This project is based on the data set that comprises several sensor data collected from a PMSM deployed on a test bench. The PMSM represents a German OEM's prototype model. The LEA department at Padeborn University collected test bench measurement. The main purpose of the data set's recording is to be able to model the stator and rotor temperatures of a PMSM in real-time. Due to the intricate structure of an electric traction drive, direct measurement with thermal sensors is not possible for rotor temperatures, and even in case of the stator temperatures, sensor outage or even just deterioration cannot administer properly without redundant modelling. In addition, precise thermal modelling gets more and more important with the rising relevance of functional safety. The main task in this project is to design a model with appropriate feature engineering that estimates four target temperatures casually.
Article purpose is predicted the temperature of a synchronous motor with a permanent
magnet using machine-learning methods [
Having accurate engine temperature estimates helps the automotive industry produce engines with lower material content and enables management strategies to use the engine to its maximum potential.
An electric motor with implicit poles has equal inductance along the longitudinal
and transverse axes, whereas an electric motor with explicit poles has a transverse
inductance not equal to the longitudinal one [
PMSM cannot started when directly connected to the network. To do this, the following options are used: Start with an additional engine. To do this, the shaft is connected to the shaft of another electric machine. This method is expensive and practically not used; Start in asynchronous mode. The rotors of such electric motors have a shortcircuited winding. The start-up takes place in asynchronous mode. After entering the synchronization, the rotor winding is disconnected; Start with a frequency converter. The frequency converter is included in the stator winding circuit and supplies voltage to them by gradually increasing the frequency. 2
The study of a permanent magnet synchronous motor is conducted in the laboratory of
the University of Paderborn, where the following results are presented in [
Maximizing the degree of thermal use of PMSM reduces the weight, volume and
cost of the engine. For this reason, real-time temperature information is required.
However, this cannot obtain solely by measuring sensors due to costs and design
flaws. Thus, in recent years, several methods of direct temperature modelling have
investigated, such as heat networks with concentrated parameters (LPTN), as well
as methods of indirect temperature estimation based on accurate models of electric
motors that detect changes in temperature-sensitive parameters. Because these
methods are usually independent of each other, fusion methods can used to
increase the accuracy and reliability of the joint assessment. In this study, a Kalman
filter (KF) is successfully combined with a low-order LPTN, an electric model
permanent magnet temperature monitor, and a built-in winding temperature sensor
to achieve this goal. Measurement results for PMSM with a capacity of 50 kW
confirm the increased productivity of KF in comparison with individual assessment
methods [
To implement the main task of this study, the method of machine learning Random
Forest is chosen [
Random forest is an ensemble machine learning method for classification,
regression, and other tasks that operate by constructing numerous decision-making trees
during model training and producing fashion for classes (classifications) or averaged
prediction (regression) of constructed trees [
Disadvantages of the Random Forest method [39-48]: The algorithm tends to relearn on some tasks, especially with a lot of noise in the data set; Learning large numbers of deep trees can be costly (but can be parallel) and use a lot of memory. 3
This study uses a data set that contains sensory data collected from the PMSM placed on a test bench. PMSM is a German prototype model from the original equipment manufacturer. The LEA department of the University of Paderborn assembled the measuring stand. The main purpose of recording a data set is to be able to simulate the temperature of the stator and rotor of the SPD in real time. Due to the complex design of the traction drive, direct measurement of the rotor temperature by thermal sensors is not possible, increase in stator temperature, sensor shutdown or even simply deterioration of the quality of work cannot properly monitor without excessive simulation. In addition, accurate thermal modelling is becoming increasingly important with the importance of functional safety. The main features of the selected data set are the next ones: ambient - The ambient temperature is measured by a temperature sensor located close to the stator; coolant - The temperature of the coolant. The motor is cooled by water. The measurement is performed at the outflow of water; u_d - Voltage of the d-component; u_q - Q-component voltage; motor_speed - Engine speed; torque - Torque induced by current; i_d - Current d-component; i_q - Current of the q-component; profile_ID - Each measurement session has a unique identifier.
Target features of the selected data set are the next ones: pm – The surface temperature of the permanent magnet, which is the temperature of the Rotor; stator_yoke – The stator yoke temperature is measured using a temperature sensor; stator_tooth – The temperature of the stator teeth is measured using a temperature sensor; stator_winding – The temperature of the stator winding is measured using a temperature sensor.
Additional information about the data set are the next ones: All recordings are selected at a frequency of 2 Hz (One row in 0.5 seconds). The data set consists of several measurement sessions, which can distinguished from each other by the column "profile_id". The measurement session can last from one to six hours. The number of sessions: 52. The engine is accelerated by manually designed driving cycles, indicating the reference engine speed and reference torque. Currents in the d / q coordinates (columns “i_d” and “i_q”) and voltages in the coordinates d / q (columns “u_d” and “u_q”) are the result of a standard control strategy that tries to follow the reference speed and torque. The columns “motor_speed” and “torque” are the resulting values achieved by this strategy, obtained from the specified currents and voltages. Most motion cycles denote random wanderings in the velocity-torque plane to simulate real motion cycles more accurately than constant excitements and difficulties.
Given that, the main task of this project is to develop a model that predicts the temperature values of such SPDM elements as stator and rotor according to already collected sensory data from the SPD prototype model, this project should not consider as a development of a global SPD control system in cars or other mechanisms. It is better to consider it as a part of this system (hereinafter: component), which is responsible for predicting stator and rotor temperatures using sensor data from other elements of PMSM, because to obtain data from stator or rotor using temperature sensors is unreliable and commercially unprofitable.
The following are two UML diagrams, namely an activity diagram that describes
the process of the machine-learning model and a sequence diagram that describes the
interaction between the control system and the model [
This diagram on Fig. 1-2 shows the following activities [
Fig. 3 shows upload data to the format pandas dataframe:
Features described above: Count is reported the number of non-empty rows in the column. Mean is reported as the average value of the data in the column. Std specifies the default value of the data deviation in the column. Min is reported as the minimum value of data in the column. 25%, 50%, and 75% are represent the percentile/quartile of each sign. Max is reported as the maximum value in the column.
Fig. 7 shows swing charts for all signs. Fig. 8 shows the correlation matrix.
A list of all test runs(profile_id) is presented in Fig.9.
After studying the data set, the following conclusions can be drawn: The data set does not contain NaN values; Indicators for test cycles are not incremental. The description of the data set does not provide references to the units of measurement used for each of the samples, which complicates the interpretation of the measured values. A statistical review of the data set and histograms shows that the data set already has some normalization. As is already known, the ambient temperature is measured by a thermal sensor located close to the stator. Therefore, it can be assumed that this will affect the ability of the motor to cool itself. Higher ambient temperatures are likely to increase the temperature for both the motor stator and the rotor. The correlation matrix shows that there is a significant correlation between three different stator temperatures. 4.2
As mentioned above, there is a significant correlation between the temperature of the stator winding, the stator yoke, and the stator teeth. This is, of course, because the stator winding is wound around the stator tooth, which in turn is connected to the stator yoke. For better understand the relationship between the three traits, we plot the values of the traits for different randomly selected test cycles.
Fig. 14. Graphs of values of stator temperature signs for profile id: 75.
These line charts show that all three temperatures correspond to the same trend. The temperature of the stator winding shows the largest changes, followed by the temperature of the stator teeth and the stator yoke. This is especially noticeable in those diagrams where the stator winding temperature varies greatly. In this case, the temperature of the tooth and the stator yoke increases and decreases more smoothly compared to the temperature recorded on the stator winding. In other words, the heat dissipated by the stator windings requires some time to heat the teeth and the stator yoke due to the thermal inertia of both parts of the stator.
The second observation that can made from these line diagrams is that sometimes the stator yoke temperature is higher than the stator winding. Nor can we determine whether this is related to the normalization method used previously mentioned, or whether these values represent higher temperatures measured per stator yoke.
Line diagrams for comparing stator temperatures with torque and motor speed are presented in Fig.18-21.
In the second part of the above test cycle, you can see that there is a relationship between stator temperature, torque, and motor speed. With increasing torque and/or engine speed, the stator temperature increases, and vice versa decreases with decreasing. However, look at the first part of the test run; it is clear that this dependence is not always fulfilled. Even at constant torque and motor speed, the stator winding temperature shows several sudden temperature changes. One or more other variables affect the stator temperature more significantly than torque and motor speed. 4.3
Since the measurement of torque, rotor, and stator temperature of an electric motor is not reliable and economically feasible in commercial programs, we will predict the stator temperature using other available functions in the data set. To do this, remove the torque, rotor and stator temperature from this data set, and use the stator winding temperature as the target value. After that, we train the Random Forest Regressor model to predict the correct stator winding temperature as the output value for the specified input variables. Input variables are: Ambient temperature; Coolant temperature; Voltage of the d-component (u_d); Q-component voltage (u_q); Engine speed (motor_speed); D-component current (i_d); The current of the q-component (i_q).
Target variable: stator winding temperature (stator_winding). Rejectable variables are: Engine torque; Rotor temperature (pm); Stator yoke temperature (stator_yoke); Stator teeth temperature (stator_tooth).
At the end of the model learning process, the values of the Mean Absolute Error (MAE) and the Mean Square Error (MSE) are calculated.
The MAE is a loss function used for regression. Loss is the average value for the absolute differences between true and predicted values, deviations in any direction from the true values are treated the same. The MAE for this model is: .
The MSE, like the MAE too, treats the deviation in any direction the same. The difference between MSE and MAE is that MSE is more likely to notice large errors because it squares all errors. The closer the values of MAE and MSE to zero, the closer the predicted values of the algorithm to the true ones. Comparing diagrams of the predicted and true values of several test runs are shown in Fig.22-25.
In these comparing diagrams, it can seen that the model is able to capture the global trend in the stator winding values, but there is still a lot of noise in the predicted values, especially when the true signal shows a large number of changes. To filter the noise generated by the model, apply the smoothing method to the output signal. MSE and MAE values and linear diagram of the output signal for test run id_72 without smoothing: MSE and MAE values and linear diagram of the output signal for test run id_72 with smoothing: In combination with smoothing, the Random Forest Regressor performs a fairly accurate prediction of the stator winding temperature. Smoothing reduced the noise level in the predicted values and had a positive effect on MSE for this particular technology.
Let's compare Random Forest with such algorithms as k-NN, SVM, and linear regression.
The figures below show the following characteristics: model training time in seconds, model accuracy for test set, MSE and MAE for test set.
Fig. 29. Characteristics of the k-NN model.
Fig. 31. SVM model characteristics.
The following are line graphs of several randomly selected test cycles depicting the models described above colours: black - original data, red - data predicted by Random Forest method, blue - data predicted by k-NN method, green - data predicted by SVM method, purple - data predicted by Linear Regression method.
Fig. 32. Comparing diagram of predicted and true values: profile_id: 6. Also, compare the work Random Forest method on different PCs. Below is a table of components of these PCs (Table 1) and a picture of the characteristics of the robots of the Random Forest method on these PCs.
Thus, comparing the characteristics of different models and line charts for different test runs, we can divide the above models into 2 groups: Random Forest and k-NN that show forecast accuracy above 90%, and Linear Regression and SVM with forecast accuracy less than 65%. K-NN is 113 seconds faster than Random Forest, but 3.1% less accurate. In addition, having tested the Random Forest model on different PCs, we can conclude that for faster learning and forecasting of the model it is necessary to use faster data carriers. 5
Since the Random Forest Regressor with smoothing performs more than sufficient prediction at the stator temperature (as shown by the various line diagrams shown below), to use a relatively modest model like this is much better than more bulky and requiring more memory alternatives such as k-NN, Linear Regression, and various neural networks. The purpose of this work was to predict the temperature of a synchronous motor with a permanent magnet using machine-learning methods. First of all, in this work, a study of the subject area and a review of publications with research established in the laboratory of the University of Paderborn SDPM. With the help of the unified UML language, diagrams are designed that show how the implemented model can act as a part of the control system of the mechanism that works on SDPM. To implement this project, the method of machine learning Random Forest Regression is chosen. The implementation tool is the Python programming language with add-ins such as NumPy, Pandas, Scikit-learn, Matplotlib, and Seaborn. A comparison of the machine learning method and the means of implementation with analogues is also performed. Because of this project, a study of data from the SDPM sensory data set is conducted, the predicted feature, which was the temperature of the stator winding, is determined, and this feature was predicted. After analysing the obtained forecasting results, we can conclude that the purpose and main objectives of this work are achieved and the trained model can be used to accurately estimate and predict the stator and rotor temperatures of a synchronous motor on permanent magnets. 33. Andrunyk, V., Berko, A., Rusyn, B., Pohreliuk, L., Chyrun, S., Dokhniak, B., Karpov, I., Krylyshyn, M.: Information System of Photostock Web Galleries Based on Machine Learning Technology. In: Computational Linguistics and Intelligent Systems, COLINS, CEUR workshop proceedings, Vol-2604, 1032-1059. (2020). 34. Veres, O., Rishnyak, I., Rishniak, H.: Application of Methods of Machine Learning for the Recognition of Mathematical Expressions. In: CEUR Workshop Proceedings, Vol-2362, 378-389. (2019) 35. Kosarevych, R.J.,Rusyn, B.P.,Korniy, V.V.,Kerod, T.I.: Image Segmentation Based on the Evaluation of the Tendency of Image Elements to form Clusters with the Help of Point Field Characteristics. In: Cybernetics and Systems Analysis,51(5), 704-713. (2015) 36. Varetskyy, Y.,Rusyn, B.,Molga, A.,Ignatovych, A.: A New Method of Fingerprint Key Protection of Grid Credential. In: Advances in Intelligent and Soft Computing, 84, 99103. (2010) 37. Zhengbing, H., Yatskiv, V., Sachenko, A.: Increasing the Data Transmission Robustness in WSN Using the Modified Error Correction Codes on Residue Number System. In: Elektronika ir Elektrotechnika, 21(1), 76-81. (2015) 38. Sachenko, A., Kochan, V., Kochan, R., Turchenko, V., Tsahouridis, K., Laopoulos,T.: Error compensation in an intelligent sensing instrumentation system. In: Conference Record IEEE Instrumentation and Measurement Technology Conference, 869-874. (2001) 39. Sachenko, S., Pushkar, M., Rippa, S.: Intellectualization of Accounting System. In: International Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applicationsm, 536 – 538. (2007) 40. Sachenko, S., Rippa, S., Krupka, Y.: Pre-Conditions of Ontological Approaches Application for Knowledge Management in Accounting. In: International Workshop on Аntelligent Data Acquisition and Advanced Computing Systems: Technology and Applications,. 605-608. (2009) 41. Oksanych, I., Shevchenko, I., Shcherbak, I., Shcherbak, S.: Development of specialized services for predicting the business activity indicators based on micro-service architecture.
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