An FSV analysis approach to verify the robustness of the triple-correlation analysis theoretical framework

Among all the gas disasters, gas concentration exceeding the threshold limit value (TLV) has been the leading cause of accidents. However, most systems still focus on exploring the methods and framework for avoiding reaching or exceeding TLV of the gas concentration from viewpoints of impacts on geological conditions and coal mining working-face elements. The previous study developed a Trip-Correlation Analysis Theoretical Framework and found strong correlations between gas and gas, gas and temperature, and gas and wind in the gas monitoring system. However, this framework's effectiveness must be examined to determine whether it might be adopted in other coal mine cases. This research aims to explore a proposed verification analysis approach—First-round—Second-round—Verification round (FSV) analysis approach to verify the robustness of the Trip-Correlation Analysis Theoretical Framework for developing a gas warning system. A mixed qualitative and quantitative research methodology is adopted, including a case study and correlational research. The results verify the robustness of the Triple-Correlation Analysis Theoretical Framework. The outcomes imply that this framework is potentially valuable for developing other warning systems. The proposed FSV approach can also be used to explore data patterns insightfully and offer new perspectives to develop warning systems for different industry applications.

As the world's largest coal producer, China's coal mine industry accounted for about 46% of global coal production in 2020 1,2 . Gas accidents are severe that must be addressed by coal mining industry managers in China 3 . Among all the gas disasters, gas concentration exceeding the threshold limit value (TLV) has been the leading cause of accidents 4 . Therefore, gas monitoring systems for real-time TLV have been adopted in China's coal mines. However, most systems still focus on exploring the methods and framework for avoiding reaching or exceeding TLV of the gas concentration from viewpoints of impacts on geological conditions and coal mining working-face elements. When the gas data outputs reach or exceed TLV, the gas monitoring system alerts the mine's safety response team 5 .
Up-to-date literature indicates that current studies mainly focus on using machine learning (ML) (including deep learning) approaches to explore warnings or predict models for avoiding exceeding the TLV of the gas concentration. However, a comprehensive literature review in the previous work appears to have at least three significant limitations on using ML methods to predict gas emissions and gas concentrations in the current coal monitoring systems model 5,6 . They include poor (dataset) inputs resulting in inadequate outputs, inaccurate interpreted prediction results, and high cost of the computing hardware for improving the efficiency and effectiveness of the ML models 5 . No published paper fully reports on systems that utilize the collected coal mine data; no attempt has been made to uncover the correlation between gas concentration and other data and apply them to predict gas concentration 4 . Therefore, a previous study developed a Trip-Correlation Analysis Theoretical Figure 1. Shown is a Triple-Correlation Analysis Theoretical Framework adopted in this research to propose a research framework comprising the correlation analyses between the gas (from T1 to Tn) and gas (from T1 and Tn), gas (from T1 and Tn) and temperature (from WD1 to WD16), and gas (from T1 to Tn) and wind (from FS1 to FSn). www.nature.com/scientificreports/ Data are obtained from each sensor for two days between 00:00:00 am on 5 February 2022 and 23:59:00 on 6 February 2022. 5760 data points are initially recorded from each sensor because data collection occurs at 15 s sampling intervals. Thus, 80,640 data points are collected in total, including gas sensors (46,080), temperature sensors (11,520), and wind sensors (23,040). The time series of the dataset outputs of all sensors (gas, temperature, and wind) on 5 February can be seen in Online Appendices 2-4. The time series of the dataset outputs of all sensors (gas, temperature, and wind) on 6 February can be seen in Online Appendices 5-7.

Methods
A mixed qualitative and quantitative research methodology is adopted, including a case study and correlational research. This research comprises five processes: data acquisition, pre-processing, data analysis, verification, and correlation analysis (see Online Appendix 1). This project adopts a mixed-analysis method for verifying data analysis-FSV.
Data acquisition. Data  Data pre-processing. Data pre-processing is necessary before data analysis since the raw data gathered in most industrial processes usually come with many dataset issues, such as out-of-range values, outliers, missing values, etc 7 . This research performs three data cleaning procedures during pre-processing: eliminating extreme values, outliers, and data standardizing.
Extreme data values (also called extreme values in this paper) are considered the out-of-range values in this research. The extreme values could lead to substantially biased inference and be omitted 8 . Other data quality issues-such as errors in measurement, noise, missing values, etc.-might be impacted by hardware relocation, sensor removal, added detectors, and/or not in-used sensors. Such issues are not discussed in this research. But they will be investigated in further studies.
Outliers come from out-of-order distributions for most datasets. They could substantially influence most parametric tests, which would profoundly impact the statistical analysis and often lead to distortion and possibly inaccurate and erroneous conclusions 9 . Anomaly data were mainly observed as the outliers were presumed to come from a different distribution within most datasets 9 . Anomaly data are considered outliers in this research. The Box-plot technique is used to eliminate extreme values and outliers. The box-plot approach uses the median, the approximate quartiles, and the lowest and highest data points to convey the level, spread, and symmetry of a distribution of data values; this approach could easily be refined to identify outlier data points 10 .  T1  3209Pre-pumping lane return air T  T060101 T5 3209Protective layer transport alley sub-airway T  T060202   T2  3209Pre-pumping Lane Coal Storage T T060102 T6 3209Protected layer transport road working face T T050203   T3  3209Pre-pumping lane split air outlet T T060103 T7 3209Protective layer transport alley return wind T T050204   T4  3209Pre-drawing lane working face T  T060104 T8 3209Protected layer transport alley drilling rig T  T050205   Table 2. Shown are WD1 and WD2 numbered to each temperature sensor and its device code given in the gas monitoring system deployed in the Case Study mine.  Two-round data analyses. Two-round data analyses are conducted by using different datasets. The obtained data's reliability and validity should separately be achieved between gas and gas, gas and temperature, and gas and wind. Several statistical significance levels have been accepted for hypothesis testing, including 0.05, 0.01, and 0.001 in social science studies 14 . P values of 0.05 have been considered acceptable for 'significance' to determine whether to reject the null hypothesis 15 . However, the smaller the significance value, the lower the risk of rejecting the null hypothesis when it is true; this needs to be balanced by the risk of accepting the null hypothesis when it is not true 16 . Recent research believes a p value of 0.01 is often considered highly significant 17 . This research verifies the value of 0.01 is a suitable cut-off for the significance level to lower the risk of rejecting the null hypothesis in developing a gas warning system.
Cronbach's Alpha confirms the data reliability. If the values of Cronbach's Alpha were above 0.6, it would be considered fair or above reliability. Exploratory factor analyses confirm the validity analysis. If Kaiser-Meyer-Olkin (KMO) value was greater than 0.6, it would be supposed to be acceptable or above measures. Bartlett's test of Sphericity should be 0.000 (p < 0.001). All average communality values should be greater than 0.6. All of the Anti-image correlations are required to be more than 0.5.
Correlational research is then conducted to indicate that two variables are influenced by a common underlying mechanism 18 . The Pearson correlation analysis method is used for this research. The correlation coefficient is used to evaluate and measure the correlation between pairs of input and output variables. The correlation coefficient's magnitude indicates that the strength of the relationship depends on how close the coefficient is to − 1 or 1, which is the correlation coefficient range 19 . The following mathematical formulas are used for calculating the Pearson correlation coefficient (see Eq. 2) 20 and computed by SPSS Statistics version 26. r will be estimated from ( x i , y i ), the mean value of standard scores of sample points, and the expression equivalent to the above formula is obtained.
Where r is the correlation coefficient. x i is the value of the x-variable in a sample. x is the mean of values of the x-variable. y i is the value of the y-variable in a sample. y is the mean of the values of the y-variable.
But recent research indicates no standard formal classification of the correlation coefficient scales 5 , which suggests using six scales to classify the degree and magnitude of correlation as great (between ± 0.9 and ± 1), very good (between ± 0.75 and ± 0.89), good (between ± 0.5 and ± 0.74), fair (between ± 0.3 and ± 0.49), poor (between ± 0.0 and < ± 0.29), and no correlation (zero). A correlation value of ± 0.3 or above indicates a correlation between two variables. Verification analysis. Verification analysis aims to investigate whether first-round data analysis outcomes might be accepted using second-round datasets simultaneously and whether second-round data analysis results might be accepted using first-round datasets. Repeated reliability and validity analysis would be conducted for the outcomes of the verification analysis between gas and gas, gas and temperature, and gas and wind.
Based on the above verification outcomes, a correlation analysis is then conducted to test and evaluate whether the degree of a strong relationship exists between two variables separately: gas and gas, gas and temperature, and gas and wind. A correlation value of ± 0.3 or above is also used to measure a correlation between two variables.

Results
The first-round analysis uses obtained data between 00:00:00 am and 23:59:00 on 5 February 2022 in the Case Study mine. The second-round analysis uses collected data between 00:00:00 am and 23:59:00 on 6 February 2022. Before conducting data analysis, three data cleaning procedures are performed during data pre-processing for the first-round analysis and second-round analysis: eliminating extreme values, outliers, and data standardizing. Measurement errors and distortion of hardware devices in the gas monitoring system cause extreme values and outliers. The data obtained from sensors T4 and T5 are eliminated due to too many zero values due to such two sensors not being used for the working-face in the Case Study mine. But they have not been removed from the gas monitoring system. Hence, both T4 and T5 are not included in this research. But they will be investigated in further studies. Data standardization solves the issues of collecting data from the different sensors with various measurements.
Thus, data obtained from six gas sensors (T1, T2, T3, T6, T7, and T8) and two temperature sensors (WD1 and WD2) are used for the following data analyses. This section presents data analyses to support the technical quality of the datasets, including analysis between gas and gas, gas and temperature, and gas and wind. www.nature.com/scientificreports/ Analysis between gas and gas. Two rounds of analysis between gas and gas data are separately conducted using obtained data on 5 and 6 February 2022.
First-round analysis between gas and gas. Data from 5 February 2022 are used for the first-round analysis between gas and gas. The reliability and validity are conducted between six items (T1, T2, T3, T6, T7, and T8) (see steps 3.1 and 3.2 in OnlineAppendix 1). All values of Cronbach's Alpha are considered to have very good reliability (above 0.6) (see Table 4).
Second-round analysis between gas and gas. Data collected on 6 February 2022 are used for the second-round analysis between gas and gas. The reliability and validity tests are conducted between the above six items (see steps 3.1 and 3.2 in Online Appendix 1). All values of Cronbach's Alpha are considered to have very good reliability (above 0.7) (see Table 5).
Verification analysis between gas and gas. The verification analysis is then conducted to compare the results of the first and second-round analyses to confirm data reliability and validity. Due to the verification analysis using the outcomes of the two-round studies rather than those obtained from the sensors, there is no need to procedure the eliminating extreme values, outliers, and data standardization. Based on Tables 4 and 5, Fig. 3 compares outcomes between the first-and second-round analyses that indicate four correlational groups, including T2 and T6, T6 and T8, T7 and T8, and T8 and T7.
Repeated reliability and validity are conducted between four correlational groups (see steps 4.1 and 4.2 in Online Appendix 1). All correlational groups satisfactorily meet the reliability and exploratory factor analysis standards. A repeated correlation analysis is followed to test whether correlations exist between items (see Table 6).
Thus, the FSV analysis verifies significant correlations exists (T2 and T6, T6 and T8, T7 and T8, and T8 and T7) (see step 5 in Online Appendix 1). The significant correlations between such items are then demonstrated in Fig. 4.
Analysis between gas and temperature. Two rounds of analysis between gas and temperature data are separately conducted using obtained data on 5 and 6 February 2022. Table 4. Shown are the reliability and exploratory factor analyses of the first-round analysis conducted between gas and gas. All Kaiser-Meyer-Olkin (KMO) values are considered greater (greater than 0.5) in the exploratory factor analysis test. Bartlett's test of Sphericity is 0.000 (p < 0.001). All average communality measures are adequate (greater than 0.6). All anti-image Correlation values are more significant than 0.5. Six correlational groups satisfactorily meet the reliability and exploratory factor analyses.  Table 5. Shown are the reliability and exploratory factor analyses of the second-round analysis conducted between gas and gas. All KMO values are considered to have a greater measure (greater than 0.8). Bartlett's test of Sphericity is 0.000 (p < 0.001). All average communality measures are adequate (greater than 0.7). All antiimage correlation values are more significant than 0.5. Six correlational groups satisfactorily meet the reliability and exploratory factor analyses. www.nature.com/scientificreports/ First-round analysis gas and temperature. The first-round analysis is conducted between gas and temperature data collected on 5 February. The results show that six gas items and two temperature items met the standards of the reliability and exploratory factor analyses, including six correlational groups (T1 and WD1, T2 and WD1, T3 and WD1, T6 and WD2, T7 and WD1, and T8 and WD2) (see Table 7). All Cronbach's Alpha values have very good reliability (above 0.7). Detailed data analyses of six correlational groups are depicted in Tables 8, 9, 10, 11, 12 and 13.
Second-round analysis gas and temperature. The second-round analysis of gas and temperature is based on data collected on 6 February. The results show that six gas items and two temperature items meet the standards of the reliability and exploratory factor analyses, including six correlational groups (T1 and WD2, T2 and WD2, T3 The horizontal x-axis presents the causing sensors (gas). Light cyan colors the correlational box to indicate existing correlations of T3 and T1 in the first-round analysis and T6 and T2 in the second-round analysis. Deep cyan colors the correlational box to show correlations of T2 and T6, T6 and T8, T7 and T8, and T8 and T7 in both round analyses. Table 6. Shown are the outcomes of the correlation analysis conducted between gas and gas. Two good correlations exist between T2 and T6 (0.617) and T6 and T8 (0.653). Two very good correlations exist between T7 and T6 (0.815) and T8 and T7 (0.815). This research uses "**" to report p values less than 0.001 as p < 0.001. **p<0.01.  www.nature.com/scientificreports/ Table 7. Shown are the reliability and exploratory factor analyses of the first-round analysis conducted between gas and temperature. All KMO values are considered a good measure (greater than 0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). All average communality values are good (greater than 0.7), and Anti-image Correlations are more significant than 0.5.  Table 9. Shown are the reliability and exploratory factor analyses conducted between T2 (affected sensor) and WD1 (causing sensor). The value of Cronbach's Alpha is 0.936 to have great reliability (above 0.6). The KMO value shows having a good measure (0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.94 (greater than 0.5). The value of the Anti-image correlation is also significant (0.5). a Measures of Sampling Adequacy (MSA). www.nature.com/scientificreports/ and WD1, T6 and WD2, T7 and WD2, and T8 and WD2) (see Table 14). Detailed data analysis of six groups is shown in Tables 15, 16, 17, 18, 19 and 20.

Factor
Verification analysis gas and temperature. Verification analysis is then conducted to compare the results of the first and second-round analyses to confirm data reliability and validity. Based on Tables 7 and 14, Fig. 5 compares the outcomes of two-round analyses between gas and temperature. Repeated reliability and validity analyses are conducted to confirm that the above three correlational groups (T3 and WD1, T6 and WD2, and T8 and WD2) satisfactorily meet the data analysis standards. A repeated correlation analysis is followed to test whether significant correlations exist between the above groups (T3 and WD1, T6 and WD2, and T8 and WD2) (Table 21).
Analysis between gas and wind. Two rounds of analysis between gas and wind data are separately conducted using obtained data on 5 and 6 February 2022. Table 11. Shown are the reliability and exploratory factor analyses conducted between T6 (affected sensor) and WD2 (causing sensor). The value of Cronbach's Alpha is 0.868 to have very good reliability (above 0.6). The KMO value shows having a good measure (0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.884 (greater than 0.5). The value of the Anti-image correlation is also significant (0.5). a Measures of Sampling Adequacy (MSA).  www.nature.com/scientificreports/ First-round analysis between gas and wind. The first-round analysis of gas and wind is based on data collected on 5 February. The results show that six gas items and two wind items meet the standards of the reliability and exploratory factor analyses, including six correlational groups (T1, FS1 and FS2, T2, FS1 and FS2, T3, FS1 and FS2, T6, FS1 and FS2, T7, FS1 and FS2, and T8, FS1, and FS2) (see Table 22). Detailed data analysis of six groups is shown in Tables 23, 24, 25, 26, 27 and 28.
Second-round analysis between gas and wind. The second-round gas and wind data analysis is based on data collected on 6 February. The results show that six gas items and three wind items meet the standards of the reliability and exploratory factor analyses, including six correlational groups (T1 and FS3, T2 and FS1, T3 and FS2, T6 and FS1, T7 and FS1, and T8 and FS1) (see Table 29). All Cronbach's Alpha values have very good reliability (above 0.6). All KMO values demonstrate a greater measure (greater than 0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). All average communality measures are adequate (greater than 0.7). Anti-image Correlations values are significant (more than 0.5). Detailed data analysis of six groups is shown in Tables 30, 31, 32, 33, 34 and 35.  www.nature.com/scientificreports/ Verification analysis between gas and wind. Verification analysis is then conducted to compare the results of the first and second-round analyses to confirm data reliability and validity. Based on Tables 22 and 29, Fig. 7 compares the outcomes of two-round analyses between gas and wind. Repeated reliability and validity are conducted between five correlational groups. Two groups (T2 and FS1, T7 and FS1) do not meet the data analysis standards. Three correlational groups satisfactorily meet the reliability and exploratory factor analysis standards. They are T3 and FS2, T6 and FS1, and T8 and FS1. A repeated correlation analysis tests whether correlations exist between such items (see Table 36). Table 17. Shown are the reliability and exploratory factor analyses of the second-round analysis conducted between T3 (affected sensor) and WD2 (causing sensor). The value of Cronbach's Alpha is 0.638 to have good reliability (above 0.6). The KMO value shows having a good measure (0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.734 (greater than 0.5). The value of the Anti-image correlation is also significant (0.5). a Measures of Sampling Adequacy (MSA).

Discussion
Based on Figs. 4, 6, and 8, a triple-correlation analysis model is established for developing a gas warning system in the Case Study mine (see Fig. 9). It incorporates ten verified correlations, including gas and gas (4), gas and temperature (3), and gas and wind (3). The result proves the correlational analysis existed between gas and gas, gas and temperature, and gas and wind. For enhancing to validate the research outcomes, four additional experiments are also conducted to test whether such correlations existed in different working-faces (no.1217 and no.3209) and other seasons (Summer and Winter) in the Case Study mine (see Table 37 and Dataset 3). All results indicate strong existing correlations between gas and gas, gas and temperature, and gas and wind. Table 20. Shown are the reliability and exploratory factor analyses of the second-round analysis conducted between T8 (affected sensor) and WD2 (causing sensor). The value of Cronbach's Alpha is 0.739 to have good reliability (above 0.6). The KMO value shows having a good measure (0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.793 (greater than 0.5). The value of the Anti-image correlation is also significant (0.5). a Measures of Sampling Adequacy (MSA).  Figure 5. Shown are the outcomes of two-round analyses between gas and temperature. The vertical y-axis gives a set of affecting sensors (gas). The horizontal x-axis presents the causing sensors (temperature). Light blue colors the correlational box to indicate correlations existed of T1 and WD1, T2 and WD1, and T7 and WD1 in the first round, and T1 and WD2, T2 and WD2, and T7 and WD2 in the second round. In both two-round analyses, deep blue colors the correlational box to indicate the correlations between T2 and WD1, T6 and WD2, and T8 and WD2. www.nature.com/scientificreports/ Thus, this research uses an explored FSV analysis approach to strongly verify the robustness of the Triple-Correlation Analysis Theoretical Framework for developing a gas warning system to improve the warning systems' sensitivity and reduce the incidence of gas explosions. To help researchers and practicians understand better the system's architectural design, a unified modeling language (UML) is developed to demonstrate how this framework is integrated into a gas system 5 , which comprises three layers (data access layer, domain layer, and view layer) and three decision-making rules (see Fig. 10).
Three decision-making rules consist of: • If the data outputs exceed the TLV, the alarming system would immediately alert the safety-response management team. • The warning system will inform the safety-responsive team if the real-time correlation analysis value (CAV) exceeds the correlation analysis limit value (CALV) between gas and gas, gas and temperature, or gas and   www.nature.com/scientificreports/ wind. This status does not state any risks, but the safety-response management team must immediately check the monitoring system to identify potential hazards. • The original data will be forwarded to the monitoring system if the CAV does not exceed the CALV.
As a result, the Triple-Correlation Analysis model (see Fig. 9) is integrated into the gas monitoring system in the Case Study mine with incorporated analysis of gas and gas, gas and temperature, and gas and wind, which is successfully adopted for developing an Innovative Integrated Gas Warning System in Dec 2021. The system's screenshot is provided in Fig. 11. Table 24. Shown are the reliability and exploratory factor analyses of the first-round analysis conducted between T2 (affected sensor) and two causing sensors (FS1 and FS2). The value of Cronbach's Alpha is 0.676 to have good reliability (above 0.6). The KMO value shows having a good measure (0.642). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.573 (greater than 0.5). All Anti-image correlation values are also significant (great than 0.5). a Measures of Sampling Adequacy (MSA).  Table 25. Shown are the reliability and exploratory factor analyses of the first-round analysis conducted between T3 (affected sensor) and two causing sensors (FS1 and FS2). The value of Cronbach's Alpha is 0.669 to have good reliability (above 0.6). The KMO value shows having a good measure (0.639). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.603 (greater than 0.5). All Anti-image correlation values are also significant (great than 0.5). a Measures of Sampling Adequacy (MSA).  Table 26. Shown are the reliability and exploratory factor analyses of the first-round analysis conducted between T6 (affected sensor) and two causing sensors (FS1 and FS2). The value of Cronbach's Alpha is 0.669 to have good reliability (above 0.6). The KMO value shows having a good measure (0.639). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.603 (greater than 0.5). All Anti-image correlation values are also significant (great than 0.5). a Measures of Sampling Adequacy (MSA).

Conclusion
This research aims to explore a proposed FSV analysis approach to verify the robustness of the Trip-Correlation Analysis Theoretical Framework for developing a gas warning system to improve the warning systems' sensitivity and reduce the incidence of gas explosions. A mixed qualitative and quantitative research methodology is adopted, including a case study and correlational research.
The first-round analysis uses data obtained on 5 February 2022 in the Case Study mine. The second-round analysis uses data collected on 6 February 2022. Verification analysis is then followed to compare the results of the first and second-round analyses to confirm data reliability and validity. Four additional experiments are also conducted to test whether such correlations existed in different working faces (no.1217 and no.3209) and other seasons (Summer and Winter). All tests indicate three significant correlations between gas, temperature, and wind that verify the robustness of the Triple-Correlation Analysis Theoretical Framework (see Fig. 1).
To help researchers and practicians better understand the system's architectural design, a UML is developed to demonstrate how this framework is integrated into a gas system (see Fig. 10). Pseudocode is also provided Table 27. Shown are the reliability and exploratory factor analyses of the first-round analysis conducted between T7 (affected sensor) and two causing sensors (FS1 and FS2). The value of Cronbach's Alpha is 0.640 to have good reliability (above 0.6). The KMO value shows having a good measure (0.641). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.582 (greater than 0.5). All Anti-image correlation values are also significant (great than 0.5). a Measures of Sampling Adequacy (MSA).  www.nature.com/scientificreports/ to describe the system's implementation, including the system's data analysis and processing logic, which may help researchers in other domains implement the methodology presented in this work (see Online Appendix 7). The outcomes imply that this framework is potentially valuable for developing other warning systems. The proposed FSV approach can also be adopted for exploring data patterns insightfully to offer new perspectives to develop warning systems for different industry applications. Another finding is that T4 and T5 sensors are not in use due to not being removed from the gas monitoring system. The implication is that they may add to the Trip-Correlation Analysis Theoretical Framework in further research to develop a more sensitive warning system. Using such findings to explore an extended Trip-Correlation Analysis Theoretical Framework in further research is more valuable.
The limitation is that gas, temperature, and wind sensors are regularly changed monthly due to the ongoing mining processing in the Case Study mine. The changes might include hardware relocation, sensor removal, and added detectors. The correlation analysis of data collected from gas, temperature and wind must be re-conducted Table 30. Shown are the reliability and exploratory factor analyses of the second-round analysis conducted between T1 (affected sensor) and FS3 (causing sensor). The value of Cronbach's Alpha is 0.626 to have good reliability (above 0.6). The KMO value shows having a good measure (0.5). Bartlett's test of Sphericity is 0.000 (p < 0.001). The average communality value is 0.835 (greater than 0.5). The value of Anti-image correlation value is also significant (0.5). a Measures of Sampling Adequacy (MSA).  www.nature.com/scientificreports/ for any sensor changes following the procedure of the FSV analysis approach. The second limitation is that this research focuses on verifying the robustness of the Trip-Correlation Analysis Theoretical Framework, which incorporates the analysis of gas and gas, gas and temperature, and gas and wind. The ambient conditions remain the same on 5 Feb and 6 Feb 2022. Further research is needed to explore whether other ambient conditions impact the performance and effectiveness of gas warning systems, such as humidity, wind, sunny, cloudy, and even human disturbance. Another limitation is that this research does not consider other data quality issues such as errors in measurement, noise, missing values, etc. They should be solved by updated hardware devices and system algorithms. For example, many studies have provided methods for solving measurement errors 21 . More effective sensors with efficient system algorithms applied to the Trip-Correlation Analysis Theoretical Framework might be used for developing an innovative gas warning system to improve the warning systems' sensitivity and reduce the incidence of gas explosions. It is valuable to investigate them further.  www.nature.com/scientificreports/ Figure 7. Shown are the outcomes of two-round analyses between gas and wind. The vertical y-axis gives a set of affecting sensors (gas). The horizontal x-axis presents the causing sensors (wind). Light navy colors the correlational box to indicate correlations between T1 and FS1, T1 and FS2, T3 and FS1, T6 and FS2, T7 and FS2, and T8 and FS2) in the first round and T1 and FS3 in the second round. Deep navy colors the correlational box to indicate correlations betweenT2 and FS1, T3 and FS2, T6 and FS1, T7 and FS1, and T8 and TS1 in two-round analyses. Table 36. Shown are the outcomes of the correlation analysis conducted between gas and wind. The results indicate three fair correlations-T3 and FS2 (0.467), T6 and FS1 (0.468), and T8 and FS1 (0.428). This research uses "**" to report p values less than 0.001 as p < 0.001. **p < 0.01. Thus, the FSV analysis verifies significant correlations (T3 and FS2, T6 and FS1, and T8 and FS1) (see Fig. 8). www.nature.com/scientificreports/ Figure 9. Shown is the Triple-Correlation Analysis model, including ten verified correlations. Four significant correlations exist between gas and gas, including two good correlations between T2 and T6 (0.617) and T6 and T8 (0.653), and two very good correlations between T7 and T6 (0.815) and T8 and T7 (0.815) (see Table 6). Three significant correlations exist between gas and temperature, including two very good correlations between T3 and WD1 (0.795) and T6 and WD2 (0.768), and one good correlation between T8 and WD2 (0.669) (see Table 21). Three fair correlations exist between gas and wind, including T3 and FS2 (0.467), T6 and FS1 (0.468), and T8 and FS1 (0.428) (see Table 36).    Figure 11. Shown is the system screenshot of the Innovative Integrated Gas Warning System deployed in the Case Study mine. The system integrates the Triple-Correlation Analysis model into the gas monitoring system with incorporated analysis of gas and gas, gas and temperature, and gas and wind. Cyan lines indicate existing correlations between gas and gas. Blue lines indicate existing correlations between gas and temperature. Navy lines indicate existing correlations between gas and wind.