Calculation of parameter estimates for nested piecewise linear regression with cross-links

Abstract

The paper provides a brief overview of publications on the development and analysis of complex systems of nonlinear model structures containing various types of cross-links between input factors in mathematical modeling. In particular, the paper considers: description of the specifics of interaction between structural divisions of an organization in order to minimize possible resource movements using a mixed integer nonlinear programming model for discrete and continuous problem statements; a model of continuous thickening of flocculated suspensions in an ideal cylindrical thickener; a model for predicting the behavior of the torque of semi-rigid connections in space structures; models of motion of an autonomous mobile robot of variable configuration taking into account the relationship of the dynamic parameters of a mechanical system; a mathematical model for determining the optimal location of the reinforcement system of a chord truss on high-rise buildings; a model for studying the dynamic behavior of a combined cable-stayed bridge system under the action of moving loads; models of hybrid composite frame systems taking into account their structural stability, constructability, economic feasibility, environmental friendliness and energy efficiency. The paper formulates the problem of calculating estimates of unknown parameters of piecewise linear regressions with cross-links of the first and second types based on the application of the least absolute values method, which is reduced to linear-Boolean programming problems. In this case, the cross-link nature of the connections is achieved by the possibility of simultaneous single or multiple entries of the same independent variables in different internal sums, minima and maxima of nested models. After solving the corresponding linear-Boolean programming problems, the values of the Boolean variables in the considered nested model indicate the order of operation of the external and internal minima and maxima, as well as their sums. A numerical illustrative example is solved.