Artificial Neural Networks for New Operating Modes Determination for Variable Energy Cyclotron

Transcription

1 Artificial Neural Networks for New Operating Modes Determination for Variable Energy Cyclotron M. Abd El- Kawy, M-Shaker Ismail, M. Abdel-Bary, and M.M.Ouda Department of Computer and system & Eng., Faculty of Eng.,Zagazig Univ., Zagazig,Egypt. Engeneering and Scientific Dep., Nuclear Research Center, Atomic Energy Authorty, Egypt. ABSTRACT An artificial neural network System (ANNS) has been designed to determine the required parameters for new Operating Modes for the MGC 20 cyclotron operation. The inputs of the ANN are the required beam parameters (the particle name, the particle energy, the beam intensity and the duty factor). The outputs of the ANN are the value of the required parameters that will be applied by the cyclotron operator to the cyclotron elements or devices. These elements are the magnetic lenses, the magnetic correctors, the concentric coils, and the harmonic coils. Four ANN have been used. The input signals are distributed to the Four ANN inputs. The outputs of the Four ANN will be calibrated and then directly applied by the operator to produce the required beam. A three layers ANN structure has been used and the feed forward back propagation algorithm has been used for training. The MATLAB software has been used to simulate the ANN structure. Key Words: Intelligent Systems / Neural Networks / Cyclotron. INTRODUCTION Artificial neural networks (ANNs) have rapidly grown in popularity. They are artificial intelligence adaptive software systems that have been inspired by how biological neural networks work. They are used because they can learn to detect complex patterns in data. In mathematical terms, they are universal function approximates meaning that given the right data and configured correctly; they can capture and model any input-output relationships. This not only removes the need for human interpretation of charts or the series of rules for generating input/output signals, but also provides a bridge to fundamental analysis, as the variables used in fundamental analysis can be used as input. As ANNs are essentially non-linear statistical models, their accuracy and prediction capabilities can be both mathematically and empirically tested. Neural networks can classify condition patterns of a system as normal or faulty. They are also highly efficient in detecting patterns and regularities in the input data. Also the inherent parallelism of these networks allows very rabid parallel search and best match computations. This methodology resulted in a great potential benefit in many applications (1). Core monitoring models have been developed with the use of neural networks to predict the core parameters for the pressurized water reactors (2). One of the important applications of neural networks is using them for modeling the complex dynamic systems to build a model that simulate the real - world processes in which empirical measurements of the external and state variables are obtained at discrete time points (3). The neural networks are used to crowd estimation at underground stations. A hybrid fast training algorithm for feed forward networks is used in the algorithm that used in this application (4).The ANN was used also in many different industrial applications especially in process control system. It was used for tuning and optimizing proportional integral derivative (PID) feedback controllers (5). In this paper, a neural network system is developed to determine the required parameters of new operating modes for the operation of the MGC 20 cyclotron. The neural network system consists of four feed forward back propagation neural networks in parallel. The back propagation training

2 algorithm (6) is used for the neural networks training. The input signals to the neural network system are the goals of the new operating mode which are the particle name, the energy, the current intensity, and the duty factor. The new operating mode goals are distributed to the inputs of the four neural networks. The outputs of the four neural networks are firstly calibrated to give the required real current values which can be applied by the operator to the lenses, correctors, concentric, internal and external harmonic coils. The outputs of artificial neural network no.1 are the currents that will be applied to the coils of the magnetic lenses. The outputs of the artificial neural network no.2 are the currents that will be applied to the coils of the magnetic correctors, the outputs of the artificial neural network no.3 are the currents that will be applied to the concentric coils. The outputs of the artificial neural network no.4 are the currents that will be applied to the internal and external harmonic coils. The Mgc-20 Cyclotron EXPERIMENTAL The MGC-20 cyclotron operating in of the nuclear research center Egypt is an azimuthally varying field cyclotron with spiral sectors. It accelerates protons, deuterons, alpha particles and helium-3 to different energies. The applications are isotope production, nuclear reaction, and nuclear spectroscopy studies. The MGC-20 cyclotron has two hollow metal accelerating electrodes, called dees, between them an oscillating electric field generated by a radio frequency generator (6, 7). The charged particles are produced by the ion source, which are located centrally between the two dees. The magnetic field of the cyclotron main magnet causes the particles to move in an approximately circular orbit. Figure (1): Schematic diagram for the MGC-20 cyclotron and beam lines components. The radius of the orbit is a function of the particle velocity, therefore the radius increases with time, so the particles follow a spiral path from the ion source to the edge of the magnet, where they pulled out from the cyclotron by an electrostatic deflector. The extracted beam is guided by the beam transportation system to the users as shown in Figure (1). The neural network system will help the operators to determine the value of a set of parameters required to accelerate a particle to certain energy and current intensity. These parameters are related to the following components of the cyclotron;

3 The magnetic lenses: every lens is a quadruple doublet. There are two lenses in the beam transport system. Every quadruple doublet lens has two coils to be able to achieve a compromise focusing for the beam. Every coil has its own DC power supply to bias it with the suitable required current to achieve the required beam focusing. The magnetic correctors: or steering magnets, they are small dipole magnets, used to change the position of the beam with respect to the axis of the beam line. It can deflect the beam in the horizontal and vertical planes with some degrees. There are two correctors in the beam transport system. Every corrector has two coils to be able to achieve a compromise centering for the beam. Every coil has its own DC power supply to bias it with the suitable required current to achieve the required beam position centering in the beam tube. The concentric coils; these coils are fixed on the front of the main magnet poles as shown in Figure (2). There are five concentric coils which are used to produce the required increase of the average magnetic field with radius to overcome the increasing of the particles mass due to the relativistic effects. The internal and external harmonic coils; the harmonic coils are used to put magnetic field bumps into the main field at desired radius to center the beam orbits (the internal harmonic coils) as well as in the center of the cyclotron to keep the extraction at the end of the accelerations Figure (2): Schematic diagram for the central region of the MGC -20 cyclotron. Conventional Method for New Operating Modes Determination Conventional method for new operating mode determination for the MGC-20 cyclotron (8) depends on the trial and error of the cyclotron human experts, who are the group responsible for the cyclotron operation and maintenance. Due to the cyclotron complexity and the many parameters affecting the particle since its extraction from the ion source by using the puller to continue in acceleration inside the cyclotron and then extraction outside the cyclotron by using the deflector to be guided inside the beam transport system to the end user. This makes a new operating mode determination for certain particle a very complex, time consuming and tedious for the operators. To save the time and simplify this complexity to achieve a new operating mode an ANN system has been designed and tested to help the operators of the cyclotron to achieve the parameters of the required operating mode. The designed ANN system will use the particle name, the required energy, the beam

4 current intensity and the duty factor to determine the operating mode parameters. The parameters are summarized in table (1) with the corresponding neural network number. Neural Networks - A Principle Review Artificial Neural Networks (ANN) is a parameterized non-linear models used for determining the required parameters of the operation modes of the MGC20 cyclotron. (ANN) is inspired by understanding of biological neural networks. ANN is composed of basic units called artificial neurons, which are the processing elements in the network (8). Each neuron receives input data, processes it and delivers a single output. The input can be a raw of data or output of other neurons. The output can be the final product or it can be an input to another neuron. The learning algorithm used for training the multilayer feed forward neural network is the Back Propagation training algorithm (BP) (8, 9, 10). It has some features that make the operation of an ANN more reliable. The first feature is that back propagation (BP) training is designed to minimize the mean squared error between the desired output and the actual values across the training set. Also it is a supervised training technique. It enables the designer to generate the desired result, if the error between the desired and the actual outputs is sufficiently small, then no training take place, otherwise training continue. (ANN) has been developed for parametric applications in a wide variety of domains. Neural networks involve fundamentally different approaches to the parametric task. This approach contains its own strengths and weaknesses. Table (1): Parameters of the operating modes to be determined by the designed ANN system. No. Parameter name of the cyclotron NN The current of the first coil of the first lens The current of the second coil of the first lens The current of the first coil of the second lens The current of the second coil of the second lens The current of the first coil of the first corrector The current of the second coil of the first corrector The current of the first coil of the second corrector The current of the second coil of the second corrector The current of the first concentric coil The current of the second concentric coil The current of the third concentric coil The current of the fourth concentric coil The current of the fifth concentric coil The current of the first internal harmonic coil The current of the second internal harmonic coil The current of the third internal harmonic coil The current of the first external harmonic coil The current of the second external harmonic coil The current of the third external harmonic coil Neural networks are fast, handle noisy data well and learn from experience. However, they are black box, operators unable to explain its own reasoning methodology, and forget past training if retrained on new data. DESIGN OF THE NEURAL NETWORK SYSTEM The developed Neural Network System (NNS) has used a multilayer feed forward back propagation neural network as the model of the neural network with three layers, input layer, hidden

5 layer, and output layer (11, 12). In order to decrease the complexity of the neural network, increasing the classification accuracy, and to reduce the required time to determine a new operating mode, four neural networks have been used in parallel. The input signals (particle type, particle energy, beam current intensity, and the duty factor) are distributed to the four neural network inputs as shown in Figure (3). The first neural network has four input neurons, four hidden neurons and four output neurons corresponding to the current values for the four coils of the two magnetic lenses. The second neural network has four input neurons, six hidden neurons and four output neurons corresponding to the current values for the four coils of the two magnetic correctors. The third neural network has four input neurons, ten hidden neurons and five output neurons corresponding to the current values for the five concentric coils. The forth neural network has four input neurons, ten hidden neurons and six output neurons corresponding to the current values for the six coils of the six harmonic coils. Fig.. (3) Shows the structure of the four neural network systems, the learning factor of the four neural networks is η= Figure (3): Schematic diagram for the artificial neural network system used to determine new cyclotron operating modes. Neural Network 1: A three layer feed forward back propagation neural network has been used to execute this network; the input layer has four neurons. The output layer has four neurons. Every output neuron corresponds to a coil from the quadruple lenses. The first output neuron signal represents the value of current to be applied to the first coil in the first quadruple lens L 11. The second output neuron signal represents the value of current to be applied to the second coil in the first quadruple lens L 12. The third and fourth output neurons signals represent the value of currents to be applied to the first and second coils in the second quadruple lens L 21 and L 22 respectively to produce the required operating mode. The signal value of the output neurons must be calibrated (to be real current values) before the operator applies them to the lenses coils. The learning is done using different values of the learning factor η, also for different numbers of the hidden layers neurons. The optimal first NN structure is achieved with four neurons in the hidden layer. Neural Network 2: A three layer feed forward back propagation neural network has been used to execute this network; the input layer has four neurons. The output layer has four neurons. Every output neuron

6 corresponds to a coil from the dipole magnets. The first output neuron signal represents the value of current to be applied to the first coil in the first dipole magnet C 11. The second output neuron signal represents the value of current to be applied to the second coil in the first dipole magnet C 12. The third and fourth output neurons signals represent the value of currents to be applied to the first and second coils in the second dipole magnet C 21 and C 22 respectively to produce the required operating mode. The signal value of the output neurons must be calibrated (to be real current values) before the operator applies them to the dipole magnets coils. The learning is done also using different values of the learning factorη, also for different numbers of the hidden layers neurons. The optimal second NN structure is achieved with six neurons in the hidden layer. Neural Network 3: A three layer feed forward back propagation neural network has been used to execute this network; the input layer has four neurons. The output layer has five neurons. Every output neuron corresponds to a coil from the concentric coils (see Figure 2). The first output neuron signal represents the value of current to be applied to the first concentric coil C 1. The second output neuron signal represents the value of current to be applied to the second concentric coil C 2. The third, fourth and fifth output neurons signals represent the value of currents to be applied to the third, the fourth and fifth concentric coils C 3, C4 and C 5 respectively to produce the required operating mode. The signal value of the output neurons must be calibrated (to be real current values) before the operator applies them to the concentric coils. The learning is done also using different values of the learning factor η, also for different numbers of the hidden layers neurons. The optimal third NN structure is achieved with ten neurons in the hidden layer. Figure (4) shows the typical final structure for the ANNS for the concentric coils. Neural Network 4: A three layer feed forward back propagation neural network has been used to execute this network; the input layer has four neurons. The output layer has six neurons. Every output neuron corresponds to a coil from the harmonic coils (see Fig. 2). The first output neuron signal represents the value of current to be applied to the first internal (Int.) harmonic coil HI 1. The second output neuron signal represents the value of current to be applied to the second internal harmonic coil HI 2. The third output neuron signal represents the value of current to be applied to the third internal harmonic coil HI 3. The fourth, fifth and six output neurons signals represent the value of currents to be applied to the first, second and third external (Ext.) harmonic coils HE 1, HE 2 and HE 3 respectively to produce the required operating mode. The signal value of the output neurons must be calibrated (to be real current values) before the operator applies them to the harmonic coils. The learning is done also using different values of the learning factor η, also for different numbers of the hidden layers neurons. The optimal fourth NN structure is achieved with 10 neurons in the hidden layer. Testing of the Neural Network System RESULTS AND DISCUSSION The testing phase examines the performance of the network using the derived weights. Measuring the ability of the network to classify the testing data correctly is done. If problems are appeared in the testing, various factors may be examined, like the format of the training data, model parameters values, and the structure of the network. For the first neural network, the number of testing patterns is 30, and the error factor of the neural network is For the second neural network, the number of testing patterns is 45, and the error factor neural network is For the neural network, the number of testing patterns is 50, and the error factor neural network is For the

7 internal and external of the forth neural network, the number of testing patterns is 50, and the error factor of internal is and external is Figure (4): The typical final structure for third NN for the concentric coils. Table (2): 10 patterns recalls for testing the trained third neural network. Pattern Neural Networks Inputs Neural Networks Outputs No. particle Energy Current Duty Intensity MeV factor µa CC1 CC2 CC3 CC4 CC Table (2) shows 10 patterns for testing the developed four neural networks. The shown output values in the table are the normalized values corresponding to the real current values to be used to start this operating mode. The operator should calibrate these normalized values to be real currents. The minus sign express only the current direction in the corresponding coil. The first pattern shows that this operating mode is for producing the particle (proton) with energy of (18 MeV) and current intensity (10 µa) at a duty factor of 10.

8 Comparison with the real corresponding mode one can realize that these operating modes are a good start for the operator and that the operator has to make fine tuning for the current values to achieve the best beam current at the end user experiments. Table (3) shows the values of the corresponding real operating mode parameters. One can realize a little difference between the real operating mode and the determined operating mode in the values of the currents. Table (4) shows the values of the error factor for the four neural networks. Table (3): Real operating modes patterns to be compared with the outputs of NN-3. Pattern Neural Networks Inputs Neural Networks Outputs No. particle Energy Current Duty Intensity MeV factor µa CC1 CC2 CC3 CC4 CC Table (4): The error factor of the four neural networks. NN Parameters I/P neurons O/P neurons Hidden neurons Error factor NN1 lenses NN2 Correctors NN3 Concentric coils NN4 Harmonic coils 4 3 Int. Har. coils Ext. Har coils CONCLUSION An artificial neural network system has been designed to determine new operating modes for the Egyptian Cyclotron MGC-20. The system was trained by using the currently used operating modes. The trained system was tested to check the suitability of the new determined operating modes. The tests showed that the new operating modes are good enough as a starting condition which followed by fine tuning by the cyclotron operator. Comparison between the parameters of real operating modes and the parameters of new operating modes showed little deviation in the currents values. The artificial neural network system consists of four parallel neural networks each has four inputs (ion name, ion energy, ion beam intensity, and the duty factor). These values are firstly calibrated and then applied to the four neural networks. The outputs of the four neural networks are the normalized values of the mode parameters. These values are calibrated to give the real values of the

9 parameters of the new operating mode. The artificial neural network system used the feed forward back propagation as the training algorithm. The Matlab software is used to simulate the neural networks structure and the training algorithm (13). REFERENCES (1) G. Dreyfus, Neural Networks Methodology and Applications, Springer-Verlag, Berlin Heidelberg (2005). (2) B.H. Koo, H.C. Kim, and S. H. Chang; IEEE Transactions on Nuclear Science; 40 (5), 1347 (1993). (3) C. A.L. Bailer-Jones and D. J.C. MacKay; Computation in Neural Systems; 9; 531 (1998). (4) T.W.S. Chow, J.Y.-F. Yam, and S.-Y Cho; Artificial Intelligence in Engineering; 13, 301 (1999). (5) K. C. Chan, S. S. Leong and G. C. I. Lin; Artificial Intelligence in Engineering; 9, 167 (1995). (6) Debrecen, Hungary, Institute of Nuclear Research (ATOMKI), Hungarian Academy of Sciences, Personal communication (1996). (7) M. S. Livingston, and J. P. Blewett, Particle Accelerators, Mc Graw- Hill Book Company (1962). (8) M. Aziz, E Massoud Conceotual Design of Neutron Radiography and Boron Neutron Capture Therapy at Mgc-20 Cyclotron" The Egyptian Society of Nuclear Sciences& Applications (2005). (9) M.M. Abd El-Bary, Aneural Network Based Expert System For Fault, Diagnosis Of Particle Accelrators M.Sc.Thesis, Department of Computer Science& Eng.,Faculty of Electronic Eng., Menoufia University, Egypt (1997). (10) Z. Kormány, I. Ander, P. Kovács, T. Lakatos and I. Szûcs Renewal and Automation of The Atomki Mgc-20 Cyclotron Proceedings of EPAC, Vienna, Austria (2000). (11) A I. Galushkin, Neural Networks Theory, Springer-Verlag, Berlin, Heidelberg (2007). (12) J.M. Zurada, Introduction To Artificial Neural Systems Manual of neural network, West Publishing Company (1992). (13) M.Hagan, H.Demuth, and M.Beale, Neural NetworkToolbox, For Use with MATLAB ", Manual of software (2006).