This research introduces a novel framework integrating stochastic finite element analysis (FEA) with advanced circular statistical methods to optimize heat pump efficiency under material uncertainties. The proposed methodologies and optimization focus on balancing the mean efficiency and variability by adjusting the concentration parameter of the Von Mises distribution, which models directional variability in thermal conductivity. The study highlights the superiority of the Von Mises distribution in achieving more consistent and efficient thermal performance compared to the uniform distribution. We also conducted a sensitivity analysis of the parameters for further insights. The results show that optimal tuning of the concentration parameter can significantly reduce efficiency variability while maintaining a mean efficiency above the desired threshold. This demonstrates the importance of considering both stochastic effects and directional consistency in thermal systems, providing robust and reliable design strategies.

Soil salinization is a difficult challenge for agricultural productivity and environmental sustainability, particularly in arid and semi-arid coastal regions. This study investigates the spatial variability of soil electrical conductivity (EC) and its relationship with key cations and anions (Na⁺, K⁺, Ca²⁺, Mg²⁺, Cl⁻, CO₃²⁻, HCO₃⁻, SO₄²⁻) along the southeastern coast of the Caspian Sea in Iran. Using a combination of field-based soil sampling, laboratory analyses, and Landsat 8 spectral data, linear Multiple Linear Regression and Partial Least Squares Regression (MLR, PLSR) and nonlinear Artifician Neural Network and Support Vector Machine (ANN, SVM) modeling approaches were employed to estimate and map soil EC. Results identified Na⁺ and Cl⁻ as the primary contributors to salinity (r = 0.78 and r = 0.88, respectively), with NaCl salts dominating the region’s soil salinity dynamics. Secondary contributions from Potassium Chloride KCl and Magnesium Chloride MgCl₂ were also observed. Coastal landforms such as lagoon relicts and coastal plains exhibited the highest salinity levels, attributed to geomorphic processes and anthropogenic activities. Among the predictive models, the SVM algorithm outperformed others, achieving higher R² values and lower RMSE (RMSE_Test = 27.35 and RMSE_Train = 24.62, respectively), underscoring its effectiveness in capturing complex soil-environment interactions. This study highlights the utility of digital soil mapping (DSM) for assessing soil salinity and provides actionable insights for sustainable land management, particularly in mitigating salinity and enhancing agricultural practices in vulnerable coastal systems.