مقایسه مدل‌سازی ریاضی، شبکه‌های عصبی مصنوعی و منطق فازی در پیش‌بینی سینتیک خشک‌کردن سیر و موسیر در خشک‌کن بسترسیال

هدف از این پژوهش، مقایسه برآورد نسبت رطوبت سیر و موسیر در طی فرآیند خشک کردن توسط خشک‌کن بسترسیال با استفاده از روش‌های مدل‌سازی ریاضی، شبکه‌های عصبی مصنوعی و منطق فازی می‌باشد. فرآیند خشک‌کردن در سه سطح دمایی (40، 55 وc °70) و سه سطح سرعت هوای ورودی (0.5 و 1.5 و ms-2.15) صورت گرفت. از 5 مدل ریاضی خشک‌کردن جهت پیش بینی نسب رطوبت سیر و موسیر استفاده شد. سرعت هوای ورودی، دمای هوای ورودی و زمان خشک‌کردن به‌عنوان پارامترهای ورودی در پیش‌بینی نسبت رطوبت، برای شبکه‌های عصبی مصنوعی و منطق فازی مورد استفاده قرار گرفت. برای ایجاد الگوهای آموزشی و ارزیابی فرآیند، از شبکه عصبی پس انتشار پیش‌خور و پیشرو با توابع آموزش لونبرگ- مارکوارت (lm) و تنظیم بیزی (br) و همچنین از سیستم استنتاجی فازی ممدانی و به‌کارگیری تابع عضویت مثلثی برای مدل‌سازی استفاده شد. با توجه به نتایج به‌دست آمده، بهترین مدل برای پیش‌بینی خشک کردن سیر مدل (page) و برای موسیر مدل midilli و همکاران انتخاب شد. نتایج بررسی‌های شبکه عصبی مصنوعی نشان داد که به‌ترتیب ضرایب تبیین 0.9994 و 0.9996، ریشه خطای میانگین مربعات 0.0036 و 0.0014 و میانگین خطای مطلق 0.044 و 0.038 در شرایط مختلف خشک‌کردن سیر و موسیر را پیش‌بینی نماید. همچنین سیستم استنتاجی فازی این مقادیر را برای سیر و موسیر به‌ترتیب (ضرایب تبیین 0.9997 و 0.9998، ریشه خطای میانگین مربعات 0.0027 و 0.0011 و میانگین خطای مطلق 0.032 و 0.029) به‌دست آورد. مقایسه نتایج به‌دست آمده از مدل‌های ریاضی، شبکه‌های عصبی مصنوعی و منطق فازی نشان داد که ریشه خطای میانگین مربعات در منطق فازی کمتر از شبکه‌های عصبی مصنوعی و مدل‌های ریاضی است.

Comparison of Mathematical Modeling, Artificial Neural Networks and Fuzzy Logic for Predicting the Moisture Ratio of Garlic and Shallot in a Fluidized Bed Dryer

<p > <strong >Introduction </strong > </p > <p >Garlic ( <em >Allium sativum </em > L.) is an important Allium crop in the world. Due to its therapeutic properties, it was cultivated in many countries. Furthermore, garlic is usually used as a flavoring agent; it may be used in the shape of powder or granule as a valuable condiment for foods. In addition to its use in food products, it was also widely used as an anticancer agent. Shallot ( <em >Allium hiertifolium Boiss </em >. L) is a perennial and bulbous plant. It is from Alliaceae family and is an important medicinal plant. The shallot is native of Iran, and grows in the high pastures. Shallot is consumed in dry areas in most parts of the country. Also shallots have been well known in Iranian folk medicine and its bulbs have been widely used for treating rheumatic and inflammatory disorders. In addition, this plant is used in the preparation of significant amounts of potassium, phosphorus, calcium, magnesium, sodium, pickles and as an additive to yogurt and pickles. ANN as a modern approach has successfully been used to solve an extensive variety of problems in the science and engineering, exclusively for some space where the conventional modeling procedure fail. A welltrained ANN can be used as a predictive model for a special use, which is a data processing system inspired by biological neural system. When mathematical equations are difficult to extrapolate, and fuzzy logic is better when decisions must be made with the estimated values below the incomplete information. The fuzzy logic theory effectively addresses the uncertainty problems that solve the ambiguity. </p > <p > <strong >Materials and Methods </strong > </p > <p >  The aim of this study was to predict moisture ratio of garlic and shallot during the drying process with fluidized bed dryer using mathematical model, artificial neural networks and fuzzy logic methods. Tests were carried out on three levels of inlet air temperature (40, 55 and 70 °C) and three inlet air velocities (0.5, 1.5 and 2.5 m/s). To estimate the drying kinetic of garlic and shallot, five mathematical models were used to fit the experimental data of thin layer drying. Three factors (air temperature, air velocity and drying time) to forecast moisture ratio in fluidized bed dryer as independent variables for artificial neural networks and fuzzy logic was considered. Cascade forward back propagation (CFBP) and feed forward back propagation (FFBP) with LevenbergMarquardt (LM), Bayesian learning (BR) algorithms for ANN and the Mamdani Fuzzy Inference System using triangular membership function were used for training patterns. </p > <p > <strong >Results and Discussion </strong > </p > <p >Consequently, the Page and Midilli <em >et al </em >. model was selected as the best mathematical model to describe the drying kinetics of the garlic and shallot slices, respectively. The results of artificial neural networks model for predicting MR showed that the R <sup >2 </sup > of 0.9994 and 0.9996; and and RMSE of 0.0036 and 0.0014 were obtained for garlic and shallot, respectively. Also, The fuzzy inference system presented the R <sup >2 </sup > of 0.9997 and 0.9998; and and RMSE of 0.0027 and 0.0011 for garlic and shallot, respectively. Comparing the results obtained from mathematical models, artificial neural networks and fuzzy logic, showed that the RMSE in the fuzzy logic was lower than artificial neural network and mathematical models. </p > <p > <strong >Conclusions </strong > </p > <p >Three factors (air temperature, air velocity and drying time) were considered for forecasting moisture ratio in fluidized bed dryer as independent variables using mathematical model, artificial neural networks and fuzzy logic. Cascade forward back propagation (CFBP) and feed forward back propagation (FFBP) with LevenbergMarquardt (LM), Bayesian learning (BR) algorithms and the Mamdani Fuzzy Inference System using triangular membership function were used for training the patterns. Comparing the results obtained from mathematical models, artificial neural networks and fuzzy logic, showed that the root mean square error in fuzzy logic was lower than others. </p >