滚动轴承乏信息试验评估方法及其应用技术研究
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摘要
乏信息指研究对象呈现的特征信息不完备与不充分。本文在综合分析现有成果基础上,研究乏信息系统理论在滚动轴承试验分析中的应用问题。在某些滚动轴承测量和性能试验中,常常难以得到大量的数据。比如一些新型航天轴承和一些特殊轴承的研制与生产,由于品种多批量小,每个品种每次需求只有十几套甚至几套,因此能用于性能试验的更少;因为缺乏概率分布和趋势项的先验信息,所以不能用流行方法解决这类轴承的试验评估问题。
考虑到概率分布未知且数据个数很少,提出静态评估的模糊范数法和基于区间数的模糊范数法。这两种方法用隶属函数和最大模范数最小化原理,获取概率分布函数,进而建立给定置信水平的区间评估模型,无需原始数据概率分布的任何信息;最大模范数最小化处理允许数据个数很少。若数据个数为偶数且大于5,则可以用基于区间数的模糊范数法提取原始数据序列的随机信息和尺度信息两个子序列。用模糊范数法分别处理这两个子序列后,再用区间数运算法则对处理结果进行融合,就可以评估总体的属性参数。若直接用模糊范数法,则数据个数可以少至3个。
提出最大熵自助法,以解决试验次数很少,但每次试验的数据个数比较多时的静态评估问题。首先建立各次试验数据的最大熵概率分布,然后用自助再抽样原理对各次试验数据得到的最大熵概率分布信息进行融合,最后得到总体的稳定状态描述,实现从个体参数识别到总体属性的推断。最大熵自助法允许试验次数可以少至3次。
有机融合灰预测GM(1,1)和自助法的优点,建立了灰自助法,以实现乏信息试验的动态评估。该方法突破了灰预报对原始数据有特殊要求的禁区,完善了区间估计的自助法。在概率分布未知和缺乏趋势项先验信息条件下,用6个指标(动态估计真值、动态估计真值的均值、估计真值变动量、动态估计区间、动态波动范围、动态波动范围平均值)全面描述系统的瞬间状态和整体特征,有效分离趋势项并实施动态评估,提高了预报的可靠性。灰自助法需要的当前数据个数少至3个。
提出两个数据序列的灰关系及其灰假设检验方法,以解决灰色系统理论要求至少有3个数据序列才能构成灰关联空间的问题。对于排序和非排序假设检验两个模型,前者用于和数据前后顺序无关的属性检验,后者则用于和数据前后顺序有关的属性检验。灰关系超越了灰关联序空间的限制,将灰关联分析提升为灰假设检验。灰关系允许小样本数据,对概率分布无任何要求,弥补了统计假设检验方法的不足。灰假设检验允许数据序列个数少至2个,每个数据序列的数据个数可以少至3个。
对所提出的方法进行了计算机仿真验证,涉及到的数据序列有正态分布,瑞利分布,均匀分布和三角分布随机变量;混合分布的平稳随机过程;趋势项;各种分布和趋势项混合的非平稳随机过程。验证结果表明,所提出的方法能比较准确地描述各种随机变量、平稳随机过程以及非平稳随机过程的瞬间状态和整体特征,有效分离趋势项,可靠实施乏信息评估。
对所提出的方法进行了试验验证,涉及到滚动轴承圆度误差,摩擦力矩,振动和噪声。验证结果表明,在没有概率分布与趋势项先验信息而只有很少数据的条件下,评估结果与试验结果很吻合,置信水平均达到95%以上。
所提出的方法还在捷联惯性测量组合的误差系数检验,武器系统效能检验与温度仪表数据分析等领域中得到很好应用。
总体而言,所提出的方法从不同侧面研究乏信息系统,形成了一个完整的评估体系。该评估体系的评估结果与实际情况一致,一般相对误差小于15%,与统计法、灰GM(1,1)、自助法、最大熵法以及算术平均法等流行方法比较,相对误差减少了9%～35%,取得了更好的效果。
Poor information means incomplete and insufficient information for the characteristic presented in the subject investigated.Based on synthesized analysis of available findings,some problems of information poor system theory applied in rolling bearing test analysis are studied in the dissertation.It is difficult to get large numbers of data in the process of measurement and performance analysis for some rolling bearings.For example,in development and manufacture of new type bearings for space using or some special type bearings,much less bearings can be made a trial because of many species and small quantity,every time only ten-odd or even several bearings are required,and prevailing methods are not used to answer the questions about test analysis and evaluation of this kinds of bearings for lack of prior information about probability distribution and trends.
Considering unknown probability distribution and very small data,two methods viz.the fuzzy norm method and the fuzzy norm method based on interval number are advanced for static evaluation.Using membership function and theory of a minimum of maximum module norm,these two methods are able to obtain a probability distribution function and then make a model for interval evaluation under the given confidence level,without any infbrmation about probability distribution of a raw data series.The number of the data can be very small for a minimum of maximum module norm.If the number of the data is even and bigger than 5,then two sub-series of random information and measure information can be extracted from the raw data series using the fuzzy norm method based on interval number.After processing these two sub-series via the fuzzy norm method,the results processed are fused by algorithm of interval numbers and the parameters of attribute of population can be evaluated.In addition,the number of the data can be down to 3 if direct using the fuzzy norm method.
The maximum entropy method is proposed to resolve the problem about static evaluation under the condition that the number of test times is small while every time the number of test data is much.First the maximum entropy distribution of each test data is established,then information about the maximum entropy distributions of all tests is fused by bootstrap resampling,and lastly the inference of attribute of population is drawn from identifying the parameters of every individual,describing the stable state of population.Investigation shows that the number of test times can be down to 3.
Organically fusing the excellences of grey forecasting modeling GM(1,1) and bootstrap,the grey bootstrap method is established to develop dynamic online evaluation of tests with poor information.It improves the bootstrap of interval estimate and breaks through forbidden zone with special requirements for raw data in grey system theory.Under the condition of unknown probability distribution and of trends without any prior information,the transient state and the global characteristic of a system are described fully,trends are separated effectively, dynamic evaluation is actualized,and reliability is increased,by developing 6 indexes,viz.dynamic estimated truth,mean of dynamic estimated truth,change quantity of estimated truth,dynamic estimated interval,dynamic fluctuant range, mean of dynamic fluctuant range.And the number of the current data can be down to 3 using the grey bootstrap method.
The grey relation between two data series and its grey hypothesis testing are introduced to resolve the problem of the grey relational space which can be structured only under the condition at least 3 data series.There are two models:one is collating sequence grey hypothesis testing and the other is non-collating sequence grey hypothesis testing.The former can verify attribute irrelative to sequencing of the data,and the latter can verify attribute relative to sequencing of the data.The grey relation goes beyond the limit of the grey relational space and advances grey relational analysis to grey hypothesis testing.In addition,the grey relation can supply some of the gaps in statistic hypothesis testing,because it allows small sample data without any requirements for probability distribution.And the number of the data series can be down to 2 and the number of the data in each data series can be down to 3.
The various methods proposed are validated by computer simulation.The data series simulated deal with random variables such as normal distribution,Rayleigh distribution,uniform distribution,and triangular distribution,deal with stationary random process of mixing distributions,deal with trends,and also deal with nonstationary random process of mixing various distributions and trends.The verified results show that the methods proposed is able to describe the transient state and the global characteristic of all kinds of random variables,of stationary random process,and of nonstationary random process,with effectively separating trends and reliably actualizing evaluation under the condition of poor information.
The various methods proposed are validated by engineering experiments. Roundness error,friction torque,vibration and noise of rolling bearings are considered.The verified results show that the methods proposed are able to evaluate rolling bearing tests,without any prior information about probability distribution and trends,only with very small data.And the confidence level can be bigger than 95%.
The methods proposed also are applied to the fields such as test of the error coefficient of the strapdown inertial measurement unit and the effectiveness check of weapon systems,and data analysis of the temperature meters.
On the whole,investigating of information poor system from different view sides,an integrated evaluation system is formed with the above methods proposed. The results using this evaluation system are coincident with the real truth of the subject investigated and the relative errors usually are less than 15%.This evaluation system can obtain better results by a 9%～35%decrease of the relative errors as compared with the prevailing methods such as statistics,grey forecasting modeling GM(1,1),bootstrap,and arithmetic mean method etc.
考虑到概率分布未知且数据个数很少,提出静态评估的模糊范数法和基于区间数的模糊范数法。这两种方法用隶属函数和最大模范数最小化原理,获取概率分布函数,进而建立给定置信水平的区间评估模型,无需原始数据概率分布的任何信息;最大模范数最小化处理允许数据个数很少。若数据个数为偶数且大于5,则可以用基于区间数的模糊范数法提取原始数据序列的随机信息和尺度信息两个子序列。用模糊范数法分别处理这两个子序列后,再用区间数运算法则对处理结果进行融合,就可以评估总体的属性参数。若直接用模糊范数法,则数据个数可以少至3个。
提出最大熵自助法,以解决试验次数很少,但每次试验的数据个数比较多时的静态评估问题。首先建立各次试验数据的最大熵概率分布,然后用自助再抽样原理对各次试验数据得到的最大熵概率分布信息进行融合,最后得到总体的稳定状态描述,实现从个体参数识别到总体属性的推断。最大熵自助法允许试验次数可以少至3次。
有机融合灰预测GM(1,1)和自助法的优点,建立了灰自助法,以实现乏信息试验的动态评估。该方法突破了灰预报对原始数据有特殊要求的禁区,完善了区间估计的自助法。在概率分布未知和缺乏趋势项先验信息条件下,用6个指标(动态估计真值、动态估计真值的均值、估计真值变动量、动态估计区间、动态波动范围、动态波动范围平均值)全面描述系统的瞬间状态和整体特征,有效分离趋势项并实施动态评估,提高了预报的可靠性。灰自助法需要的当前数据个数少至3个。
提出两个数据序列的灰关系及其灰假设检验方法,以解决灰色系统理论要求至少有3个数据序列才能构成灰关联空间的问题。对于排序和非排序假设检验两个模型,前者用于和数据前后顺序无关的属性检验,后者则用于和数据前后顺序有关的属性检验。灰关系超越了灰关联序空间的限制,将灰关联分析提升为灰假设检验。灰关系允许小样本数据,对概率分布无任何要求,弥补了统计假设检验方法的不足。灰假设检验允许数据序列个数少至2个,每个数据序列的数据个数可以少至3个。
对所提出的方法进行了计算机仿真验证,涉及到的数据序列有正态分布,瑞利分布,均匀分布和三角分布随机变量;混合分布的平稳随机过程;趋势项;各种分布和趋势项混合的非平稳随机过程。验证结果表明,所提出的方法能比较准确地描述各种随机变量、平稳随机过程以及非平稳随机过程的瞬间状态和整体特征,有效分离趋势项,可靠实施乏信息评估。
对所提出的方法进行了试验验证,涉及到滚动轴承圆度误差,摩擦力矩,振动和噪声。验证结果表明,在没有概率分布与趋势项先验信息而只有很少数据的条件下,评估结果与试验结果很吻合,置信水平均达到95%以上。
所提出的方法还在捷联惯性测量组合的误差系数检验,武器系统效能检验与温度仪表数据分析等领域中得到很好应用。
总体而言,所提出的方法从不同侧面研究乏信息系统,形成了一个完整的评估体系。该评估体系的评估结果与实际情况一致,一般相对误差小于15%,与统计法、灰GM(1,1)、自助法、最大熵法以及算术平均法等流行方法比较,相对误差减少了9%～35%,取得了更好的效果。
Poor information means incomplete and insufficient information for the characteristic presented in the subject investigated.Based on synthesized analysis of available findings,some problems of information poor system theory applied in rolling bearing test analysis are studied in the dissertation.It is difficult to get large numbers of data in the process of measurement and performance analysis for some rolling bearings.For example,in development and manufacture of new type bearings for space using or some special type bearings,much less bearings can be made a trial because of many species and small quantity,every time only ten-odd or even several bearings are required,and prevailing methods are not used to answer the questions about test analysis and evaluation of this kinds of bearings for lack of prior information about probability distribution and trends.
Considering unknown probability distribution and very small data,two methods viz.the fuzzy norm method and the fuzzy norm method based on interval number are advanced for static evaluation.Using membership function and theory of a minimum of maximum module norm,these two methods are able to obtain a probability distribution function and then make a model for interval evaluation under the given confidence level,without any infbrmation about probability distribution of a raw data series.The number of the data can be very small for a minimum of maximum module norm.If the number of the data is even and bigger than 5,then two sub-series of random information and measure information can be extracted from the raw data series using the fuzzy norm method based on interval number.After processing these two sub-series via the fuzzy norm method,the results processed are fused by algorithm of interval numbers and the parameters of attribute of population can be evaluated.In addition,the number of the data can be down to 3 if direct using the fuzzy norm method.
The maximum entropy method is proposed to resolve the problem about static evaluation under the condition that the number of test times is small while every time the number of test data is much.First the maximum entropy distribution of each test data is established,then information about the maximum entropy distributions of all tests is fused by bootstrap resampling,and lastly the inference of attribute of population is drawn from identifying the parameters of every individual,describing the stable state of population.Investigation shows that the number of test times can be down to 3.
Organically fusing the excellences of grey forecasting modeling GM(1,1) and bootstrap,the grey bootstrap method is established to develop dynamic online evaluation of tests with poor information.It improves the bootstrap of interval estimate and breaks through forbidden zone with special requirements for raw data in grey system theory.Under the condition of unknown probability distribution and of trends without any prior information,the transient state and the global characteristic of a system are described fully,trends are separated effectively, dynamic evaluation is actualized,and reliability is increased,by developing 6 indexes,viz.dynamic estimated truth,mean of dynamic estimated truth,change quantity of estimated truth,dynamic estimated interval,dynamic fluctuant range, mean of dynamic fluctuant range.And the number of the current data can be down to 3 using the grey bootstrap method.
The grey relation between two data series and its grey hypothesis testing are introduced to resolve the problem of the grey relational space which can be structured only under the condition at least 3 data series.There are two models:one is collating sequence grey hypothesis testing and the other is non-collating sequence grey hypothesis testing.The former can verify attribute irrelative to sequencing of the data,and the latter can verify attribute relative to sequencing of the data.The grey relation goes beyond the limit of the grey relational space and advances grey relational analysis to grey hypothesis testing.In addition,the grey relation can supply some of the gaps in statistic hypothesis testing,because it allows small sample data without any requirements for probability distribution.And the number of the data series can be down to 2 and the number of the data in each data series can be down to 3.
The various methods proposed are validated by computer simulation.The data series simulated deal with random variables such as normal distribution,Rayleigh distribution,uniform distribution,and triangular distribution,deal with stationary random process of mixing distributions,deal with trends,and also deal with nonstationary random process of mixing various distributions and trends.The verified results show that the methods proposed is able to describe the transient state and the global characteristic of all kinds of random variables,of stationary random process,and of nonstationary random process,with effectively separating trends and reliably actualizing evaluation under the condition of poor information.
The various methods proposed are validated by engineering experiments. Roundness error,friction torque,vibration and noise of rolling bearings are considered.The verified results show that the methods proposed are able to evaluate rolling bearing tests,without any prior information about probability distribution and trends,only with very small data.And the confidence level can be bigger than 95%.
The methods proposed also are applied to the fields such as test of the error coefficient of the strapdown inertial measurement unit and the effectiveness check of weapon systems,and data analysis of the temperature meters.
On the whole,investigating of information poor system from different view sides,an integrated evaluation system is formed with the above methods proposed. The results using this evaluation system are coincident with the real truth of the subject investigated and the relative errors usually are less than 15%.This evaluation system can obtain better results by a 9%～35%decrease of the relative errors as compared with the prevailing methods such as statistics,grey forecasting modeling GM(1,1),bootstrap,and arithmetic mean method etc.
引文
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