2.1. The Working Principle of φ-OTDR Coherent Detection System
The narrow linewidth laser (PL-NLWM-1550-C-2-SA-A-M) from LD-PD INC SINGAPORE generates continuous light with a narrow linewidth of <3 kHz, a wavelength of 1550 nm and a power of 60 mW. The continuous light is divided into two parts by the 90/10 coupler. The 90% part of it enters the acoustic-optic modulator (AOM, SGTF100-1550-1P) to modulate into a pulse signal with a frequency shift of Δ
f = 100 MHz [
21,
22]. The AOM is driven by an arbitrary waveform generator (AWG) to generate repetitive laser pulses. After being amplified by an erbium-doped fiber amplifier (EDFA), it enters the sensing fiber through an optical circulator (CIR) and undergoes Rayleigh scattering. The other 10% of the light passes through a polarizer scrambler (PS) and is used as the principal oscillator light with the backscatter Rayleigh (RBS) returning from the CIR to produce a beat-frequency signal in a 3 dB coupler. It is detected using a photodetector (PD, MBD-200M-AM) with a bandwidth of 200 MHz and converted into a high-gain electrical signal. The system schematic diagram is illustrated in
Figure 1a. The voltage
V(
t) of the PD output beat signal can be simply expressed as follows:
Here,
AL(
t) represents the amplitude of the local oscillator.
φt(
t) represents the phase information that contains the vibration signal. In this process, several factors can influence the spatial resolution, sensitivity, and frequency response of the system, including the line width of the laser, the stability of the light source, the optical pulse width, and the bandwidth range of the PD. There are several demodulation methods available for φ-OTDR systems. Among them, the adoption of a digital in-phase and quadrature (IQ) demodulation scheme [
23] can truly achieve phase demodulation, enabling the precise restoration of vibration signals and improving the signal-to-noise ratio (SNR) of the system. The demodulation schematic diagram is depicted in
Figure 1b. The PD output signal performs IQ phase demodulation. After passing through a low-pass filter (LPF), the demodulated components,
I(
t) and
Q(
t) can be represented as follows:
The amplitude
A(
t) and phase
φt(
t) of the vibration signal can be represented as
According to the above formula, the phase
φt(
t) of RBS can be obtained. Given that the range of the arctangent function is (−
π/2,
π/2), the result needs to be transformed into a range (−
π,
π) based on the quadrants where
I and
Q are located. Through phase unwrapping, the final phase result can be achieved. The DAS tested in this paper was provided by Wuxi BuLiYuan Electronic Technology Co., Ltd., located in Wuxi, China, with the model identified as BLY pDAS-100P. The corresponding detection parameters are outlined in
Table 2.
2.3. The Performance Evaluation of Indicators
DAS devices involve numerous indicators, and these indicators are interrelated, which can lead to confusion for users in different application fields when selecting and using DAS. Conducting a comprehensive evaluation of DAS performance is crucial to provide users with a reference that meets their specific requirements.
The evaluation of DAS performance, indeed, requires both quantitative and qualitative analysis. This evaluation approach aligns with the concept of AHP [
27], which is commonly used to evaluate comprehensive and complex problems. The AHP is a comprehensive evaluation approach that incorporates both quantitative and qualitative analysis. It is employed to tackle complex evaluation problems by breaking them down into multiple levels and elements. Within each level, the elements are compared, assessed, and computed against one another. By utilizing analytical methods, the weight parameters of each level can be determined [
28]. This methodology provides a solution to the systemic problems encountered in scenarios involving multiple objectives, multiple levels, and challenges that cannot be entirely evaluated through quantitative methods.
In this paper, a set of AHP steps is designed specifically based on the characteristics of DAS indicators and engineering requirements. These steps are outlined as follows:
First, construct a hierarchical model. The comprehensive evaluation model of DAS performance is divided into the following three layers: the top layer (H), the middle layer (M), and the bottom layer (L). In the context of evaluating DAS indicators, the top layer is defined as the target layer. The target layer sets only one factor, which is typically referred to as the “DAS performance evaluation”. The middle layer consists of six factors that are crucial to consider, including M
1 frequency response, M
2 sensitivity, M
3 spatial resolution, M
4 sensing distance, M
5 multi-point perturbation, and M
6 temperature influence. The bottom layer, also referred to as the criterion layer, establishes the following three factors: K
1 (excellent), K
2 (fair), and K
3 (poor). The AHP model, as illustrated in
Figure 2, is designed to illustrate the evaluation process.
Next, the judgment matrix is constructed for a factor concerning the subsequent layer of associated factors. Let us take the construction of the judgment matrix for the target layer and the middle layer as an example. In this process, we compare two factors, Mi and Mj, from the middle layer at a time. The resulting judgment matrix is as follows:
Here, the relative importance of the factors Mi and Mj in the middle layer concerning the target layer is represented by the comparison scale
aij. The quantization method in reference [
20] was used to determine the value of
aij. The value
aij was determined simultaneously according to the given conditions:
aij > 0,
aji = 1/
aij (
i ≠
j),
aii = 1(
i,
j = 1, 2, …,
n).
We constructed judgment matrices B, C, D, E, F, G, and H to evaluate M1 frequency response, M2 sensitivity, M3 spatial resolution, M4 sensing distance, M5 multi-point perturbation, and M6 temperature influence concerning the criterion layer. The order of this judgment matrix was 3, indicating that it is a square matrix with dimensions of 3 rows and 3 columns.
After constructing the judgment matrices, we proceed with hierarchical single ranking and conduct a consistency test. To solve for the eigenvalues
λ and eigenvectors
WA of the judgment matrix
A according to Equation (6), we needed to perform the following calculations. The weight value
WA represents the weight value of all factors in the middle layer concerning the target layer.
Similarly, the eigenvalues and eigenvectors of the judgment matrices B, C, D, E, F, G, and H can be determined to complete the hierarchical single-sorting process.
A consistency check of the judgment matrix is necessary after the hierarchical single-sorting process. To calculate the stochastic consistency ratio CR, we can use Equation (7).
Here, the variable CR represents the consistency indicator, n denotes the order of the judgment matrix, and RI represents the average random consistency indicator. When the order of the judgment matrix is three, the consistency indicator is represented by RI as a value of 0.58. However, when the order is seven, the consistency indicator changes to a value of 1.32.
If the consistency indicator CI is less than 0.10, the consistency test of the judgment matrix is considered successful. However, if the CI exceeds 0.10, the judgment matrix needs to be readjusted until the CI is less than 0.10.
Finally, a hierarchical total ranking was performed. The weight values of all factors in the middle level and the criterion level, relative to the top level, were calculated separately to complete the hierarchical total ranking process. This process considers the importance of each factor at different levels and combines them to determine the DAS performance evaluation results.