Optimal Estimation of the Motion Parameters of a Precision Rotating Stand by Maximum Likelihood Method

Ermakov, R. V.; Seranova, A. A.; Львов, А. А.; Kalikhman, D. M.

doi:10.1007/s11018-019-01598-x

Cited by 10 publications

(2 citation statements)

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“…The simplest classical one is the local non-adaptive random search algorithm [1,3,7], shown in figure 1.…”

Section: Developing the Search For Optimal Solution Proceduresmentioning

confidence: 99%

Control algorithm for decision making in multi-criteria optimization problems

Grishko

2022

J. Phys.: Conf. Ser.

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The main feature of the multi-criteria optimization of the design processes of complex electronic devices is that they are all interconnected, heterogeneous in nature and, as a rule, non-linear. That is, by changing some of them by varying the corresponding parameters, we inevitably change other parameters of the system, and not always in the right direction. The purpose of the work is to propose a way to organize the procedure for finding the optimal solution to multicriteria design problems. When developing and creating new schemes, structures and systems, the task of determining the optimal values of the parameters of the designed technical device or system is reduced to the task of finding the extremum of a certain function, called the quality function. Usually, it is a non-linear function of many independent variables, which, as a rule, cannot be investigated by analytical methods. In this situation, it is advisable to search for a solution to the problem using special algorithms. At the early stages of designing complex radio electronic devices, an algorithm for finding the optimal solution based on the application of search optimization theory methods is proposed. The paper describes the procedure for finding the optimal solution, the distinctive feature of which is that during the search for a solution, information is accumulated and a search direction vector is constructed. This vector offers options for changing weights for subsequent search procedures. The algorithm developed on its basis is used in the information system for the complex analysis of the designs of radio-electronic facilities. The use of random search provides the algorithm with global properties, reduces the number of objective function calculations by one step, which is especially noticeable with a large number of optimized parameters. Allows you to quite simply include any restrictions on the set of valid values of the vector of optimized parameters, which is not always possible when using regular search methods. The proposed algorithm is simply tuned to search for a global extremum by selecting the appropriate parameters. For each specific case, there are some optimal ratios of the values of these algorithm parameters, which, when searching for a solution, reduce the number of working steps. The developed algorithm is less critical to the optimal values of its own parameters, which makes it much easier to tune it when solving practical problems of optimizing design processes.

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“…The simplest classical one is the local non-adaptive random search algorithm [1,3,7], shown in figure 1.…”

Section: Developing the Search For Optimal Solution Proceduresmentioning

confidence: 99%

Control algorithm for decision making in multi-criteria optimization problems

Grishko

2022

J. Phys.: Conf. Ser.

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“…When the prior information of the parameters identified is unknown, the maximum likelihood method is often used to identify structural parameters or load parameters. In the maximum likelihood method, the parameter value when the maximum value is taken by the likelihood function is used as the identification result, and the corresponding confidence interval is calculated [8][9][10]. Liu et al [11] proposed the maximum likelihood method based on the sensitivity matrix method (SMM), which is suitable for dealing with the uncertainty inverse problems with insufficiency and imprecision in the input and/or output parameters.…”

Section: Introductionmentioning

confidence: 99%

Eccentricity Parameters Identification for a Motorized Spindle System Based on Improved Maximum Likelihood Method

Mao

et al. 2020

Shock and Vibration

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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.

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