مقایسۀ عملکرد رگرسیون خطی چندمتغیره و مدل‏ های هوش ‏مصنوعی در تخمین تابش کل خورشیدی

در این پژوهش، برای اولین ‏بار در ایران، تابش کل خورشیدی (gsr) با به‏کارگیری داده‏های ساعتی رطوبت خاک و بدون استفاده از داده‏های ساعت آفتابی و مقدار ابرناکی برآورد شد. بدین منظور، از هشت متغیر روزانه شامل میانگین دمای هوا، بیشینه دما، کمینه دما‏، فشار هوا، رطوبت نسبی هوا، بارندگی، دمای میانگین خاک، و رطوبت خاک در کنار تابش کل روزانه‏ در ایستگاه تحقیقاتی هواشناسی دانشگاه بوعلی سینا در یک دوره 435روزه (ثبت‏شده توسط واقعه‏نگاشت geonica) و مدل‏های رگرسیون خطی، سیستم استنتاج عصبی فازی تطبیفی (anfis)، شبکه عصبی پرسپترون چندلایه (mlp)، و شبکه عصبی رگرسیون تعمیم‏یافته (grnn) استفاده‏ شد. نمونه‏های ورودی هدف به دو صورت تصادفی و غیرتصادفی وارد مدل‏ها شد که نتایج گواه بر دقت بهتر مدل‏ها در نمونه‏های تصادفی‏شده تحت شرایط استفاده از کل متغیرها به‏عنوان ورودی بود. بررسی‏ها حاکی از برتری مدل mlp با rmse=3.04 مگاژول بر متر مربع در روز و %86.33=r2 بود. افزون‏براین، به‏کارگیری کمترین متغیرهای هواشناسی شامل سه متغیر دمای میانگین هوا، رطوبت نسبی هوا، و دمای خاک در مدل grnn توانست با rmse=3.45 مگاژول بر مترمربع در روز و %82.52r2= عملکرد بسیار مطلوبی در تخمین gsr ارائه دهد. رگرسیون خطی چند‏متغیره نیز فقط توانست یافتن ورودی‏ها را تسهیل کند.

Comparison of Multiple Linear Regression and Artificial Intelligence Models in Estimating Global Solar Radiation

IntroductionSolar radiation is the main source of all energies on the Earth and is an important parameter in hydrology studies, water resource management, water balance equations, and plant growth simulation models. In the areas where ground measurements are not available, the Global Solar Radiation (GSR) can be estimated by empirical and semiempirical models, satellite techniques, artificial intelligence models and other geostatistical approaches. In artificial intelligence models such as neural networks, various meteorological parameters like air temperature, relative humidity, sunshine hours, etc. are easily integrated to estimate global solar radiation.In most commonly used radiation models (e.g. Angstrombased models) for estimating daily GSR, the sunshine hours and cloud cover are two important input parameters. Unfortunately, those parameters are not measured very accurately in weather sites. Moreover, for time scales less than daily (e.g., hourly) using sunshine hour as an input, is not possible for predicting the subscale temporal GSR.The main purpose of this study is to compare Multiple Linear Regression model and three types of artificial intelligence models (MLP, GRNN, and ANFIS) against each other to estimate GSR in cold semiarid climate of Hamedan, Iran. This is to present the most accurate model by including the soil data and ignoring the sunshine hours.Materials and methods According to the Extended DeMartonne climate classification model, Hamedan is located in a semiaridvery cold area and has a mean altitude of 1851 meters above sea level. In this study, GSR and meteorological variables (daily values of maximum air temperature, mean air temperature, minimum air temperature, air pressure, air relative humidity, soil temperature and rainfall) are recorded at BuAli Sina University weather site, located at latitude 34°48″ and longitude 48° 28″. These data were recorded every 10 minute during 31 Dec. 2016, to 10 Mar. 2018 by using an automated Spanish GEONICA Logger.  Multiple Linear Regressions (MR): This model is a simple and linear model that estimates the target variable by assigning a constant optimized coefficient for each input variable.Adaptive NeuroFuzzy Inference System (ANFIS): A multilayered network model that uses advanced neural network learning algorithms and fuzzy logic to describe the relationships between inputs and outputs. This model uses the neural network’s Learning ability and fuzzy rules to define the relationships between inputoutput variables.Generalized Regression Neural Network (GRNN): This is a threelayered neural network, which the number of neurons in the first and last layers like other neural networks, is respectively equal to the input and output vectors. But, unlike other networks, the number of hidden layers of neurons in GRNN model is equal to the number of observational data.Evaluation criteria: To evaluate the model performances against actual field measurements, we have used the Root Mean Square Error (RMSE) and Coefficient of Determination (R2).Results and discussionThe correlations of models input variables (eight independent variables) versus GSR (dependent variable) were evaluated. The results revealed that maximum air temperature; average air temperature, relative humidity and soil temperature are the most influencing inputs for modeling GSR, using minimum numbers of meteorological parameters. Among them, maximum air temperature, minimum air temperature, atmospheric relative humidity and soil temperature, were selected as the best inputs for modeling least parameters. The percentages of train and test data were 75% and 25%, respectively. In this research, the models were run using two different samples. The results of the evaluations showed that random samples had higher accuracy in GSR estimates. In MR model, the 4variables input, and in three artificial intelligence models (GRNN, ANFIS, MLP), 3variables input showed the superior performances.Finally, the models were evaluated by using all the eight inputs. At this stage, MLP with RMSE=3.04 Mj.m2.day1 and R2=86.33%, ANFIS with RMSE=3.26 Mj.m2.day1 and R2=84.43%, GRNN with RMSE=3.41 Mj.m2.day1 and R2=82.86%, and MR with RMSE=4.11 Mj.m2.day1 and R2=75.20%, provided the best GSR estimates, respectively.ConclusionThe results showed that in all input variables, random and nonrandom samples, artificial intelligence models have better performance than linear regression. By availability of the whole eight meteorological variables (daily values of maximum air temperature, mean air temperature, minimum air temperature, air pressure, air relative humidity, soil temperature and rainfall), MLP model can present the best GSR estimates. If all input parameters are not available, employing Generalized Regression Neural Network (GRNN) model and 3variable inputs of mean air temperature, relative air humidity, and soil temperature is suggested for estimating the Global Solar Radiation (GSR) in cold semiarid climate of Hamedan.It is noteworthy that in estimating GSR, two important parameters of sunshine hours and cloud cover were not used in our research. Testing the models performances in other climate types is suggested as future works.