Owing to increasing interest in the environment, particularly on air quality, regulations in the automobile industry have become stricter. Test cycles have been substituted to simulate real driving conditions, and they offer opportunities for researchers to satisfy regulations and predict emissions using models.

The objective of this study is to develop a deep neural network (DNN) model, optimize its hyperparameters using the Bayesian optimization method, and use hidden-node determination logic to predict engine-out NO${}_{\mathrm{x}}$ emissions by using the worldwide harmonized light vehicles test procedure (WLTP) of diesel engines. A DNN network learns the internal relationships between inputs and target outputs even though they are complicated. However, the hyperparameters of DNNs are typically determined by researchers before training, and they affected the accuracy of the model. In this study, the hyperparameters of the DNN model such as the number of hidden layers, number of nodes in each hidden layer, learning rate, learning rate decay, and batch size are automatically optimized using the Bayesian optimization method. Some logical equations are combined with the number of nodes in the first hidden layer and the number of hidden layers to realize the model’s structure instead of using the number of hidden nodes in each hidden layer.

Compared with grid search and random sampling, the Bayesian optimization method is a promising solution to optimize hyperparameters. In addition, a hidden-node determination logic further improved the accuracy of the model. The accuracy of the optimized model is indicated by an R² value of 0.9675 with 14 input features. The result of cycle prediction shows that the mean absolute errors are approximately 16–17 ppm for four WLTP cycles, which are 1.6% of the maximum NO${}_{\mathrm{x}}$ value. These results indicate that the accuracy of the model is comparable to that of a physical NO${}_{\mathrm{x}}$ measurement device whose linearity is 1% of the full scale (5,000 ppm).

由于对环境特别是对空气质量的兴趣不断提高，汽车行业的法规变得更加严格。测试周期已被用来模拟实际驾驶条件，它们为研究人员提供了满足法规和使用模型预测排放的机会。

这项研究的目的是开发一个深度神经网络（DNN）模型，使用贝叶斯优化方法优化其超参数，并使用隐藏节点确定逻辑来预测发动机输出NO${}_{\mathrm{X}}$通过使用全球范围内的柴油发动机协调一致的轻型车辆测试程序（WLTP）来实现排放。DNN网络学习输入和目标输出之间的内部关系，即使它们很复杂。但是，DNN的超参数通常是由研究人员在训练之前确定的，它们会影响模型的准确性。在这项研究中，使用贝叶斯优化方法自动优化DNN模型的超参数，例如隐藏层数，每个隐藏层中的节点数，学习率，学习率衰减和批量大小。一些逻辑方程式与第一隐藏层中的节点数和隐藏层数结合在一起，以实现模型的结构，而不是使用每个隐藏层中的隐藏节点数。

与网格搜索和随机抽样相比，贝叶斯优化方法是优化超参数的有前途的解决方案。另外，隐藏节点确定逻辑进一步提高了模型的准确性。具有14个输入要素的R ²值为0.9675，表明了优化模型的准确性。循环预测的结果表明，四个WLTP循环的平均绝对误差约为16-17 ppm，这是最大NO的1.6％${}_{\mathrm{X}}$值。这些结果表明，该模型的准确性与物理NO的准确性相当。${}_{\mathrm{X}}$ 线性度为满刻度（5,000 ppm）的1％的测量设备。