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. 2025 Mar 20;15:9659. doi: 10.1038/s41598-025-94287-5

Sub pulse length event measurement in BOTDR system using slope assisted Brillouin frequency shift

Shuangshuang Liu 1, Jianzhong Zhang 1,2,✉, Zhe Ma 2,✉, Jinglang Xu 1, Zhikun Wang 1, Yubo Zhang 1, Mingjiang Zhang 1,2
PMCID: PMC11926342  PMID: 40113883

Abstract

To overcome the limitations by pulse width on the event zone measurement capability, a novel temperature demodulation scheme was proposed and validated to measure sub-pulse length event zones based on the slope-assisted Brillouin frequency shift (SA-BFS). Unlike the conventional BFS-based methods, this approach leverages the BFS slope for temperature demodulation, enabling precise measurement of sub-pulse-length event zones. We developed a theoretical model that established a linear relationship between the BFS slope and temperature, validated through simulations and experiments across various event zone lengths and pulse widths. Ultimately, the system’s measurement capability was improved from 2 to 0.49 m, achieving a temperature demodulation of 57.75 °C on a 10.2 km sensing fiber, with a temperature accuracy approximately ten times higher than that of conventional demodulation schemes. The method of SA-BFS provided a transformative approach to measure physical quantities along the fiber, serving as a valuable tool for distributed optical fiber sensors such as BOTDR and BOTDA.

Keywords: Brillouin optical time domain reflectometer, The Brillouin frequency shift slope, Sub-pulse-length event, Temperature demodulation

Subject terms: Nonlinear optics, Optical sensors, Optical metrology

Introduction

Brillouin optical time domain sensing technology has attracted much attention due to its advantages in structural health monitoring and industrial production including Brillouin optical time domain reflectometer (BOTDR)1–3 and Brillouin optical time domain analyzer (BOTDA)4–7 based on spontaneous and stimulated Brillouin scattering, respectively. Compared with the BOTDA system, BOTDR system has the advantages of single-ended optical injection, which greatly reduces the system cost and structural complexity. And it can still work even if there is a break in the fiber8,9. Brillouin scattering is an inelastic scattering which occurs between the probe wave and acoustic wave. And there is frequency shift for the Brillouin scattering signal comparing to the incident signal, which is defined as Brillouin frequency shift (BFS) corresponding to the maximum gain of Brillouin gain spectrum (BGS). For BOTDR system, temperature is demodulated based on the linear relationship between BFS and temperature. It should be noted that the length of the event zone should be larger than the nominal resolution spatial, which is decided by the pulse width10,11. This is because that the measurement of BOTDR system is based on the localization principle of OTDR. It will lead to great measurement errors because the measured BFS will be much smaller than real BFS, when the length of event zone is less than the nominal spatial resolution. For BOTDR systems, the ability to measure the event zone is limited primarily by the pulse width, which is larger than 10 ns corresponding to the nominal spatial resolution of 1 m due to the phonon lifetime. However, with the expansion of application scenarios, there is a higher demand of measurement capabilities for strain and temperature change of the smaller event zone12,13. Therefore, it is necessary to develop a technique to detect the small event zone.

In order to break through the limitations of pulse width, there are two methods to enhance the measurement capabilities. One effective method is to reduce the effective pulse width by pulse modulation techniques, such as double-pulse method (DP-BOTDR), synthetic spectrum method (S-BOTDR), phase-shifted pulses method (PSP-BOTDR), differential cross spectrum method (DCS-BOTDR) and differential pulse pair (DPP-BOTDR). DP-BOTDR achieved a measurement of 0.2-m-long heated range on a 16 m sensing distance by injecting two pulses with the same width and a certain interval into the fiber14. Four measurements were performed with pulses of different pulse widths and phase shifts by S-BOTDR which distinguished 400 sensing points on a sensing distance of 40 m15. PSP-BOTDR measured a 0.2 m temperature zone on 354.4 m of test fiber by two pairs of pulses, one with short pulses of a phase difference of π and the other with long pulses of the same width16,17. DCS-BOTDR was based on PSP-BOTDR that replace pulse combination with long pulses, avoiding the complexity of phase modulation18. The effective pulse width of the method of differential pulse pair was determined by the difference in the pulse width and a nominal spatial resolution of 0.2 m was achieved along a sensing distance of 3 km19,20. Although the above methods improved the detection capability for the small event zone by decreasing the effective width of the pulse, these techniques undoubtedly increased the system complexity and measurement time. The other method is post-processing techniques where long optical pulses are still acted as probe signals instead of complex constructed pulses. The iterative subdivision method achieved a measurement of 1.5 m using a 100 ns pulse by restoring the Brillouin signal based on the energy density distribution21. Similarly, pulse subdivision superposition treated a single pulse as a combination of several subdivided pulses22. Using partitioned BGS analysis method, a 3 m strain test section in the 28.5-km-long BOTDR was achieved by a 100 ns probe pulse and23,24. Besides, some algorithms can also be used for signal restoration, such as quadratic time–frequency transforms, image deconvolution and high-order self-convolution25–27. These methods optimized the measurement capabilities by adjusting the algorithm parameters, such as the number of subdivided segments for iterative subdivision method, partitioned BGS analysis method and the estimated value of the signal-to-noise ratio for image deconvolution. However, these parameters are very sensitive to noises in practical applications.

In this paper, to realize the measurement of sub-pulse-length event, a novel temperature demodulation scheme was proposed based on the slope-assisted Brillouin frequency shift (SA-BFS). A linear relationship between the slope of the BFS distribution and the temperature was established through analyzing the BFS distribution characteristics when the length of the event zone was smaller than the nominal spatial resolution. And the length of event zone was measured based on the BFS perturbation zone and pulse width. The proposed scheme effectively breaks through the limitation of the pulse width without increasing the structure complexity and complicating data processing, only with the calibration process of the linear coefficients once at the time of first use. Finally, a sub-pulse-length event of 0.49 m was identified on a 10.2 km sensing fiber using a pulse width of 20 ns corresponding to 2 m. The effective sensing point was 20,800, which was superior than the existing technology.

The organization of this paper is given as follows. In the section of introduction, the research background was presented. In the section of principle and simulation results, the fundamental principles of Brillouin scattering signal measurement were analyzed and numerical simulations were carried out. In the section of experiments and results, the experimental setup was constructed and the experimental results were achieved. In the section of discussion, the limitations of the proposed scheme were thoroughly examined. Finally, the conclusions of this study were summarized.

Principle and simulation results

The intensity of Brillouin scattering signal measured at a certain moment is the superposition of the scattering signals from different points within pulse width which corresponds to the length of the optical fiber from z0 ~ z0-Δz, where z0 is a random position of fiber, Δz = cTpulse/2 is the nominal spatial resolution and Tpulse is the pulse width, c is the light velocity in a vacuum, as shown in Fig. 1a. The BGS measured by changing the scanning frequency is the superposition of the BGSs over the fiber length of Δz, demonstrated in Fig. 1b. If the fiber length of Δz is divided into n segments with the same length, the measured BGS can be expressed as28,29:

graphic file with name d33e377.gif 1

where G(v, z0) is the measured BGS by BOTDR system, gBi(v, vBi) is sub-Brillouin signal generated by the i th segment whose spectrum has a Lorentzian profile with the BFS of vBi, the full width at half maximum (FWHM).

Fig. 1.

Fig. 1

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The superposition principle of Brillouin scattering signal.

of ΔvBi and the peak gain of g0. And v represents the range of the scanning frequency. Equation (1) showed the measured BGSs along the fiber, demonstrating that the Brillouin signal was a superimposed result. When temperature/strain is applied to an event zone, the BFS of vBi will be changed. The characteristics of the BFS distribution is analyzed in detail at different locations in and around the event zone. As shown in Fig. 1c, Δz represents the length of the nominal spatial resolution which is larger than the length of the event zone. To simplify the analysis, we only introduce the change of the BFS caused by the temperature without considering the strain in the following analysis. This is because the influences on the BFS by temperature and strain are the same, which both are linear relationship. It should be noted that the different colors are used to distinguish the BGS with different BFS in essence. The blues curves represent the BGSs in the non-event zone with vBi(T0) and the red curves denote the BGSs in the event zone with vBi(T) = vBi(T0) + CT(T-T0), where CT is the temperature coefficient of the BFS, T0 and T denotes the temperatures in the non-event zone and event zone, respectively. When the pulse is in the non-event zone, corresponding to the parts of ① and ⑤ of the BFS curve, the measured BGSs are the superposition of n BGSs with the center frequency vB(T0). As the pulse enters the event zone, the superimposed area covers both the non-event and event zones, Eq. (1) is further expressed as:

graphic file with name d33e535.gif 2

From Eq. (2), it can be seen that the measured BGSs of the event zone are the superimposed results of the two-part BGSs of the non-event and event zones, respectively. Therefore, when the event zone length was smaller than the pulse width, the results of BFS were affected by both the temperature and the event zone length, resulting in an inability to measure temperature information by the BFS distribution. To further demonstrate the effect of temperature on the BFS, Eq. (2) can be transformed into the following representation through the process of normalization30:

graphic file with name d33e553.gif 3

where

graphic file with name d33e560.gif 4
graphic file with name d33e566.gif 5
graphic file with name d33e573.gif 6
graphic file with name d33e579.gif 7

where r is the ratio of the length of the event zone within the nominal spatial resolution. The normalized frequency scanning range is indicated by x and a indicates the normalized BFS. Equation (3) quantified the Brillouin gain distribution at every position along the fiber. Then, performing a Taylor series expansion for Eq. (3) and ignoring higher-order terms above quadratic, the expression of BFS is as follows.

graphic file with name d33e602.gif 8

From the Eq. (8), it can be seen that the BFS was influenced by both temperature and the length of event zone for the sub-pulse-length event measurement, which was the fundamental reason for the limitations of the conventional BOTDR systems31. As the pulse moves into the event zone, the percentage of the event zone of r gradually increases and the measured xp(zn) gradually increases. When the length of Δz completely covers the event zone, the value of r reaches the maximum, corresponding to the curve shown in the part of ③. This state will be maintained until the pulse leaves the event zone. The part of ④ corresponds to the process of leaving the event zone, which is similar to the part of ②. However, it is different in that the occupation of the event zone gradually decreases for the part of ④. For the conventional BOTDR system, the information of temperature or strain is demodulated based on the BFS value of the part of ③. However, when the length of the event zone is smaller than Δz, the BGSs used for the superposition still include the part of the non-event zone and the BFS is decided by both vBi(T0) and vBi(T). Therefore, the conventional demodulation scheme is unable to measure the information of temperature/strain based on the BFS.

In order to achieve sub-pulse-length event measurement, the method of variable elimination was used for Eq. (8). By introducing a new indicator of the BFS slope, the measurement scheme of SA-BFS is proposed. The BFS slope was defined as the change of the BFS at any two positions as Eq. (9).

graphic file with name d33e670.gif 9

where zn and zn+1 are the starting and ending positions for calculating the slope of BFS distribution of kslope. Introducing Eqs. (7) and (8) into the Eq. (9), the relationship between the slope of BFS distribution and temperature is:

graphic file with name d33e707.gif 10

According to Eq. (10), there is a linear relationship between kslope and T, so temperature can be demodulated by measuring kslope. Different from the conventional demodulation scheme, the proposed scheme achieves the measurement of temperature based on the slope of BFS distribution rather than the BFS. Equation (10) established a novel temperature measurement mechanism, decoupling it from event zone length—an advancement over the conventional BFS-based methods. In the experiment, the falling edge of the BFS curve is selected as the linear region to calculate the slope of BFS distribution instead of the rising edge. The reason is that the pulse was not the ideal rectangular due to the limitation of the equipment and it takes some time to establish the acoustic field when the pulse enters into the fiber32.

To verify the feasibility of the scheme, numerical simulations were firstly performed based on the above theoretical model. The parameters in the simulation were as follows: the sensing fiber was 10 km, the pulse width was 60 ns and the temperature was 25 ℃ for the room and 40 ℃ for the event zone, respectively. The length of hotspot was 4, 5 and 6 m for Fig. 2b,c,d, respectively. And the starting position of hotspot was from 8001 m. The frequency range of BGS was from 10.7 to 10.9 GHz with the step of 1 MHz and the center frequency of BGS was 10.8 GHz. The accurate BFS was indicated by the red dotted line which was 10. 8165 GHz computed according to the temperature coefficient of 1.1 MHz/℃. The red dotted box represented the measured BFS, which were 10.8113, 10.8140 and 10. 8165 GHz, respectively. It can be seen that the part of ③ of the BFS curve becomes a single point when the length of the hotspot increased to 6 m being equivalent to the nominal spatial resolution. The BFS at this point can accurately reflect the temperature information of the event zone. However, this state only existed for a moment. When the lengths of hotspot were less than the nominal spatial resolution shown in Fig. 2b,c, the results demonstrated that the BFSs were smaller than the true BFS and cannot be used to accurately measure the temperature information of the event zone, which limited the measurement of the sub-meter event zone for the BOTDR system.

Fig. 2.

Fig. 2

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The simulation results of BFS with pulse width of 60 ns. (a) The comparison of BFS distributions under different lengths of hotspot with (b) 4 m (c) 5 m and (d) 6 m.

However, there is a linear relationship between the slope of BFS distribution and temperature, which can be used for the extraction of temperature according to Eq. (10). Figure 3 demonstrated the simulation results of the BFS distribution under different temperatures. The room temperature was 25 °C and temperatures of hotspot were from 30 to 70 °C with the step of 10 °C. As can be seen from the figure, the speed of BFS changes was different in the event zone and the higher the temperature was, the faster the BFS changed. The calculation results of the slope of BFS were shown in Fig. 3b. The fitting results showed that the slope of BFS and temperature presented a linear relationship, validating the theory described in Eq. (10).

Fig. 3.

Fig. 3

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(a) Simulation results for the slope of BFS distributions under different temperatures. (b) The linear relationship between the slope of BFS distribution and temperature.

In addition, the characteristic of the BFS perturbation zone defined as the length of the parts from ② to ④ in Fig. 1c was analyzed. Figure 4a displayed the results of the BFS distribution of different pulse widths and Fig. 4b demonstrated the fitting result between the change region of BFS and the total length of pulse width and hotspot. Combining the theory with the simulation results, it found that the length of the BFS perturbation zone was equal to the sum of the pulse width and the length of hotspot. Therefore, the length of hotspot can be computed by measuring the BFS perturbation zone, effectively avoiding the dependence on the pulse width.

Fig. 4.

Fig. 4

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(a) Simulation results for the BFS perturbation zone under different pulse widths. (b) The fitting result between the BFS perturbation zone and the total length.

Experiments and results

Based on the above theory and simulation, experimental validation was performed based on the experimental setup of BOTDR system with microwave heterodyne detection, as shown in Fig. 5. A narrow-linewidth laser (NLL) with 4.5 kHz was used as the light source and the output power was 18.7 mW. The continuous wave was divided into two paths by a 90:10 coupler. The lower branch was used as the reference light to perform coherent detection and passed through a polarization scrambler (PS) to eliminate polarization-related noise. The upper branch of 90% entered into the semiconductor optical amplifier (SOA) to generate a high extinction ratio probe pulse. The peak power of the probe pulse was amplified to 479.2 mW by an Er-doped fiber amplifier (EDFA1) and the Brillouin signal was amplified by EDFA2. The pulse passed through an optical circulator (OC) before launching into the fiber under the test (FUT). The reference signal and the Brillouin signal were beaten in a 50:50 coupler. Fiber Bragg gratings (FBG1 and FBG2) were used to filter out the spontaneous radiation noise generated by EDFA1 and EDFA2, respectively. The optical beat signal underwent coherent detection via a 12 GHz bandwidth photodetector, followed by signal conditioning through a low-noise amplifier (LNA) with 26 dB gain. The operation of frequency downshifted to 200 MHz for the center frequency was implemented by an arbitrary waveform generator (AWG) with an output power of 15 dBm and the frequency range of 10.52–10.72 GHz. The intermediate frequency signal passed through the band-pass filter (BPF) and envelope detector and was sampled and processed on the computer.

Fig. 5.

Fig. 5

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Experimental setup. NLL narrow-linewidth laser, SOA semiconductor optical amplifier, EDFA Er-doped fiber amplifier, FBG fiber Bragg grating, OC optical circulator, FUT fiber under test, PS polarization scrambler, PD photoelectric detector, LNA low noise amplifier, AWG arbitrary waveform generator, BPF band-pass filter.

Based on the above experimental setup, experimental validations were carried out. Firstly, the distribution of the BFS perturbation zone were measured with the hotspot of 3 m and the pulse widths of 30, 40, 50, 60 and 70 ns, respectively. The sensing length was 10.2 km and sampling rate was 250 Ms/s. Figure 6a showed the BFS results under different pulse widths and Fig. 6b was the fitting results between the BFS perturbation zone and the total length of pulse width plus hotspot. Both simulation and experimental results showed that the length of the BFS perturbation zone was equal to the sum of the length of hotspot and the nominal spatial resolution. It should be noted that the length of the BFS perturbation zone was 80% of the length of the parts from ② to ④ in the experiment, because the pulse was not a standard rectangular with the rising and falling edges. Figure 6 demonstrated that the length of the event zone can be obtained by measuring the length of the BFS perturbation zone with the knowledge of the pulse width.

Fig. 6.

Fig. 6

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(a) The BFS distributions under different pulse widths with hotspot of 3 m. (b) The fitting results between the length of the BFS perturbation zone and the total length of the nominal spatial resolution plus hotspot.

Next, the linear relationship between the slope of BFS distribution and temperature was experimentally verified. Figure 7a–d analyzed the effect on the characteristics of the BFS distribution by the lengths of hotspot. Pulse with a width of 60 ns was injected into the fiber with different lengths for hotspot of 6, 5, 4, and 3 m, respectively, which were placed in a thermostat at the end of 10, 070 m. From the figure, it can be seen that the stabilization zones of the BFS were not obvious compared with the simulation results of the part of ③ in Fig. 2. On the one hand, it was that the pulse injected into the fiber was not an ideal rectangular square wave owing to the equipment limitations. On the other hand, noise inevitably was introduced during the process of data acquisition which deteriorated the ideal distribution of the BFS. Consequently, this is one of the vital reasons to propose the temperature demodulation scheme based on the method of SA-BFS. Additionally, the experimental results demonstrated that the maximum value of the BFS decreased with the reducing lengths of hotspot at the same temperature. This indicated that the BFS values were influenced by both temperature and the length of hotspot when the lengths of hotspot were smaller than the nominal spatial resolution. Therefore, it was not possible to distinguish two parameters only based on the BFS values. Figure 7e–h described the linear region for the calculation of kslope. The regions around 50% of the maximum BFS value were used to calculate the slope of BFS distribution, effectively avoiding the influence of the rising and falling edges of the pulse. The slopes of BFS distribution under different lengths were calculated and fitted in Fig. 8a–d. It was found the slope of BFS distribution was different under the increasing temperature and there was a great linear relationship between kslope and T. Moreover, this linear relationship was the same in different lengths of hotspot. This indicated that the linear relationship between kslope and T was universal and not affected by the length of the event zone.

Fig. 7.

Fig. 7

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The BFS distributions along the fiber under different lengths for hotspot of (a) 6 m, (b) 5 m, (c) 4 m and (d) 3 m. The calculation regions for kslope of (e) 6 m, (f) 5 m, (g) 4 m and (h) 3 m.

Fig. 8.

Fig. 8

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The relationship between kslope and temperature under different lengths for hotspot of (a) 6 m, (b) 5 m, (c) 4 m and (d) 3 m.

Figure 9a–d studied the characteristics of superimposed BFS traces near the region of hotspot under different pulse widths from 80 to 20 ns, respectively. And Fig. 9e–h showed the linear regions which were used to calculate kslope. Furthermore, the relationship between kslope and T was established in Fig. 10. From the results of different pulse widths, it can be seen that the linear relationship between kslope and T was maintained. Different from the conclusion of Fig. 7. where the fitting coefficients were the same for different lengths of hotspot, the results in Fig. 10. showed that the fitting coefficients were changed with the varied pulse widths. The smaller the pulse width was, the larger the absolute value of the fitting coefficient was. This indicated there were different fitting coefficients for different pulse widths. In practice, the parameter of pulse width is often known and determined. Once the pulse width is fixed, the coefficient of kslope and T can be determined.

Fig. 9.

Fig. 9

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The BFS distributions along the fiber under different pulse widths of (a) 80 ns, (b) 60 ns, (c) 40 ns and (d) 20 ns. The calculation regions for kslope of (e) 80 ns, (f) 60 ns, (g) 40 ns and (h) 20 ns.

Fig. 10.

Fig. 10

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The relationship between kslope and temperature under different pulse widths of (a) 80 ns, (b) 60 ns, (c) 40 ns and (d) 20 ns.

Through comprehensive theoretical analysis and experimental validation, the innovative of the method of SA-BFS has been successfully demonstrated. Finally, a measurement was performed on a 10.2 km sensing fiber by a 20 ns pulse. In the experiment, a section of the fiber was placed on a heated platform at the position of 10,068 m at the end of the fiber. Figure 11 displayed the BFS distribution, showing pronounced variation near the temperature zone. Conventional BOTDR registered a 3.43 °C variation (BFS: 10,810.91 MHz at the hotspot vs. 10,807.07 MHz at room temperature). However, the SA-BFS method, leveraging a 2.49 m BFS perturbation zone and a − 4.57 MHz/m slope, precisely measured a 0.49 m hotspot at 57.75 °C. The experimental results identified that the method of SA-BFS was feasible and effective to demodulate the temperature information.

Fig. 11.

Fig. 11

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(a) The measured results for 0.49 m hotspot by 20 ns and (b) a zoom of the BFS distributions around the event zone.

Discussion

The results demonstrated that an event zone of 0.49 m over a sensing distance of 10.2 km was measured based on the method of SA-BFS. Compared with the existing technology as shown in Fig. 12, the result of the work was superiority but the further optimization is required. In theory, the measurement of arbitrary length of the event zone less than the pulse width can be realized under an ideal state. However, it is difficult due to the limitation of equipment and noise. Here, the limitations impeding system optimization were revealed. When a pulse with the power of P is input into the fiber, the power of the Brillouin scattering signal is expressed as33:

graphic file with name d33e1151.gif 11

where c is the speed of light, n represents the refractive index of the fiber, α is the loss coefficient of the fiber and z is the length of the fiber. The BGS of gB should be amended GB according to Eq. (1), then the expression of Eq. (11) is as follows:

graphic file with name d33e1190.gif 12

where ΔLT is the event length, ΔL represents the sampling interval and Δz means the nominal spatial resolution. Combining with Eq. (8), the power at position xp is:

graphic file with name d33e1219.gif 13

Fig. 12.

Fig. 12

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The comparison of the work with the existent techniques.

Equation (13) demonstrates the influencing factors for the theoretical power at the position of BFS. It can be seen that the level of noise, the sampling rate and the percentage of the event zone all have an impact on the results. In practical measurements, BFS is extracted by Lorentzian curve fitting which needs to identify an initial maximum value. However, there is a deviation from the initial maximum value due to the presence of noise and the broadening effects of the pulse. This deviation directly affects the calculated results for the slope of BFS distribution. This deterioration is more pronounced when the event zone is far smaller than the Δz or the signal-to-noise ratio is relatively low. Unfortunately, there is no comprehensive theory that can accurately quantify the error, so the influence is qualitatively analyzed. But this phenomenon suggests a new direction for our future work.

Conclusion

A novel scheme based on the slope of BFS distribution was proposed and validated to demodulate temperature and the length of the BFS perturbation zone was used to measure the length of event zone. The proposed scheme broke through the limitation of pulse width and achieved the sub-pulse-length event measurement. Firstly, the BFS distribution at different positions were analyzed according to the principle of superposition of Brillouin scattering signals. And the linear relationship between kslope and T was established. Secondly, numerical simulation was conducted under the different lengths of the event zone and temperatures. The experimental results revealed a novel demodulation mechanism wherein the slope of BFS distribution demonstrates statistically significant superiority over the conventional BFS amplitude in temperature extraction. Meanwhile, it was found that the length of the BFS perturbation zone was equal to the sum of the event zone length and the nominal spatial resolution. Then the above conclusions were verified on the sensing fiber of 10.2 km. When the pulse width is fixed, it can be to measure the arbitrary length after calibrating the linear relationship between the slope of BFS distribution and temperature. The scheme improved the measurement capability of the event zone from 2 to 0.49 m over a sensing distance of 10.2 km. The temperature demodulation result was 57.75 °C, while a variation of 3.43 °C was measured by the conventional demodulation scheme. The innovative scheme of SA-BFS was proposed and verified to achieve the sub-pulse-length event measurement. The proposed scheme provides a new mechanism for temperature demodulation for designing a distributed optical fiber sensor based on the OTDR not only the BOTDR system but also the BOTDA system, providing a new perspective for the measurement of temperature or strain in Brillouin optical fiber sensing technology.

Author contributions

Shuangshuang Liu: Methodology, Validation, Methodology, Writing—Original Draft, Review & Editing. Jianzhong Zhang: Resources, Supervision,Writing-Original Draft. Zhe Ma: Formal Analysis, Funding Acquisition, Writing-Original Draft. Jinglang Xu: Validation, Software. Zhikun Wang : Data Curation. Yubo Zhang: Investigation. Mingjiang Zhang: Supervision, Funding Acquisition.

Funding

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 62075153, 62205237 and 62075151, in part by the Shanxi Provincial Key Research and Development Project under Grant 202102150101004, in part by Shanxi Provincial Central Leading Local Science and Technology Development Fund under Grants YDZJSX20231A019, in part by the Shanxi Province Basic Research Program Jointly Funding Project (Lu An) 202403011241001, in part by the Shanxi Province Basic Research Program Jointly Funding Project (Traffic Control) 202303011222005, in part by the China Postdoctoral Science Foundation 2024M761889 and in part by National Key Research and Development Program of China under Grants 2023YFF0715700.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Contributor Information

Jianzhong Zhang, Email: zhangjianzhong@tyut.edu.cn.

Zhe Ma, Email: mazhe@tyut.edu.cn.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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