Characterization of Acoustic Source Signal Response in Oxidized Autocombusted Coal Temperature Inversion Experiments

Abstract

The measurement error of sound travel time, one of the most critical parameters in acoustic temperature measurement, is significantly affected by the type of sound source signal. In order to select more appropriate sound source signals, a sound source signal preference study of loose coal acoustic temperature measurement was performed and is described herein. The results showed that the absolute error of the swept signal and the pseudo-random signal both increased with increased acoustic wave propagation distance. The relative error of the swept signal showed a relatively stable upward trend; in comparison, the pseudo-random signal showed a general decrease with a large fluctuation in the middle section, and both the relative and absolute errors for the pseudo-random signal were larger than those of the swept signal. Therefore, the swept signal is expected to perform better than the pseudo-random signal in the loose coal medium. Based on the experimental results, the linear sweep signal was selected as the sound source signal for the loose coal temperature inversion experiments: the average error between the inverted temperature value and the actual value was 4.86%, the maximum temperature difference was 2.926 °C, and the average temperature difference was 1.5949 °C.

1. Introduction

Coal has long been the ballast and stabilizer of China’s energy supply [1,2]. Based on the Statistical Bulletin of the People’s Republic of China on National Economic and Social Development in 2022 released by the National Bureau of Statistics of China, coal consumption accounted for 56.2% of China’s total energy consumption in 2022, an increase of 0.3 percentage points from the previous year [3]. A total of 130 coal mines in China’s 25 major coal-producing provinces and autonomous regions are potentially at risk of spontaneous coal combustion [4,5]. With the increase in mining depth and intensity, the area of the hollow zone is expanding and the danger of spontaneous combustion of coal is becoming increasingly strong [6,7,8]. At present, the detection of hidden fire sources in coal mining airspace, coal piles, and coal bunkers is commonly accomplished through the use of geological radar, radon detection, and drilling to determine the temperature and index gas concentration, etc. These traditional techniques have different degrees of equipment aging, operation, and maintenance difficulties and are often limited by the physical and chemical properties of different coal bodies. The measured data often contain errors when compared with real-life conditions [9]. Each technique is affected by the environmental conditions in the area in which it is employed, and when faced with more complex coal seam conditions, multiple points simultaneously, and the presence of anomalous high-temperature points, a greater number of defects are produced [10]. Acoustic temperature measurement techniques are characterized by significant advantages, such as high measurement accuracy, wide temperature measurement range, large measurement space, no contact, real-time continuity, and simple operation. They are one of the few techniques that can be used to obtain a large amount of temperature information with low input requirements, and they are a highly promising method for accurately detecting the location of hidden fire sources, such as air mining areas, coal piles, and coal silos [11]. Acoustic temperature measurement has been successfully applied in numerous fields, such as the atmosphere, oceans, power plant boilers, and grain storage; however, there are few reports on the application of temperature monitoring of crushed and stacked coals [12,13,14,15]. The authors of one study concluded that the mechanical properties of loose coal, porous media, and other characteristics are similar to those of stored particles of grain. It is anticipated that acoustic temperature measurement will be applied to restricted and complex underground environments to enable the comprehensive real-time monitoring of loose coal temperature [8].

It has been demonstrated in the literature that sound travel time measurements are impacted by a number of factors during sound wave propagation, with the type of sound source signal being an important source of measurement error [16,17]. The ability to accurately measure the acoustic signal of TOF within loose coals therefore directly determines the application of acoustic temperature measurement technology in concealed fire detection. Since acoustic temperature measurement technology in China is still in its infancy in the field of coal temperature detection, the application of relevant research methodology employed in other fields is used as a reference. Signal selection for acoustic temperature measurement in different media has been performed by numerous scholars. Shen et al. [18] performed sound travel time measurements of cold-state power station boilers using swept signals, uniform white noise signals, and sinusoidal signals in conjunction with the intercorrelation calculation method. It was found that a cross-correlation algorithm with only swept signals can be successfully applied to sound travel time measurements. Luo et al. [19] performed simulation experiments to study the selection of sound source signals in the measurement of furnace sound travel time, and the simulation results showed that when the linear frequency sweep signal was used as the sound source signal, the obtained travel time was more accurate compared with the pseudo-random sequence signals, quadratic frequency sweep signals, and logarithmic frequency sweep signals. It also exhibited a strong anti-interference ability. Wang et al. [20] combined the pseudo-random sequence coding technique with the intercorrelation analysis method to design a high-precision, rapid measurement system of sound travel time in gaseous media and performed a corresponding simulation study. The results showed that when a pseudo-random sequence was not included, the sound travel time could not be derived and the sampling accuracy was not as high as expected. Zhang et al. [21] used linear swept frequency signals as the sound source and mutual correlation as the sound travel time estimation algorithm to conduct experiments on flue gas temperature measurement in boiler hearths and flues, confirming that it is feasible to use swept frequency signals with mutual correlation functions to calculate sound travel times. Kleppe et al. [22] successfully measured sound travel time using a pseudo-random sequence. Ewan et al. [23] found that the accuracy and stability of using a linear swept signal as the source signal for the system resulted in higher values at higher SNRs; however, at lower SNRs (SNR −10 dB), pseudo-random binary sequences as the source signal outperformed the swept signal in their measurements. Zhang et al. [24] used pseudo-random signals for the temperature monitoring of high-temperature boilers to study the accuracy and stability of pseudo-random signals with correlation tests under a single path. Deng et al. [25] used lignite, coking coal, and anthracite as the research objects in their study, with white noise from 250 to 1600 Hz used as the test signal, and used the sound transmission loss experimental test system to test the sound transmission loss of three types of coal samples under six types of particle sizes and determined the optimal frequency range of the sound transmission in the loose coals to be from 600 Hz to 900 Hz.

By analyzing the current research landscape of acoustic temperature measurement and sound source signal selection, it can be observed that, in China, research on the application of acoustic temperature measurement technology in the field of coal fire disaster detection remains in the initial stage and lacks systematic evaluation. In this paper, we analyze the basic principle of acoustic temperature measurement technology and the propagation characteristics of the acoustic source signal and independently design an experimental system for temperature measurement using the acoustic method of loose coals under the action of multi-factor coupling. The swept frequency signal and pseudo-random sequence signal were selected as the experimental sound source signals, and experiments on sound travel time measurement of different sound source signals in loose coals were performed. The sound source signals suitable for the loose coal medium were given preference based on the experimental results. Our research results can significantly enhance the application of acoustic temperature measurement technology in the field of temperature monitoring of loose coals in the air-mining zone, which is of great significance to guarantee the safe, efficient, and sustainable mining of coal resources.

2. Basic Theory of Experiments

2.1. Basic Principles

Loose coal body refers to the original coal body whose integrity has been damaged by external forces such as geological structures or artificial mining, turning the coal body from a complete state to a loose state, resulting in a significant increase in grain size and porosity [26]. Acoustic waves propagate in a gaseous medium and temperature as a function of the speed of sound is the principle of acoustic temperature measurement, as shown in Figure 1 [27,28]. Acoustic temperature measurement is based on the propagation speed of sound in a medium, which primarily depends on the absolute temperature of the medium. The correspondence between the rate of propagation of sound waves in a gaseous medium and the temperature of the gas is utilized to solve for the temperature or temperature field. When acoustic methods are employed in the temperature monitoring of loose coals, the precise measurement of the sound travel time is crucial to ensuring the accuracy of the measured medium’s temperature. Therefore, how to improve the measurement accuracy of sound travel time becomes the key to the application of acoustic temperature measurement technology in the field of coal mine hidden fire detection.

2.2. Acoustic Source Signal Type

Owing to harsh environmental conditions, high temperature, and strong noise during the spontaneous combustion of coal, it is vital to choose a suitable form of sound source signal. The experimental system for measuring sound travel time can be used with two different forms of sound source signals: pneumatic and electrodynamic [29]. A pneumatic sound source is a device that uses sound waves generated by gas flow to produce sound; however, the output sound stability is poor, significantly affected by the environment and conditions of use, and not applicable to the current loose coal sound travel time measurement [29,30]. An electric sound source in the generation of sound waves can offer more precise control of frequency and amplitude, and the output of the sound wave is highly stable, with it being less susceptible to environmental airflow and other factors. Based on the accuracy of the experimental results and the real-life mining environment, we selected an electric sound source as the form of sound source signal generation.

There are many types of signals for electrodynamic sound sources, and in this study, we searched for suitable sound source signals for coal body medium and inter-correlation function such as time delay estimation algorithms from well-established and widely used sound source signals. Among them, sine, triangular, square, and sawtooth waves, in addition to slope and triangular signals, are not suitable as sound source signals for sound travel time measurements of loose coals due to the lack of obvious peaks or unstable peaks in their cross-correlation curves [31,32]. The loose coal medium contains a large amount of Gaussian noise, and under these conditions, the most suitable signals for efficient and reliable transmission are special signals with white noise statistics [32]. However, there remain numerous technical challenges and difficulties related to the generation, processing, and reproduction of white noise signals. With more in-depth research on the types of sound source signals, pseudo-random signals with a wide frequency range, good periodicity, uniform power spectral density and simple processing have been designed through computer programming, and their randomness provides great benefit in distinguishing the strong background noise from the sound source signals; they therefore have great potential to be used as a sound source signal for sound travel time measurements in loose coals. The swept frequency signal has been widely used in boiler temperature measurement and other sound travel time measurement sites; we therefore selected the swept frequency signal and the pseudo-random sequence signal as the sound source signal to perform the sound travel time measurement experiment.

2.2.1. Pseudo-Random Sequence Signal

The pseudo-random sequence, as a periodic sequence, generally consists of a feedback shift register, as shown in Figure 2 [24]. Under the action of a time pulse, $a_n,a_{n-1},a_{n-2},\dots ,a_3,a_2,a_1$ acts as a memory sequentially outputting a sequence from left to right that possesses the properties of a two-valued autocorrelation function. These properties are very close to the autocorrelation function property of white noise when $K\to 0$ in Equation (1):

$$R(j)=\{\begin{array}{c}1,(j=0)\\ K,(j=1,2,\dots ,P-1)\end{array}$$

(1)

where P is periodicity of sequences, K < 1.

When the pseudo-random signal is used for acoustic fly-through time measurement, its randomness prevents measurement deviation due to external interference, noise, and other factors, and the generation speed is fast enough to realize real-time signal measurement and processing. In addition, the pseudo-random signal has a wide frequency range, which can meet the necessary requirements in different environments. In addition, the periodicity of the pseudo-random signal is outstanding, which ensures accuracy and stability, with its power spectral density being uniform to ensure the accuracy and reliability of the measurement results. The generation and processing of pseudo-random signals obtained using computer programming are very simple, and automated measurements can be easily realized. In this study, we used the hybrid programming of MATLAB and LABVIEW, adopted the eigen polynomials projected, and produced the pseudo-random sequences as the acoustic source signals of loose coals according to the principle of linear shift register.

2.2.2. Sweep Signal

Sweep signal is a continuous sine wave signal whose frequency changes according to a certain law, and it is also a broadband signal with variable frequency [31]. By designing them accordingly, they can be made to correlate weakly with various ambient noises and are therefore very easy to detect. Sweep signals have been widely used with good results in many areas of signal detection, monitoring of high temperature environments in industrial high temperature furnaces, and measurements in grain storage of particles, and are expected to be used as source signals in sound travel time measurements in loose coals.

Sweep signals are usually divided into three types, namely, linear sweep signals, quadratic sweep signals, and logarithmic sweep signals, and the mathematical expressions of these three typical sweep signals are shown in

Table 1. Mathematical expressions for typical swept signals [24].

Sweep Signal Form	Mathematical Expression	Parameter Description
Linear swept signal	f(t) = f0 + βt(t ∈ [0, tg])	β = [f(tg) − f0]/tg
Secondary type sweep signal	f(t) = f0 + βt2(t ∈ [0, tg])	β = [f(tg) − f0]/tg2
Logarithmic sweep signal	f(t) = f0 + 10βt(t ∈ [0, tg])	β = [log10f(tg) − f0]/tg

.

Where f₀ is the instantaneous frequency of the swept signal at the start, f(t_g) is the instantaneous frequency of the swept signal at t_g, and [0, t_g] is the duration of the swept signal. Sweep signals provide very accurate time measurements with very high time resolution due to the very stable, controlled, and subtle changes in frequency. In addition, swept signals can be filtered and removed from interfering signals to enhance their immunity to interference to ensure the accuracy of the measurement results. Lastly, the sweep signal can be programmed to generate and control its frequency and sweep range in real time to suit different measurement needs. The swept frequency signal is therefore highly suitable as a sound source signal for sound travel time measurement in loose coals, and the linear swept frequency signal (hereinafter referred to as the swept frequency signal) was selected for the study described herein [19,21].

3. Experimental Systems and Methods

3.1. Design Ideas

Based on the above basic principles of acoustic temperature measurement experiments and after investigating the existing temperature measurement experimental devices, the main considerations for applying acoustic temperature measurement to loose coals in designing the experimental bench are as follows: ① Lab bench specification size; ② Experimental temperature; ③ Experimental test signals and signal frequencies; and ④ Experimental equipment hardware. After selecting the size of the test rig, acoustic testing was performed, and the acoustic signals received by the acoustic microphones were selected to undergo testing at different distances and the results were compared. The experimental temperature is based on the warning level of spontaneous coal combustion at Xi’an University of Science and Technology, and the temperature range of the early stage of spontaneous coal combustion was selected for this experiment. Signal and frequency selection was based, experimentally, on previous experience of acoustic wave measurements on grain particles and particles in quasi-porous media. With regard to hardware, we selected the domestic equipment of Beijing Shengwang Acoustic and Electric Company. In the system, the loudspeaker and microphone are positioned at the same horizontal line in the coal sample box to form a single path for sound travel time measurement, which provides experimental data for the study of sound travel time measurement in loose coals.

3.2. System Components and Parameter Settings

To construct the multi-factor coupling effect of a loose coal acoustic temperature measurement experimental system, as shown in Figure 3, its components primarily include the following:

(1) Coal sample chamber and soundproofing system

The box containing the coal samples is 50 cm × 50 cm × 180 cm in size, composed of 316 stainless steel with a thickness of 2 mm to simulate the environment of the underground mining area. The sound insulation system consists of an industrial grade acoustic material, polyester fiber acoustic cotton, which is uniformly fixed to the inner wall of the coal sample chamber using a stainless steel grid to weaken the effect of reflected sound waves on the experimental results.

(2) Programmed heating system

The programmed temperature rise system consists of a programmed temperature rise device, a thermocouple with a type K probe with a diameter of 1 mm, and an MT500 temperature recorder. The temperature of the coal sample to be tested was set to 20 °C, 30 °C, 35 °C, 40 °C, 45 °C, and 50 °C using the programmed temperature-raising device to meet the requirements of different stages of the experiment, and the temperature of the coal sample was transmitted to the temperature recorder by the thermocouple.

(3) Acoustic test systems

The acoustic test system includes a D8.4MKII bass-medium dynamic loudspeaker (with an impedance of 4 Ω, a power rating of 100~200 W, a voice coil diameter of 76 mm, and a sensitivity of 86 dB/W. The power rating is 4 Ω, the power output is 100~200 W, and the voice coil diameter is 76 mm), an MPA416 microphone (frequency range of 20 Hz~20 kHz, sensitivity of 50 mV/Pa (−26 dBre1V/Pa), and dynamic range of 29~127 dB), PA300 power amplifier (peak output power up to 295 W, bandwidth of 20 Hz~20 kHz, 102 dB dynamic range, and total power efficiency of 73~80%), XCQ108 expandable multi-channel data collector (input frequency response range 2 Hz~20 kHz (±0.5 dB, input sampling rate 51.2 kHz), dynamic range 101 dB, and sensitivity 50 mV/Pa), BSWA sound level calibrator (with 1 kHz calibration frequency, outputs 94 dB and 114 dB SPL, calibrator accuracy ±0.3 dB, applicable to all frequency weighting networks), upper computer, and BSWA RX 1.0.0.184 acoustic measurement software developed by Beijing Shengwang Acoustic Electric Technology Co. (Beijing, China). The equipment has a linear layout and forms a single path for sound travel time measurements. The experimental sound source signal frequency was set to 20 Hz~20 kHz, the minimum sampling frequency was 6 kHz, and the sound source signal acquisition frequency fs was 51,200 Hz [20].

When using the cross-correlation function as the sound travel time delay estimation algorithm, if the number of sound travel time delay points is $n_0=D\cdot fs$, then the number of sampling points and the number of sound travel time delay points should satisfy N > 4n₀ [33]. Based on the experimental system described in this paper and a large amount of data acquired during a previous study, the sound travel time in the experimental loose coals is roughly D = 3~6 ms. For a sampling frequency of 51,200 Hz, the calculation indicates the number of sampling points of the sound source signal N > 4 n0 = 4 D·fs = 4 × 6 × 51.2 ≈ 1229.

3.3. Experimental Conditions and Methods

The experiments described in this paper can primarily be divided into two parts: (1) Experiments on acoustic fly-through time measurement with different types of sound source signals and (2) coal temperature inversion experiments using swept frequency signals as acoustic source signals.

Before the commencement of the experiment, the system must be commissioned. During debugging of the system, attention should be paid to calibrating the microphone sensitivity, because the air quality is unstable due to the influence of the environment, and other factors, including temperature, humidity and atmospheric pressure, and other parameters can change at any time. Therefore, in order to ensure that the metal diaphragm of the microphone receives accurate air vibration wave signals, the sensitivity of the microphone must be adjusted accordingly. Once the calibration is completed, the specific experimental steps and methods are as follows:

(1) Experiments on acoustic fly-through time measurement with different types of sound source signals

a. Open the acoustic test software with the microphone and modulate the sound source signals as pseudo-random sequence signals and swept frequency signals, respectively.

b. The long flame coal is crushed and sub-divided into four particle sizes of 0.5–0.8 cm, 0.8–1 cm, 1–3 cm, and 3–5 cm, each of which is 300 kg, and evenly spread in the box.

c. Maintain the thermocouple and microphone at the same depth, 28.5 cm from the top cover, and set the initial temperature to 20 °C and the microphone spacing to L1 = 0.70 m, L2 = 0.85 m, L3 = 1.00 m, L4 = 1.15 m, and L5 = 1.30 m, respectively.

d. Adjust the sampling parameter to 51,200 Hz [34,35], and use FIR filters to filter the two sound source signals separately. A bandpass filter of order 502 was selected, and the design method is the Kaiser window function with a passband frequency of 1000~3000 Hz and a passband amplitude of 1 dB.

e. Adjust the acoustic wave frequency to 1000–3000 Hz [36], the preparation time to 2 s, the acoustic wave one-shot time to 4 s, the silence time to 1 s, and the acoustic wave emission time to 3 s as a control variable, to ensure that the attenuation coefficient α(k) of the original signal and the delayed signal is 1, and the acoustic wave is repeated 3 times and stored.

f. The data were imported into MATLAB 2016 software, and after wavelet noise suppression [37] was applied to the data results, the quadratic correlation PHAT-β algorithm was utilized for the processing and output of acoustic signal results [21,36,37,38].

g. The experimental data were calculated using RX 1.0.0.184 software in I.C.C. RX software in the I.C.C. The reference values and reasonable ranges of the acoustic fly-through times on different paths were obtained, as shown in

Table 2. Theoretical values of acoustic fly-through time at different distances with theoretical time delay sampling points (unit ms).

Route Number	Theoretical Value of TOF t (ms)	Theoretical Delay Sampling Points (ms)
L1	2.041	104
L2	2.478	126
L3	2.916	149
L4	3.353	171
L5	3.791	194

. The data shown in Table 2 are derived from 100 acoustic TOF measurements taken during a pervious study using MATLAB simulation and processed using the inter-correlation time delay estimation algorithm.

Due to the simultaneous presence of absorption attenuation and scattering attenuation during the propagation of sound waves in the granular medium, in addition to the fluctuation in the ambient noise, the recalibration of the microphone position and sensitivity in the process of filling coal samples will induce a certain degree of error. The fly-through times of the sound waves in different paths in the coal samples measured in the experimental process therefore generally vary within a reasonable range.

(2) Coal temperature inversion experiment using a swept signal as an acoustic source signal

a. Turn on the programmed heating system and set the temperature to 20 °C, 30 °C, 35 °C, 40 °C, 45 °C, and 50 °C using the control panel. Once the temperature detection device shows that the temperature has reached the preset temperature, repeat the steps of experiment (1) to derive the time delay estimation using the swept signal as the sound source signal;

b. Through the already constructed loose coal body quasi-porous medium sound velocity–coal temperature mapping relationship model ${(\lambda C_g^I/\phi \epsilon )}^2=T_L$, in addition to when the coal sample particle size is 0.6–1.5 cm, 1–3 cm, and 3–5 cm to determine the equivalent path conversion factor $\lambda$, the value of the gas component medium correction coefficient $\phi$ [39], and substituting the results of the time-delay estimation into the Equation to derive the results of coal temperature inversion.

4. Experimental Results and Analysis

Take the longest distance of the sound travel time measurement system of the sound wave propagation path in the loose coals as an example of the path L₅ = 1.30 m. The temperature inside the box is 20 °C at room temperature, and the propagation speed of the sound wave in the air can be obtained from the approximate formula c = 20.03 T^1/2, c₀ = 342.95 m/s. The theoretical value of the sound travel time under path L₅ is t₀ = L₅/c₀ = 3.791 ms and the sampling frequency fs is 51,200 Hz. The number of theoretical delay estimation points is 194, and the theoretical values of sound travel time at different distances with their corresponding delay sampling points are shown in Figure 4.

4.1. Pseudo-Random Sequence Signal Accuracy Analysis in Loose Coals

(1) Analysis of pseudo-random signal cross-correlation results

Let the sound source signal be a pseudo-random sequence signal, corresponding to 56,320 sampling points. Taking the distance l between the two microphones as 0.7 m as an example, the pseudo-random signal waveforms received by the near-end microphone and the far-end microphone are shown in Figure 5. The data obtained after the experimental measurements were calculated using the quadratic correlation PHAT-β algorithm and the results are shown in Figure 6.

As can be seen from Figure 6, when the distance between the near-end microphone and the far-end microphone is 0.7 m, the pseudo-random signal is no longer distinguishable from the original waveform after attenuation and laboratory noise in the empty box, and the amplitude of the signal is also slightly reduced by attenuation in the air medium. As can be observed in Figure 6, when the pseudo-random signal is used as the sound source signal of the sound travel time measurement experimental system, the peaks of the curves are obvious and almost no sidelobes are generated after the time delay estimation of the pseudo-random signal at different distances using the quadratic correlation PHAT-β algorithm. The estimated number of time-delay points when pseudo-random signals are used as sound source signals at five distances are 107, 130, 149, 174, and 190, which do not vary considerably from the theoretical sampling points, proving that the pseudo-random signals can be used as sound sources to determine the accurate sound travel time inside the loose coals.

(2) Pseudo-random signal accuracy analysis

Continuously make 30 measurements of the sound travel time inside the box at different distances and use the quadratic correlation PHAT-β algorithm for time delay estimation of the measurement results to obtain data on the sound travel time when the pseudo-random signals are used as the sound source signals at different distances, as shown in Figure 7. The results of 30 times delay estimations were averaged to determine the variation in sound travel time when the pseudo-random signal was used as the sound source signal, as shown in Figure 8.

When analyzing the pseudo-random signal as the sound source signal, the results of the above 30 times delay estimations were averaged to obtain the acoustic fly-through time data at different distances, as shown in Figure 8. The absolute error of the sound travel time when the pseudo-random signal is used as the source signal ranges from 0.019 to 0.031 ms. As the distance increases, the absolute error gradually increases. The factor responsible for this change is the fact that as the distance increases, the signal propagation time increases and the attenuation is larger; the relative error ranges from 0.72 to 0.93%, and with the increase in distance, the relative error decreases gradually in general, and reaches the minimum value when the microphone spacing is 1 m. Similarly, the experimental data of pseudo-random signal fly-through time at different distances were fitted linearly, and the curve of pseudo-random signal propagation distance l fitted with fly-through time t based on MATLAB software is shown in Figure 9.

The fitted regression equation is as follows:

$$l=2.8940t-0.0020$$

(2)

The R² of the fitted curve was calculated to be 0.99999. We were able to prove that the pseudo-random signal propagation distance l is highly correlated with the sound travel time t, and the experimental data of the pseudo-random signal propagation time at different distances are accurate and reliable.

4.2. Accuracy Analysis of Frequency Sweep Signals in Loose Coals

(1) Analysis of inter-correlation results for swept signals

Designate the swept signal as the sound source signal of the sound travel time system, the frequency range is 1000~3000 Hz, the number of sampling points is 56,320 points, L₁ = 0.70 m, for example, the two microphones receive the signal waveform as shown in Figure 10.

When L₁ = 0.70 m, the waveform of the swept signal is clearly visible, and the signal amplitude is slightly reduced after attenuation. Measure the fly-through time of the swept signal at different distances, respectively, and calculate it using the quadratic correlation PHAT-β algorithm. The results are shown in Figure 11.

As can be seen in Figure 11, the peaks of the swept signal curves at the five different distances are distinct, and almost no sidelobes are generated. The number of time delay points after the time delay estimation of the swept signal at the five distances are 105, 127, 146, 166, and 192, respectively, which are not much different from the corresponding theoretical sampling points in Figure 11, proving that the swept signal can be used as the source signal for the measurement of the loose sound travel time of the coals.

(2) Sweep signal accuracy analysis

Continuously make 30 measurements of the sound travel time within the loose coals at different distances, estimate the time delay of the measurement results using the quadratic correlation PHAT-β algorithm, and take the average value of the 30 time delay estimation results to determine the change in the sound travel time when the swept signal is used as the sound source signal, as shown in Figure 12.

When analyzing the swept signal as the sound source signal, the results of the above 30 times delay estimates were averaged to obtain the acoustic fly-through time data at different distances, as shown in Figure 13. When analyzing Figure 12 and Figure 13, it can be seen that the absolute error in the fly-through time of the swept signal ranges from 0.002 to 0.019 ms and increases gradually with distance. The factor responsible for this change is the fact that the sweeping signal propagation time increases and the attenuation is greater when the distance increases. The relative error of the swept signal fly-through time ranges from 0.01 to roughly 0.50 percent, exhibiting the same trend as the absolute error as the distance increases.

Considering the accuracy of the sound travel time measurements during the experiment, the curve based on MATLAB software fitting the swept signal propagation distance l to the travel time t is shown in Figure 14. The regression equation for the fitted distance x versus time y can be approximated as follows:

$$y=2.8820x+0.0264$$

(3)

The R² of the fitted curve is calculated to be 0.99996, which proves that the sweeping signal propagation distance l is strongly correlated with the sound travel time t, and the experimental data are accurate and reliable.

Comparing the calculation results of pseudo-random sequences as sound source signals described in Section 4.1, it can be seen that the peaks of the time delay estimation curves of the pseudo-random signals and the swept signals when they are used as sound source signals are obvious, with almost no side-valve generation, and the error between the actual time delay sampling points and the theoretical sampling points is extremely small, which proves that the two signals can be used as the sound travel time measurement of the sound source signals. After the two signals were used as sound source signals for sound travel time measurement experiments at different distances for 30 runs, the measured time delay estimates were averaged and analyzed for absolute and relative errors, as shown in Figure 8 and Figure 13. As the acoustic wave propagation distance increases, the absolute error of the measurement results of the swept frequency signal and the pseudo-random signal increases, and the absolute error of the pseudo-random signal is larger than that of the swept frequency signal. Comparing the relative errors, as the acoustic transmission distance increases, the calculation results of the swept signal show a more stable upward trend; in comparison, the pseudo-random signal calculation results gradually decrease in general, with larger peaks and pits in the middle section, and reach their minimum value when L3 = 1.00 m; however, they are all larger than the swept signal. In summary, it can be seen that the swept signal performs better than the pseudo-random signal for the sound travel time measurement experiments within loose coals.

4.3. Verification of the Inversion of Coal Temperature by Swept Frequency Acoustic Source Signals

By analyzing the experimental results detailed in Section 4.1 and Section 4.2, we concluded that the error in the calculation results of the swept frequency signal is the result of the sound travel time source signal being less than the pseudo-random signal under the loose coal medium. In order to more effectively illustrate the accuracy of the swept signal as an acoustic source signal for the inversion of coal temperature, the swept signal was configured to be an acoustic source signal based on the experimental method described in Section 3.3 Summary combined with the principle of temperature rise. The microphone interval L₄ = 1.30 m was selected, the particle sizes of the coal samples were 0.5–0.8 cm, 0.8–1.5 cm, 1–3 cm, and 3–5 cm, and the temperature of the coal samples was set to 30 °C, 35 °C, 40 °C, 45 °C, and 50 °C using the programmed heating system to perform coal temperature inversion experiments, with the results of the experiments shown in Figure 15. From the experimental results, it can be seen that the average absolute error between the temperature inverted by the swept frequency acoustic source signal and the temperature of coal samples with different grain sizes is 4.86%, with a maximum temperature difference of 2.926 °C and an average temperature difference of 1.5949 °C. The results show that the swept frequency signal, when used as the sound source signal for the temperature measurement of loose coals, exhibits strong accuracy and stability, and is able to invert the coal temperature more accurately and reliably.

5. Conclusions

(1) Based on the principles of acoustic temperature measurement and acoustic source signal generation, an experimental system of acoustic temperature measurement of loose coals using an acoustic method under multi-factor coupling was designed and built. The pseudo-random sequence and the swept frequency signal were, respectively, used as sound source signals for the sound travel time measurement experiments in loose coals, and the results demonstrate that the two signals correlate well with one another, and the estimated number of measured time delay points is very small compared with the theoretical value.

(2) The absolute errors of the sound travel time measurements of the swept and pseudo-random signals increase with an increase in the sound traveling distance, with maximum values of 0.019 and 0.031, respectively. The relative error of the swept signal exhibits a more stable upward trend, with the maximum and minimum values of 0.5 and 0.01, respectively, while the pseudo-random signal decreases in general, with larger peaks and pits in the middle section, with the minimum value of 0.72, all of which are larger than that of the swept signal. From the above results, it is considered that, within the medium of loose coals, the swept signal performs better than the pseudo-random signal.

(3) The average error between the inverted temperature and the temperature of coal samples with different grain sizes was 4.86%, the maximum temperature difference was 2.926 °C, and the average temperature difference was 1.5949 °C. This method exhibits strong accuracy and stability and can invert coal temperature more accurately and reliably.