链式回转弹仓区间不确定性动力学模型

doi:10.12382/bgxb.2023.0379

摘要/Abstract

摘要：

针对具有区间不确定性参数的辨识问题,提出一种基于区间可能度转换模型的区间不确定性参数的双层嵌套辨识(Double-layer Nested Identification,DNI)方法。通过将待辨识参数分为两类,利用DNI方法辨识出第1类确定性参数,再通过基于DNI思想的区间优化方法优化第2类区间不确定性参数的区间范围;面向嵌套策略类型方法计算量庞大且效率低的问题,选用贝叶斯优化-粒子群优化(Bayesian Optimization-Particle Swarm Optimization,BO-PSO)方法作为内层算法以提高求解效率。DNI方法的内层利用BO-PSO方法计算区间上下界,外层利用改进型布谷鸟搜索(Improved Cuckoo Search,ICS)方法辨识特定参数。为进一步缩短求解时间,提出一种ICS多核极限学习机(ICS-Multiple Kernel-Extreme Learning Machine,ICS-MK-ELM)代理模型,ICS-MK-ELM代理模型克服了人工调节每个核函数超参数的困难,并且模型预测精度明显高于核ELM(Kernel ELM,KELM)和MK-ELM;将DNI方法应用于链式回转弹仓的参数辨识,解决了链式弹仓具有区间不确定性参数的辨识困难的问题,参数辨识结果表明所提DNI方法以及基于DNI思想的区间优化方法具有更高的精度和稳定性。

关键词: 不确定性, 区间可能度, 弹仓, 参数辨识, 多核极限学习机, 贝叶斯优化, 布谷鸟搜索方法

Abstract:

For the identification problem with interval uncertain parameters, a double-layer nested identification (DNI) method based on an interval possibility degree transformation model is proposed. By dividing the parameters to be identified into two categories, the first type of deterministic parameters are identified by DNI method, and the interval range of the second type of interval uncertainty parameters is optimized by the DNI-based interval optimization method. The BO-PSO algorithm is chosen as the inner-layer algorithm to improve the efficiency of the nested strategy type method. For the inner layer of DNI method, BO-PSO method is used to calculate the upper and lower bounds of interval, and for the outer layer, ICS method is used to identify the specific parameters. In order to shorten the solving time, an ICS-MK-ELM agent model is proposed. The ICS-MK-ELM agent model overcomes the difficulty of manually adjusting the hyper-parameters of each kernel function, and the prediction precision of the model is obviously higher than those of KELM and MK-ELM. Finally, the DNI method is applied to the parameter identification of the rotational chain shell magazine, which solves the problem of the parameter identification of the chain-type magazine with interval uncertainty. The results of parameter identification show that the DNI method and the interval optimization method based on DNI have higher accuracy and stability.

Key words: uncertainty, interval possibility degree, shell magazine, parameter identification, multiple kernel extreme learning machine, Bayesian optimization, cuckoo search algorithm

中图分类号:

TJ301

赵伟, 侯保林, 闫少军, 鲍丹, 林瑜斌. 链式回转弹仓区间不确定性动力学模型[J]. 兵工学报, 2024, 45(6): 1991-2002.

ZHAO Wei, HOU Baolin, YAN Shaojun, BAO Dan, LIN Yubin. A Dynamic Model of Interval Uncertainty of Rotational Chain Shell Magazine[J]. Acta Armamentarii, 2024, 45(6): 1991-2002.

图/表 16

图1 链式回转弹仓的简化图

Fig.1 Structure sketch of rotational chain shell magazine

图2 摩擦模型改进效果图

Fig.2 Improvement effect diagram of friction model

图3 DNI方法流程图

Fig.3 Flowchart of DNI method

图4 区间的6种位置关系

Fig.4 Six position relations of Intervals A and B

图5 基于MK-ELM的代理模型结构

Fig.5 Agent model structure based on MK-ELM

图6 ICS-MK-ELM的流程图

Fig.6 Flowchart of ICS-MK-ELM

图7 代理模型预测结果对比图

Fig.7 Comparison of predicted results of agent model

图8 电机转速

Fig.8 Motor speed

图9 电机电流

Fig.9 Motor current

图10 区间上下界对比图

Fig.10 Comparison of upper and lower bounds of the interval

表1 第1类参数的辨识结果(空载)

Table 1 Identifiied results of the first type of parameters (no load)

方法	M_fc/(N·m)	M_fs/(N·m)	ω_s/(rad·s^-1)	A_s	B_e/(N·m·s·rad^-1)	标准差	极差	离散系数	相似度区间
区间	[0,10]	[0,10]	[0.1,3]	[0,100]	[0.1,10]
DNI	0.0457	7.7283	1.7906	88.14504	7.962252	0	0	0	[0.0354,0.1398]
文献[14]	2.1565	8.5718	1.6062	56.8612	7.2311	0.0152	0.0792	0.0285	[0.0353,0.1750]
文献[15]	0.0190	7.9256	2.6388	19.5739	8.0893	0.0161	0.0025	0.0756	[0.0354,0.1475]

表2 第1类参数的辨识结果(半载)

Table 2 Identified results of the first type of parameters (half load)

方法	M_fc/(N·m)	M_fs/(N·m)	ω_s/(rad·s^-1)	A_s	B_e/(N·m·s·rad^-1)	标准差	极差	离散系数	相似度区间
区间	[0,20]	[0,20]	[0.1,3]	[0,100]	[0.1,10]
DNI	5.8666	12.6646	0.5839	0.0009	8.6948	0	0	0	[0.0241,0.1264]
文献[14]	3.7937	15.0262	1.4869	53.77662	8.3186	0.1468	0.3602	0.1590	[0.0231,0.3121]
文献[15]	3.0889	13.2096	1.1470	0.0228	9.5951	0.0178	0.0515	0.0876	[0.0216,0.1733]

表3 第2类参数辨识结果(空载)

Table 3 Identified results of the second type of parameters (no load)

方法	ε	J_e/(kg·m²)	$J · e$ /(kg·m²·s^-1)	标准差	极差	离散系数	相似度区间
	0.15	[2.0140,2.9750]	[-2.9764,1.4157]	0.0011	0.0020	0.0056	[0.0358,0.1368]
DNI	0.1	[2.4942,2.8982]	[-2.4516,0.8382]	0.0012	0.0022	0.0081	[0.0366,0.0998]
	0.05	[2.6867,2.9641]	[-1.6102, -0.5150]	0.0007	0.0014	0.0083	[0.0359,0.0486]
	0.15	[2.0146,2.9847]	[-2.9798,1.4808]	0.0260	0.0907	0.0005	[0.0355,0.1465]
文献[15]	0.1	[2.4384,2.9884]	[-2.7622,0.5517]	0.0345	0.1439	0.0108	[0.0354,0.1018]
	0.05	[2.6380,2.9943]	[-1.9418,-0.7364]	0.0109	0.1001	0.0071	[0.0354,0.0508]

表3 第2类参数辨识结果(空载)

Table 3 Identified results of the second type of parameters (no load)

方法	ε	J_e/(kg·m²)	$J · e$ /(kg·m²·s^-1)	标准差	极差	离散系数	相似度区间
	0.15	[2.0140,2.9750]	[-2.9764,1.4157]	0.0011	0.0020	0.0056	[0.0358,0.1368]
DNI	0.1	[2.4942,2.8982]	[-2.4516,0.8382]	0.0012	0.0022	0.0081	[0.0366,0.0998]
	0.05	[2.6867,2.9641]	[-1.6102, -0.5150]	0.0007	0.0014	0.0083	[0.0359,0.0486]
	0.15	[2.0146,2.9847]	[-2.9798,1.4808]	0.0260	0.0907	0.0005	[0.0355,0.1465]
文献[15]	0.1	[2.4384,2.9884]	[-2.7622,0.5517]	0.0345	0.1439	0.0108	[0.0354,0.1018]
	0.05	[2.6380,2.9943]	[-1.9418,-0.7364]	0.0109	0.1001	0.0071	[0.0354,0.0508]

表4 第2类参数辨识结果(半载)

Table 4 Identified results of the second type of parameters (half load)

方法	ε	J_e/(kg·m²)	$J · e$ /(kg·m²·s^-1)	标准差	极差	离散系数	相似度区间
	0.15	[4.0301,4.9414]	[-5.9923,2.9921]	0.0027	0.0014	0.0008	[0.0246,0.1258]
DNI	0.1	[4.0025,4.9070]	[-0.3079,2.9863]	0.0019	0.0002	0.0009	[0.0241,0.0981]
	0.05	[4.0689,4.2069]	[0.8067,2.9926]	0.0033	0.0015	0.0013	[0.0252,0.0488]
	0.15	[4.0210,4.9750]	[-5.9676,2.9744]	0.0251	0.0661	0.0025	[0.0217,0.143]
文献[15]	0.1	[4.0204,4.9040]	[-0.4373,2.9504]	0.0526	0.1423	0.0123	[0.0244,0.1017]
	0.05	[4.0686,4.2515]	[0.8364,2.9583]	0.0805	0.2448	0.0341	[0.0253,0.0495]

表4 第2类参数辨识结果(半载)

Table 4 Identified results of the second type of parameters (half load)

方法	ε	J_e/(kg·m²)	$J · e$ /(kg·m²·s^-1)	标准差	极差	离散系数	相似度区间
	0.15	[4.0301,4.9414]	[-5.9923,2.9921]	0.0027	0.0014	0.0008	[0.0246,0.1258]
DNI	0.1	[4.0025,4.9070]	[-0.3079,2.9863]	0.0019	0.0002	0.0009	[0.0241,0.0981]
	0.05	[4.0689,4.2069]	[0.8067,2.9926]	0.0033	0.0015	0.0013	[0.0252,0.0488]
	0.15	[4.0210,4.9750]	[-5.9676,2.9744]	0.0251	0.0661	0.0025	[0.0217,0.143]
文献[15]	0.1	[4.0204,4.9040]	[-0.4373,2.9504]	0.0526	0.1423	0.0123	[0.0244,0.1017]
	0.05	[4.0686,4.2515]	[0.8364,2.9583]	0.0805	0.2448	0.0341	[0.0253,0.0495]

图11 空载工况下的辨识曲线族

Fig.11 Identification curve family under no-load condition

图12 半载工况下的辨识曲线族

Fig.12 Identification curve family under half load condition

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