TAKING INTO ACCOUNT A PRIORI INFORMATION ON PARAMETER IN MAXIMUM LIKELIHOOD METHOD

2016 ◽  
Vol 13 (3) ◽  
pp. 403-409
Author(s):  
Viktor V. Garbaruk ◽  
◽  
Viktor N. Fomenko ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wengui Mao ◽  
Chaoliang Hu ◽  
Jianhua Li ◽  
Zhonghua Huang ◽  
Guiping Liu

As a kind of rotor system, the electric spindle system is the core component of the precision grinding machine. The vibration caused by the mass imbalance is the main factor that causes the vibration of the grinding machine. Identifying the eccentricity parameters in an electric spindle system is a key issue in eliminating mass imbalances. It is difficult for engineers to understand the approximate range of eccentricity by experience; that is, it is difficult to obtain a priori information about eccentricity. At the same time, due to the geometric characteristics of the electrospindle system, the material factors and the randomness of the measurement response, these uncertain factors, even in a small case, are likely to cause large deviations in the eccentricity recognition results. The search algorithm used in the maximum likelihood method to identify the eccentricity parameters of the electrospindle system is computationally intensive, and the sensitivity in the iterative process brings some numerical problems. This paper introduces an Advance-Retreat Method (ARM) of the search interval to the maximum likelihood method, the unknown parameter increment obtained by the maximum likelihood method is used as the step size in the iteration, and the Advance-Retreat Method of the search interval is used to adjust the next design point so that the objective function value is gradually decreasing. The recognition results under the three kinds of measurement errors show that the improved maximum likelihood method improves the recognition effect of the maximum likelihood method and can reduce the influence of uncertainty factors on the recognition results, and the robustness is satisfactory.


2016 ◽  
Vol 29 (2) ◽  
pp. 119 ◽  
Author(s):  
Evgeny V. Mavrodiev

Three-taxon statement matrices can be analysed using the maximum-likelihood method. In the present paper, it is demonstrated that groups based solely on putative reversals are always recognisable after maximum-likelihood analysis of three-taxon statement matrices, even without a priori recoding of the putative reversals as new character states or fractional weighting of three-taxon statements. Parametric implementations of three-taxon statement analysis still require more investigation. However, it must be highlighted that a focus on the set of hypotheses, rather than on the ‘actual data’, is required.


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