Introduction. The study of heat exchange transients in the climate system “Heater-Ventilator-Room”, when ventilator capacity varies step-wise, is presented. The construction of functional relations between inputs and outputs of the system is the object of special attention. This allows for a non-parametric identification of impulse responses in the system for simulation and control.
Materials and methods. The climate system is represented by a combination of several different-type elements with step inputs and experimental data as outputs. Mathematical models of the elements are governed by Volterra integral equation of the 2nd kind. Solution of this equation is an ill-posed problem, and specifics of identification experiments do not allow applying computational methods of classical regularization algorithms. A non-parametric identification of impulse responses for the elements is performed by the authors’ stable algorithm with due regard for real technical systems specifics. The algorithm is founded on stable differentiation by smoothing cubic splines with optimal smoothing parameter estimation and special type boundary conditions.
Results. Non-parametric identification algorithm is adapted for the investigated climate system. The inverse problems of impulse responses identification and the direct problems of heat flux reactions prediction are solved. A high convergence of theoretical and experimental data is shown.
Conclusions. The behavior of the transients is predictable for the climate system under the particular operation mode. The algorithm proposed takes proper account of practical problems specifics. The results obtained suggest the efficiency of the algorithm for applied identification problems solutions in real complex technical systems.
The thermal control system “Heater-Fan-Room” is represented by three different-type interconnected simpler subsystems. In this paper, a “black-box” whose structure is not specified is used as a mathematical model of the system and subsystems due to complexity of physical processes proceeding in these subsystems. For stationary linear systems, the connection between an input and an output of the “black-box” is defined by the Volterra integral equation of the first kind with an undetermined difference kernel also known as impulse response in the automatic control theory. In such a case, it is necessary to evaluate an unknown impulse response to use the “black-box” model and formulate all subsystems and the system as a whole. This condition complicates significantly the solution search of non-parametric identification problems in the system because an output of one subsystem is an input of another subsystem, so active identification schemes are unappropriated. Formally, an impulse response evaluation is a solution of the integral equation of the first kind for its kernel by registered noise-contaminated discrete input and output values. This problem is ill-posed because of the possible solution instability (impulse response evaluation in this case) relative to measurement noises in initial data. To find a unique stable solution regularizing algorithms are used, but the specificity of the impulse response identification experiment in the “Heater-Fan-Room” system do not allow applying computational methods of these algorithms (a system of linear equations or discrete Fourier transformation). In this paper, the authors propose two specific identification algorithms for complex technical systems. In these algorithms, impulse responses are evaluated using first derivatives of identified system signals that are stably calculated by smoothing cubic splines with an original smoothing parameter algorithm. The results of the complex “Heater-Fan-Room” system modeling and identification prove the efficiency of the algorithms proposed. Acknowledgments: The reported study was funded by RFBR, project number 20-38-90041.
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