Design of Sustainable Construction Cost Estimation System Based on Grey Theory - BP Model

China's construction industry is developing rapidly, and market investment is out of control. Therefore, accurate and rapid project cost estimation is the focus of the industry. The grey theory system is a method to study the uncertainty problem of little data and poor information. It can excavate different information hidden in the system observation data to achieve correct description and understanding. The research will improve the BP neural network based on grey theory, and verify the exactitude and advantage of the model from performance comparison and empirical analysis. This study can make the project cost forecast more reasonable. Results show that compared with the traditional model, the maximum error value decreased by 0.52, the research model's maximum mean square error decreased by 0.09, and the variance decreased by 0.13. In the regression analysis, the R-value of the model fitting was above 0.95, the R-value of the verification fitting reached 0.9205. The R-value of the overall fitting reached 0.9475, and the fitting effect was excellent. The convergence speed of the research model is faster than other models, and the fitness value is stable at 1.36. In the empirical analysis, this model can review project cost investment budgets in some areas and reduce project costs. This can improve work efficiency. The model also has certain practical significance for the sustainable development of construction project cost estimates.