High-confidence Minimum Acquisition Mileage of Durability Load Spectrum of Off-road Special Vehicles

doi:10.12382/bgxb.2023.0817

Abstract

Abstract:

With respect to the problem of acquiring the service loads during the durability development of special vehicles,a high-confidence (above 90%) minimum acquisition mileage model is proposed for the durability load spectrum with the characteristic parameter obeying the Weibull distribution. The Weibull distribution and parameter estimation of this characteristic parameter are studied based on the cumulative power spectral density which comprehensively characterizes the energy distribution and damage distribution of load spectrum. And then a high-confidence minimum acquisition mileage model of durability load spectrum is constructed. Taking the minimum mileage of load spectrum acquisition for durability development of special vehicles as an example, the minimum mileage of acquisition is calculated by taking the wheel six-axis force signal acquired under two journeys as an object. The calculation is performed by specifying the accuracy indexes and confidence requirements between the measured load spectrum samples and the sample population. The minimum acquisition mileages of the load spectrum of special vehicles can be obtained under typical working conditions and are validated with each other. The results show that the proposed model which uses the load spectrum feature parameters obeying the Weibull distribution can effectively realize the calculation of minimum mileage for load spectrum acquisition with high confidence and high accuracy.

Key words: special vehicle, durability load spectrum, Weibull distribution, minimum acquisition mileage, cumulative power spectral density

CLC Number:

TJ306

ZHENG Guofeng, WAN Yinqing, WEI Hanbing, ZHAO Shu’en. High-confidence Minimum Acquisition Mileage of Durability Load Spectrum of Off-road Special Vehicles[J]. Acta Armamentarii, 2024, 45(9): 3017-3028.

Figures/Tables 9

Fig.1 Schematic diagram of calculating the minimum acquisition mileage of load spectrum with high confidence

Fig.2 Durability load spectrum acquisition for special vehicle

Fig.3 Driving speeds and measured wheel six-component load spectra on two roads

Fig.4 APSD of the left front wheel load spectrum on Road Ⅰ

Fig.5 Statistics and critical values of load spectrum characteristic parameter samples

Fig.6 Sample fitting results of the characteristic parameters of load spectrum of Fz channel

Table 1 Weibull fitting results of feature parameter based on different wheel load spectra

通道	路段Ⅰ拟合结果		路段Ⅱ拟合结果
通道	形状参数	尺度参数	形状参数	尺度参数
左前轮	7.3864×10¹⁰	2.0809	7.0215×10¹⁰	2.2541
右前轮	7.8590×10¹⁰	1.9344	7.2240×10¹⁰	2.1566
左中轮	3.6829×10¹⁰	1.9799	4.0985×10¹⁰	2.2011
右中轮	3.7494×10¹⁰	1.9923	4.0719×10¹⁰	2.0911
左后轮	3.4083×10¹⁰	1.7282	3.7642×10¹⁰	2.2959
右后轮	3.4083×10¹⁰	1.7045	3.7642×10¹⁰	2.1260

Fig.7 The change of minimum acquisition mileage with relative deviation and confidence based on different wheel load spectra

Table 2 Minimum acquisition mileage calculated based on six rounds of Fz direction load spectrum under different relative deviations and confidence requirements

通道	路段Ⅰ		路段Ⅱ
通道	相对偏差15% 置信度90%	相对偏差1% 置信度99%	相对偏差15% 置信度90%	相对偏差1% 置信度99%
左前轮	25434.7	51097.6	24062.5	49068.5
右前轮	10425.3	19940.5	13329.1	26308.4
左中轮	13755.4	26714.6	9927.1	19277.5
右中轮	14830.1	28921.4	6170.4	11671.6
左后轮	2971.5	5303.9	18557.6	37303.8
右后轮	2572.0	4554. 5	10109.6	19651.5

References 22

[1]	郑国峰, 杨思宇, 陈柏先, 等. 基于极值外推的特种车辆疲劳耐久性多轴载荷谱编制[J]. 兵工学报, 2024, 45(7):2414-2425. doi: 10.12382/bgxb.2023.0431
	ZHENG G F, YANG S Y, CHEN B X, et al. Compilation of multiaxial load spectra for fatigue durability of special vehicle based on extreme value extrapolation[J]. Acta Armamentarii, 2024, 45(7):2414-2425. (in Chinese) doi: 10.12382/bgxb.2023.0431
[2]	WANG J X, WANG N X, WANG Z Y, et al. Determination of the minimum sample size for the transmission load of a wheel loader based on multi-criteria decision-making technology[J]. Journal of Terramechanics, 2012, 49:147-160.
[3]	ABEBE T H. The derivation and choice of appropriate test statistic(Z, t, F and Chisquare test) in research methodology[J]. Mathematics Letters, 2019, 5(3):33-40.
[4]	MOREIRA E E, MEXIA J T, MINDER C E. F tests with random sample sizes. theory and applications[J]. Statistics & Probability Letters, 2013, 83(6):1520-1526.
[5]	崔卫民, 薛红军, 喻天翔, 等. 试验数据服从Weibull分布时可靠性试验最少试件的确定[J]. 机械工程学报, 2008, 44(1):51-55.
	CUI W M, XUE H J, YU T X, at al. Determination of sample size for Weibull distribution in structural reliability tests[J]. Journal of Mechanical Engineering, 2008, 44(1):51-55. (in Chinese)
[6]	王继新, 季景方, 胡际勇, 等. 基于贝叶斯理论的工程车辆载荷样本长度计算方法[J]. 农业工程学报, 2011, 27(6):148-151.
	WANG J X, JI J F, HU J Y, et al. Bayesian method for determination of load sample size in engineering vehicles[J]. Transactions of the CSAE, 2011, 27(6):148-151. (in Chinese)
[7]	赵新, 纪永祥, 刘社锋, 等. 基于贝叶斯方法的兰利法测试引信解除保险距离数据处理[J]. 兵工学报, 2021, 42(1): 26-32.
	ZHAO X, JI Y X, LIU S F, et al. Data processing of test of fuze arming distance measured using langlie method based on bayesian method[J]. Acta Armamentarii, 2021, 42(1): 26-32. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.01.003
[8]	ZHENG G F, WANG Q Y, CAI C. Criterion to determine the minimum sample size for load spectrum measurement and statistical extrapolation[J]. Measurement, 2021, 178:109387.
[9]	GOPE P C. Determination of sample size for estimation of fatigue life by using Weibull or log-normal distribution[J]. International Journal of Fatigue, 1999,21:745-752.
[10]	XIONG J J, SHENOI R A. A reliability-based data treatment system for actual load history[J]. Fatigue & Fracture of Engineering Materials & Structures, 2005,28: 875-889.
[11]	JOHANNESSON P, SPECKRT M. Guide to load analysis for durability in vehicle engineering[M]. New York,NY, US: John Wiley & Sons, 2014.
[12]	阎楚良, 高镇同. 飞机高置信度中值随机疲劳载荷谱的编制原理[J]. 航空学报, 2000, 21(2):118-123.
	YAN C L, GAO Z T. Compilation theory of median stochastic fatigue load-spectrum with high confidence level for airplane[J]. Acta Aeronautica et Astronautica Sinica, 2000, 21(2):118-123. (in Chinese)
[13]	PRATUMNOPHARAT P, LEUNG P S, COURT R S, Extracting fatigue damage parts from the stress-time history of horizontal axis wind turbine blades[J]. Renewable Energy, 2013,58:115-126.
[14]	樊新海, 王战军, 安钢, 等. 基于连续小波变换的柴油机气缸工作状态检测[J]. 兵工学报, 2010, 31(7):971-974.
	FAN X H, WANG Z J, AN G, et al. Condition detection of diesel engine cylinders based on continuous wavelet transform[J]. Acta Armamentarii, 2010, 31(7):971-974. (in Chinese)
[15]	郑国峰, 上官文斌, 韩鹏飞, 等. 基于小波变换的汽车零部件加速耐久性多轴载荷谱编辑方法研究[J]. 机械工程学报, 2018, 54(10):157-166.
	ZHENG G F, SHANGGUAN W B, HAN P F, et al. Study of multi-axis load spectrum edition method based on the wavelet transform to the accelerated durability test of the vehicle components[J]. Journal of Mechanical Engineering, 2018, 54(10): 157-166. (in Chinese)
[16]	ZHENG G F, PAN H R, CHEN B X, et al. Methods for editing random load spectra based on multi-parameter index preservation for accelerated durability testing[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2022, 236(14):7657-7673.
[17]	BALAKRISHNAN R, KATERI M. On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data[J]. Statistics and Probability Letters, 2008, 78: 2971-2975.
[18]	FELLER W. An introduction to probability theory and its application[M]. 2nd edition. New York,NY, US: John Wiley & Sons,1957.
[19]	盛骤, 谢式千, 潘承毅. 概率论与数理统计[M]. 第4版. 北京: 高等教育出版社, 2008.
	SHENG Z, XIE S Q, PAN C Y. Probability theory and mathematical statistics[M]. 4th edition. Beijing: Higher Education Press, 2008. (in Chinese)
[20]	郑国峰, 朱红国, 伍晨波, 等. 极值超出量服从广义 Pareto分布的载荷谱外推方法研究[J]. 中国机械工程, 2020, 18(31): 2262-2267.
	ZHENG G F, ZHU H G, WU C B, et al. Study to load spectrum extrapolation method based on generalized pareto distribution[J]. China Mechanical Engineering, 2020, 18(31): 2262-2267. (in Chinese)
[21]	WANG Q S, ZHOU J S, GONG D. Fatigue life assessment method of bogie frame with time-domain extrapolation for dynamic stress based on extreme value theory[J]. Mechanical Systems and Signal Processing, 2021, 159:107829.
[22]	ZHENG G F, LIAO Y L, CHEN B X, et al. Multi-axial load spectrum extrapolation method for fatigue durability of special vehicles based on extreme value theory[J]. International Journal of Fatigue, 2024,178:108014.