A Probability Integral Parameter Inversion Method Integrating a Selection-Weighted Iterative Robust Genetic Algorithm
Abstract
1. Introduction
2. Methods
2.1. The PIM Prediction Model
2.2. Construction and Solution of Conditional Equations
2.3. Prediction Parameters of PIM Solution Based on Robust Genetic Algorithm
3. Simulated Experiment
3.1. A Brief Introduction to the Mining Working Face
3.2. Overview of Data for Simulated Experimental Geological Mining Conditions
3.3. Simulation Application Experiment and Results
4. 1312(1) Working Face Experiment
4.1. A Brief Introduction to the 1312(1) Working Face
4.2. Engineering Application Experiments and Results
5. Discussion
5.1. The Impact of Changes in k Value on the Proposed Method
5.2. The Influence of Different Layout Forms of Survey Lines on Parameter Inversion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
Symbol | Meaning |
Wmax | maximum subsidence value |
subsidence value of the strike section of the coal mining working face | |
subsidence value of the trend profile of the coal mining working face | |
ds, dt | length and width of unit mining |
M | thickness of the mining face in a coal mine |
q | subsidence coefficient |
α | inclination angle of the coal seam |
(x,y) | coordinates at any point on the surface |
H | average mining depth of the working surface |
Tanβ | main influence tangent |
θ | greatest subsidence angle |
D1 | length of inclination of working face |
D3 | length of strike of working face |
S1, S2, S3, and S4 | upper, lower, left, and right inflection point offsets of the working face, respectively |
B = [q,tan β,θ,S1,S2,S3,S4] | estimated parameter for subsidence using probability integration method |
G = [m,H,x,y,α,D3,D1] | geological and mining condition parameter of the working face |
difference between the true value and the fitted value | |
measured subsidence value | |
predicted subsidence value | |
Vmin | minimum residual sum of squares after adding weights |
Pi | weight of the i-th observation value |
j | total number of observed values |
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Parameter | Design Value | Plan 1 | Plan 2 | Plan 3 | ||||
---|---|---|---|---|---|---|---|---|
GA Method | Proposed Method | GA Method | Proposed Method | GA Method | Proposed Method | |||
q | IV | 0.64 | 0.6395 | 0.6405 | 0.6417 | 0.6400 | 0.6600 | 0.6403 |
RE | 0.08% | 0.09% | 0.26% | 0.00% | 3.12% | 0.04% | ||
tan β | IV | 1.5 | 1.5322 | 1.4804 | 1.5339 | 1.5000 | 1.4171 | 1.5013 |
RE | 2.15% | 1.31% | 2.26% | 0.00% | 5.52% | 0.09% | ||
θ/° | IV | 86.5 | 1.5322 | 85.5932 | 85.2471 | 85.9763 | 85.5607 | 85.6825 |
RE | 2.15% | 1.05% | 1.45% | 0.61% | 1.09% | 0.95% | ||
S1/m | IV | 45 | 49.9317 | 45.2301 | 39.7648 | 44.8008 | 47.2286 | 45.1187 |
RE | 10.96% | 0.51% | 11.63% | 0.44% | 4.95% | 0.26% | ||
S2/m | IV | 45 | 50.1448 | 44.8294 | 34.3203 | 45.1991 | 47.0186 | 45.5513 |
RE | 11.43% | 0.38% | 23.73% | 0.44% | 4.49% | 1.23% | ||
S3/m | IV | 45 | 44.3203 | 44.9171 | 45.7279 | 45.5575 | 46.5879 | 46.2037 |
RE | 1.51% | 0.18% | 1.62% | 1.24% | 3.53% | 2.67% | ||
S4/m | IV | 45 | 44.3203 | 47.0725 | 47.1754 | 45.4753 | 49.7983 | 45.3857 |
RE | 1.51% | 4.61% | 4.83% | 1.06% | 10.66% | 0.86% | ||
RMSE/mm | 22.5 | 2.8 | 33.8 | 1.7 | 28.7 | 1.4 |
Parameter | Reference Value | Engineering Application Plan 1 | Engineering Application Plan 2 | |||
---|---|---|---|---|---|---|
GA Method | Proposed Method | GA Method | Proposed Method | |||
q | IV | 1.2672 | 1.5533 | 1.2404 | 1.3798 | 1.2889 |
RE | 17.94% | 34.47% | 27.10% | 31.91% | ||
tan β | IV | 1.8928 | 1.6547 | 1.8700 | 1.9113 | 1.8721 |
RE | 12.58% | 1.20% | 0.98% | 1.09% | ||
θ/° | IV | 86.5266 | 87.4652 | 85.3094 | 86.8843 | 85.5449 |
RE | 1.08% | 1.41% | 0.41% | 1.13% | ||
S1/m | IV | 14.0062 | 36.5795 | 17.0370 | 43.2282 | 23.7842 |
RE | 161.17% | 21.64% | 208.64% | 69.81% | ||
S2/m | IV | 44.5606 | 52.0727 | 42.7824 | 26.5384 | 34.7214 |
RE | 16.86% | 3.99% | 40.44% | 22.08% | ||
S3/m | IV | −2.9398 | 10.6886 | 15.6669 | −11.2751 | 9.6938 |
RE | 463.58% | 632.92% | 283.53% | 429.74% | ||
S4/m | IV | 6.2964 | 3.3455 | −21.3161 | 21.0065 | −4.0305 |
RE | 46.87% | 438.54% | 233.63% | 164.01% | ||
RMSE/mm | 69.7 | 101.2 | 76.8 | 107.3 | 69.8 |
Parameter | q | tan β | θ/° | S1/m | S2/m | S3/m | S4/m | RMSE/mm | |
---|---|---|---|---|---|---|---|---|---|
k | Design value | 0.6400 | 1.5000 | 86.5000 | 45.0000 | 45.0000 | 45.0000 | 45.0000 | |
k = 10 | IV | 0.6405 | 1.6011 | 85.6798 | 44.0935 | 46.3629 | 45.2836 | 46.2499 | 15.2 |
RE | 0.08% | 6.74% | −0.95% | −2.01% | 3.03% | 0.63% | 2.78% | ||
k = 1 | IV | 0.6400 | 1.5101 | 85.8538 | 44.4956 | 45.7281 | 46.7030 | 44.5848 | 1.6 |
RE | 0.00% | 0.67% | −0.75% | −1.12% | 1.62% | 3.78% | −0.92% | ||
k = 0.1 | IV | 0.6403 | 1.5013 | 85.6825 | 45.1187 | 45.5513 | 46.2037 | 45.3857 | 1.4 |
RE | 0.04% | 0.09% | 0.95% | 0.26% | 1.23% | 2.67% | 0.86% | ||
k = 0.01 | IV | 0.6414 | 1.5363 | 85.1924 | 45.4640 | 43.7179 | 45.9748 | 46.3232 | 7.5 |
RE | 0.22% | 2.42% | −1.51% | 1.03% | −2.85% | 2.17% | 2.94% | ||
k = 0.001 | IV | 0.6407 | 1.5794 | 86.0870 | 44.7540 | 44.0796 | 45.0884 | 44.7858 | 12.9 |
RE | 0.11% | 5.29% | −0.48% | −0.55% | −2.05% | 0.20% | −0.48% |
Parameter | q | tan β | θ/° | S1/m | S2/m | S3/m | S4/m | RMSE/mm | |
---|---|---|---|---|---|---|---|---|---|
k | Design value | 0.6400 | 1.5000 | 86.5000 | 45.0000 | 45.0000 | 45.0000 | 45.0000 | |
k = 10 | IV | 0.6404 | 1.6268 | 86.0113 | 46.1155 | 45.3005 | 43.8490 | 47.2080 | 18.8 |
RE | 0.06% | 8.45% | −0.56% | 2.48% | 0.67% | −2.56% | 4.91% | ||
k = 1 | IV | 0.6444 | 1.5001 | 85.3051 | 44.8297 | 44.3856 | 43.7977 | 47.5408 | 9.2 |
RE | 0.69% | 0.01% | −1.38% | −0.38% | −1.37% | −2.67% | 5.65% | ||
k = 0.1 | IV | 0.6405 | 1.4804 | 85.5932 | 45.2301 | 44.8294 | 44.9171 | 47.0725 | 2.8 |
RE | 0.09% | 1.31% | 1.05% | 0.51% | 0.38% | 0.18% | 4.61% | ||
k = 0.01 | IV | 0.6390 | 1.5257 | 85.2503 | 43.8192 | 45.1534 | 46.4601 | 46.0842 | 3.9 |
RE | −0.15% | 1.71% | −1.44% | −2.62% | 0.34% | 3.24% | 2.41% | ||
k = 0.001 | IV | 0.6368 | 1.5205 | 85.6139 | 43.0816 | 46.2739 | 47.1941 | 44.4129 | 4.8 |
RE | −0.50% | 1.37% | −1.02% | −4.26% | 2.83% | 4.88% | −1.30% |
Parameter | q | tan β | θ/° | S1/m | S2/m | S3/m | S4/m | RMSE/mm | |
---|---|---|---|---|---|---|---|---|---|
k | Design value | 0.6400 | 1.5000 | 86.5000 | 45.0000 | 45.0000 | 45.0000 | 45.0000 | |
k = 10 | IV | 0.6505 | 1.5557 | 85.7074 | 42.4913 | 45.6933 | 44.8361 | 44.8234 | 25.8 |
RE | 1.64% | 3.72% | −0.92% | −5.57% | 1.54% | −0.36% | −0.39% | ||
k = 1 | IV | 0.6427 | 1.5000 | 85.4679 | 43.9696 | 46.1892 | 46.7253 | 45.0778 | 5.0 |
RE | 0.42% | 0.00% | −1.19% | −2.29% | 2.64% | 3.83% | 0.17% | ||
k = 0.1 | IV | 0.6400 | 1.5000 | 85.9763 | 44.8008 | 45.1991 | 45.5575 | 45.4753 | 1.7 |
RE | 0.00% | 0.00% | 0.61% | 0.44% | 0.44% | 1.24% | 1.06% | ||
k = 0.01 | IV | 0.6407 | 1.5314 | 86.1272 | 44.4732 | 46.4933 | 43.4665 | 46.6973 | 5.8 |
RE | 0.11% | 2.09% | −0.43% | −1.17% | 3.32% | −3.41% | 3.77% | ||
k = 0.001 | IV | 0.6399 | 1.5000 | 85.1070 | 44.6436 | 45.1770 | 45.0159 | 46.3817 | 2.8 |
RE | −0.01% | 0.00% | −1.61% | −0.79% | 0.39% | 0.04% | 3.07% |
Parameter | q | tan β | θ/° | S1/m | S2/m | S3/m | S4/m | RMSE/mm | |
---|---|---|---|---|---|---|---|---|---|
Plan | Design value | 0.6400 | 1.5000 | 86.5000 | 45.0000 | 45.0000 | 45.0000 | 45.0000 | |
Layout Plan 1 | IV | 0.6403 | 1.4982 | 84.7213 | 44.4317 | 46.8088 | 45.4997 | 48.2903 | 1.2 |
RE | 0.05% | 0.12% | 2.06% | 1.26% | 4.02% | 1.11% | 7.31% | ||
Layout Plan 2 | IV | 0.6400 | 1.5008 | 84.4382 | 46.1015 | 43.8334 | 43.5677 | 50.5812 | 0.2 |
RE | 0.00% | 0.05% | 2.38% | 2.45% | 2.59% | 3.18% | 12.40% | ||
Layout Plan 3 | IV | 0.6398 | 1.5048 | 84.9745 | 43.9372 | 46.2053 | 46.0874 | 46.9935 | 0.8 |
RE | 0.03% | 0.32% | 1.76% | 2.36% | 2.68% | 2.42% | 4.43% | ||
Layout Plan 4 | IV | 0.6402 | 1.4991 | 85.2291 | 41.6217 | 48.4276 | 44.1853 | 48.4487 | 0.4 |
RE | 0.03% | 0.06% | 1.47% | 7.51% | 7.62% | 1.81% | 7.66% | ||
Layout Plan 5 | IV | 0.6403 | 1.4996 | 85.3239 | 46.7982 | 43.9935 | 49.2968 | 43.0575 | 1.6 |
RE | 0.05% | 0.03% | 1.36% | 4.00% | 2.24% | 9.55% | 4.32% | ||
Layout Plan 6 | IV | 0.6128 | 1.5080 | 85.9702 | 39.7584 | 45.5032 | 40.3865 | 45.9748 | 45.0 |
RE | 4.25% | 0.53% | 0.61% | 11.65% | 1.12% | 10.25% | 2.17% |
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Jiang, C.; Liu, W.; Wang, L.; Zhu, X.; Tan, H. A Probability Integral Parameter Inversion Method Integrating a Selection-Weighted Iterative Robust Genetic Algorithm. Appl. Sci. 2025, 15, 8102. https://doi.org/10.3390/app15148102
Jiang C, Liu W, Wang L, Zhu X, Tan H. A Probability Integral Parameter Inversion Method Integrating a Selection-Weighted Iterative Robust Genetic Algorithm. Applied Sciences. 2025; 15(14):8102. https://doi.org/10.3390/app15148102
Chicago/Turabian StyleJiang, Chuang, Wei Liu, Lei Wang, Xu Zhu, and Hao Tan. 2025. "A Probability Integral Parameter Inversion Method Integrating a Selection-Weighted Iterative Robust Genetic Algorithm" Applied Sciences 15, no. 14: 8102. https://doi.org/10.3390/app15148102
APA StyleJiang, C., Liu, W., Wang, L., Zhu, X., & Tan, H. (2025). A Probability Integral Parameter Inversion Method Integrating a Selection-Weighted Iterative Robust Genetic Algorithm. Applied Sciences, 15(14), 8102. https://doi.org/10.3390/app15148102