# Hybrid Improved PSO Algorithm for Soil Property Parameter Estimation
## 5 Conclusions  
This paper proposes a soil property parameter estimation method based on the integration of a wheel-soil mechanical model with the PSO-EDO algorithm. First, the mechanical interaction between the wheel and soil was analyzed, and a wheel-soil model was developed using calculus, followed by the simplification of the governing equations. Next, SPM chaotic mapping was introduced for population initialization, and the inertia weight was updated based on the fitness values during the iterative process. Subsequently, the strengths of the EDO and SPSO algorithms were combined to develop the improved PSO-EDO algorithm. The performance of the proposed algorithm was tested using common benchmark functions and compared with basic PSO, SPSO, PSO-GA, PSO-WOA, and EDO algorithms. The experimental results indicate that the PSO-EDO algorithm performs well for both unimodal and multimodal functions. Although its computation speed is slightly slower, it achieves higher accuracy.  
In the soil property parameter estimation simulation, the PSO-WOA, EDO, and PSO-EDO algorithms, which performed well in the benchmark function tests, were compared. The PSO-EDO algorithm's average computation time was 1.9487 s, 18.0% shorter than that of the PSO-WOA algorithm and 14.5% shorter than that of the EDO algorithm. The PSO-EDO and PSO-WOA algorithms showed similar convergence speeds, both completing convergence within 10 iterations, approximately five generations faster than the EDO algorithm. The error rate for soil property parameter estimation was generally within 10%, indicating good performance and demonstrating the feasibility and superiority of the proposed method. In future work, the structure of the PSO-EDO algorithm needs to be further refined to enhance its performance.  
Despite these promising results, several limitations should be acknowledged. First, the current validation is based on simulation data under idealized conditions. In real-world applications, data noise, missing values, and heterogeneous soil conditions may affect performance. Second, the algorithm's scalability for large-scale or high-dimensional terrain data remains to be further tested.  
Future work should aim to: (1) validate the algorithm with field-collected data in diverse environments; (2) extend the method to accommodate various complex soil types and dynamic terrain characteristics; and (3) explore the integration of deep learning or hybrid intelligent systems to further enhance estimation accuracy, robustness, and computational efficiency.  
Conceptualization, M.L. and L.Y.; Methodology, M.L. and C.Q.; Software, M.L.; Validation, A.S.; Formal analysis, Y.S. and L.Y.; Investigation, T.Z.; Resources, A.S.; Data curation, M.L.; Writing--original draft, M.L.; Writing--review & editing, M.L., A.S. and L.Y. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.