نوع مقاله : مقاله پژوهشی

نویسندگان

• سید رضا غفاری رزین ¹
• نوید هوشنگی ²

¹ استادیار گروه مهندسی نقشه‌برداری، دانشکده مهندسی علوم زمین، دانشگاه صنعتی اراک

² استادیارگروه مهندسی نقشه برداری، دانشکده مهندسی علوم زمین، دانشگاه صنعتی اراک

چکیده

در این مقاله کارائی مدل‌های شبکه عصبی مصنوعی (ANN)، سیستم استنتاج عصبی-فازی سازگار (ANFIS)، رگرسیون بردار پشتیبان (SVR) و مدل شبکه عصبی رگرسیون عمومی (GRNN) در تعیین ارتفاع ژئوئید محلی مورد ارزیابی قرار می‌گیرد. برای انجام اینکار، مختصات ژئودتیکی 26 ایستگاه از شبکه شمال‌غرب ایران که ارتفاع اورتومتریک (H^o) آنها نیز با ترازیابی درجه یک توسط سازمان نقشه‌برداری کشور (NCC) اندازه‌گیری شده، مورد استفاده قرار گرفته است. در این ایستگاه‌ها، تفاضل ارتفاع اورتومتریک از ارتفاع نرمال (h)، به عنوان ارتفاع ژئوئید (N) در نظر گرفته شده است. بنابراین ورودی مدل‌های ANN، ANFIS، SVR و GRNN مختصات طول و عرض ژئودتیکی ایستگاه‌ها بوده و خروجی متناظر با آن، ارتفاع ژئوئید است. آموزش مدل‌ها با استفاده از 22 و 19 ایستگاه انجام گرفته است. به عبارت دیگر تعداد ایستگاه‌های آموزش متغیر بوده تا بتوان آنالیز دقیق‌تری از دقت مدل‌ها را ارائه نمود. به منظور ارزیابی دقیق‌تر، نتایج با ژئوئید حاصل از مدل IRG2016 که توسط سازمان نقشه‌برداری کشور تولید شده، مقایسه می‌شوند. ارزیابی‌های انجام گرفته نشان می‌دهد که در حالت 22 ایستگاه آموزش و 4 ایستگاه آزمون، RMSE مدل‌های ANN، ANFIS، SVR، GRNN و IRG2016 در مرحله آزمون به ترتیب برابر با 37/32، 19/83، 49/34، 53/82 و 29/65 سانتی‌متر شده است. اما در حالت 19 ایستگاه آموزش و 7 ایستگاه آزمون، مقادیر خطای مدل‌ها به ترتیب برابر با 36/63، 58/31، 39/64، 41/29 و 24/68 سانتی‌متر به دست آمده است. مقایسه RMSE نشان می‌دهد که مدل ANN با تعداد ایستگاه‌های آموزش کمتر، دقت بالاتری نسبت به مدل‌های ANFIS، SVR و GRNN ارائه می‌دهد. نتایج این مقاله نشان می‌دهد که با استفاده از مدل‌های ANN و ANFIS می‌توان ارتفاع ژئوئید را با دقت بالایی به صورت محلی برآورد کرده و مورد استفاده قرار داد.         

کلیدواژه‌ها

• ژئوئید
• مدل ANN
• مدل ANFIS
• مدل SVR
• مدل GRNN
• ارتفاع اورتومتریک

موضوعات

• ژئودزی

عنوان مقاله [English]

Efficiency of machine learning models in estimation of local geoid height with GPS/Leveling measurements

نویسندگان [English]

• Seyyed Reza Ghaffari-Razin ¹
• Navid Hooshangi ²

¹ Assistant professor , Department of Geo-science Engineering, Arak University of Technology, Arak, Iran

² Assistant professor, Department of Geoscience Engineering, Arak University of Technology

چکیده [English]

Extended Abstract
Introduction
In geodesy, three levels are considered: the physical surface of the earth on which mapping measurements are made, the ellipsoidal reference surface (geometric datum) which is the basis of mathematical calculations, the geoid physical surface (physical datum) which is the basis for measuring heights. Satellite positioning systems measure the height of points relative to the ellipsoid surface. The geoid is one of the equipotential surfaces of the earth's gravity field, which approximates the mean sea level (MSL) by least squares. Geoid is very important in geodesy as a representative of the physical space or the space of observations made on the earth and also as the base level of elevations. The separation between the geoid and the geocentric reference ellipse is called geoid height (N). Although there is only one equipotential surface called geoid, various methods are used to determine it. These methods include: geometric method, geoid determination by satellite method, Gravimetric methods and geoid determination using GPS/leveling.
 Materials and Methods
In this paper, the aim is to estimate the height of the local geoid using machine learning models. To do this, artificial neural network (ANN), adaptive neuro-fuzzy inference model (ANFIS), support vector regression (SVR) and general regression neural network (GRNN) models are used. The geodetic coordinates of 26 GPS stations in the north-west of Iran along with their orthometric height (H⁰) and normal height (h) were obtained from the national cartographic center of Iran. In all stations, the difference of orthometric height and normal height is considered as geoid height (N). Therefore, the geodetic longitude and latitude of the GPS stations are considered as the input of the machine learning models, and the corresponding geoid height was considered as the output. In order to test the results of machine learning models, two modes of 4 and 7 test stations are considered. Also, the output of the models is compared with the local geoid model IRG2016 presented by Saadat et al. for the Iranian region and also the global geoid model EGM2008.
Results and Discussion
Due to the availability of a complete set of observations of GPS stations along with orthometric height obtained from leveling in the north-west region of Iran, the study and evaluation of the models proposed in the paper has been carried out in this region. Observations of 26 GPS stations of North-west of Iran were prepared from the national cartographic center (https://www.ncc.gov.ir/). Two modes are considered for training and testing of ANN, ANFIS, SVR and GRNN models. In the first case, the number of training stations is 22 and the number of test stations is 4. But in the second case, by increasing the number of test stations to 7 stations, the error evaluation of the models has been done. It should be noted that the distribution of training and test stations is completely random.
After the training step of machine learning models and choosing the optimal structure, the test step is performed in two different modes (4 and 7 stations). At this step, the value of the geoid height in the test stations is estimated and compared with the value obtained from the difference of orthometric height and normal height as a basis. Two statistical indices of relative error in percentage and RMSE in centimeters were calculated for all models and presented in Table (1) for the first case.
Table 1. Relative error (%) of ANN, ANFIS, SVR, GRNN and IRG2016 models in the test stations considered for the first case
  
 
According to the results of Table (1) and comparing the relative error values of all models in the test stations, it shows that the ANFIS model was more accurate than other models. After ANFIS model, IRG2016 model has higher accuracy than ANN, SVR and GRNN models. It should be noted that the IRG2016 local model uses the observations of all Iranian plateau stations to model the local geoid, and therefore it is expected that this model will be more accurate in the study area than other models.
 Conclusion
The evaluations show that in the case of 22 training stations and 4 test stations, the RMSE of ANN, ANFIS, SVR, GRNN and IRG2016 models in the test step are 37.32, 19.83, 49.34, 53.82 and 29.65 cm, respectively. However, in the case of 19 training stations and 7 test stations, the error values of the models are 36.63, 58.31, 39.64, 41.29 and 24.68 cm, respectively. Comparison of RMSE shows that ANN model with less number of training stations provides higher accuracy than ANFIS, SVR and GRNN models. The results of this paper show that by using ANN and ANFIS models, geoid height can be estimated and used with high accuracy locally in civil and surveying applications.

کلیدواژه‌ها [English]

• Geoid
• ANN
• ANFIS
• SVR
• GRNN
• Orthometric height