When the CNC servo press presses the positioning nut, it is necessary to determine its quality based on the collected data signals, which are easily affected by composite noise and can lead to misjudgment of the nut. To address the difficulty in extracting signal envelope features and determining parameters in VMD under complex noise interference, a method is proposed that combines the capuchin search algorithm to optimize VMD parameters and effectively reconstruct data signals. Firstly, select MCCI as the objective optimization function. Secondly, adaptive modal decomposition is performed on the composite signal, and low noise components are filtered out using the permutation entropy algorithm and correlation coefficient for signal reconstruction. Then, using simulated and measured signals as samples, objective comparisons were made using specific values of RMSE and SNR, and reconstructed signals were visually compared using EMD, CEEMDAN, and CapSA-VMD methods, respectively. The results show that CapSA-VMD decomposition does not contain false components, and the denoising effect is significantly better than the other two. The accuracy of nut quality detection is as high as 97.8%. The research results can provide useful reference for denoising composite signals of pressed positioning nuts and improving the accuracy of envelope threshold judgment.