Determining the Risk Level Regarding to the Positioning of an Exam Machine Used in the Nuclear Environment, based of polynomial regression Mihai OPROESCU1, Vasile-Gabriel IANA1, Mirela GHERGHE2, Mirel-Dorin STANICA3, Ioan LITA1 1. University of Pitesti, 2. Nuclear Medicine Laboratory, IOB, 3. University POLITEHNICA of Bucharest ABSTRACT In this paper is presented a computational algorithm, based on polynomial regression, used to predict the positioning of a universal exam machine. The universal exam machine works in nuclear environment, which makes it impossible to control using positioning sensors or cameras. In the same time, the exam machine is used for non-destructive analysis of nuclear materials. The exam machine operates with a stepper motor. The control parameters of the stepper motor have resulted from different conditions operation of stepper motor. Based on these parameters, a predictive polynomial method was developed to optimize the positioning of the exam machine controlling the stepper motor. This method is trained off-line using previously acquired data. This method is a part of predictive machine learning that is trained offline using previously acquired data. For hardware validation is implemented a circuit that use current sensors coupled to each phase of the stepper motor. The information received from those current sensors is sufficient to achieve, based on the prediction method, a very accurate prediction system respecting operating conditions of the exam machine. SPECIFIC PARAMETERS VALUES DETERMINATION OF STEPPER MOTOR Within the Institute of Nuclear Research (ICN), Piteşti, there is a system which control the universal exam machine for different non-destructive examination methods. This system is equipped with stepper motors to move the universal exam machine. A prototype at small scale similar to the one present in the ICN Pitesti was created, Figure 1, with a single axe drive according to the block diagram of Figure 2. Figure 1. Prototype of control Figure 2. Schematic bloc of system for stepper motor control system for stepper driving motor driving The information was obtained by testing a NEMA 17 stepper motor with the following specifications: step angle - 0.9 °, two phases; current / phases - 1.7A. Through this system was tracked the positioning error of stepper motor for different driving conditions: • the frequency of steps variable; • variable number of steps; • direction of rotation; • current through the phases of stepper motor. The set test parameters are as follows: Number of steps: 400, 800 and 1200 steps, where 400 steps representing a complete rotation; The stepper motor used has a resolution of 0.9 ° / step; The frequency of the steps is correlated with the time t = 55, 60, 65, ..., 120 ms. The stepper motor command was used in full step mode. Current through the stepper motor phases was chosen at follow values: 0.25A, 0.5A, 0.75A and 1 A Figure 3. Positioning error for Figure 4. Positioning error for 400 de steps 800 steps Figure 5. Positioning error for 1200 steps The engine was driven both clockwise and anti-clockwise, ranging the number of steps, time between 2 steps, and current through the stepper motor. From the result graphs it can be seen that the error increases with the reduction of the time between 2 steps and the decrease of the current value by the phase. REGRESSION POLYNOMIAL METHOD APPLIED There are several machine learning techniques that use advanced statistical methods to achieve regression modes with one or more input variables and a single output variable. To estimate the positioning error, is proposed a multiple regression to determine the relationship of the input variables (the time between the two steps and the value of the current through the phase) and the output variable representing the positioning error. In order to represent relations where the independent values versus predictor values give a non-linear function, a polynomial regression is used. Assuming there is only one predictive variable, the regression model can be represented by the relationship (3) Y = β0 + β1X1 + β2X2 + β3X12 + β4X22 +…+ βmX1n + βm+1X2n (3) The proposed evaluation using polynomial regression was used to predict the estimation error of stepper motor. The βm coefficients of the polynomial were obtained using scikit-learn Machine Learning in Python. The values of the time between 2 steps and the value of the current through the stepper motor phase were previously obtained, the training of the model realizing offline. Later, these coefficients are used directly in the control algorithm for prediction of the stepper motor positioning error. Figure 6. Predicted value of Figure 7. Prediction error of the positioning error regression model THE CONTROL SYSTEM PROPOSED BASED ON ERROR ESTIMATION Through a signal acquisition interface, the sensors value are applied to the predictive algorithm running on a PC. The error will be interpreted to modify stepper motor drive parameters following the rules in below table. TABLE 1. RULES TO CONTROL THE STEPPER MOTOR TABLE 2. THE PHASECURRENT RANGES, RESPECTIVELY STEPTIME, ARE: Parameter increment is proportional based on positioning estimated error. INTRODUCTION A specific feature to nuclear activities is that it cannot use any type of sensors or measurement and control equipment in radiated area. Universal exam machines are robots powered by stepper motors that have to position high-precision the nuclear material in a totally unfriendly environment. For the most part, these robots are operated in the open loop, without having any information about the current position. That is the reason for development of a prediction algorithm of positioning error. Several control techniques using stepper motors have been presented in the literature [1-5]. These techniques present both closed-loop control [1] and open-loop control [3, 4, 5] for stepper motors with position sensors [3] or without sensors [2]. Several control techniques for stepper motor have been presented in the literature [1-5]. These techniques present both closed-loop control [1] and open-loop control [3, 4, 5], for stepper motors with position sensors [3] or without sensors [2]. In second part of the paper is present the way in which the data from the stepper motor is acquired and the results obtained. In the third part is presented the predictive method of the positioning error. At the end of the paper is proposed a stepper motor control circuit based on estimated positioning error and stepper motor drive parameters. Copyright Colin Purrington (http://colinpurrington.com/tips/academic/posterdesign). Step Time Phase Current Error Decision low nothing HIGH 1. Increase StepTime 2. Increase PhaseCurrent Increase StepTime Increase PhaseCurrent STOP PhaseCurrent low   HIGH StepTime Conclusions This paper describes a method for predicting the positioning error of a stepper motor from a universal exam machine that works in the nuclear environment. To simulate the method, a prototype was made for providing the input data: the time between two phases and the value of the current through the phase. The result of the predictive error positioning method will be input for a motor stepper control circuit. The next step of the research is the practical implementation of the proposed method and the proposed control algorithm in order to validate the theoretical approach. The novelty of the paper is the combination between the machine learning and the circuit elements in Processor in Loop (PIL) systems to command and control, as accurately as possible, the universal exam machine in the nuclear environment, where it is impossible to use sensors or cameras to control the positioning Acknowledgments This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI – UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0419 / 71PCCDI, within PNCDI III The research that led to the results shown here has received funding from the following research projects of the Romanian National Authority for Scientific Research and Innovations, CNCS/CCCDI-UEFISCDI within PNCDI III: “Experimental validation of a propulsion system with hydrogen fuel cell for a light vehicle - Mobility with Hydrogen Demonstrator”, 53PED, ID: PN-III P2-2.1-PED-2016-1223; and European Space Agency within STAR (Space Technology and Advanced Research): “Concept Development of an Energy Storage Unit Using High Temperature Superconducting Coil for Spacecraft Power Systems (SMESinSpace)