Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm
Abstract
:1. Introduction
2. Proposed Methodology
2.1. Causal Diagnosability Based on Structural Analysis
2.1.1. Structural Model
2.1.2. Causal Diagnosability
2.2. Quantitative Assessment of Diagnosability Based on MMCD
2.2.1. MMCD
2.2.2. Quantitative Assessment
2.3. Diagnosability Optimization Design Using GWO Algorithm
2.3.1. Optimization Design Model
- Step 1: Build the system structure model ;
- Step 2: Using the causal MSO algorithm from the literature [27], obtain the under different causal conditions;
- Step 3: Design the residual set that satisfies the diagnosability requirement;
- Step 4: Construct the vector ;
- Step 5: Assume that the design cost of is . Then, the design cost of is expressed as follows:
2.3.2. Diagnosability Optimization Design Strategy Based on the GWO Algorithm
- Step 1: For parameter initialization, set the gray wolf population as , maximum iteration number , and parameters , , and . The parameters of MMCD are selected from the optimal parameter settings verified in the literature [40];
- Step 2: Based on Equation (26), initialize the position of the gray wolf population ;
- Step 3: If the constraints shown in Equation (29) are satisfied, calculate its fitness value based on Equation (28); otherwise, its fitness value is infinity. Second, determine the wolf, wolf, and wolf according to the merit of fitness;
- Step 4: Update the location of the gray wolf population based on Equation (35);
- Step 5: Update the parameters , , and ;
- Step 6: Judge whether the maximum number of iterations has been reached. If so, stop the algorithm and return as the optimal solution ; otherwise, return to step 3.
3. Results and Analysis
3.1. Causal Diagnosability of Fixed-Wing UAVs
3.2. Diagnosability Impact Factor Analysis
3.3. MMCD-Based Diagnosability Quantitative Assessment
3.4. Diagnosability Optimization Design Based on the GWO Algorithm
4. Summary
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Gu, X.; Shi, X. Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm. Math. Comput. Appl. 2025, 30, 55. https://doi.org/10.3390/mca30030055
Gu X, Shi X. Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm. Mathematical and Computational Applications. 2025; 30(3):55. https://doi.org/10.3390/mca30030055
Chicago/Turabian StyleGu, Xuping, and Xianjun Shi. 2025. "Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm" Mathematical and Computational Applications 30, no. 3: 55. https://doi.org/10.3390/mca30030055
APA StyleGu, X., & Shi, X. (2025). Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm. Mathematical and Computational Applications, 30(3), 55. https://doi.org/10.3390/mca30030055