Design of experiment for sensitivity analysis of mathematical models from different classes
- Autores: Sysoev A.S.1, Saraev P.V.1, Pogodaev A.K.1
-
Afiliações:
- Lipetsk State Technical University
- Edição: Nº 117 (2025)
- Páginas: 103-118
- Seção: Systems analysis
- URL: https://bakhtiniada.ru/1819-2440/article/view/360559
- DOI: https://doi.org/10.25728/ubs.2025.117.5
- ID: 360559
Citar
Texto integral
Resumo
The article focuses on design of experiment for conducting Sensitivity Analysis of mathematical models used in forecasting and controlling complex systems. Special attention is given to cases where factors are unevenly distributed in space, which is typical for problems with nonlinear dependencies, local features, and high computational complexity. In such situations, the application of mathematical remodeling is justified, whereby models with a complex structure are replaced (remodeled) by objects of a selected remodeling class that have a predefined structure, which allows unificating system research. The purpose of the study is the development and comparison of the design of experiment strategies aimed at improving the efficiency of Sensitivity Analysis. Methods adapted to uneven data distribution are considered. The foundation of sensitivity research is the analysis of finite fluctuations, built upon the application of the Lagrange mean value theorem. Numerical experiments on a test function and its neural network approximation confirmed that the proposed algorithms (central composite design and an adaptive Latin hypercube sampling-based method) enable highly accurate identification of significant factors, aligning with classical methods (Sobol indices, Morris method), while significantly reducing computational costs. It is shown that the remodeling approach refines sensitivity estimates and ensures a unified analysis procedure for models of complex structure.
Palavras-chave
Sobre autores
Anton Sysoev
Lipetsk State Technical University
Email: ysoev_as@stu.lipetsk.ru
Lipetsk
Pavel Saraev
Lipetsk State Technical University
Email: psaraev@yandex.ru
Lipetsk
Anatoly Pogodaev
Lipetsk State Technical University
Email: pak@stu.lipetsk.ru
Lipetsk
Bibliografia
1. АДЛЕР Ю.П., МАРКОВА Е.В., ГРАНОВСКИЙ Ю.В. Пла-нирование эксперимента при поиске оптимальных усло-вий. – М.: Наука, 1976. – 279 с. 2. СОБОЛЬ И.М., СТАТНИКОВ Р.Б. Выбор оптимальных па-раметров в задачах со многими критериями. – М.: Дрофа,2006. – 176 с. 3. ЩЕГЛЕВАТЫХ Р.В., СЫСОЕВ А.С. Исследование ней-росетевой модели обнаружения аномальных наблюдений вмассивах данных // Прикладная математика и вопросыуправления. – 2021. – №1. – C. 23–40. 4. HORIGUCHI A., PRATOLA M.T., SANTNER T.J. Assessingvariable activity for Bayesian regression trees // ReliabilityEngineering & System Safety. – 2021. – No. 207. – P. 107391. 5. PETELET M., IOOSS B., ASSERIN O. et al. Latin hypercubesampling with inequality constraints // AStA – Advances inStatistical Analysis. – 2010. – No. 94(4). – P. 325–339. 6. SALTELLI A. Global Sensitivity Analysis: the Primer. –Chichester: John Wiley & Sons, 2008. 7. SARAEV P., BLYUMIN S., GALKIN A. et al. Mathematicalremodeling concept in simulation of complicated variablestructure transportation systems // Transportation ResearchProcedia. – 2020. – No. 45. – P. 475-482. 8. SIN G., GERNAEY K.V. Improving the Morris methodfor sensitivity analysis by scaling the elementary effects //Computer aided chemical engineering. – 2009. – No. 26. –P. 925–930. 9. SOBOL I.M. Global sensitivity indices for nonlinearmathematical models and their Monte Carlo estimates //Mathematics and computers in simulation. – 2001. – No. 1–3. –P. 271–280. 10. SYSOEV A. Sensitivity analysis of mathematical models //Computation. – 2023. – No. 11(8). – P. 159. 11. SZPISJAK-GULYAS N., AL-TAYAWI A.N., HORVATH Z.H.et al. Methods for experimental design, central compositedesign and the Box–Behnken design, to optimise operationalparameters: A review // Acta Alimentaria. – 2023. – No. 52(4). –P. 521–537.
Arquivos suplementares
