A Multi-Optional Hybrid Functions Entropy as a Tool for Transportation Means Repair Optimal Periodicity Determination

Abstract

The paper considers theoretical explanation and construction of some mathematical models of a transportation mean operational process in reference to maintenance optimal periodicity. The important finding is that the objectively existing engineering transportation means maintenance optimal periodicity is determined in the different from the probabilistic methods way. There is a scientifically proven explanation for the mentioned above periodicity optimization with the help of the specially introduced hybrid-optional effectiveness functions distribution. The developed doctrine uses the entropy paradigm conditional extremization approach. This contribution allows obtaining the wanted optimal periodicities sidestepping the related states probabilities determination and their further extremization. The essential breakthrough of the developed doctrine is that the optional objective effectiveness functions, in such a case, are the corresponding combinations of the intensities of the studied system’s possible transitions from state to state, which relates with the set of the considered operational options. Corresponding limit solutions for the zero-to-zero ratio indeterminate forms are analyzed. Theoretical speculations are illustrated with the example calculation experiments. The necessary diagrams are plotted.

The User-Preferred Optimal Flight Parameters in an Active Navigational System in a Multi-Alternative Situation

“…It is considered a certain kind of a hybrid combination of the Gibbs-Jaynes principle [17][18][19] with the classical theory of calculus of variations embodied in monograph [1], implemented in works [21][22][23][24][25][26][27], and proposed to application for aircraft control systems in aspects reflected in [2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

“…Therefore, it is proposed to model mathematically the following situation in the framework of SeMP [1,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

“…Then: (15) At the given problem setting for the second alternative individual's subjective preference function first complete derivative with respect to time: (16) Since the preferences functions do not depend upon time t in the explicit view, then: (17) hence, instead of ( 16) with taking into consideration condition of (17), one can use just: (18) Where: (19) Thus for equation ( 19): (20) And (21) Therefore for equation ( 21) the proposed approach yields: (22) Now, substituting the obtained expressions of ( 20) and (22) for their corresponding values into the complete derivative equation ( 18) satisfactorily for the presented problem setting, one can have: (23) Substituting the result of ( 23) for its corresponding value into the second equation of ( 15), it gives: (24) Canceling in the expression of ( 24) for π ≠ 0, one can get: (25) And from (25) at x ≠ 0.…”

“…The advantages of such approach were demonstrated in works [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Hybrid-Optional Effectiveness Functions Entropy Conditional Extremization Doctrine Contributions into Engineering Systems Reliability Assessments

“…Nevertheless, evolution of scientific approaches has no end. It looks prospective to implement the developed Doctrine to the problems discussed in references [31][32][33][34] since the recent research [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] gives a good background for that.…”