Artificial intelligence methods for MT data processing are

proposed. Distortions having a complex structure created by external

artificial sources such as, for example, passing train were investigate. In

the first part of this paper the time intervals with such type of

distortions were found by using a special neuronal system. Next for time

intervals found in the first stage the measure curve fragment is removed

and then it is replied by the fragment created by a trained perceptron.

The experiment showed that used method are effective

Baran, Grzegorz

Bielecka, Marzena

Danek, Tomasz

Wojdyła, Marek

Schedae Informaticae

English

Jagiellonian Univeristy Repository

       S C H E D A E   I N F O R M A T I C A E   VOLUME 17/18  2009  Neural Networks Application to Reduction of Train Caused Distortions in Magnetotelluric Measurement Data  MARZENA BIELECKA1, TOMASZ. DANEK1, MAREK WOJDYŁA2, GRZEGORZ BARAN3 1Departament of Geoinformatics and Applied Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland 2PBG Geophysical Exploration Company Ltd., Jagiello ska 76,  03-301 Warszawa, Poland 3Institute of Computer Science, Jagiellonian University  Prof. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland e-mail: bielecka@agh.edu.pl, danek9@geolog.geol.agh.edu.pl  Abstract. Artificial intelligence methods for MT data processing are proposed. Distortions having a complex structure created by external artificial sources such as, for example, passing train were investigate. In the first part of this paper the time intervals with such type of distortions were found by using a special neuronal system. Next for time intervals found in the first stage the measure curve fragment is removed and then it is replied by the fragment created by a trained perceptron. The experiment showed that used method are effective. Keywords: MT data, neural network. 1.  Introduction Magnetotelluric (MT) is a one of the most popular and commonly used passive geophysical method. It is widely used in deep lithosphere research but recently a growing number of examples of using MT method in hydrocarbon        76 prospecting and earthquake prediction are observed. Magnetotelluric applies measuring of fluctuations in natural electric (E) and magnetic (H) fields in orthogonal directions at the surface of the Earth to determining the conductivity structure of the Earth at depths ranging from tens of meters to several hundreds of kilometers.     Fig. 1. Simplified scheme of MT processing and interpretation        77 The fundamental theory of magnetotelluric was first proposed by Tikhonov [1], and Cagniard [2]. Magnetotelluric data, called amplitude and phase sounding curves, are usually obtained by processing of measured time series, which describe electromagnetic variations in particular point on Earth surface. Sounding curves are next interpreted with various inversion methods (Fig. 1). But quality of magnetotelluric data often suffers from high noise level. The most common sources of this noise such as railways, electrical devices, thunderstorms etc. are very hard to avoid especially in urbanized areas. Typically MT signals are recorded in two separated points (measuring point and remote reference point) and then these two records are processed together. Fragments with high noise level are simply removed. But sometimes noise sources like for example DC railways are so intensive that whole record is affected and traditional processing is pointless. In this case, to obtain a solid sounding curve with limited error from raw and very noisy time series other, more effective and sophisticated method of noise reduction is needed. Nowadays the most promising ways of reduction of steady shape intensive noises are based on methods of artificial intelligence [3, 4, 5].  2.  Recognition and elimination distortions caused by trains In order to implement automatic system for train caused distortions recognition and elimination, 121 data sets have been collected. Each set consists of two measurements: (a) The first one consists of two time series – )(tEx  and ),(tH y  without distortions. (b) The second one consists of two time series – )(tE x  and ),(tH y  has been done at the same place, with distortions caused by trains.   The time series consist of 57 till about 5000 measurement points. It was input date for the system. 2.1.  Recognition of train caused distortions The distorted intervals marking in the time series )(tEx  was the first task of the implemented system.         78 The data analysis showed that distortions caused by trains have a characteristic shape on the time series )(tEx – see Fig. 2.   Fig. 2.  Train caused distortions on the xE  time series  Fig. 3. An example of effect of approximating algorithm using – the time series is approximated by a broken line         79 2.1.1.  Train caused distortions recognition using artificial neural networks (ANNs) Learning and testing sets were prepared in the following way: a) The approximating broken line is calculated for each time series )(tE x (Fig. 3). b) Sequences of n  ( )1≥n  points satisfying a given criterion were chosen. In this paper three various criteria were used to choose sequences for input data: ,):(),...,( 1 qpplappG mmnmmq ≥→⇔ ++  ,):(),...,( 1 qpplappD mmnmmq ≤→⇔ ++  ),,...,(),...,(),...,( nmmqnmmqnmmq ppDppGppO +−++ ∨⇔  where: ):( 1+→ mm ppla  is a slope of a straight line containing points mp  and 1+mp , Rd ∈ . The criteria were applied in order to divide the set nS  into various classes of problems which are solved by specialized ANNs. Thus, the criterion qG  describes sequences in which the first line segment is described by the ascending affined function with great value of differential coefficient whereas qD  corresponds to sequences in which the first line segment is described by the descending affined function with great absolute value of differential coefficient. The criterion qO  describes sequences in which the first line segment is described by the ascending or descending affined function with great absolute value of differential coefficient. The above criteria were used because train caused distortion begins from big increase or big decrease of the measured value xE . c) For each sequence )(),...,( KSpp nnmm ∈+  input vector was made. It was calculated in two following ways:   )](),(),...,(),([),...,( 1111 nmnmnmnmmmmmnmmw ppyppxppyppxppW +−++−++++ →→→→=   )],(),:(),...,,(),:([),...,( 1111 nmnmnmnmmmmmnmmk ppdpplappdpplappW +−++−++++ →→=   where: )( 1+→ mm ppx  – the first component of the vector 1+→ mm pp , )( 1+→ mm ppy  – the second component of the vector 1+→ mm pp ,        80 ):( 1+→ mm ppla  – slope of a straight line to which points mp  and 1+mp  belong, ),( 1+mm ppd  – Euclidean distance between points mp  and 1+mp .  d) A number value was assigned to each input vector in dependence on the investigated fragment of the time series )(tEx  was distorted or not:  1)( =Wf  if vector W  has been obtained from distorted time series ),(tEx   0)( =Wf  if vector W has been obtained from undistorted time series )(tEx . About ¾ elements from the obtained set of pairs ))(,( WfW  were selected randomly and they constituted the learning set. Other elements were used as testing set. 2.1.2.  ANNs architectures Two types of ANNs were used:  a) Multilayered perceptron with one hidden layer consisting of sigmoid neurons [7]: xexf−+=11)( .        The output layer consists of linear neurons. b) Multilayer network with radial basis neurons in the hidden layer [6]: )),...,((),...,( 11 kk xxrfxxg = ,               where:      2)(kwxxr −= β ,    ],...,[ 1 kxxx =  – input vector,    ],...,[ 1 kwww =  – a neuron weights vector,    kwx −  – distance in k-dimensional Euclidean space,    0>β  – a parameter.         An activation function: xexf −=)( .        There are linear neurons in the output layer.   The efficiency of ANNs prediction was measured using Mean Absolute Error.         81 2.1.3.  The system recognizing train caused distortions For a given time series )(tEx  the train caused distortions recognizing algorithm is of the following form: 1. Estimate the time series )(tEx  for a parameter δ  given by the user or calculated using statistic methods. 2. For each sequence of n  broken line segments:  a. check if the sequence satisfies one of the established criterion        ( qG , qD  or qO ); b. check the proper neural network in dependence of which criterion is satisfied; if none is satisfied interrupt the algorithm; c. construct input vector according to kW  or wW ; d. activate ANN for the obtained input vector; e. remember of the output ANN value for each point kt  from the investigated interval.  3. For each point kt  of the graph the output value of the system is equal to arithmetic mean of all ANNs output values obtained in point 2.e.  4. Mark intervals of time series )(tEx  on which the output value of the system is greater than a given bias 10 ≤≤ γ  (default value is equal  to 0.5) as intervals with distortions. The scheme of the system is shown in Fig. 4.   Fig. 4. The scheme of train caused distortions recognizing system using criteria qG  and qD         82 2.1.4.  Obtained results The results are shown in Tab. 1. In systems number 4, 8, 9, 11 and 18 two various ANNs were used for line segments sequences satisfying criterion 4,0G  and 4,0−D . System 18 was the best one – its efficiency is equal to 75,13%. 2.2.  Train caused distortions elimination The data set consists of 121 subsets. Each of them it is a double measurement of the electric Earth field with and without train caused distortions. The distorted signal was put onto the ANN input. To return a time series like to the corresponding one without distortions was the ANN task.  The ANN has one hidden layer with sigmoidal neurons or radial-based neurons and linear neurons in the output layer. The number of neurons in the output layer was equal to the size of the input vector.   Tab. 1.  Distortions recognition results. Notations: RFB – radial based network – neural Network with radial neuron in the hidden layer; WP – multilayer perceptron; δ  parameter determined for each time series using statistic methods  The system number  Parameter  δ  Input vector size How the input vector was determined Criterion Number of neurons in hidden layer  ANN type MAE for testing set  Efficiency 1 0,8 20 kW  4,0G  120 RFB 0,3833 72,15% 2 0,8 20 kW  4,0G  6 WP 0,3961 71,81% 4,0G  30 WP 0,3621 3 0,8 30 kW  4,0−D  31 RFB 0,3773 74,43% 4,0G  5 WP 0,3649 4 0,8 30 kW  4,0−D  8 WP 0,3941 73,51% 5 1,3 10 wW  4,0G  15 WP 0,368 61,49% 6 1,3 20 wW  4,0O  63 RFB 0,3689 68,01%        83 The system number  Parameter  δ  Input vector size How the input vector was determined Criterion Number of neurons in hidden layer  ANN type MAE for testing set  Efficiency 7 1,3 20 wW  4,0G  6 WP 0,3912 63,36% 4,0G  22 WP 0,3769 8 1,3 20 kW  4,0−D  5 WP 0,3877 68,03% 4,0G  3 WP 0,39 9 1,3 20 kW  4,0−D  5 WP 0,3877 67,52% 10 1,3 30 kW  4,0O  5 WP 0,3727 65,35% 4,0G  2 WP 0,3487 11 1,3 30 kW  4,0−D  4 WP 0,3669 66,17% 12 1,3 30 wW  4,0G  23 WP 0,3545 67,22% 13 1,3 40 wW  4,0O  18 RFB 0,359 61,59% 14 1,3 40 wW  4,0G  43 WP 0,3396 66,17% 15 1,3 40 wW  4,0−D  102 RFB 0,302 62,03% 16 variable 10 kW  4,0G  6 WP 0,4119 64,79% 17 variable 30 kW  4,0O  46 RFB 0,401 70,46% 4,0G  50 WP 0,378 18 variable 30 wW  4,0−D  8 WP 0,3831 75,13% 19 variable 40 wW  4,0G  51 RFB 0,3901 71,55% 20 variable 40 kW  4,0−D  24 RFB 0,3922 68,82% 21 variable 40 kW  4,0−D  6 RFB 0,3992 68,40%   Learning and testing sets were constructed in the following way: 1. Each time series )(tEx  was divided into fragments consisted of M  points. 2. Each obtained fragment )(tFk  was divided into m sub-fragments and the integral of each fragment has been calculated.         84 ∑−=+=10)()(mikk imtFtG , 1≥m , .1,...,2,1,0 −=mMt  3. The data set was composed of input vectors with       −1),...,0(mMGG kk  and corresponding output vectors       −1'),...,0('mMGG kk  without distortions. 4. The ¾ of the data set was used as the learning set and ¼ as the testing set.   The used data it is about 15% of needed data being necessary for learning the ANNs with the highest efficiency. Results are shown in Tab. 2 and Tab. 3. In Tab. 2 there are results that were obtained for the smaller data set consisted of 74 measurement subsets. In Tab. 3 there are result for bigger data set consisted of 121 measurement subsets. It is noticed that for the bigger data set the result is changed significantly.   Tab. 2.  Neural networks training results. The networks were used for elimination of train caused distortions. Notations: RFB – radial based network – neural Network with radial neuron in the hidden layer; WP – multilayer perceptron  Index M  m  Number of neurons in the last layer   ANN type Number of hidden neurons MAE for learning set MAE for testing set Cardinality of the learning set Cardinality of the testing set Weights number in the neural network 1 600 12 50 RFB 12 11,409 19,899 49 16 1200 2 300 12 25 RBF 10 19,89 23,565 142 47 500 3 300 6 50 RFB 11 10,108247 13,112735 142 47 1100 4 150 6 25 WP 20 152,93 179,178 324 108 1000 5 150 6 25 RFB 10 11,003 13,101 324 108 500 6 150 6 25 RFB 21 11,061 12,044 324 108 1050              85 Tab. 3.  Results for ANNs used for train caused distortions elimination. Notations: RFB – radial based network – neural Network with radial neuron in the hidden layer; WP – multilayer perceptron  Index M  m  Number of neurons in the last layer ANN type Number of hidden neurons MAE for learning set MAE for testing set Cardinality  of the learning set Cardinality of the testing set Weights number in the neural network 1 600 12 50 RFB 6 16,367 24,855 38 12 600 2 300 12 25 RBF 10 22,959 28,115 105 35 500 3 300 6 50 RFB 16 10,020 15,669 105 35 1600 4 150 6 25 RFB 27 11,070 15,294 239 80 1350 3.  Concluding remarks In the case of train caused distortions the results should be regarded as preliminary because the number of learning examples is about 15% of the needed number. However, even is such situation the system achieved 75% efficiency, which, in this context, is a quite good result. In the case of ANNs which removes train caused distortions the results are very promising. To enlarge the learning set of about 50 examples improved outcomes signifi-cantly. This probably means that the obtained results can be improved by adding next examples to the learning set.  Acknowledgements. This article was written within the framework of a research grant founded by the Polish Ministry of Science and Higher Education, no N525 029 32 /2768.  4.  References [1] Cagniard L.; Basic theory of the magnetotelluric method of geophysical prospecting, Geophysics, 18, 1953, pp. 605–637.  [2] Tikhonov A.N.; The determination of the electrical properties of deep layers of the Earth’s crust, Dokl. Acad. Nauk. SSR, 73, 1950, pp. 295–297.         86  [3]  Manoj C., Nagarajan N.; The application of artificial neural networks to magnetotelluric time-series analysis, Geophysical Journal International, 153, 2003, pp. 409–423.  [4] Moorkamp M., Jones A.G., Rao C.K.; Processing magnetotelluric time series with adaptive filters and neural networks, 18th EM Induction Workshop, El Vendrell, Spain, 2006.  [5] Popova I.V., Ogawa Y.; Application of a modified Hopfield neural network to noisy magnetotelluric data, Izvestiya Physics of the Solid Earth, Vol. 43,3, 2007, pp. 217–224.  [6] Yee P.V., Haykin S.; Regularized Radial Basis Function Networks, Theory and Applications, 2001.  [7] Tadeusiewicz R.; Sieci neuronowe, Akademicka Oficyna Wydawnicza, 1993.     Received December 29, 2008 

Neural networks application to reduction of train caused distortions in magnetotelluric measurement data

https://ruj.uj.edu.pl/xmlui/bitstream/handle/item/78136/baran_neural_networks_application_to_reduction_of_train_2009.pdf?sequence=1&isAllowed=y

Neural networks application to reduction of train caused distortions in magnetotelluric measurement data

Abstract

Similar works

Full text

Available Versions

Jagiellonian Univeristy Repository