Latin Hypercube Sampling Method for Correlated Wind Speed Sequences

This example demonstrates the Latin Hypercube Sampling (LHS) method for generating correlated wind speed sequences, incorporating Cholesky decomposition and correlation ranking procedures. The implementation addresses the critical need for accurate simulation of wind speed dependencies, which is essential for predicting wind pattern variations and turbine performance. The method utilizes historical wind speed observations and their correlation structure to generate synthetic sequences that maintain statistical properties. Key implementation aspects include: using Cholesky decomposition to factorize the correlation matrix, ensuring positive semidefinite properties; applying ranking techniques to preserve correlation structures in the sampled data; and generating stratified random samples that cover the entire distribution space efficiently. These simulated values serve crucial roles in wind energy research, particularly for performance forecasting of wind turbines and other applications requiring precise wind speed modeling. The approach enhances traditional Monte Carlo methods by ensuring better space-filling properties while maintaining correlation constraints through proper matrix transformation and sample ordering techniques.