Research on an IMODE-NLSF hybrid parameter fitting method for pile-up double-exponential nuclear pulses

By addressing the issues of nonlinear amplitude distortion and spurious spectrum tailing caused by pulse pile-up in nuclear radiation detection systems, this paper proposes a serially coupled parameter fitting and separation algorithm combining Improved Differential Evolution (IMODE) and Nonlinear Least Squares Fitting (NLSF). Utilizing the double-exponential model as the basis function for nuclear pulses, this algorithm first leverages the robust global search capability of IMODE to locate the optimal solution neighborhood within a broad parameter space. It then smoothly transitions to NLSF for localized, fine-grained iteration. This strategy effectively overcomes the non-convex and multi-local-minima optimization challenges inherent in multiple pile-up signal models. Monte Carlo simulation results demonstrate that, under severe pile-up conditions with a signal-to-noise ratio of 30 dB and a pulse time interval of only 20 sampling points, IMODE-NLSF exhibits a significantly faster convergence rate of the Root Mean Square Error (RMSE) compared to single NLSF, GA-NLSF, and PSO-NLSF algorithms. The standard deviation of the relative amplitude extraction error is controlled within 0.54%, exhibiting improved convergence efficiency and noise-resistant robustness. Practical energy spectrum reconstruction experiments using an ²⁴¹Am source confirm that the proposed algorithm effectively corrects waveform distortion caused by pile-up, significantly suppresses the spurious high-energy tailing in the energy spectrum, and successfully recovering 1039 hidden piled-up pulses (approximately 3.46%) from 30,000 raw recorded events. This study provides a reliable algorithmic solution for nuclear radiation signal processing and spectrum analysis.