تو موگرافي يونوسفر بكمك روش كمينه‌سازي توابع هدف و شبكه‌هاي عصبي مصنوعي در منطقه ايران

Ionosphere Tomography using Minimization of Objective Functions Method and Neural Networks over Iran

ر اين مقاله روش كمينه‌سازي توابع هدف با كمك شبكه‌هاي عصبي موجك چند لايه، جهت مدل‌سازي توموگرافي يونوسفر به عنوان يك روش جديد ارائه شده است. براساس روش توموگرافي، تابع هدفي تعريف گرديده و سپس با كمك شبكه‌هاي عصبي موجك چند لايه (WNN) طراحي شده، مقدار اين تابع هدف به كمترين ميزان خود مي‌رسد. جهت بهينه‌سازي وزن‌ها و باياس‌ها در شبكه‌هاي عصبي، مي‌بايستي از يك الگوريتم آموزش مناسب بهره گرفت. به همين جهت در اين مقاله از الگوريتم‌هاي آموزش پس انتشار خطا (BP) و بهينه‌سازي انبوه ذرات (PSO) استفاده شده است. سه روش تركيبي براي كمينه‌سازي توابع هدف كه جزو نوآوري‌هاي اصلي اين مقاله است مورد بررسي و آناليز قرار گرفته است. در روش اول (RMTNN) از شبكه عصبي مصنوعي پرسپترون 3 لايه با الگوريتم آموزش پس انتشار جهت مدل‌سازي توزيع چگالي الكتروني استفاده شده است. در روش دوم (MRMTNN) يك شبكه عصبي موجك 3 لايه بهمراه الگوريتم آموزش پس انتشار خطا جهت مدل‌سازي توزيع چگالي الكتروني بكار گرفته شده و نهايتاً در تركيب سوم (ITNN) از شبكه عصبي موجك 3 لايه بهمراه الگوريتم آموزش بهينه‌سازي انبوه ذرات جهت مدل‌سازي تغييرات زمان-مكان چگالي الكتروني بهره گرفته شده است. مشاهدات مربوط به شبكه مبناي ژئوديناميك دائمي ايران (32 ايستگاه GPS به همراه يك ايستگاه اندازه‌گيري مستقيم يونوسفر) جهت آزمون و ارزيابي هر سه تركيب مورد استفاده قرار گرفته‌اند. تمامي نتايج بدست آمده از سه روش با اندازه‌گيري‌هاي ايستگاه‌ يونوسوند و مدل هارمونيك‍‌هاي كلاه كروي (SCH) مقايسه شده است. همچنين شاخص‌هاي آماري خطاي نسبي و مطلق، جذر خطاي مربعي ميانگين (RMSE)، باياس، انحراف معيار و ضريب همبستگي براي هر سه روش پيشنهادي اين مقاله مورد محاسبه و بررسي قرار گرفته است. آناليزهاي انجام گرفته در مورد روش‌هاي RMTNN، MRMTNN و ITNN بيانگر اين موضوع است كه روش ITNN نسبت به دو روش ديگر داراي سرعت همگرايي بالا به جواب بهينه و همچنين دقت و صحت بالاست. مقايسه‌هاي صورت گرفته نشان‌دهنده بهبود مدل‌سازي محتواي الكترون كلي توسط روش ITNN به مقدار 5/0 الي 65/5 TECU در منطقه ايران نسبت به مدل‌هاي تجربي يونوسفر مي‌باشد. همچنين متوسط ضريب همبستگي 901/0 مابين خروجي‌هاي روش ITNN و اندازه گيري‌هاي ايستگاه‌هاي يونوسوند، حاكي از كارائي بالاي روش پيشنهادي اين مقاله در مدل‌سازي تغييرات زمان-مكان چگالي الكتروني اس

دIn the last two decades, knowledge of the distribution of the ionospheric electron density considered as a major challenge for geodesy and geophysics researchers. To study the physical properties of the ionosphere, computerized ionosphere tomography (CIT) indicated an efficient and effective manner. Usually the value of total electron content (TEC) used as an input parameter to CIT. Then inversion methods used to compute electron density at any time and space. However, CIT is considered as an inverse ill-posed problem due to the lack of input observations and non-uniform distribution of TEC data. Many algorithms and methods are presented to modeling of CIT. For the first time, 2-dimensional CIT was suggested by Austin et al., (1988). They used algebraic reconstruction techniques (ART) to obtain the electron density. Since, other researchers have also studied and examined the CIT. Although the results of all studies indicates high efficiency of CIT, but two major limitations can be considered to this method: first, due to poor spatial distribution of GPS stations and limitations of signal viewing angle, CIT is an inverse ill-posed problem. Second, in most cases, observations are discontinuous in time and space domain, so it is not possible determining the density profiles at any time and space around the world. In this paper, the method of residual minimization training neural network is proposed as a new method of ionospheric reconstruction. In this method, vertical and horizontal objective functions are minimized. Due to a poor vertical resolution of ionospheric tomography, empirical orthogonal functions (EOFs) are used as vertical objective function. To optimize the weights and biases in the neural network, a proper training algorithm is used. Training of neural networks can be considered as an optimization problem whose goal is to optimize the weights and biases to achieve a minimum training error. In this paper, back-propagation (BP) and particle swarm optimization (PSO) is used as training algorithms. 3 new methods have been investigated and analyzed in this research. In residual minimization training neural network (RMTNN), 3 layer perceptron artificial neural networks (ANN) with BP training algorithm is used to modeling of ionospheric electron density. In second method, due to the use of wavelet neural network (WNN) with BP algorithm in RMTNN method, the new method is named modified RMTNN (MRMTNN). In the third method, WNN with a PSO training algorithm is used to solve pixel-based ionospheric tomography. This new method is named ionospheric tomography based on the neural network (ITNN). The GPS measurements of the Iranian permanent GPS network (IPGN) (1 ionosonde and 4 testing stations) have been used for constructing a 3-D image of the electron density. For numerical experimentation in IPGN, observations collected at 36 GPS stations on 3 days in 2007 (2007.01.03, 2007.04.03 and 2007.07.13) are used. Also the results have been compared to that of the spherical cap harmonic (SCH) method as a local ionospheric model and ionosonde data. Relative and absolute errors, root mean square error (RMSE), bias, standard deviations and correlation coefficient computed and analyzed as a statistical indicators in 3 proposed methods. The Analyzes show that the ITNN method has a high convergence speed and high accuracy with respect to the RMTNN and MRMTNN. The obtained results indicate the improvement of 0.5 to 5.65 TECU in IPGN with respect to the other empirical methods. The GPS measurements of the Iranian permanent GPS network (IPGN) (1 ionosonde and 4 testing stations) have been used for constructing a 3-D image of the electron density. For numerical experimentation in IPGN, observations collected at 36 GPS stations on 3 days in 2007 (2007.01.03, 2007.04.03 and 2007.07.13) are used. Also the results have been compared to that of the spherical cap harmonic (SCH) method as a local ionospheric model and ionosonde data. Relative and absolute errors, root mean square error (RMSE), bias, standard deviations and correlation coefficient computed and analyzed as a statistical indicators in 3 proposed methods. The Analyzes show that the ITNN method has a high convergence speed and high accuracy with respect to the RMTNN and MRMTNN. The obtained results indicate the improvement of 0.5 to 5.65 TECU in IPGN with respect to the other empirical methods.