Weighing fusion method for truck scale based on an optimal neural network with derivative constraints and a lagrange multiplier

•We propose a novel method for optimizing a neural network based on PD-LMNN.•Improve the NN’s generalization ability while lack of training samples.•Develop the detail algorithm of PD-LMNN and discuss the PD-LMNN’s performances.•Construct a weighing fusion model of a truck scale based on PD-LMNN.•Verify this fusion model’s its effectivity and accuracy.

This paper presents a novel weighing fusion method for a truck scale based on an optimal neural network with partial derivative constraints and a Lagrange multiplier (PD-LMNN). In this proposed method, firstly, the constraints for optimizing neural network (NN) are constructed via the truck scale’s prior knowledge that the partial derivative of the truck scale’s input–output function is positive. Secondly, the neural network’s performance index is created by using the augmented Lagrange function with a multiplier and a penalty factor. Thirdly, the detail algorithm of training the constrained-optimization NN is given. This proposed method can improve the NN’s generalization ability in case of the lacking training samples. The comparative experimental results show that the weighing errors of the truck scale with PD-LMNN are far less than those of DINN (DINN is a method for training a NN only by using the data samples, not the prior knowledge), and the PD-LMNN’s generalization ability is better than that of DINN when the training samples are lacking.