs have found applications in transforming a one-dimensional sensor into a device that can sense impact events in three-dimensional space [26–28] or turning a multimode fiber into a spatially resolved sensor [29,30]. More importantly, mapping the entire transmission spectrum of a multimodal interferometric sensor (i.e., the well-known SMS configuration) to the measurand of interest (temperature variation in this case) using a deep learning-based approach was reported in [31]. Thanks to the direct mapping, accurate temperature measurements were realized in the presence of strong noise from other perturbations (e.g., vibrations). Thus, the performance of the OFS in terms of immunity to environmental noise was significantly boosted by the deep learning-based signal analysis. The idea proposed in [31] reveals a new dimension of strategies for developing advanced OFSs, which also prompted us to further explore the potential of machine learning for optical fiber sensing.

In addition to the enhanced robustness against environmental perturbations as demonstrated in [31], in this work, we seek to show that by using machine learning (e.g., ANNs) as a tool for OFSs, new functionalities and enhanced performance (e.g., larger dynamic ranges) can be achieved in existing OFSs, which have been not possible by using conventional methods (e.g., curve fit and Fourier transform). Rather than examining single or a few spectral features in the spectral response (e.g., shift in a trough wavelength or change in its magnitude), the proposed approach, that is machine learning, exploits the rich information buried in the whole spectrum. We demonstrate this concept using a simple and well-studied sensing configuration, the SMF-HCF-SMF (single-mode fiber-hollow core fiber-single-mode fiber) structure, for measurements of bending. ANN models trained by the spectral responses of the prototype sensor can not only predict the curvature of the sensor in a large dynamic range with high accuracy but also identify the bending direction directly based on the measured raw spectrum. Thus, with the assistance of machine learning, we demonstrate for the first time that a simple SMF-HCF-SMF device (with a regular capillary) can achieve accurate directional bending sensing in an extensive dynamic range.

Another interesting aspect presented in this study is that the requirement of the hardware of the sensor interrogation unit (e.g., the bandwidth of the light source) can be alleviated by using machine learning to analyze the sensor’s spectral responses. We envision that the work reported here will be a cornerstone and open a new direction for advanced optical fiber sensing.

2. Materials and methods

2.1. Experimental setup and sensor characterization

The SMF-HCF-SMF-based sensor is fabricated by splicing a 10 mm-long HCF (i.e., a capillary tube, inner/outer diameter: 55/125 um) with two SMFs (corning SMF-28) using a commercial fusion splicer (SUMITOMO ELECTRIC INDUSTRIES, TYPE-36) with a manual operation mode. Detailed splicing conditions can be found in [32]. The transmission spectrum of the sensor is measured using a broadband light source (1530-1610 nm, Thorlabs ASE-FL7002-C4) and an optical spectrum analyzer (OSA, ANDO AQ6317B). The sensor is mounted on two optical fiber rotation modules, which are fixed to two translation stages, as illustrated in Fig. 1(a). The initial separation distance between the two stages is 120 mm. By translating one of the stages inwards, the separation distance between the two stages decreases, leading to an increase in the curvature of the sensor. The bending direction of the sensor can be controlled by adjusting the two rotation modules. In this study, two bending directions are defined and investigated, i.e., up and down, as indicated in Fig. 1(a). Figure 1(b) illustrates the measured transmission spectrum of the sensor when no bending is applied. Multiple fringe troughs, i.e., optical features that can be potentially utilized for sensing, can be observed in the spectral response of the sensor. The complex spectrum is a result of multiple optical mechanisms involved in the structure, such as anti-resonance, multimode interference [33,34], which, in turn, endow the sensor with potentially multiple functionalities. Figure 1(c) and 1(d) show the representative spectral responses of the sensor to different settings of curvature in up- and down-bend directions, respectively. The presented spectral responses illustrate the idea that how much the spectrum of the sensor can get distorted when subject to external perturbations (bending in this case), making it challenging to use conventional techniques to map the response to the measurand of interest. An interesting phenomenon is that the sensor exhibits somewhat different responses when it is bent up and down due to the fact that the two fusion-splicing interfaces between the HCF and SMF are not identical. If advanced demodulation algorithms are utilized to analyze the spectral responses and extract relevant features, it is possible that such a simple sensor can be used for directional bending sensing. Note that the prototype SMF-HCF-SMF-based device with a 10-mm HCF is not fully optimized, where the two connection points, the length of the HCF, and the inner diameter of the HCF, can be further adjusted to improve the measurement sensitivity of the device.

 

Fig. 1. Experimental setup and characterization of the SMF-HCF-SMF structure-based bending sensor. (a) Schematic of the experimental setup. (b) Measured transmission spectrum of the sensor. Measured spectral responses of the sensor to different curvatures in (c) up-bend direction and (d) down-bend direction.

Download Full Size | PDF

2.2. Spectral analysis with ANN

A schematic representation of a shallow ANN with a single hidden layer and with five nodes in its hidden layer is illustrated in Fig. 2, which is used throughout this study. The measured transmission spectrum of the sensor is used as the input data for the ANN, and the transmission at each of the sampled wavelengths is considered a variable in the input data array. The input data flows forward from the input layer to the hidden layer, and then to the output layer. Each of the layers performs operations on the data using various weight /bias values and an activation function; for example, in this work, the activation function for the hidden layer and the output layer are the sigmoid and the linear function, respectively. The model predicts the output (i.e., curvature in this case) based on the input spectrum. The weight/bias values connected to each node in the model are optimized based on Bayesian regulation back-propagation algorithm to obtain minimal mean squared error (MSE) between the predicted output and the true values (applied curvatures in the experiment) [35]. In the experiment, a total of 48 spectral responses of the sensor were recorded and used as data samples to train and test the ANN model. The 48 spectra corresponded to 47 settings of curvature (including up and down bending; two spectra were recorded for 0 m^-1). The wavelength sampling points were 2001 in the range 1530-1610 nm, corresponding to a wavelength sampling interval of 0.04 nm. 80% of the data samples were randomly selected to train the model and the remaining 20% of the data samples that were unseen by the model were used to test the trained ANN regression model. The ANN training processes were implemented using MATLAB 2020a.

 

Fig. 2. Schematic representation of a shallow ANN with five nodes in the hidden layer employed in this study. The measured transmission spectrum is directly used as the input, and the model predicts the curvature of the sensor.

Download Full Size | PDF

3. Results

3.1. Directional bending sensing with high accuracy and a large dynamic range by ANN analysis

The spectral responses of the sensor were first analyzed using the conventional dip tracking method. As shown in Fig. 1(d), the evolution of the fringe trough at ∼1606 nm is relatively tractable compared to other troughs in the spectrum. Figure 3(a) shows the transmission of the fringe trough at ∼1606 nm as a function of curvature. Note that positive curvatures and negative curvatures represent up-bending and down-bending, respectively. Conventionally, the transmission response shown in Fig. 3(a) can be divided into several sub-sections. To be specific, an exponential curve fit can be applied to the response in the curvature range -13.67-0 m^-1; a linear curve can be utilized to fit the response in the curvature range 0-8.8 m^-1; and, a third-order polynomial fit can be applied to the response in the curvature range 8.8-13.67 m^-1. The curve-fitted models are shown in Fig. 3(b). When a measurement is performed, the transmission of the fringe trough at ∼1606 nm has to be determined first and then the curvature is obtained based on the transmission of the trough and the curve-fitted models. However, the non-monotonic responses of the sensor fundamentally limit the capability of the sensor for directional bending sensing in a broad dynamic range (indicated by the green dashed line). Also, the conventional approach involving multiple curve fits is cumbersome and requires careful extraction of the dip transmission from the measured raw spectra, which can introduce significant errors.

 

Fig. 3. Spectral responses of the sensor analyzed using the conventional dip tracking method. (a) Transmission of the dip at ∼1606 nm as a function of curvature. (b) Curve-fitted models for the sensor’s responses.

Download Full Size | PDF

We also employed another commonly used method, i.e., the fast Fourier transform (FFT), to analyze the sensor’s responses to curvatures. Figure 4(a) shows the FFT results of the measured spectra when the applied curvatures were 0, -13.67, and 13.67 m^-1. Distinct peaks can be observed in the spatial domain plots, corresponding to multiple dominant modes guided by the sensor structure. Amplitude evolutions of the three peaks (peak A, B, and C), indicated in Fig. 4(a), are plotted as a function of curvature in Fig. 4(b). Again, the non-monotonic relationships limit the capability of the sensor for directional bending measurements in the investigated dynamic range. As shown in Figs. 3 and 4, the conventional dip tracking and FFT-based analyses detrimentally affect the ability of the sensor. Thus, we propose to use an ANN model to automatically learn the relevant features and directly map the raw spectrum to the applied curvature, to make full use of the spectral response of the sensor.

 

Fig. 4. Frequency responses of the sensor analyzed using the conventional FFT method. (a) Frequency responses of the sensor obtained by FFT for different settings of curvatures. (b) Amplitude evolution of several distinct peaks in the frequency response of the sensor as a function of curvature.

Download Full Size | PDF

Figure 5(a) illustrates a scatter plot where the predicted curvatures of the sensor obtained from the ANN model are plotted against their actual values recorded in the experiment. Each of the circles corresponds to a single data point, i.e., a single measurement for an applied curvature. For an ideal model, these data points should be exactly aligned along the y = x curve, as indicated by the dashed line. Note that the data points shown in Fig. 5(a) are only the dataset used for training the ANN regression model. As can be seen, for the training dataset (80% of all data samples), the trained ANN model successfully mapped the measured raw spectra to their corresponding curvatures even with relatively small numbers of data samples, indicating that the model can effectively extract the relevant features included in the sensor’s whole spectrum and can memorize the complex mapping between a spectral response and its corresponding curvature. At epoch 32 of the model training, the MSE reached satisfactory values (< 0.01) for both training and test datasets, as shown in the inset of Fig. 5(a), where the model training process was manually stopped. Figure 5(b) shows the scatter plot for the test dataset that was not seen by the model in the training process. The predicted and actual curvatures are close, having small errors with a correlation coefficient of 0.99994, meaning that the trained ANN model is able to generalize well for an unseen dataset. Figure 5(c) shows the error histogram for all data samples predicted by the model. Approximately 94% of the data samples were predicted with an error less than 0.07 m^-1 based on the ANN analysis, whereas only 52% was achieved with the same accuracy based on the conventional dip tracking and curve-fitting approach shown in Fig. 3.

 

Fig. 5. Spectral responses of the sensor analyzed by machine learning. (a) Scatter plot of the training dataset produced by the ANN model. The inset shows the plot of MSE obtained with respect to epochs during the training process. (b) Scatter plot of the test dataset produced by the ANN model. (c) Error histogram between applied curvatures and predicted curvatures obtained from the trained ANN.

Download Full Size | PDF

Comparing Figs. 3, 4, and 5, it is clear that the ANN-based analysis outperformed the conventional dip tracking-based and FFT-based methods. The ANN analysis makes the sensor able to not only measure curvature in a large dynamic range from 0 to 13.67 m^-1 but also identify the bending direction of the sensor, which has not been possible in previous work [36–43]. The results demonstrate that by directly learning the relationship between the sensor’s raw spectral response and the measurand of interest via a machine learning technique, new functionalities (e.g., directional bending sensing) and enhanced performance (e.g., broader dynamic range and higher accuracy) can be added to existing OFSs. Note that typically a large amount of data is required for training an ANN, especially when the ANN has many hidden layers and the associated nodes. However, collecting a large dataset in the sensor calibration is sometimes challenging, thereby posing a limitation on the effectiveness and efficiency of using machine learning for optical fiber sensors, given that traditional approaches (e.g., the FFT and curve fit analyses) do not require the acquisition of a huge amount of data. In this work, we performed the standard sensor calibration process where the sensor’s responses to a few discrete curvatures were recorded. The performances of the traditional demodulation approaches and a simple shallow ANN with only 5 nodes in its hidden layer were compared. It is shown that the ANN outperformed the conventional approaches based on the same data set. The simple shallow ANN was used to avoid overfitting due to the limited training data set. On the other hand, as demonstrated in [31], we envision that by collecting more data from the prototype sensor, for example, in environments with different conditions (e.g., temperatures, vibration, etc.) and using the data to train a more advanced machine learning model, the simple SMF-HCF-SMF structure-based sensor will be able to unambiguously sense curvature at an arbitrary setting of the environment. For different sensor devices with different lengths of HCF, different machine learning models must be trained for each of the sensors.

3.2. Relaxed requirement on the sensor interrogator by ANN analysis

When performing a measurement, for example using an OSA, more wavelength sampling points generally yield a more accurate result. However, more sampling points require more time for the OSA to accomplish one sweep in the desired wavelength range, i.e., 1530-1610 nm in this case, which may compromise the performance of the sensor, especially when the measurand of interest changes dynamically. In this section, we seek to demonstrate that conventional requirements on the sensor interrogator (i.e., the bandwidth of the light source and the sampling points of the OSA) can be significantly relieved by using machine learning as a tool to analyze the sensor’s spectral response and importantly, without comprising the accuracy of the measurement.

In section 3.1, each of the input datasets for the ANN model is composed of 2001 sampling points spreading linearly from 1530 nm to 1610 nm. We down-sampled the original spectrum from 2001 points to 501 and 21 points, where the wavelength interval correspondingly increased to 0.16 and 4 nm, respectively. The down-sampled spectra were then used to train and test new ANN models. Figure 6(a) and 6(b) show the applied curvatures and their corresponding predicted curvatures obtained from the trained ANN models. The predicted curvature matched well with the applied curvatures in both cases with a correlation coefficient greater than 0.9999 and MSE lower than 0.01. It is worth noting that as the sampling points decreased down to 21, it is even challenging to tell the shape of the sensor’s spectrum, as illustrated in the inset Fig. 6(b), let alone use conventional techniques for demodulation. However, the machine learning-based analysis successfully one-to-one mapped the discrete spectral response to an applied curvature, which once again demonstrates its potential for OFSs.

 

Fig. 6. Spectral responses of the sensor analyzed by ANN models with reduced sampling points for each input dataset: (a) 501 points and (b) 21 points. The inset shows an exemplary spectral response with 21 sampling points.

Download Full Size | PDF

Another important aspect for an OFS interrogator is the wavelength bandwidth of the light source. A light source with tens of nm bandwidth (e.g., >30 nm) is always preferred for optical fiber interferometric sensors. More importantly, the wavelength range of the source must cover the distinct fringe troughs of the sensor’s spectral response, which are typically tracked for sensing applications. We seek to show that with the assistance of machine learning techniques, the stringent requirement on the wavelength and the bandwidth of the light source can be greatly relaxed. We extracted the sensor’s spectral responses (see Figs. 1(c) and 1(d)) in a 20-nm wavelength range from the measured raw spectra which had an 80-nm range (1530-1610 nm), and the extracted dataset (501 points in a 20-nm range for each input) was used to train and test new ANN models. Figure 7(a) and 7(b) present the prediction results from two ANN models when trained using the spectral responses from 1540-1560 nm and 1590-1610 nm, respectively. Once again, satisfactory prediction results with a correlation coefficient greater than 0.9999 and MSE lower than 0.01 are obtained in both cases. Note that the range 1590-1610 nm covers the distinct troughs at ∼1606 nm that are tractable with respect to curvature, while the wavelength range 1540-1560 nm does not include distinct features that respond well to curvature, as can be seen in Figs. 1(c) and 1(d). Through machine learning analyses, relevant features buried in the spectral responses within a narrow wavelength range with/without distinguishable spectral features can be effectively extracted and thereby lead to the successful one-to-one mapping between a spectral response and a value of the measurand of interest. Note that since the requirements on the sensor interrogator could be significantly relieved based on the ANN analysis, the system update rate could be improved by decreasing the sampling points and wavelength monitoring span of the OSA.

 

Fig. 7. Spectral responses with a 20-nm wavelength range of the sensor analyzed by ANN models: (a) 1540-1560 nm and (b) 1590-1610 nm.

Download Full Size | PDF

4. Conclusion

In conclusion, we have proposed the use of machine learning to learn directly the relationship between the recorded raw spectral data of an OFS and the measurand of interest to achieve high-accuracy and large dynamic-range measurements. We have achieved a proof-of-concept demonstration where the complicated transmission spectrum of an SMF-HCF-SMF-based structure is one-to-one mapped to a curvature exerted on the device. With machine learning as the tool for demodulation, the simple structure is able to realize vector bending sensing (up and down) in a large dynamic range 0-13.67 m^-1, which has not been possible based on conventional signal analyses. We have also shown that machine learning-based analysis negates the need to carefully choose the bandwidth of the light source and sampling points of the detector, as is often the case for traditional techniques.

In this proof-of-concept study we have focused on a simple OFS for the measurement of a single parameter, whereas the proposed technique can be readily extended to other OFSs for simultaneously sensing multiple quantities, provided a training data set can be obtained. We envision that new functionalities and enhanced performance can be realized in existing OFSs when assisted with machine learning in the sense that a simple OFS can potentially function as a sensor network. We believe that the work presented in this article provides a new data-driven strategy to advance optical fiber sensing. The majority of previous efforts are focused on increasing the complexity in the sensor fabrication and interrogation unit (i.e., hardware) in order to improve system performance, whereas the proposed technique is software-based exploiting advances in data science, that is machine learning.