## 1 Introduction
This provides new ideas for performance degradation and lifetime prediction. The NOx simulation model based on data-driven construction is less dependent on the mechanism and can achieve satisfactory accuracy under appropriate algorithm selection and optimization. The research on intelligent algorithm modeling of the NOx simulation model mainly focuses on the following: (1) Using different artificial intelligence algorithms (such as artificial neural networks (ANN), deep neural networks (DNN), convolutional neural networks (CNN), long and short-term memory neural networks (LSTM), etc.) and optimization algorithms to construct different models to predict the emissions and characteristic parameters of gasoline engines or medium and high-speed diesel engines [16; 17; 18; 19; 20; 21; 22; 23]. (2) Use appropriate algorithms to study the performance characteristics and predicted emissions of dual-fuel engines (such as isoamyl alcohol/gasoline, biodiesel/diesel, etc.) under different fuel ratios [24; 25; 26; 27; 28; 29]. (3) Research into the promotion and adaptive optimization of artificial intelligence algorithm model prediction abilities [30; 31; 32; 33; 34; 35; 36]. From the modeling characteristics and applications of the physical and data-driven models described above, it is clear that the modeling process of the data-driven model is relatively simple because it does not rely on complex mathematical physical equations based on the working principles of the object. Therefore, it facilitates the exploration of research questions that lack detailed theoretical support, such as the characterization of dual-fuel or new-fuel engines. Many algorithms can use complex computing models and algorithms based on large data sets to achieve high prediction accuracy, which is not conducive to the adaptive expansion of the model and the practical application of the model. In this paper, a NOx calculation model for marine diesel engines is developed using a data-driven modeling construct. Compared to CNN and DNN, a backpropagation neural network (BPNN) has a simpler structure. After a BPNN learns the data samples, each data undergoes multilayer and multinode repeated operations to realize data regression prediction. Compared with the simple feedforward ANN, BPNN optimizes and adjusts the weight matrix and bias matrix of the neural network by introducing error feedback backpropagation. Selecting an appropriate activation function makes the input and output have a highly nonlinear mapping relationship, and the BPNN can approximate any nonlinear function with arbitrary precision. For non-time series data, such as diesel engine operating conditions, the BPNN is more suitable for the nonlinear regression prediction of multidimensional input and output systems such as diesel engines than LSTM. Meanwhile, to make the structure of the BPNN as simple as possible, the BPNN is optimized using the group method of data handling (GMDH), and the final GMDH-BP model-based NOx calculation model is constructed. The main contents of this paper are as follows: (a) establishing a three-dimensional simulation model using experimental data and conducting simulation experiments to provide data samples for the NOx calculation model; (b) selecting variables related to NOx emissions from the perspective of mechanism generation, using the grey relational analysis correlation method to initially select influencing factors with strong correlation and using the principal component analysis method to reduce the dimensionality of influencing factors to obtain low-dimensional input data; (c) establishing three computational models to compare the computational accuracy: the GMDH-BPNN NOx computational model using GMDH adaptive optimization of the structure of the BPNN neural network model; the GA-BPNN NOx computational model using the genetic algorithm (GA) to optimize the weights and bias of the BPNN; and, finally, the GMDH-BPNN, GA-BPNN, and unoptimized BPNN models are compared.