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Porównanie przydatności sieci neuronowych typu GRNN i RBF do prognozowania poprawek dla krajowej skali czasu UTC(PL)

Sobolewski Ł.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 11

972--974

PL

W pracy przedstawiono wyniki badań sieci neuronowych typu GRNN zastosowanych do prognozowania poprawek dla krajowej skali czasu UTC(PL). Wyniki te porównano z wynikami otrzymanymi przy użyciu sieci neuronowej typu RBF, a także z wynikami otrzymanymi w GUM z zastosowaniem metody regresji liniowej. Prognozowanie poprawek prowadzono w oparciu o metodę regresji dla danych wejściowych powstałych na bazie dwóch szeregów czasowych sc1 (bez eliminacji trendu opisanego równaniem regresji liniowej) oraz sc2 (z eliminacją tego trendu). Prognozy zostały wykonane na 15 dzień dla 5 kolejnych miesięcy 2008 począwszy od stycznia (MJD 54479) do maja (MJD 54599) Z przeprowadzonych badań wynika, że otrzymane wartości błędu prognozy dla sieci neuronowej typu GRNN są zdecydowanie gorsze od błędów prognozy otrzymanych przy użyciu sieci neuronowej typu RBF.

EN

The paper discusses the results of comparison of the usefulness of GRNN and RBF neural networks for predicting the corrections for the national time scale UTC(PL). The first chapter describes the national time scale UTC(PL), and also presents the problem of maintaining the best compatibility of the UTC(PL) with UTC. The second chapter describes the basic idea and principle of operation of the GRNN neural networks. The third chapter shows how the input data for the neural networks was prepared. Based on historical measurement data from the cesium atomic clock Cs2 and corrections of the UTC(PL) relative to UTC two time series (ts1 and ts2) were prepared, which were the basis for determining the input data for the neural networks. The fourth chapter describes the research results. The obtained research results shown that in the case of predicting the corrections for the polish time scale UTC(PL) using GRNN and RBF neural networks and the input data based on time series ts1 prediction errors have reached very large values. Predicting the corrections for the UTC(PL) based on time series ts2 was carried out in two ways. The first method assumed using the input data prepared on the basis of time series ts2 with values of two coefficients a0 and a1, which are the coefficients of linear regression equation. In the second case only coefficient a1 was used with the input data prepared on the basis of time series ts2. The best results was obtained using RBF neural network for the input data prepared on the basis of time series ts2 with a1 coefficient. For the GRNN neural network the obtained value of maximum prediction error for both method of data preparation was larger than in the case of using RBF neural network. Obtained values of prediction errors using GRNN neural network are on the same level with prediction errors obtained in the GUM using linear analytical regression method.

2

Wpływ dodatkowych danych wejściowych w sieci neuronowej na wynik prognozowania poprawki dla krajowej skali czasu UTC(PL)

Miczulski W., Sobolewski Ł.

Pomiary Automatyka Kontrola

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2013

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R. 59, nr 4

312--315

PL

W artykule przedstawiono wyniki badań, których celem było sprawdzenie, czy wprowadzenie na wejście sieci neuronowej (SN) typu MLP i GMDH dodatkowych danych wejściowych, charakteryzujących pracę zegarów atomowych, wpłynie korzystnie na wynik prognozowania poprawki dla UTC(PL). Otrzymane wyniki wskazują, że kluczowym aspektem jest dobór SN. Dla SN typu GMDH wpływ dodatkowych danych jest niewielki. SN tego typu osiąga lepsze wyniki w prognozowaniu poprawki dla UTC(PL), niż sieć typu MLP.

EN

The paper presents the results of investigations whose aim was to examine whether the insertion of additional input data for MLP and GMDH neural networks would increase compliance of the UTC(PL) with UTC. The primary input vector in the training process of the network included historical data of measurements of the phase time between the UTC and atomic clock (Cs2). Additional input vectors were made in two ways. The first way results from the rules of determining the UTC time scale, which is computed as a weighted average based on continuous comparisons of more than 300 atomic clocks located in laboratories of many countries around the world. Hence, the input data containing the historical data, characterizing the behavior of two additional atomic clocks whose results are available in the Central Office of Measures (GUM), was added to the study. These clocks are to "imitate" the gait of atomic clocks used to calculate the UTC time scale. The second way is related to the results of previous studies, which indicate that the quality of predicting the corrections for the UTC(PL) depends on the atomic clock gait instability. The measure of this instability is the Allan deviation. That is why, an additional input data containing the Allan deviation gait characterizing the atomic clock Cs2 gait instability was added to the study. Selection of a neural network has very large impact on the results. In the case of the MLP neural network the insertion of additional input data resulted in a smaller value of the prediction error, and in the case of the GMDH networks insertion of an additional input data affected the final prediction result to a small extent.

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Porównanie metod prognozowania zastosowanych w sieci neuronowej GMDH przeznaczonej do wyznaczania prognozy poprawek dla krajowej skali czasu UTC(PL)

Sobolewski Ł.

Pomiary Automatyka Kontrola

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2013

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R. 59, nr 1

23--25

PL

W pracy zostały porównane metody prognozowania poprawek dla krajowej skali czasu UTC(PL). Badania dotyczące prognozowania poprawek prowadzono w oparciu o sieci neuronowe GMDH dwoma metodami, metodą analizy szeregów czasowych i metodą regresji. Prognozowanie poprawek zostało wykonane na 15 dzień miesiąca dla 20 kolejnych miesięcy. Otrzymane wyniki prognoz przy użyciu sieci neuronowej GMDH zestawione z wynikami prognoz otrzymanymi przez Główny Urząd Miar z zastosowaniem metody regresji liniowej pokazują, że lepszą metodą prognozowania poprawek dla krajowej skali czasu okazała się metoda analizy szeregów czasowych.

EN

The paper discusses the results of predicting the corrections for the national time scale UTC(PL), using GMDH neural networks. The aim of the research was to examine the influence of the GMDH neural network prediction methods on the prediction result. The first section describes the national time scale UTC(PL) and presents the problem of maintaining the best compatibility of the UTC(PL) with UTC. It also presents the method of predicting the corrections used in the Central Office of Measures (GUM), and a new method for predicting the corrections for the UTC(PL) based on GMDH neural network. The second section shows how the input data for the GMDH neural network was prepared. Based on historical measurement data from the cesium atomic clock Cs2 and corrections of the UTC(PL) relative to UTC, two time series (sc1 and sc2) which were the basis for determining the input to GMDH neural network were prepared. The third section describes the predicting methods used in the GMDH neural network and a training data for both methods. The fourth section focuses on the method of predicting the corrections using GMDH neural networks, and contains the research results. The research on predicting the corrections were carried out using two methods, the time series analysis and the regression method. Prediction of the corrections was made on the 15th day of month for 20 consecutive months. The prediction results using the GMDH neural network were compared with the results received by the GUM with use of the linear regression method. The research show that the GMDH neural networks can be used to predict the corrections for the national time scale UTC(PL). A better method of predicting the corrections for the national time scale proved to be the method of time series analysis. The results were better than the prediction results obtained in the GUM for both time series sc1 and sc2. In the case of using the regression method only for times series sc1, the obtained results were better than those obtained in the GUM.

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Wpływ doboru parametrów sieci neuronowej GMDH na wyniki prognozy poprawek dla krajowej skali czasu UTC(PL)

Sobolewski Ł.

Pomiary Automatyka Kontrola

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2012

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R. 58, nr 10

869-871

PL

W pracy omówiono wyniki badań dotyczących prognozowania poprawek dla krajowej skali czasu UTC(PL), z wykorzystaniem sztucznych sieci neuronowych GMDH. Przedstawiono wyniki badań, których celem było sprawdzenie, jak dobór funkcji przejścia neuronu sieci GMDH oraz stosunku danych uczących do danych testujących wpływają na wynik prognozy. Opisano wyniki prognozowania poprawek otrzymane na podstawie przeprowadzonych badań, uzyskane na 15 dzień dla 28 kolejnych miesięcy, począwszy od stycznia 2008 roku (MJD 54479) do kwietnia 2010 roku (MJD 55299).

EN

The paper discusses the results of predicting the corrections for the national time scale UTC(PL), using GMDH neural networks. The aim of the research was to examine the influence of the GMDH neural network parameters, ie. the transfer function of the neuron and the ratio of training to test data on the prediction result. The first section describes the national time scale UTC(PL), and presents the problem of maintaining the best compatibility of the UTC(PL) with UTC. It also presents the method for predicting the corrections used in the GUM as well as a new method for predicting the corrections for the UTC(PL) based on GMDH neural network. The second section shows how the input data for the GMDH neural network was prepared. Based on historical measurement data from the cesium atomic clock Cs2 and corrections of the UTC(PL) relative to UTC, two time series (sc1 and sc2) were prepared. They were the basis for determining the input to the GMDH neural network. The third section describes the basic idea and principle of operation of GMDH neural networks, which belong to the group of self-organizing networks. In the fourth section there is presented the method for predicting the corrections using GMDH neural networks and there are given the research results. There were carried out investigations whose aim was to examine the influence of the transfer function of the neuron and the ratio of training to test data on the prediction result. Based on those investigations the prediction of the corrections on the 15th day of 28 consecutive months was performed. The research show that the GMDH neural networks can be used for predicting the corrections for the national time scale UTC(PL). The obtained prediction errors are significantly smaller than those obtained from the analytical linear regression method used in the GUM. It is shown that a significant influence on obtaining small prediction errors has a proper selection of the GMDH neural network parameters.