Sensorless Coil Temperature Measurements using Neural Networks

for Voltage Control

Linus Taenzer

1 a

, Chaﬁc Abu-Antoun

2 b

and Jasmin Smajic

1 c

Institute of Electromagnetic Fields, ETH Zurich, R

amistrasse 101, Zurich, Switzerland

DAS Data Science, ETH Zurich, R

amistrasse 101, Zurich, Switzerland

Keywords:

Linear Induction Actuator, Virtual Sensor, Artiﬁcial Intelligence, Neural Network, Gaussian Process

Regression, System Simulation, Voltage Control.

Abstract:

Voltage and current measurement data based deep learning as a method to conduct sensorless coil temperature

prediction of an embedded linear induction actuator is being proposed and validated in this work. Generated

numerical data from Finite Element ﬁeld simulations are used to train a neural network which in turn predicts

temperatures at non-accessible places e.g. at an embedded coil. The network is demonstrated and the compar-

ison to experimental data shows the potential of virtual sensing. Even though the number of physical sensors

have increased enormously in the last decades, the measurement of desired temperatures at certain locations is

limited by accessibility and by the application itself, for example, if a coil is used as a moving part in an actu-

ator. This work proposes an indirect method based on measurable quantities in the device, such as voltage and

current, to quantify precisely temperatures and hot spots in sensitive parts of the device. As high temperatures

can have a huge effect on the device’s performance, a controllable voltage to compensate the performance re-

duction instantaneously is desired. Applications based on the principle of an inductive linear actuator show a

strong performance dependency on the temperature of the conducting material or coil. The authors present an

Artiﬁcially Intelligent voltage controller to achieve the desired performance based on measurable variables in

the device and supported by sensorless methods like temperature prediction with Artiﬁcial Intelligence (AI).

1 INTRODUCTION

Induction actuators cover a wide range of applica-

tions such as arc suppression, high-speed mechanical

switches and hybrid DC circuit breakers where very

fast operating cycles are required (Vilchis-Rodriguez

et al., 2019). Different concepts exist using the ad-

vantages of coils and repulsion disks. The character-

istics of such processes are a very short energizing

time and fast movements within milliseconds. In DC

circuit breakers, current pulses are created by the dis-

charge of a capacitor. With the generation of eddy

currents, a repulsive force drives a rod up and down

to ensure the stability of power grids, in case of volt-

age drops or power failures (Dong et al., 2011). The

induction actuator is a standard concept for switches

such as circuit breakers. By using a circuit breaker,

the load can be disconnected. This leads to the occur-

rence of electric arcs. The inductive linear actuator’s

https://orcid.org/0000-0003-3574-9241

https://orcid.org/0000-0001-8644-7281

https://orcid.org/0000-0002-1209-7570

principle is attractive as it allows simple designs and

high speed actuation while providing reliability and

stability (Lim et al., 2013).

An induction actuator based application with iter-

ative cycles is investigated for a wide range of appli-

cations and thermal conditions. The repetitive peri-

ods during operation can lead to overheating of the

system. Due to the excited coils and induced eddy

currents, the temperature rise in the coils is huge

and therefore affects the resistance of the coils. The

temperature levels in a fast repetitive mode typically

require active cooling. For further heat reduction,

a voltage controller is needed to deﬁne the voltage

charging level of the capacitor during every cycle.

The measurement of the temperature in an embedded

coil is very difﬁcult due to limited space and would

lead to fast failure of the sensor due to high temper-

atures and forces. Instead of the temperature other

properties such as current and voltage can be mea-

sured and based on these data, the demperature can be

determined. There are many applications that use AI

for integrating virtual sensors to determine complex

830

Taenzer, L., Abu-Antoun, C. and Smajic, J.

Sensorless Coil Temperature Measurements using Neural Networks for Voltage Control.

DOI: 10.5220/0010251708300836

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 2, pages 830-836

ISBN: 978-989-758-484-8

Figure 1: Linear induction actuator.

variables using already existing sensor data. Some

authors (Gonzaga et al., 2009) use a feed-forward ar-

tiﬁcial neural network for the design of a soft sensor

to estimate the PET viscosity in real time and then

control the polymerization process. Neural networks

as well as Kalman ﬁlters are suitable methods to de-

termine the temperature for highly non-linear systems

such as batteries (Charkhgard and Farrokhi, 2010).

2 LINEAR INDUCTION

ACTUATOR

In Fig. 1, the design of the induction actuator is shown

in detail. The system consists of a coil surrounded

by a stator which guides the magnetic ﬁeld closely

through the coil. The conductive ring is placed in-

side the coil guided by a shaft. When the switch is

turned on, the loaded capacitor is discharged through

the coil. The current in the coil causes a time vary-

ing magnetic ﬁeld and induces eddy currents in the

conductive ring in the opposite direction to the coil

current. Due to the magnetic ﬁeld and the current

in the coil and conductive ring, a repulsion force is

generated between the two conductors and the ring

moves away. The capacitor is charged with an en-

ergy E

max

and generates a current pulse that reaches

a maximum value I

max

. The main target of this sys-

tem is always a constant desired kinetic energy of the

conductive ring, regardless of the frequency of repet-

itive loadings. Under operating conditions with sev-

eral cycles per minute, the accompanying heat gen-

eration leads to a signiﬁcant temperature rise, which

results in a limited performance as the temperature di-

rectly inﬂuences the coil resistance. The time interval

in Fig. 2 consists of two different segments. On the

one hand, the stroke period P

, on the other hand the

waiting period P

wait

in which the system expects new

input. For the control of cooling and the capacitor’s

input charging voltage, the measurement of the tem-

perature is required and a relationship between this

temperature and the kinetic energy must to be known.

The full system was previously optimized to achieve

the desired performance even at the end of its life-

time, e.g. the conductive ring will still have sufﬁcient

kinetic energy. Consequently, the capacitor is over-

sized. However, this oversizing leads to excessive

kinetic energy, high forces and wear, which in turn

cause the coil to break earlier. Additionally, too much

kinetic energy would overload the system and lead to

faster failure and shorter life time.

Figure 2: Repetitive cycles during operation.

Temperature sensors are widely used due to their low

price, but reach their limits with limited installation

space and ofﬂine calibration. In addition, other prob-

lems such as own heat development, contamination

by ions or damage during the process become appar-

ent (Charkhgard and Farrokhi, 2010). In the case of

the investigated induction actuator, a sensor for tem-

perature measurements would have a big impact on

the physical behaviour and performance of the system

as the ﬁll factor of the coil is important to stay high

and the initial position between the coil and conduc-

tive ring has to be precise at the beginning of a cycle.

Further, high accelerations and forces would destroy

the sensor quickly.

Sensorless Coil Temperature Measurements using Neural Networks for Voltage Control

831

Figure 3: The neural network precisely represents the FEM curves.

Virtual sensors have evident advantages over real

physical sensors in terms of cost and implementa-

tion. In addition, certain installation places can also

lead to rapid sensor failure. Regarding virtual tem-

perature measurements, (Guzm et al., 2018) use a

CFD model and a model based on transfer functions

to predict the real time temperature of a greenhouse

from real sensor data. (Boulandet, 2016) introduces a

lumped-parameter model of an electric circuit to pre-

dict the front-side acoustic radiation impedance of a

loudspeaker using the measured electric impedance of

the loudspeaker and additional parameters deﬁned by

experimental data using curve ﬁtting. As alternative

to transfer functions, simpliﬁed models and regres-

sion methods as well as neural networks get more and

more attention as precise, fast and reliable methods.

(Hussein, 2018) shows a sensorless way to estimate

the surface temperature and the battery cell’s termi-

nal voltage using ANNs with current measurements

as input.

3 MODELLING

3.1 Finite Element Method (FEM)

Due to the complexity of the electromechanical sys-

tem involving eddy currents and changing inductance

caused by a ﬂying ring, the induction actuator is sim-

ulated with FEM. This numerical method offers a pre-

cise model and captures all relevant effects that can-

not be implemented and modelled so far with meth-

ods such as system identiﬁcation. By varying rele-

vant system parameters, e.g. lifetime dependencies of

the capacitor, thermal inﬂuences such as the coil re-

sistance, the conductive ring resistance and voltage of

the capacitor, many different data points with differ-

ent voltage and current curves of a predeﬁned geomet-

ric concept are simulated. Subsequently, the voltage

can be used to regulate the kinetic energy of the ﬂy-

ing conductive ring to achieve the target performance.

The key parameters are:

• Capacitance of capacitor C

cap

• Resistance of the capacitor R

cap

• Voltage of the capacitor V

cap

• Resistance of the coil R

coil

• Resistance of the conductive ring R

Using these input parameters, the corresponding tran-

sient currents, voltages in the coil and the forces act-

ing on the conductive ring are calculated by using

FEM. The idea of this sensorless measurements is

based on the following equations from a coil’s elec-

tric circuit, modelled by an inductance and a resistor,

using Faraday’s law (Galili et al., 2012).

u = iR +

dΦ

= iR +

B(t)dA

(1)

In the coil, the inductance is changing with the po-

sition x of the conductive ring and the current of the

coil. The inductance is a highly complex term that

cannot be calculated in advance. As the magnetic ﬁeld

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

832

is a result of the changing current and the position in-

ﬂuences the changing area A directly, the ﬂux linkage

is deﬁned as λ(...).

coil

= i

coil

dλ(i

coil

, x)

(2)

coil

= i

coil

δλ(i

coil

, x)

δi

coil

δλ(i

coil

, x)

δx

(3)

coil

δλ(i

coil

,x)

δi

coil

δλ(i

coil

,x)

δx

coil

(4)

The voltage and the current of the coil depend on the

constant resistances and varying inductances. Calcu-

lating the resistance from the varying parameters is

complex and leads to numerical instabilities such as

divisions by zero. However, these equations are sim-

pliﬁed engineering equations which are included in a

weak form in the ﬁnite element solver model. Using

variables such as position, voltage and current, neural

networks are applied as a regression model that pre-

dicts any output for any combination of inputs in a

very fast way.

After predicting the resistance, the temperature

can be deﬁned by R

coil

∼ ρ

coil

∗ l

(5)

coil

= ρ

(1 + α ∗ (T − T

)) (6)

T =

(

coil

− 1) + T

(7)

3.2 Neural Network Integration

Due to the fact, that neural networks are able to

learn highly complex dependencies, they are ideal to

solve non-linear relationships between input and out-

put variables. Its properties make it relatively easy to

solve the complicated induction equation. As men-

tioned in (Kumar et al., 2020), physical data can be

used in both predictive directions, using a forward

and an inverse model. Due to the physical equations

shown above, the dataset generated by FEM includes

the scalar values (input) and the time dependent volt-

age and current curves (output).

3.2.1 Forward Model

The forward direction can be used to investigate the

system dynamics from the ﬁve scalar inputs described

in 3.1 and integrate the outputs such as current and

Figure 4: Varying coil resistance inﬂuences the voltage

curves.

Figure 5: Varying coil resistance inﬂuences the current

curves.

voltage curve in a system simulation procedure. This

forward model is realized by a feed-forward neural

network, which is trained on the FEM-data of 600

data points created with Latin-Hypercube sampling to

cover a homogenous range of variables. As the FEM

model is being developed over several years and has

an error of less than three percent to experimental re-

sults, it can be used for validation as seen in Fig. 3.

The required accuracy is obtained with three layers

of 2’000 neurons each. The use of dropout and three

folds of cross-validation reduces the risk of overﬁt-

ting. A trained neural network, using the scalar inputs

mentioned above, is able to capture the effect of resis-

tance in the coil as seen in Fig. 4 and Fig. 5. The coil

and current pulses are scaled over the stroke period P

The heat generation in the coil results in higher resis-

tances and therefore has a signiﬁcant impact on the

current pulse. This forward model can be used later

in a system simulation for predicting various operat-

ing cycles within a few milliseconds instead of vari-

ous hours for one cycle using FEM simulations.

Sensorless Coil Temperature Measurements using Neural Networks for Voltage Control

833

Figure 6: Predicted and true data responses of ρ

coil

comparing GPR, Trees (Boosting and Bagging) and ANN.

3.2.2 Inverse Model

For the prediction of the temperature, an inverse

model is necessary. Current and voltage curves serve

as input to predict the coil resistance. By using all

these data points, a neural network is trained to ﬁnd

the coil resistance’s inﬂuence on the current and volt-

age curve.

The neural network is constructed with several

hidden layers using Rectiﬁed Linear Units (ReLU) as

the activation function. The convergence algorithm

Adam, a stochastic gradient descent algorithm avail-

able in the Python library Tensorﬂow, turned out to

be the most suitable. A wide range of different neu-

ral network conﬁgurations was trained and analysed,

taking into account parameters as the number of hid-

den layers, the number of neurons, dropout, and batch

normalization. Fig. 6 shows the comparison of using

different Machine Learning methods for the predic-

tion of the coil’s resistivity ρ

coil

. GPR and ANN both

achieve high accuracy results on noisy input data. The

comparison was done using ﬁve cross folds and doing

hyperparameter optimization for each model. Addi-

tionally, white noise was added on normalized input

data to get the problem robust also for experimental

and predicted data. By applying white noise with a

maximum amplitude of 3% on the input data, each

model was optimized by training the hyperparame-

ters, e.g. the learners and number of leafs for decision

trees, standard deviation and kind of kernel for GPR

and hidden layers and number of neurons for neural

networks. Three percent noise on normalized data is

used so that this model can be also applied to experi-

mental data.

Figure 7: Potential applications of a virtual sensor are a sys-

tem simulation models using data predicted by ANN and a

real integration on a microcontroller using sensor data.

4 USE CASES

Our proposed virtual sensor can be either applied to

a real induction actuator application and monitor the

temperature of the coil using real sensor measure-

ments or it can be integrated into a system simulation

as seen in Fig. 7.

Figure 8: System simulation model with integrated voltage

control.

In this work, the AI-based system simulation of

this process is realized as shown in Fig. 8. The

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

834

temperature behaviour is represented by a thermal

lumped parameter model predicting the input energy

with Gaussian Process Regression (GPR) during one

operation cycle and then solving the ordinary differ-

ential equation for each cycle. The electromagnetic

coupling is described by the neural network based

forward model. For performance regulation voltage

control is introduced. The purpose of the system

simulation is to investigate the system’s performance

under different operating conditions.

Figure 9: Physical models represented by machine learning

techniques.

As seen in Fig. 9, a system simulation procedure

is created by implementing time series neural net-

work as fast and accurate representation of the time-

consuming ﬁnite element calculations. Long Short

Term Memory (LSTM) networks are used in a cou-

pled way to predict the forces of the conductive ring

to calculate the kinetic energy.

5 VALIDATION

Figure 10: Validation of the thermal model using the tem-

perature of the ferromagnetic base.

In a system simulation procedure, the performance

control can be tested. As seen in Fig. 10, the sys-

tem simulation is validated with experiments by exe-

cuting more than 200 operation cycles in a laboratory

and comparing them to the simulation results. As the

temperature in the coil cannot be measured, it is com-

pared to the measurements of the ferromagnetic base.

Although the system simulation assumes a homoge-

nous temperature of the ferromagnetic base, it clearly

captures the trend. The temperature of the ferromag-

netic base is measured radially outside the base. The

performance of the virtual sensor can be compared

with the validated system simulation, Fig. 11. It is

shown that after every operation cycle the initial tem-

perature can be predicted based on the voltage and

current of the coil.

Figure 11: Comparing the coil temperature of the thermal

model in the system simulation with the virtual sensor.

6 VOLTAGE CONTROL

By predicting the force of the conductive ring, its ve-

locity can be derived and the kinetic energy is cal-

culated. For a desired kinetic energy at an optimal

performance point, the input voltage of the capacitor

can be regulated with a controller in a system sim-

ulation model. Due to the knowledge of decreasing

lifetime parameters of the capacitor and the tempera-

ture measurements, the expected performance of the

system is predicted and a controller can adapt the in-

put energy. Based on the FEM data, artiﬁcial intelli-

gence is used once more in form of GPR to predict the

corresponding input voltage of the capacitor for the

above deﬁned input parameters. For this voltage con-

trol, a real time thermal model is necessary to monitor

the transient behaviour of the coil temperature over

time and use it as new input for the machine learn-

ing model. After every operational cycle, the voltage

control gets the lifetime and thermal input parameters

and predicts the needed voltage for a desired input

energy. In Fig. 12, the inﬂuence of voltage control

is shown. For the investigated device with an oper-

ational time interval of two seconds, the heat gener-

Sensorless Coil Temperature Measurements using Neural Networks for Voltage Control

835

Figure 12: During 40 operation cycles, voltage control has a signiﬁcant inﬂuence on the heat generation in the system. It leads

to a continuous character of the kinetic energy and requires less energy in the capacitor.

ation in the system leads to increasing coil tempera-

tures, although the system is already cooled. By using

a constant input voltage of 100% to make the system

reaching 100% kinetic energy of the conductive ring

even at the end of the lifetime, a lot of energy is un-

necessarily invested leading to longer charging times

in the capacitor. If voltage control is included, less

voltage is needed and the system can adapt to tem-

perature changes and decreasing capacitance due to

abrasion of the capacitor. The optimal performance

at 100% kinetic energy is achieved with errors of less

than 2% and, therefore, makes the whole system more

efﬁcient and achieves reliably the desired optimal per-

formance point.

7 CONCLUSIONS

A virtual sensor is proposed for the temperature deter-

mination in the coil of an induction actuator to con-

trol its performance. Beside the introduced system

simulation model, the sensor can be used for predict-

ing the temperature of a coil when physical hardware

sensor measurements of the coil current and volt-

age are available. A validated and highly accurate

FEM model is used to generate training data for an

AI-based virtual sensor. The electromagnetic FEM

model takes hours to calculate the system response of

one single operation cycle. In contrast, a trained ML

model predicts the temperature of the coil within mil-

liseconds in places where no sensor can be integrated

without reducing the performance. When consider-

ing thousands of working cycles, excessive comput-

ing equipment would be needed to describe the tem-

perature accurately and efﬁciently with FEM models.

The virtual sensor therefore not only allows measure-

ments in places that are difﬁcult to reach, but also en-

ables a fast and very accurate calculation method.

REFERENCES

Boulandet, R. (2016). Sensorless Measurement of the

Acoustic Impedance of a Loudspeaker. (1):7353–

7360.

Charkhgard, M. and Farrokhi, M. (2010). State-of-charge

estimation for lithium-ion batteries using neural net-

works and EKF. IEEE Transactions on Industrial

Electronics, 57(12):4178–4187.

Dong, E., Tian, P., Wang, Y., and Liu, W. (2011). The de-

sign and experimental analysis of high-speed switch

in 1.14kV level based on novel repulsion actuator.

2011 4th International Conference on Electric Utility

Deregulation and Restructuring and Power Technolo-

gies (DRPT), (50807006):767–770.

Galili, I., Kaplan, D., and Lehavi, Y. (2012). physics course.

337.

Gonzaga, J. C. B., Meleiro, L. A. C., Kiang, C., and Filho,

R. M. (2009). ANN-based soft-sensor for real-time

process monitoring and control of an industrial poly-

merization process. 33:43–49.

Guzm, C. H., Carrera, J. L., Dur, A., Berumen, J., Ortiz,

A. A., Guirette, O. A., Brizuela, J. A., and Fabio, G.

(2018). Implementation of Virtual Sensors for Mon-

itoring Temperature in Greenhouses Using CFD and

Control.

Hussein, A. A. (2018). A Sensorless Surface Tempera-

ture Measurement Method for Batteries using Artiﬁ-

cial Neural Networks. pages 3560–3564.

Kumar, S., Tan, S., Zheng, L., and Kochmann, D. M.

(2020). Inverse-designed spinodoid metamaterials.

npj Computational Materials, 6(1):1–10.

Lim, D.-k., Woo, D.-k., Kim, I.-w., Shin, D.-k., Ro, J.-s.,

Chung, T.-k., and Jung, H.-k. (2013). Characteris-

tic Analysis and Design of a Thomson Coil Actuator

Using an Analytic Method and a Numerical Method.

49(12):5749–5755.

Vilchis-Rodriguez, D. S., Shuttleworth, R., Smith, A. C.,

and Barnes, M. (2019). Performance of high-power

thomson coil actuator excited by a current pulse train.

2019:3937–3941.

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

836