Accurate forecasting of urban domestic waste clearance in China is essential for advancing the sustainable development of urbanization. To this end, this paper proposes a novel nonlinear grey convolution model that incorporates background value optimization. Firstly, this model introduces power exponents to enhance its ability to capture the nonlinear characteristics of the system. And then, it also analyzes the sources of errors in the background value calculation of traditional models and effectively addresses this issue by incorporating dynamic interpolation coefficients. Besides, the optimal hyperparameters of the model are determined using particle swarm optimization (PSO). In two distinct case studies, the proposed model was rigorously compared with five forecasting models across three distinct domains, consistently demonstrating its superior performance.