A Novel Method for Source Tracking of Chemical Gas Leakage: Outlier Mutation Optimization Algorithm
Abstract
:1. Introduction
- Traditional gas leakage accident application examples usually take the position and number of the storage tank or environmental variables as known conditions. In order to illustrate that the OMO algorithm has the best comprehensive performance in the gas leakage traceability problem under flat terrain conditions, randomness is introduced to the various variables that will affect the calculation results of the Gaussian plume model, which can make the application examples created in this article to be strongly representative.
- The introduction of sensor information defect conditions: the number of sensors in the three types of application examples is 16, 9, 4, respectively, and the intensity of the information defect increases in turn, which is a challenge to the exploration integrity of the optimization algorithm, but it is also an important part to prove the advantages of OMO algorithm.
- The OMO algorithm is different from other swarm intelligence algorithms. The exploration phase of the OMO algorithm is dominated by outliers, and the exploration method introduces the Levi flight, which aims to avoid the local optimum with a high degree of exploration. In the exploitation phase of the OMO algorithm, two-way selection improves the convergence speed and accuracy. The complementarity of the encirclement and mutation strategies has become a major feature of the algorithm.
- The research on the parameter law of the OMO algorithm and the introduction of precision control parameters enable the OMO algorithm to adjust parameters reasonably in practical applications and quickly adapt to various application scenarios.
2. Methodology
2.1. Gaussian Plume Model
- The concentration of leaking gas conforms to Gaussian distribution in the y-axis section and the z-axis section;
- The leakage intensity of the leaking gas is continuous and uniform;
- The ambient wind speed remains constant during the gas leak process, and the default direction is along the positive x-axis;
- The model ignores the effects of any chemical reactions, including sedimentation and decomposition;
- The leaked gas follows the ideal gas equation of state and the law of conservation of mass.
2.2. Outlier Mutation Optimization (OMO) Algorithm
- ;
- ;
- , independent of .
3. Experimental Design
3.1. Chemical Gas Leakage Accident Application Example
3.2. Chemical Gas Leakage’s Source Tracking Model
3.3. Other Details and Pseudocode of OMO Algorithm
Algorithm 1. Pseudocode of OMO algorithm. |
Inputs: The population size N, maximum number of iterations T, Speed Control Constant SH, SR Outputs: Data required for drawing plotData, the location of prey preyLocation and its fitness value preyEnergy |
Initialize the random population Xi(i = 1, 2, …, N), plotData, preyLocation, preyEnergy and step parameters α, β for (each iteration t) do for (each predator Xi) do Update the escape energy E and Epara using Equations (3) and (4) if (|E| ≥ 1) then Exploration phase Update the location vector using Equation (8) if (|E| < 1) then Exploitation phase if (r > 0.5) then Besiege strategy Update the location vector using Equations (13), (14), (16), (17) if (r ≤ 0.5) then Mutant strategy Update the location vector using Equations (13)–(17) Checkup population boundary and correct individual Calculate the fitness values of predator population Set preyLocation and preyEnergy as the location of prey and its fitness based on the minimum value between last prey and current population Update plotData and record them Return plotData, preyLocation, preyEnergy |
4. Results and Discussion
4.1. Results
4.1.1. Qualitative Results of OMO Algorithm
4.1.2. Relationship between OMO Algorithm and Population Number N
- The time-requirement of the OMO algorithm is approximately proportional to the population number N;
- The accuracy of the OMO algorithm gradually increases as the population number N increases;
- When the population number 3 < N < 5, the accuracy of the OMO algorithm is relatively low; when the population number 3 < N < 25, the accuracy of the OMO algorithm is significantly improved with the increase of N; when the population number N > 25, the increased speed of OMO algorithm’s accuracy with the increase of N gradually decreases and stabilizes.
4.1.3. Relationship between OMO Algorithm and Iterations
- The time-requirement of the OMO algorithm is approximately proportional to the iterations;
- The accuracy of the OMO algorithm gradually increases as the iterations increase;
- When the iterations <100, the accuracy of the OMO algorithm is significantly improved with the increase of iterations; when the 100 < iterations < 500, the accuracy of the OMO algorithm is slightly improved with the increase of iterations; when the iterations >500, the increased speed of the OMO algorithm’s accuracy with the increase of iterations gradually decreases and stabilizes.
4.1.4. Relationship between OMO Algorithm and Speed Control Constant
- Changing the values of SH and SR will have a certain impact on the accuracy of the OMO algorithm, but random values of SH and SR will have a high probability to get a more satisfactory result.
- High-precision OMO algorithm results are often accompanied by suitable exploration steps (influenced by SH), and low-precision OMO algorithm results are often accompanied by too-large exploration steps. The reason why some SH are too large but can also achieve accuracy of the algorithm is mainly due to the random allocation of super boundary data, but in the chemical gas leakage accident model established by this paper, the best value of SH is 1–60.
- High-precision OMO algorithm results are often accompanied by suitable exploitation steps (influenced by SR), and low-precision OMO algorithm results are often accompanied by too large exploitation steps. Logarithmic processing has been performed in the step length parameter of the standard Brownian motion to ensure that the exploitation space is small enough in the final stage and the space has been explored completely; therefore, a small-range change of SR will have little effect on the accuracy of the OMO algorithm. In the chemical gas leakage accident model established by this paper, the best value of SR is 1–100.
4.1.5. Robustness Analysis under the Influence of White Gaussian Noise (WGN)
4.1.6. Comparative Analysis among Optimization Algorithms
4.2. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Ammonia | Chlorine | Phosgene | |
---|---|---|---|
AEGL-1 | 30 | 0.5 | NR |
AEGL-2 | 160 | 2.0 | 0.3 |
AEGL-3 | 1100 | 20 | 0.75 |
Algorithm Classification | Strengths | Weaknesses | Instances |
---|---|---|---|
Swarm Intelligence (SI) algorithms based on gas dispersion models | High degree of freedom in the exploration phase, fast calculation speed, and accurate result in the exploitation phase | Insufficient random exploration may make the result fall into local optimal solution | Particle Swarm Optimization (PSO) Algorithm [30,31] Ant Colony Optimization (ACO) Algorithm [30] Firefly Algorithm [30] Harris Hawks Optimization (HHO) Algorithm [32] |
Evolutionary algorithms based on gas dispersion models | No need to distinguish the exploration and exploitation phases; controllable search ability (coefficient of variation) | High evolutionary generations will reduce population diversity | Genetic Algorithm (GA) [17,33] Differential Evolution (DE) Algorithm [34] |
Direct optimization algorithms based on gas dispersion models | Low algorithm complexity and fast calculation speed | Easy to fall into local optimal solution | Pattern Search (PS) Algorithm [35,36] Simulated Annealing (SA) Algorithm [37,38,39] Least Squares Algorithm [15,16] |
Methods based on big data or probabilistic analysis | No need to build a scene model, not restricted by geographical conditions | Need for much prior knowledge and observation data, slow calculation speed | Deep Neural Networks [18] Big Data with Probability Function [19] Sequential Monte Carlo Methods [40] K-Nearest Neighbor Classifier [41] |
Other methods | Advanced technology, high accuracy | High technical and economic requirements | Drone-Enabled Participation [6] Random Walk Robot Participation [42,43] Hybrid Optimization Algorithm [44,45,46,47] |
Cloud Condition | Solar Radiation Angle α | ||
---|---|---|---|
α > 60° | 35°< α ≤ 60° | 15° < α ≤ 35° | |
Cloud cover 4/8, or thin clouds at high altitude | Strong | Medium | Weak |
Cloud cover 5/8–7/8, cloud height 2134–4877 m | Medium | Weak | Weak |
Cloud cover 5/8–7/8, cloud height lower than 2134 m | Weak | Weak | Weak |
Wind Speed | Under Sunshine | Without Sunshine | |||
---|---|---|---|---|---|
Strong | Medium | Weak | Cloud Cover ≥4/8 | Cloud Cover ≤3/8 | |
0–2 | A | A–B | B | F | F |
2–3 | A–B | B | C | E | F |
3–4 | B | B–C | C | D | E |
4–6 | C | C–D | D | D | D |
>6 | D | D | D | D | D |
Stability Level | ||
---|---|---|
A–B | ||
C | ||
D | ||
E–F |
Function Name | Function Equation | Range | Optimal Solution and Value |
---|---|---|---|
Sphere | |||
Rosenbrock | |||
Rastrigin | |||
Griewank | |||
Schaffer | |||
Ackley |
Optimization Algorithm | Parameter | Value |
---|---|---|
DE/GA | Scaling factor F | 0.5 |
Crossover probability Cr | 0.5 | |
HHO | σν | 1 |
β | 1.5 | |
PS | Initial point | (0, 0, 0) |
SA | Initial point | (0, 0, 0) |
PSO | Inertia factor | 0.3 |
1 | ||
1 | ||
Grey Wolf Optimization (GWO) [63] | Convergence constant a | [2, 0] |
Slap Swarm Algorithm (SSA) [64] | Convergence constant a | [2, 0] |
Whale Optimization Algorithm (WOA) [65] | Convergence constant c1 | [2, 0] |
Target Parameter | Expected Value | Calculated Value | Relative Error (%) |
---|---|---|---|
Time (s) | − | 12.743 | − |
(m) | 8 | 8.158 | 1.971 |
(m) | 15 | 15.020 | 0.131 |
Q (kg/s) | 80 | 79.045 | 1.193 |
Optimal value | 0 | 2.464e-15 | − |
Target Parameter | Expected Value | Calculated Value | Relative Error (%) |
---|---|---|---|
Time (s) | − | 10.304 | − |
(m) | 8 | 8.287 | 3.593 |
(m) | 15 | 15.444 | 2.960 |
Q (kg/s) | 80 | 76.909 | 3.864 |
Optimal value | 0 | 2.356e-13 | − |
Target Parameter | Expected Value | Calculated Value | Relative Error (%) |
---|---|---|---|
Time (s) | − | 8.644 | − |
(m) | 8 | 10.725 | 34.068 |
(m) | 15 | 14.190 | 5.401 |
Q (kg/s) | 80 | 84.612 | 5.765 |
Optimal value | 0 | 5.694e-23 | − |
Target Parameter | Expected Value | Calculated Value | Relative Error (%) |
---|---|---|---|
Time (s) | − | 6.697 | − |
(m) | 8 | 8.285 | 3.568 |
(m) | 15 | 15.069 | 0.459 |
Q (kg/s) | 80 | 79.896 | 0.131 |
Optimal value | 0 | 2.029e-10 | − |
Population Number N | Optimal Value | Time (s) |
---|---|---|
3 | 8.450e-6 | 1.678 |
5 | 2.130e-7 | 2.490 |
8 | 9.622e-10 | 3.712 |
10 | 3.253e-10 | 4.561 |
15 | 1.187e-11 | 6.591 |
20 | 7.940e-13 | 8.680 |
25 | 7.228e-15 | 10.723 |
30 | 2.464e-15 | 12.743 |
50 | 2.339e-16 | 21.753 |
100 | 4.073e-17 | 42.479 |
Iterations | Optimal Value | Time (s) |
---|---|---|
50 | 1.384e-10 | 2.249 |
100 | 1.457e-13 | 4.405 |
200 | 3.067e-14 | 8.623 |
300 | 2.464e-15 | 12.743 |
400 | 7.305e-16 | 16.975 |
500 | 4.157e-16 | 21.311 |
1000 | 5.238e-16 | 43.213 |
SH | SR | Optimal Value |
---|---|---|
4 | 6 | 1.447e-11 |
23 | 3 | 1.690e-11 |
2 | 43 | 2.405e-11 |
15 | 2 | 2.683e-11 |
1 | 3 | 3.602e-11 |
137 | 1 | 3.679e-11 |
422 | 440 | 4.382e-4 |
709 | 469 | 4.384e-4 |
495 | 844 | 4.396e-4 |
869 | 42 | 6.804e-4 |
865 | 76 | 7.124e-4 |
973 | 329 | 7.846e-4 |
SNR (dB) | Q (kg/s) | Optimal Value | ||
---|---|---|---|---|
0 | 14.916 | 12.956 | 61.406 | 5.565e-2 |
0.3 | 15.173 | 14.886 | 54.400 | 6.340e-2 |
0.6 | 11.520 | 13.130 | 82.052 | 3.102e-2 |
1 | 12.125 | 13.927 | 57.669 | 2.614e-2 |
5 | 11.808 | 14.294 | 78.303 | 1.128e-2 |
10 | 9.047 | 14.618 | 73.611 | 3.658e-3 |
15 | 9.563 | 15.179 | 71.538 | 1.071e-3 |
20 | 7.383 | 14.727 | 77.701 | 3.932e-4 |
30 | 8.405 | 15.271 | 80.032 | 8.574e-5 |
50 | 8.175 | 14.977 | 79.100 | 4.209e-7 |
100 | 7.906 | 14.848 | 81.372 | 3.680e-11 |
Target Parameters | OMO | PS | SA | PSO | GA | DE | HHO | GWO | SSA | WOA |
---|---|---|---|---|---|---|---|---|---|---|
Time (s) | 12.743 | 4.910 | 3.028 | 2.223 | 6.049 | 10.129 | 12.373 | 13.196 | 13.514 | 13.160 |
(m) | 8.158 | 6.207 | 5.565 | 7.410 | 6.379 | 7.435 | 8.528 | 5.276 | 6.849 | 8.779 |
(m) | 15.020 | 14.501 | 10.905 | 14.175 | 13.890 | 15.028 | 14.530 | 14.740 | 15.026 | 13.188 |
(kg/s) | 79.045 | 62.406 | 43.929 | 83.694 | 75.824 | 81.038 | 76.953 | 83.620 | 84.956 | 76.095 |
relative error (%) | 1.971 | 22.418 | 30.433 | 7.379 | 20.262 | 7.064 | 6.606 | 34.044 | 14.391 | 9.741 |
relative error (%) | 0.131 | 3.326 | 27.297 | 5.497 | 7.399 | 0.186 | 3.132 | 1.732 | 0.171 | 12.080 |
relative error (%) | 1.193 | 21.993 | 45.089 | 4.617 | 5.220 | 1.298 | 3.809 | 4.525 | 6.195 | 4.882 |
Optimal value | 2.464e-15 | 2.309e-6 | 9.492e-3 | 5.625e-8 | 3.302e-4 | 3.697e-13 | 8.531e-7 | 2.712e-7 | 6.317e-9 | 2.434e-5 |
Target Parameters | OMO | PS | SA | PSO | GA | DE | HHO | GWO | SSA | WOA |
---|---|---|---|---|---|---|---|---|---|---|
Time (s) | 10.304 | 4.429 | 2.990 | 1.638 | 3.867 | 8.406 | 10.263 | 11.170 | 11.364 | 11.083 |
(m) | 8.287 | 4.111 | 10.667 | 9.549 | 5.668 | 8.854 | 9.644 | 1.855 | 7.312 | 4.460 |
(m) | 15.444 | 12.990 | 12.908 | 13.352 | 13.661 | 15.001 | 15.533 | 10.150 | 13.190 | 12.100 |
(kg/s) | 76.909 | 95.762 | 52.081 | 90.098 | 79.938 | 85.554 | 73.722 | 92.250 | 83.853 | 83.342 |
relative error (%) | 3.593 | 48.618 | 33.335 | 19.363 | 29.151 | 10.675 | 20.544 | 76.814 | 8.598 | 44.252 |
relative error (%) | 2.960 | 13.400 | 13.947 | 10.986 | 8.926 | 0.010 | 3.555 | 32.332 | 12.065 | 19.336 |
relative error (%) | 3.864 | 19.703 | 34.899 | 12.622 | 0.077 | 6.943 | 7.847 | 15.313 | 4.816 | 4.178 |
Optimal value | 2.356e-13 | 9.689e-7 | 6.450e-4 | 5.182e-8 | 6.226e-6 | 1.459e-11 | 2.012e-7 | 4.987e-7 | 1.960e-8 | 3.161e-4 |
Target Parameters | OMO | PS | SA | PSO | GA | DE | HHO | GWO | SSA | WOA |
---|---|---|---|---|---|---|---|---|---|---|
Time (s) | 8.644 | 3.206 | 2.954 | 1.341 | 3.046 | 7.219 | 8.833 | 9.301 | 9.536 | 9.390 |
(m) | 10.725 | 2.677 | 12.369 | 2.101 | 6.126 | 4.446 | 10.669 | 3.628 | 12.061 | 4.878 |
(m) | 14.190 | 7.641 | 15.168 | 9.720 | 10.597 | 9.392 | 15.471 | 9.127 | 8.076 | 11.870 |
(kg/s) | 84.612 | 127.404 | 43.551 | 106.466 | 100.159 | 101.978 | 58.645 | 80.567 | 104.305 | 72.035 |
relative error (%) | 34.068 | 66.536 | 54.607 | 73.732 | 23.427 | 44.428 | 33.368 | 54.653 | 50.768 | 39.026 |
relative error (%) | 5.401 | 49.060 | 1.121 | 35.200 | 29.354 | 37.386 | 3.137 | 39.151 | 46.160 | 20.864 |
relative error (%) | 5.765 | 59.255 | 45.562 | 33.082 | 25.199 | 27.472 | 26.694 | 0.709 | 30.382 | 9.956 |
Optimal value | 5.694e-23 | 1.401e-11 | 1.384e-6 | 5.373e-10 | 3.371e-10 | 1.075e-11 | 9.049e-19 | 5.915e-12 | 7.136e-14 | 2.514e-9 |
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Xia, Z.; Xu, Z.; Li, D.; Wei, J. A Novel Method for Source Tracking of Chemical Gas Leakage: Outlier Mutation Optimization Algorithm. Sensors 2022, 22, 71. https://doi.org/10.3390/s22010071
Xia Z, Xu Z, Li D, Wei J. A Novel Method for Source Tracking of Chemical Gas Leakage: Outlier Mutation Optimization Algorithm. Sensors. 2022; 22(1):71. https://doi.org/10.3390/s22010071
Chicago/Turabian StyleXia, Zhiyu, Zhengyi Xu, Dan Li, and Jianming Wei. 2022. "A Novel Method for Source Tracking of Chemical Gas Leakage: Outlier Mutation Optimization Algorithm" Sensors 22, no. 1: 71. https://doi.org/10.3390/s22010071
APA StyleXia, Z., Xu, Z., Li, D., & Wei, J. (2022). A Novel Method for Source Tracking of Chemical Gas Leakage: Outlier Mutation Optimization Algorithm. Sensors, 22(1), 71. https://doi.org/10.3390/s22010071