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.

10.22052/scj.2021.242830.0

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 4-10×617/1، 6-10×528/2 و 015/0 و در ابعاد 128×128 نیز برابر با 4-10×046/2، 6-10×253/7 و 0058/0 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 Approaches of Feature Extraction for Two-dimensional Steady State Heat Transfer Data Set

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]

Since the formation and Direct solving the governing equations requires high time and computational cost, this study seeks to provide an equation free model based on deep learning algorithm that simulates steady state heat transfer in two-dimensional space and a relatively large size using order reduction method. Principal component analysis is a linear method and autoencoder is a nonlinear methods. The results of comparing their performance on different data sets showed that in reducion of order to very low dimensions, autoencoder and in reducion of order to very high dimensions, principal component analysis has a higher accuracy. Of course, the number of dimensions to order reduction and the characteristics of the data set such as size and number of dimensions of the data will affect the accuracy of the dimensional reduction. These two methods were used to order reduction of thermal data in order to faster simulate the phenomenon of Steady State Heat Transfer and were compared with a model based on convolutional neural network with a number of layers and multiple filters. The results showed that the models based on order reduction methods have much less computational volume and simulation time, and the outputs obtained from them, especially the model based on the autoencoder method, have a much higher accuracy.

کلیدواژه‌ها [English]

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