Research Of Evaluation Method And Its Application Technology In Rolling Bearing Test With Poor Information

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.