dsaitЦифровые решения и технологии искусственного интеллектаDigital Solutions and Artificial Intelligence Technologies3033-7097Финансовый университет при Правительстве Российской Федерации10.26794/3030-7097-2026-2-3-41-50dsait-74Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ, ЧИСЛЕНЫЕ МЕТОДЫ И КОМПЛЕКСЫ ПРОГРАММMATHEMATICAL MODELING, NUMERICAL METHODS AND SOFTWARE PACKAGESИнженерия данных и машинное обучение для решения обратной задачи по результатам CAE-моделированияData engineering and machine learning for solving the inverse problem based on CAE simulation resultshttps://orcid.org/0000-0002-8621-0724ТулуповаО. П.TulupovaO. P.

Ольга Павловна Тулупова — кандидат технических наук, доцент кафедры ИТ факультета информационных технологий и анализа больших данных

Москва

Olga P. Tulupova — Cand. Sci. (Tech.), Assoc. Prof. of Artificial Intelligence Department of the Faculty of Information Technology and Big Data Analysis

Moscow

optulupova@fa.ruhttps://orcid.org/0009-0006-6082-1347ЖолобоваГ. Н.ZholobovaG. N.

Галина Николаевна Жолобова — кандидат технических наук, доцент кафедры ИТ, заместитель заведующего кафедрой информационных технологий по учебной работе факультета информационных технологий и анализа больших данных

Москва

Galina N. Zholobova — Cand. Sci. (Tech.), Assoc. Prof., Deputy Head of Artificial Intelligence Department for acadtmic affairs of the Faculty of Information Technology and Big Data Analysis

Moscow

nzholobova@fa.ruhttps://orcid.org/0000-0002-0362-4121ЕникеевФ. У.EnikeevF. U.

Фарид Усманович Еникеев — доктор технических наук, профессор кафедры вычислительной техники и инженерной кибернетики

Уфа

Farid U. Enikeev — Dr. Sci. (Tech.), Prof. Department of Computer Science and Engineering Cybernetics

Ufa

kobros@yandex.ruФинансовый университет при Правительстве Российской ФедерацииРоссияFinancial University under the Government of the Russian FederationRussian FederationУфимский государственный нефтяной технический университетРоссияUfa State Petroleum Technological UniversityRussian Federation202607092026234150Copyright © Тулупова О.П., Жолобова Г.Н., Еникеев Ф.У., 20262026Тулупова О.П., Жолобова Г.Н., Еникеев Ф.У.Tulupova O.P., Zholobova G.N., Enikeev F.U.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.digitarin.ru/jour/article/view/74

Применение машинного обучения в решении прямых задач прогнозирования становится альтернативой применению ресурсоемкого конечно-элементного моделирования. Однако применение машинного обучения для решения обратной задачи в литературе практически не рассматривается. Традиционные подходы основаны на итерационных расчетах, которые требуют многократных прогонов моделей и не работают в реальном времени, что ограничивает создание цифровых двойников.

Цель исследования — решение обратной задачи путем разработки и верификации модели гауссовской регрессии (GPR) для определения параметров K и m по геометрии готового изделия на основе конечно элементных данных ANSYS. В качестве источника данных использовались результаты конечно-элементного моделирования процесса сверхпластической формовки в CAE-пакете ANSYS. Было выполнено 120 конечно-элементных симуляций, по 40 для каждого из трех режимов давления. Общий объем данных, полученных из решений ANSYS, составил 7571 строку. Были разработаны две GPR-модели. Одна для определения K с ядром Matern, вторая для m с ядром RBF. Масштабирование данных выполнялось методом RobustScaler. Показано, что замена RBF-ядра на ядро Matern (ν = 2,5) снижает медианную относительную неопределенность прогноза для параметра K с 50 до 16%. На тестовой выборке получены следующие метрики качества: R2 = 0,91 для K и R2 = 0,92 для m, относительная среднеквадратичная ошибка составляет 20% для K и 7% для m. Выполненный корреляционный анализ выявил наиболее значимое влияние давления формовки на параметр K (r = –0,32).

Разработанная модель может быть использована для неразрушающего контроля качества, встраивания в цифровые двойники и оптимизации режимов сверхпластической формовки.

The use of machine learning in solving direct forecasting problems is becoming an alternative to the use of comprehensive finite element modeling. However, the solutions of inverse problem by means of machine learning is conventionally not considered in the literature. Traditional approaches are based on iterative calculations that require multiple runs of models and do not work in real time, which limits the creation of digital doubles.

The objective of this study is to solve the inverse problem by developing and verifying a Gaussian regression (GPR) model for determining the strain rate sensitivity index of superplastic material from the results of bulge tests based on the results of finite element calculations. The results of finite element modeling of the superplastic forming process in the ANSYS CAE package were used as a data source. 120 finite element simulations were performed, 40 for each of the three pressure modes. Two GPR models have been developed. One is for defining K with the Matern kernel, the second is for m with the RBF kernel. It is shown that replacing the RBF kernel with the Matern kernel (ν = 2,5) reduces the median relative uncertainty of the forecast for parameter K from 50 to 16%. The following quality metrics were obtained on the test sample: R2 = 0.91 for K and R2 = 0.92 for m, the relative RMS error is 20% for K and 7% for m.

The developed model can be used for non-destructive quality control, integration into digital twins, and optimization of superplastic forming processes.

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The authors declare that there are no conflicts of interest present.