توسعه یک مدل رتبه کاسته بدون معادله مبتنی بر الگوهای متفاوت استخراج ویژگی‌ روی مجموعه داده انتقال حرارت دو بعدی پایا

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی کامپیوتر و فناوری اطلاعات، دانشگاه قم، قم، ایران.

2 گروه مهندسی مکانیک، دانشگاه قم، قم، ایران.

چکیده

با توجه به هزینه زمانی و محاسباتی بالای روش‌های حل مستقیم یا عددی معادلات دیفرانسیل حاکم بر پدیده‌ها، پژوهش حاضر به ارائه روشی بدون معادله و مبتنی بر الگوریتم‌های یادگیری عمیق با استفاده از روش‌های کاهش بعد می‌پردازد. دو روش تحلیل مؤلفه‌های اصلی (خطی) و خودرمزنگار (غیرخطی) برای شبیه‌سازی پدیده انتقال حرارت پایا با استفاده از مجموعه داده‌های انتقال حرارت پایای دو بعدی در ابعاد 64×64 و 128×128 بکار رفت و از طریق ابزارها و کتابخانه‌های موجود در محیط پایتون پیاده‌سازی شد. طبق نتایج حاصل، در کاهش مرتبه شدید، خودرمزنگار و در کاهش مرتبه جزئی، تحلیل مؤلفه‌های اصلی دقت بالاتری دارد. همچنین خروجی‌های حاصل از مدل رتبه کاسته پیشنهادی با شبیه‌سازی‌های حاصل از مدلی مبتنی بر شبکه عصبی کانولوشنی با تعداد لایه‌ها و فیلترهای متعدد مقایسه شد. نتایج حاصل از شبیه‌سازی توزیع دمای پایا برحسب خطای میانگین مربعات (MSE) با استفاده از مدل‌های مبتنی بر تحلیل مؤلفه‌های اصلی، خودرمزنگار و مدل مبتنی بر شبکه‌های عصبی کانولوشنی در ابعاد 64×64 به ترتیب برابر با 4-10×1.617، 6-10×2.528 و 0.015 و در ابعاد 128×128 نیز برابر با 4-10×2.046، 6-10×7.253 و 0.0058 درجه سلسیوس در هر پیکسل است. بنابراین، مدل‌های رتبه کاسته پیشنهادی به‌ویژه مدل مبتنی بر روش خودرمزنگار از دقت بسیار بالاتری نسبت به مدل مبتنی بر شبکه‌های عصبی کانولوشنی برخوردار می‌باشد.

کلیدواژه‌ها

عنوان مقاله [English]

Development of an equation-free reduced-order model based on different feature extraction patterns on the two-dimensional steady-state heat transfer dataset

نویسندگان [English]

  • Somaye Afzali 1
  • Mohammad Kazem Moayyedi 2
  • Faranak Fotouhi 1
1 Department of Computer Engineering and Information Technology, University of Qom, Qom, Iran.
2 Department of Mechanical Engineering, University of Qom, Qom, Iran.
چکیده [English]

Due to the high computational cost and time of the direct or numerical methods of the partial differential equations governing phenomena, this paper proposes an equation-free model based on deep learning algorithms using dimension reduction methods. Two methods of the principal component analysis (linear) and the autoencoder (nonlinear) were used to simulate the steady-state heat transfer phenomenon using the two-dimensional steady-state heat transfer dataset of size 64×64 and 128×128. These methods were implemented using the tools and libraries available in the Python environment. According to the results, autoencoder has higher accuracy in reduction of order to very low dimensions, while principal component analysis has a higher accuracy in reduction of order to very high dimensions. Additionally, the outputs of the proposed reduced-order model were compared with simulation results obtained from a model based on convolutional neural network with a large number of layers and filters. The simulation results of the temperature distribution of the steady-state heat transfer phenomenon in terms of mean square error (MSE) using principal component analysis, autoencoder, and convolutional neural network-based models at dimensions of 64×64 were equal to 1.617×10-4, 2.528×10-6, and 0.015 °C per-pixel, respectively. At dimensions of 128×128, the results were equal to 2.046×10-4, 7.253×10-6, and 0.0058 °C per-pixel, respectively. Therefore, the proposed reduced-order models, especially the autoencoder-based model, have significantly higher accuracy than the convolutional neural network-based model.

کلیدواژه‌ها [English]

  • Steady-state heat transfer modeling
  • Dimensionality reduction
  • Principal component analysis
  • Autoencoder
  • Mean squared error

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سابقه مقاله

  • تاریخ دریافت: 01 خرداد 1400
  • تاریخ بازنگری: 21 مهر 1400
  • تاریخ پذیرش: 01 آذر 1400

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