# Hybrid Improved PSO Algorithm for Soil Property Parameter Estimation
## 1 Introduction  
In recent years, there has been a notable increase in the prevalence of special engineering vehicles designed for use on unpaved roads, off-road vehicles, and agricultural vehicles [1, 2]. This has led to a corresponding rise in the number of vehicles that are required to operate on soft ground. The low bearing capacity and poor traction of soft ground present a significant challenge for vehicles, often impeding their ability to move. Consequently, the study of soil parameter estimation has become a crucial aspect of assessing potential hazardous driving areas and enabling the use of unmanned vehicles in such environments. Terrain mechanics are crucial for solving the problem of vehicle mobility on soft ground, with researchers investigating the relationship between wheel subsidence and interaction forces by creating a semi-empirical model. [PERSON] [3] systematically studied the fundamental theory of terrain-vehicle mechanics and proposed formulas for calculating wheel sinkage and compression resistance. [PERSON] (2001) and [PERSON] (1965) [4, 5] improved [PERSON]'s formulas based on experimental data, while [PERSON] [6] proposed a formula torepresent shear stress distribution. These formulas involve soil and empirical parameters, and the model requires efficient and accurate estimation of soil parameters through inverse prediction. Hybrid PSO methods have been extensively studied for parameter optimization. Early works integrated PSO with other evolutionary algorithms: [PERSON] et al. [7] combined PSO, GA, and neural networks (PSO-GA-BP) for forest fire prediction, while [PERSON] et al. [8] proposed PSO-ACO for energy scheduling. [PERSON] et al. [9] further introduced PSO-WOA to address high-dimensional convergence issues. Recent advancements demonstrate broader applicability. In microseismic source localization, [PERSON] et al. [10] developed a PSO-GA algorithm with dynamic learning factors, achieving 59% higher accuracy than GA. For medical hyperthermia, [PERSON] et al. [11] utilized stochastic PSO (SPSO) to minimize thermal damage through adaptive laser parameter tuning. In computer vision, [PERSON] et al. [12] proposed SPSO-Pruner for YOLOv5 network pruning, reducing the parameters by 50% with an improved F1-score. Multi-objective frameworks also emerged: [PERSON] and [PERSON] [13] combined WOA, PSO, and Levy flight (WOALFVWPSO), outperforming benchmarks in 19/23 functions, while [PERSON] and [PERSON] [9] applied PSO-WOA to cloud-fog workflows, reducing execution cost by 18%. Despite the significant potential of these hybrid PSO algorithms (e.g., PSO-WOA and GA-PSO) across diverse domains, they still face core challenges in convergence efficiency, computational cost, and local optima avoidance. The existing methods exhibit critical trade-offs--PSO-GA-BP [7] and WOALFVWPSO require manual parameter tuning, while SPSO-Pruner and PSO-WOA struggle with scalability in high-dimensional spaces. Specifically, PSO-WOA suffers from insufficient convergence speed in high-dimensional optimization due to static parameter configurations, and PSO-GA is prone to local optima entrapment in multimodal problems owing to fixed crossover and mutation rates; moreover, complex adaptation rules further amplify computational burdens. To address these limitations, this paper proposes a novel hybrid algorithm, PSO-EDO (Particle Swarm Optimization-Exponential Distribution Optimizer), which integrates dynamic inertia weight adjustment for adaptive exploration-exploitation balance, leverages the memoryless property of the Exponential Distribution Optimizer (EDO) [14] to prevent premature convergence, and employs SPM chaotic mapping to enhance initial population diversity. Compared to recent studies (e.g., PSO-WOA in cloud-fog scheduling and PSO-GA in microseismic source localization), PSO-EDO eliminates the need for complex parameter tuning, ensures computational efficiency, significantly improves global search capability by reducing local optima risks, and provides an advanced solution for real-time engineering applications.