Gearbox Fault Diagnosis Based On Rough Sets Theory

Gearbox is one of the most important transmission parts in the mechanical systems, but, for some uncertain reasons, the failure rate is higher, the vibration signal shows nonlinear and nonstationary, fault type and location as well as extent affect the characteristic parameters greatly. While monitoring and diagnosing the gearbox, selecting monitoring points improperly usually fails to gain the fault information effectively, determine the fault position, extract sensitive characteristic parameters and obtain high fault recognition rate. The method of local wave decomposition(LMD) could decompose the nonstationary signal adaptively and map to the time-frequence analysis plane, which could display signals in time domain and frequence domain simultaneously. Attributes reduction technology in rough sets (RS) could optimize the characteristic parameter set and extract the sensitive fault characteristic parameters. Least squares support vector machine (LSSVM) has good function approximation and high pattern recognition ratio. A method of combining RS with LSSVM through studying on LWD and RS deeply is proposed, intelligent fault diagnosis system of gearbox based on RS and LSSVM is established. The main work is as follows:(1) LWD is employed to process the vibration signal of gearbox and extract the initial characteristic parameters based on analying the vibration property. A method of combining mirror extension with window function is used to relieve endpoint effect, ensemble empirical mode decomposition (EEMD) method is utilized to solve the mode mixing problem effectively, experiments show that these methods have achieved good results in fault signal decomposition. According to the measurable indicators of fault characteristic parameter set, it is proposed to use the rms values of the fault characteristic parameters to measure the stability and the minimal mean difference of each characteristic parameters in six working conditions to measure the sensitivity. The normalized energy and approximate entropy characteristic parameter sets based on EEMD are extracted in the paper, calculating results show that the sensitivity of the former and the latter are basically the same, but the stability is superior to the latter, so the normalized energy characteristic parameter set would be used for gearbox fault diagnosis. (2) A global dynamic optimization algorithm for discretization based on improved Naive Scaler is proposed. The process of Naive Scaler algorithm is improved so that all breakpoints which warranties indiscernible relation would be got. The method of selecting breakpoints from the candidate set dynamically through separating the samples evenly by breakpoints and increasing the breakpoints gradually ensures the least breakpoints under the condition of keeping the classification ability of the whole information system. The experimental results show that the algorithm got the least breakpoints by comparison with other algorithms, which reflects the superiority in discretization aspects.(3) A new reduction algorithm based on condition equivalence classifications is proposed to delete the redundant features. The minimal attributes reduction set can be got through finding the attributes in the rest of the properties which can distinguish the samples in the condition equivalence classifications not assigned to decision classes properly only by the core attributes. Attribute reduction algorithms based on heuristic information can not guarantee the minimal attributes reduction set, experimental results show that computational complexity of the algorithm proposed in the paper is low relatively, which improves the reduction efficiency.(4) A method based on condition attribute reduction technology in Rough Sets is proposed to optimize the sampling points. The minimal attribute reduction sets of six fault monitoring points fuse into one big decision table for reduction, the classification ability of every monitoring point is determined according to the frequency of fault characteristic parameters in each point which appear in the final reduction set of the big decision table. Experimental results show the method needs neither modeling for the monitoring object nor dynamics analysis, but selects the effective sampling point directly according to the relationship between the fault characteristic parameters and fault types through processing the vibration signal, which is convenient and efficient to optimize the measuring points.(5) The method of extracting decision rules based on rough set theory does not possess the ability to learn and induction, so fault pattern recognition rate is low relatively. Attribute reduction technique in rough set theory could extract sensitive fault characteristic parameters, least squares support vector machine has strong pattern recognition ability, so in order to make full use of their advantages in the characteristic parameter extraction and pattern recognition, the intelligent fault diagnosis system is constructed based on RS and LSSVM. The theoretical and practical results have proved that the system improves the gearbox fault diagnosis performance and provides a relatively generic solution for processing and recognizing nonlinear and non-stationary fault signal.