# Experimental Study of Extracting Weak Infrared Signals of Rock Induced by Cyclic Loading under the Strong Interference Background

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental System

#### 2.2. Experimental Environment

#### 2.2.1. Monotonic Changes in the Ambient Temperature

#### 2.2.2. Fluctuations in Ambient Temperature

#### 2.3. Experimental Method

^{3}and the top and bottom faces of each sample were parallel within an error of 0.1 mm. The specific processing parameters of the samples are shown in Table 1.

#### 2.4. Data-Processing Method

#### 2.4.1. Difference Processing

#### 2.4.2. Wavelet Analysis

_{j,k}(x).

^{2}(R), any given signal f(x) ∈ L

^{2}(R) can be decomposed into different frequency bands by scale as follows:

_{j}(x) is the component of f(x) at scale j. If h is an orthogonal wavelet, the components of Equation (3) are orthogonal, i.e.,

_{i}(x), g

_{j}(x)> denotes the inner product of the two components g

_{i}(x) and g

_{j}(x). If it is 0, then the components are not related and can be arbitrarily combined without being affected by other components. The wavelet analysis method has been a common signal-processing method to extract weak signals from strong noisy backgrounds, and it is applied to many practical applications [53].

_{high}, ΔAIRT

_{mid}, and ΔAIRT

_{low}denote the components in high, middle, and low frequency, respectively. The orthogonal Coiflet 5 wavelet basis was selected to decompose ΔAIRT. According to the loading period and the sampling frequency of AIRT, the suitable decomposition level for the wavelets is 11. ΔAIRT

_{mid}belonged to the detailed component at level 11, and the ΔAIRT

_{low}belonged to the approximation component at level 11. The remaining detailed components from level 1 to 10 belonged to ΔAIRT

_{high}. The absolute error of the postdecomposition synthesis is on the order of 10

^{−9}.

#### 2.4.3. Statistical Analysis

_{mid}is the component which is most related to the stress change because the influence of the background and the noise has been removed. To evaluate the effect and accuracy of extracted weak infrared radiation signals induced by stress from the strong interference environment, the following two aspects in temporal and amplitude were taken into consideration:

_{mid}should be consistent with that of the stress [47]. Therefore, both the correlation between the ΔAIRT and the stress, and the correlation between the ΔAIRT

_{mid}and the stress were analyzed.

_{mid}was consistent with the calculated theoretical result. Therefore, both the maximum amplitudes of ΔAIRT and ΔAIRT

_{mid}were analyzed.

## 3. Results

#### 3.1. Stress-Strain Analysis

#### 3.2. Photos for Experimental Conditions

#### 3.3. Temperature Variation and ΔAIRT

#### 3.3.1. Results in ‘EM1’

_{low}, ΔAIRT

_{mid}, and ΔAIRT

_{high}plotted in Figure 5a–c, respectively.

_{low}decreased monotonically with a value of 0.27 K, which was consistent with the change in the ambient temperature (Figure 4a). The ΔAIRT

_{low}could be used to represent the change in the ambient temperature. Figure 5b shows that the ΔAIRT

_{mid}was consistent with the stress curve with temporal cyclic changes. The maximum amplitude of ΔAIRT

_{mid}was 0.05 K, which was only approximately 15% of the change amplitude in the ambient temperature. Figure 5c shows that the ΔAIRT

_{high}changed drastically with large fluctuations. Apart from the influence of the background and stress, the fluctuations of ΔAIRT

_{high}were mainly due to instrumental noise and wind in the range of 0.05 K. The standard error of ΔAIRT

_{high}is about 8 mK, indicating that the experimental condition was relatively stable in ‘EM1’.

#### 3.3.2. Results in ‘EF2’

_{low}shows a similar trend with that of the ambient temperature. The trend of ΔAIRT

_{mid}was consistent with the stress curve in period as well with the maximum amplitude of 0.076 K in Figure 7b, which is approximately 40% of the amplitude of the ambient temperature change (0.19 K). Figure 7c shows that the ΔAIRT

_{high}changed with large fluctuations due to instrumental noise, wind, and sunlight in the range of 0.1 K. The standard error of ΔAIRT

_{high}is about 15 mK, indicating that the experimental condition was relatively more complex than that in ‘EM1’.

#### 3.4. Statistical Results

_{mid}were calculated and are listed in Table 2. It is found that the correlation coefficients between original ΔAIRT and the stress were poor with the maximum value less than 0.6. However, the correlation coefficients between the decomposed ΔAIRT

_{mid}and the stress increased significantly with the minimum value larger than 0.8. The average values of correlation coefficient in ‘EM1’ and ‘EF2’ were 0.93 and 0.90, respectively.

_{mid}were approximately 0.2–1.6 mK/MPa during the elastic deformation stage in the two experimental environments. This is similar to the results obtained in a stable indoor experimental condition without obvious ambient temperature change [22,23,24,27,28,29].

## 4. Discussion

#### 4.1. The Relationship between the Change in the TIR and Stress

^{−1}), ρ is the density (kg/m

^{3}), C

_{p}is the specific heat capacity (J/kg·°C), and T is the absolute temperature of a unit object (K). According to the literature [47,54], the values of thermal parameters for sandstone are as follows: α = 7.8 × 10

^{−6}°C

^{−1}, ρ = 2230 kg/m

^{3}, and C

_{p}= 710 J/kg·°C. Those for granite are: α = 7.5 × 10

^{−6}°C

^{−1}, ρ = 2640 kg/m

^{3}, and C

_{p}= 820 J/kg·°C. According to Equation (6), when the initial temperature of the granite was 20.3 °C, and the main stress variation was 60 MPa, the temperature increase can be calculated as 0.061 K. For sandstone, when the main stress variation was 35 Mpa, the temperature increased by 0.051 K. The increasing rate of ΔAIRT

_{mid}for sandstone is higher than that for granite. Figure 4a and Figure 6a show that the amplitude of ambient temperature change was about 0.2 K, and that the amplitude of ΔAIRT

_{mid}was only 15–40% of the ambient temperature. It was relatively weak compared to the ambient temperature.

_{mid}changed consistently with the change in stress with the average correlation coefficient larger than 0.9. As there was no cyclic component with the same period of stress change during the loading process, it can be inferred that the ΔAIRT

_{mid}was caused by the stress change.

#### 4.2. The Relationship between AIRT and Physical Temperature

^{−2}), ε is the emissivity in the range of 0–1, e is the Stefan–Boltzmann constant, and T is the physical temperature (K). For blackbody, the radiant temperature is equal to T. For an actual object, the relationship between the two temperatures is:

_{s}is the radiant temperature (K). Based on the TIR theory, the TIR intensity changes linearly with the physical temperature change with the correlation coefficient greater than 0.99, and it was confirmed by the experimental results in the laboratory condition with slight changes in ambient temperature [35,36]. As the emissivity is less than 1, the value of radiant temperature change is lower than that of the physical temperature, though both of the temperatures could be used to represent the thermal change. Figure 4a shows that the ambient temperature change was 0.33 K, whereas the ΔAIRT

_{low}was 0.27 K (Figure 5a). Similarly, the ambient temperature change in Figure 6a was 0.19 K, whereas the ΔAIRT

_{low}was 0.17 K (Figure 7a). When taking the emissivity of the rock samples (ε ≈ 0.9) into consideration, the two temperatures were generally consistent according to Equation (8). It is noted that the emissivity of the rock was changed obviously in the stress condition in the range of 8.0–10.0 μm [38]. However, as the AIRT was obtained in the range of 3.7–5.0 μm, the emissivity change was not considered here.

#### 4.3. Significance of the Experimental Results

#### 4.4. The Difficulty and Further Improvement

- (1)
- The cyclic loading mode and the relatively high loading rate in this study are just one type of crustal stress condition. However, the actual crustal stress conditions are complex and variable, and the loading rate is uncontrollable in reality. Additionally, the wavelet method is not suitable for extracting the TIR signal related to the aperiodic crustal stress from a relatively strong background.
- (2)
- In addition, most of IR radiation recorded by satellite sensors is emitted by vegetation, soil, and unconsolidated sediments on the Earth’s surface. Moreover, the received radiation is influenced by many nonseismic factors including climate, topography and landscape, geophysics, and geography. It is difficult to observe the TIR signal from the loaded rock on the ground directly.
- (3)
- The distance between the spectrometer and the specimen is at the level of meters in the experimental condition, which is much less than the orbit height at the level of hundreds of kilometres for satellite observations. The influence of the atmosphere effect is inevitable.

- (1)
- For the experimental design, the cyclic loading mode at a relative slow rate can be considered to simulate the actual crustal stress condition [46]. In addition, more types of rock samples can be selected to confirm the magnitude of the stress-related TIR signal.
- (2)
- (3)

## 5. Conclusions

- (1)
- The AIRT is strongly influenced by the ambient temperature and environmental radiation. The AIRT related to stress is relatively weak and submerged by the ambient temperature, which cannot be identified directly.
- (2)
- The stress-induced infrared radiation signal from the cyclic loaded rock can be extracted via wavelet analysis method. The correlation coefficient between the decomposed ΔAIRT and stress is larger than 0.8, and the amplitude of the extracted stress-induced infrared radiation is close to the theoretical result. Therefore, it is feasible to extract the weak TIR signals induced by stress in a strong interference background.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Experimental scene: (

**a**) schematic of the instrument arrangement, (

**b**) photo of the experimental system under outdoor conditions at night.

**Figure 3.**The photos of the samples and the arrangement of the temperature probes in these two types of environments: (

**a**) HG-1 in the ‘EM1’; (

**b**) HG-4 in the ‘EF2’.

**Figure 4.**The measured results of sample HG-1 in the cyclic loading process: (

**a**) The ambient temperature change; (

**b**) ΔAIRT change.

**Figure 5.**Results of decomposed ΔAIRT using wavelet analysis in the cyclic loading process of sample HG-1: (

**a**) ΔAIRT

_{low}; (

**b**) ΔAIRT

_{mid}; (

**c**) ΔAIRT

_{high}.

**Figure 6.**The measured results of sample HG-4 in the cyclic loading process: (

**a**) The ambient temperature change; (

**b**) ΔAIRT change.

**Figure 7.**Results of decomposed ΔAIRT using wavelet analysis in the cyclic loading process of sample HG-4: (

**a**) ΔAIRT

_{low}; (

**b**) ΔAIRT

_{mid}; (

**c**) ΔAIRT

_{high.}

Sample No. | Rock Type | Cyclic Loading Range (MPa) | Loading Rate (MPa/s) | Environmental Conditions |
---|---|---|---|---|

HG-1 | Granite | 10–60 | 0.3 | Night, ‘EM1’, Day 1 |

HG-2 | 10–70 | 0.4 | Night, ‘EM1’, Day 2 | |

HG-3 | 10–70 | 0.4 | Night, ‘EF2’, Day 3 | |

HG-4 | 10–70 | 0.5 | Daytime, ‘EF2’, Day 3 | |

SY-1 | Sandstone | 5–40 | 0.4 | Daytime, ‘EF2’, Day 1 |

SY-2 | 5–40 | 0.4 | Daytime, ‘EF2’, Day 2 |

**Table 2.**Statistical results of the correlation coefficients between both of ΔAIRT and ΔAIRT

_{mid}and stress and the maximum amplitude.

Sample No. | Correlation Coefficient | Maximum Amplitude (K) | ||
---|---|---|---|---|

ΔAIRT | ΔAIRT_{mid} | ΔAIRT | ΔAIRT_{mid} | |

HG-1 | 0.18 | 0.91 | 0.27 | 0.05 |

HG-2 | 0.12 | 0.94 | 0.09 | 0.03 |

HG-3 | 0.59 | 0.93 | 0.11 | 0.04 |

HG-4 | 0.45 | 0.91 | 0.29 | 0.08 |

SY-1 | 0.24 | 0.90 | 0.33 | 0.06 |

SY-2 | 0.09 | 0.84 | 0.23 | 0.06 |

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**MDPI and ACS Style**

Huang, J.; Liu, S.; Ni, Q.; Mao, W.; Gao, X.
Experimental Study of Extracting Weak Infrared Signals of Rock Induced by Cyclic Loading under the Strong Interference Background. *Appl. Sci.* **2018**, *8*, 1458.
https://doi.org/10.3390/app8091458

**AMA Style**

Huang J, Liu S, Ni Q, Mao W, Gao X.
Experimental Study of Extracting Weak Infrared Signals of Rock Induced by Cyclic Loading under the Strong Interference Background. *Applied Sciences*. 2018; 8(9):1458.
https://doi.org/10.3390/app8091458

**Chicago/Turabian Style**

Huang, Jianwei, Shanjun Liu, Qiang Ni, Wenfei Mao, and Xiang Gao.
2018. "Experimental Study of Extracting Weak Infrared Signals of Rock Induced by Cyclic Loading under the Strong Interference Background" *Applied Sciences* 8, no. 9: 1458.
https://doi.org/10.3390/app8091458