Estimation of trapezoidal-shaped overlapping nuclear pulse parameters based on a deep learning CNN-LSTM model

The Long Short-Term Memory neural network (LSTM) has excellent learning ability for the time series of the nuclear pulse signal. It can accurately estimate the parameters (such as amplitude, time constant, etc.) of the digitally shaped nuclear pulse signal (especially the overlapping pulse signal). However, due to the large number of pulse sequences, the direct use of these sequences as samples to train the LSTM increases the complexity of the network, resulting in a lower training efficiency of the model. The convolution neural network (CNN) can effectively extract the sequence samples by using its unique convolution kernel structure, thus greatly reducing the number of sequence samples. Therefore, the CNN-LSTM deep neural network is used to estimate the parameters of overlapping pulse signals after digital trapezoidal shaping of exponential signals. Firstly, the estimation of the trapezoidal overlapping nuclear pulse is considered to be obtained after the superposition of multiple exponential nuclear pulses followed by trapezoidal shaping. Then, a data set containing multiple samples is set up; each sample is composed of the sequence of sampling values of the trapezoidal overlapping nuclear pulse and the set of shaping parameters of the exponential pulse before digital shaping. Secondly, the CNN is used to extract the abstract features of the training set in these samples, and then these abstract features are applied to the training of the LSTM model. In the training process, the pulse parameter set estimated by the present neural network is calculated by forward propagation. Thirdly, the loss function is used to calculate the loss value between the estimated pulse parameter set and the actual pulse parameter set. Finally, a gradient-based optimization algorithm is applied to update the weight by getting back the loss value together with the gradient of the loss function to the network, so as to realize the purpose of training the network. After model training was completed, the sampled values of the trapezoidal overlapping nuclear pulse were used as input to the CNN-LSTM model to obtain the required parameter set from the output of the CNN-LSTM model. The experimental results show that this method can effectively overcome the shortcomings of local convergence of traditional methods and greatly save the time of model training. At the same time, it can accurately estimate multiple trapezoidal overlapping pulses due to the wide width of the flat top, thus realizing the optimal estimation of nuclear pulse parameters in a global sense, which is a good pulse parameter estimation method.