Method for Predicting the Satisfaction and Utilization Rates of Spare Based on BP Neural Networks

doi:10.3969/j.issn.1009-086x.2025.02.019

Abstract

Abstract:

By leveraging the correspondence between spares configuration schemes and equipment support performance， the BP（back propagation） neural network model is used to adjust the mapping relationship between spares configuration schemes and their corresponding satisfaction and utilization rates. This facilitates the evaluation of the rationality of spares configuration scheme design. Using three types of equipment with different structural compositions as examples， the corresponding neural network prediction models for the satisfaction and utilization rates of spares are designed and trained with data samples. This achieves fast and high-precision calculations of the satisfaction and utilization rates of spare parts， with both the mean error and mean square error being less than 0.05%， demonstrating the effectiveness of the proposed method.

Key words: spares configuration scheme, BP（back propagation） neural network, support efficiency, spares satisfaction rate, spares utilization rate

摘要：

针对备件满足率与利用率的计算、预测问题，提出了一种基于BP神经网络的预测方法。依据备件配置方案与装备保障效能之间存在的影响关系，设计神经网络模型拟合备件配置方案与其对应满足率、利用率之间的映射关系，实现备件配置方案设计合理性的评估。以3类不同组成结构的装备为例，设计对应的备件满足率与利用率神经网络预测模型，并通过数据样本进行训练，实现了快速、高精度的备件满足率与利用率的预测。算法耗时短且平均误差与均方误差均小于0.05%，证明了所提方法的有效性。

关键词: 备件配置方案, BP神经网络, 保障效能, 备件满足率, 备件利用率

CLC Number:

Xinru WANG, Shaokang TANG, Jianjun YANG. Method for Predicting the Satisfaction and Utilization Rates of Spare Based on BP Neural Networks[J]. Modern Defense Technology, 2025, 53(2): 175-182.

王欣汝, 唐少康, 杨建军. 基于BP神经网络的备件满足率与利用率预测方法[J]. 现代防御技术, 2025, 53(2): 175-182.

Figures/Tables 12

Fig. 1 Working diagram of neural network

Fig. 2 Schematic diagram of neuron computational logic simplification

Table 1 Activation function

类别	激活函数	函数表达式	导数
线性	Linear函数	$f (x) = a x$	$f' (x) = a$
非线性	Sigmoid函数	$f (x) = 1 1 + e - x$	$f' (x) = f (x) (1 - f (x))$
	tanh函数	$f (x) = e x - e - x e x + e - x$	$f' (x) = 1 - f (x) 2$
	ReLU函数	$f (x) = x, x ≥ 0 0, x < 0$	$f' (x) = 1, x ≥ 0 0, x < 0$
	ELU函数	$f (x) = x, x ≥ 0 a (e x - 1), x < 0$	$f' (x) = 1, x ≥ 0 f (x) + a, x < 0$

Table 1 Activation function

类别	激活函数	函数表达式	导数
线性	Linear函数	$f (x) = a x$	$f' (x) = a$
非线性	Sigmoid函数	$f (x) = 1 1 + e - x$	$f' (x) = f (x) (1 - f (x))$
	tanh函数	$f (x) = e x - e - x e x + e - x$	$f' (x) = 1 - f (x) 2$
	ReLU函数	$f (x) = x, x ≥ 0 0, x < 0$	$f' (x) = 1, x ≥ 0 0, x < 0$
	ELU函数	$f (x) = x, x ≥ 0 a (e x - 1), x < 0$	$f' (x) = 1, x ≥ 0 f (x) + a, x < 0$

Fig. 3 Neural network model

Table 2 Reliability information for the units

部件类型	可靠性分布类型	失效率/h^-1	平均维修时间/h
1	指数分布	0.001 4	0.5
2	指数分布	0.002 1	0.5
3	指数分布	0.003 2	0.5
4	指数分布	0.003 5	0.5
5	指数分布	0.004 1	0.5
6	指数分布	0.004 5	0.5
7	指数分布	0.004 9	0.5
8	指数分布	0.005 1	0.5
9	指数分布	0.005 2	0.5
10	指数分布	0.005 5	0.5

Fig. 4 Principle of component task simulation

Fig. 5 Simulation flow chart

Table 3 Equipment composition information

装备类型	A	B	C
部件组成	1~6	1~8	1~10

Fig. 6 Training and testing results of the neural network model

Fig. 7 Distribution of test set errors forclass C equipment neural network model

Table 4 Errors in the test set of the neural network model

装备类型	评估指标	备件满足率/%	备件利用率/%
A	平均误差	0.015 61	0.013 13
A	均方误差	0.002 03	0.013 12
B	平均误差	-0.009 01	0.007 04
B	均方误差	0.001 02	0.007 15
C	平均误差	-0.008 71	0.038 38
C	均方误差	0.000 80	0.004 57

Table 5 Algorithm time statistics

方法	1组方案/s	10组方案/s
BP神经网络	0.000 473	0.004 775
蒙特卡罗仿真（3 000次）	0.030 614	0.318 128

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