Стохастична багатокритеріальна оптимізація систем мікроклімату будівель з урахуванням невизначеності вхідних параметрів

Abstract

The paper is devoted to the analysis of multi-objective optimization methods for building microclimate systems under irreducible uncertainty of input parameters — weather and climatic conditions, occupancy patterns, actual thermal characteristics of envelopes and equipment. A brief overview of main formalization approaches is given: scalarization of objective functions, Pareto-dominance methods based on evolutionary algorithms (NSGA-II, SPEA2), robust optimization using min-max and Taguchi criteria, and fuzzy-set models. It is shown that deterministic design solutions obtained for nominal parameter values often lose their optimality in real operating conditions due to the nonlinear and asymmetric influence of disturbances on objective functions and constraints. The main focus is on the stochastic formulation with chance constraints, which allows explicit control of the reliability level of normative microclimate requirements. The mathematical framework is presented: replacement of deterministic constraints by their probabilistic analogues, numerical implementation using the Monte Carlo method with Latin hypercube sampling, the Taguchi mean-variance criterion, and quantile-based objectives. A case study is performed for the central supply-exhaust ventilation system of an administrative building with a floor area of 2000 m² in the climatic conditions of the Vinnytsia region. Monte Carlo simulation with N = 5000 realizations is used to compare two solutions: the deterministic one, optimal for nominal parameter values, and the stochastic one, obtained under a chance constraint on indoor carbon dioxide concentration. It is demonstrated that the stochastic solution, at the cost of only a 7 % increase in the expected objective function value, provides more than a twelvefold reduction in the probability of normative air quality violation. The dependence of optimal control variables and minimum expected objective function on the specified reliability level is constructed, enabling the designer to make an informed trade-off between energy efficiency and reliable fulfillment of normative requirements. The results can be used at the design and optimization stages of HVAC systems for public buildings