目的 提高BP神经网络对电喷印过程中液滴铺展行为的预测能力。方法 提出一种鲸鱼优化算法(WOA)优化BP神经网络的液滴铺展预测模型。首先，采用相场方法建立电场作用下液滴铺展的数值模型，并通过实验验证仿真结果的准确性。然后，选取初始直径、撞击速度、接触角和电场强度作为神经网络的输入参数，将最大铺展直径作为神经网络的输出参数，利用鲸鱼优化算法优化神经网络中的初始权值和阈值，构建液滴铺展预测模型。最后，基于仿真结果对预测模型进行训练与测试，并将其与传统的BP神经网络模型进行对比分析。结果 相较于传统BP神经网络预测模型，WOA–BP神经网络预测模型的平均绝对误差、均方根误差分别降低了72.60%、77.60%，而平均绝对百分比误差则从15.029 3%减小为4.585 3%。结论 WOA–BP神经网络预测模型可以更好地预测液滴铺展，可为液滴铺展的预测提供新的方法。

The work aims to improve the prediction ability of BP neural network for droplet spreading behavior during electrojet printing. A whale optimization algorithm (WOA) was proposed to optimize the droplet spreading prediction model based on BP neural network. Firstly, the numerical model of droplet spreading under the action of electric field was established by the phase field method, and the accuracy of the simulation results was verified by experiments. Then, the initial diameter, impact velocity, contact angle and electric field strength were selected as input parameters for the neural network, the maximum spreading diameter was taken as the output parameter of the neural network, and the initial weights and thresholds in the neural network were optimized by the whale optimization algorithm to construct the droplet spreading prediction model. Finally, the prediction model was trained and tested based on the simulation results, and was compared and analyzed with the traditional BP neural network model. Compared with the traditional BP neural network prediction model, the mean absolute error and root mean square error of the WOA-BP neural network prediction model were reduced by 72.60% and 77.60% respectively, while the mean absolute percentage error was reduced from 15.029 3% to 4.585 3%. It is demonstrated that the WOA-BP neural network prediction model can better predict the droplet spreading and can provide a new method for the prediction of droplet spreading.