An adaptive calibration technique for thermistor with varying temperature coefficient and reference resistance

1. Introduction

Temperature is an essential process measurement parameter. Temperature dependency is prevalent in practically all chemical processes and reactions. In chemical plants, temperature indicates the progress of a process. Incorrect temperature measurement may result in considerable loss of product in temperature-critical reactions. At times, failing to control temperature can result in catastrophic plant failure and loss of life. A thermistor is a commonly used temperature sensor because of its high sensitivity and low power dissipation.³⁸

The functionality of thermistors can be understood through a literature survey. In a proposed adaptive system,¹ complementary metal-oxide-semiconductor technology was used to design and integrate the system building blocks. The high-level models obtained after experimental characterization were verified for acceptable electronic behavior within a well-defined multilayer perceptron architecture. Enhanced sensing behavior observed in CaTiO₃ processed through high energy ball milling was much higher than that observed in CaTiO₃ processed through solid-state reaction method.² A 555 timer in the astable multivibrator mode has been used³ as a simple and economical signal conditioning circuit for negative temperature coefficient (NTC) thermistor temperature sensors. A substrate membrane has been fabricated to improve sensitivity using back etching technology,⁴ beneath the hot area. The performance of the microcalorimeter, transfer standard, and measuring system⁵ allowed Centro Nacional de Metrología to achieve efficiency measurement and uncertainties analogous to or even less than reported by other national metrology institutes. Analysis of changes in the thickness, growth rate, and temperature profile of ice was performed⁶ through data collected using an NTC thermistor.

A diamond thermistor was fabricated⁷ for high-temperature sensing with a high-pressure, high-temperature, and chemical vapor deposition technique. An NTC thermistor junction temperature estimation technique has been discussed⁸ for power metal–oxide–semiconductor field-effect transistors considering the temperature-sensitive electrical parameter as the ON-state voltage. For indoor and outdoor applications, the printing of disposable and degradable temperature sensors is possible using temperature-sensitive substrates incompatible with conventional inks, as proposed in.⁹ The fabrication of a liquid crystal thermistor was presented in.¹⁰ Based on the heat loss of self-heated NTC thick-film segmented thermistors and their operation, a novel heat loss flowmeter prototype has been proposed¹¹ that operates in the power-save regime. A linearization method in¹² demonstrated thermistor measurement results with a linearity error below ±0.5%.

Based on a thermal tracer, a flow velocity measurement method has been reported in,¹³ temperature information is used to solve the problems in flow velocity monitoring due to the presence of sand in oil-water two phase flow. A proposed measurement system for a wide-range flow sensor was developed by¹⁴ to determine the thermal characteristics of the flow. The results can be used in developing and designing measurement systems for micro-electromechanical-system-based thermal gas flow sensors.

A fast and accurate method has been presented in¹⁵ to predict the junction temperature of insulated-gate bipolar transistor module chips with no additional temperature sensors. In,¹⁶ the authors simulated a thermistor’s neural network-based signal conditioning circuit. Neural network algorithms have been used to design a linear compensation circuit for a resistance temperature detector.¹⁷ A support vector machine was used to develop a nonlinear compensation technique for a resistance temperature detector.¹⁸

Delay time of a negative temperature coefficient device has a significant reliance on the accuracy of the radiation measurement. An experiment consisting of double-thermistor structure for potassium tantalate niobate deflectors has been proposed in¹⁹ to suppress effect on delay time caused due to ambient temperature dependence. The results showed that the double-thermistor structure decreases the ambient temperature dependence by half compared with a conventional thermistor.

A temperature-compensated anemometer has been designed and tested based on an NTC thermistor couple in.²⁰ The fluid’s temperature measured in this configuration is convenient for wind turbine testing. A new method has been presented in²¹ to fabricate a diamond-based thermistor that consists of ohmic contacts on sintered Si₃N₄ ceramics. The characteristic voltage–current curves display a linear variation over wide temperature and voltage ranges. A transient compensation method has been proposed in²² for thermistor-based sensors in a constant temperature configuration.

For temperatures in the 70–190°C range, a glass substrate with thin films of HCl-doped PO-Mn₃O₄ nanocomposites were fabricated in²³ and displayed flexibility, conformability, and fire resistance. Estimating the bulk physical parameters describing the behavior of thermo-electrical modules and their dependence on varying operating conditions was shown to be highly accurate²⁴ in employing the improved version of the unified method for transmission electron microscope based characterization. Apart from making the sensor smaller or more spherical and decreasing its radiation sensitivity, no improvements over the sensor in²⁴ were possible for the sensor in²⁵ using gold sputtering.

The drift of conductivity and temperature sensors fastened with the Ocean Moored Network for the northern Indian Ocean buoy system in the Arabian sea was investigated using pre- and post-deployment calibration.²⁶ During a heat tracing experiment in a groundwater flow simulator, fiber Bragg gratings, distributed temperature sensing, and continuous fiber Bragg gratings based temperature measuring techniques were compared, and it was reported that distributed temperature sensing produces more accurate results over the other type.²⁷ A novel circuit solution has been proposed in²⁸ for temperature measurement. The temperature of a pick tip was obtained in a coal rock cutting experiment along with the circuit design and calibration, showing that the wear rate of the polycrystalline diamond compact bit increases at a critical temperature of 700°C. Nanomaterials and conductive polymer-based flexible temperature sensors have been evaluated in²⁹ with the temperature response, sensitivity, and production methods. Calibration of NTC thermistors using the residual compensation method was discussed in.³⁰

In,³¹ four-wire measurements were used to eliminate errors and maximize resolution and current consistent with the thermistor’s input voltage range and self-heating. Results showed that the number of parameters could considerably influence the interpolation error. A thermistor was developed by³² with a guard heater to minimize heat loss for accurately measuring the surface temperature of a material. The results show good performance and accuracy. Thermal conditions for the small-sized, long-stroke, low-speed stages of piston compressors have been investigated in.³³ The reading stability of the thermistor was studied for 120 hours at 90°C. The impact of different thermistor linearization techniques on the temperature uncertainty is presented in³⁴ for the temperature history characterization of phase-change materials. A method was proposed by³⁵ to minimize the resolution per analog-to-digital converter step for a specified temperature range using the thermistor resistance and its derivative at the boundary.

From the reported literature, it is clear that most studies discuss the linearity of sensors over a certain range rather than full scale, and the calibration process must be repeated every time a thermistor is replaced. These calibrations are time-consuming and may require a change in hardware, increasing the overall cost of the instrument. This paper overcomes these problems by proposing a method using the artificial neural network (ANN) concept. The ANN model is cascaded to the buffer circuit and trained to achieve a linear output independent of physical parameters like the temperature coefficient (β) and reference temperature resistance (R₀). An optimized ANN is developed using diverse algorithms and schemes and comparing their mean square error (MSE) and regression (R). The optimized ANN model provides the lowest MSE and a R close to one. The proposed technique is validated in this extended version by subjecting it to practical data implemented on the embedded platform for online temperature measurement.

The organization of the remainder of this paper is as follows. A brief description of the challenges faced in using thermistors for temperature monitoring is provided in Section 2. Section 3 describes the proposed solution, followed by results and discussion in Section 4. Finally, the conclusions of the study are provided in Section 5.

2. Problem statement

Thermistors are temperature–sensitive resistors, having either a negative or positive resistance–temperature coefficient. A decaying exponential function best describes an NTC thermistor’s resistance–temperature (R–T) characteristics, and interpolation can be performed using different equations.^36–39 The Steinhart-Hart equation, shown in Equation (1), is considered here:

R_T: Thermistor’s resistance at temperature T

R₀^: Reference resistance at a specified reference temperature T₀ (T₀ = 25°C)

β: Temperature coefficient

This work uses a 5 kΩ thermistor (Sowparnika Thermistors and Hybrids Pvt Ltd, make) with a temperature coefficient of 4000 K. Output resistance obtained for the change in temperature from 20 to 200°C derived from equation 1 is shown in Figure 1. A signal conversion circuit in the form of a voltage divider and amplifier is used to convert the resistance obtained from the thermistor to a voltage, as shown in Figure 2. Mathematical equations for the voltage divider are given in Equations (2) and (3). The outputs obtained from the voltage divider and amplifier are shown in Figure 3a and b, respectively.³⁵

Figure 1. Simulated response of 5 kΩ thermistor.

Figure 2. Signal conversion circuit used for testing thermistors with different temperature coefficients.

Figure 3. (a) Output obtained from voltage divider circuit; (b) Output obtained from amplifier circuit.

V is the source voltage of 5 V

R₁ and R₂: amplifier resistance of 470 Ω and 1 kΩ potentiometer

Several types of thermistors are available commercially. These thermistors are classified based on their reference resistance (R₀) and temperature coefficient (β) values. The most commonly available thermistors have 5, 10, and 20 kΩ reference resistances. Thermistors are also available,^37–39 with varying temperature coefficients. Characteristics of various thermistors are included in this section and are tested to understand the difficulties involved in available measurement techniques. For this purpose, measurement is carried out with three different thermistors with reference resistances (R₀) of 5, 10, and 20 kΩ and a temperature coefficient of 4000 K. Results obtained for variation with temperature are shown in Figure 4.

Figure 4. Measured output voltages as a function of temperature for different thermistors with a temperature coefficient of 4000 K and varying reference resistances (R₀) measured in Ω.

Tests were also conducted using thermistors with different temperature coefficient values of β = 4000, 8000, and 12000 K, and a reference resistance (R₀) of 5 kΩ. The output obtained for temperature measurements is shown in Figure 5. All the available thermistors were tested with the signal conversion circuit shown in Figure 2.

Figure 5. Measured output voltages as a function of temperature for different thermistors with a reference resistance (R₀) of 5 kΩ and varying temperature coefficients (β) measured in K.

The output obtained from the amplifier for varying temperatures for different thermistors is shown in Figures 4 and 5. From these graphs, it is clear that the amplifier output has a nonlinear relation with temperature. The output varies with changing reference resistance and temperature coefficient. Because of the high nonlinearity of the thermistor, it is only used over 10%–60% of its full-scale range in practice. Users must perform repeated calibrations whenever a thermistor with a different reference resistance (R₀) or temperature coefficient (β) is used. These conventional techniques are time-consuming because they must be calibrated every time a thermistor is changed in the system.

Objectives: With an arrangement for temperature measurement in a system consisting of a thermistor in cascade with a signal converter circuit, as shown in Figure 2, design an intelligent temperature measurement technique using an optimized neural network model and with the following properties:

3. Methods

The objectives defined in section 2 are achieved by cascading a neural network model with a data converter unit by switching the conventional calibration circuit, as shown in Figure 6. The practical setup of the implemented calibration technique is shown in Figure 7. The experimentation setup consists of a muffle furnace (BML instruments ltd make) to heat the sensor. The sensor output is connected to the signal conditioning circuit designed on Elvis board. The Elvis board is interfaced to the computer. For computation MATLAB⁴⁰ (RRID:SCR_001622), LabVIEW tools⁴⁰ (RRID:SCR_01325) are used to develop neural network model and interface with the system. Alternatively, an open-source alternative SCILAB model has also been develop and archived in.⁵¹ The measurement technique is implemented in the LabVIEW program,⁴⁰ with the front panel window shown in Figure 8.

Figure 6. Block diagram of the proposed technique.

Reference resistance - R₀ and temperature coefficient -β.

Figure 7. Experimental setup.

Figure 8. Front panel window of the proposed LabVIEW program.

The front panel window consists of two numerical controls to feed the neural network with the R₀ and β values. Two numerical indicators display the temperature of the system calculated using the conventional method and calibrated using the ANN. Two graphical indicators display the temperatures, display titled “Uncalibrated” will display the output from conventional technique and display titled “Calibrate” display’s the output of ANN-calibrated techniques. A block diagram of the proposed technique is shown in Figure 9.

Figure 9. Block diagram window of the proposed LabVIEW program.

The block diagram window consists of the data acquisition (DAQ) assistant to acquire real-time data from the buffer output and feed it to the LabVIEW MATLAB script window, which is programmed with the trained ANN model using the net function. The ANN is trained on the MATLAB platform, and the executed net function is used to calculate the output value for varying input temperatures with various R₀ and β. The computed output using the ANN is displayed using numerical and graphical indicators. The values computed using the conventional method are also displayed for reference.

Training is the process of obtaining the weights to achieve the desired output. Consideration of different algorithms with varying hidden layers results in an optimized ANN. The average of the squared difference between outputs and targets gives the MSE. Lower MSE values are better, with a zero MSE meaning no error. The correlation between output and target is measured by R. A close relationship is when R is one, and a random relationship is zero.

Different schemes and algorithms have been used to find the optimized ANN. These are back propagation trained with particle swarm optimization (AL1), radial basis function trained by ant colony optimization (AL2), radial basis function trained by artificial bee colony (AL3), radial basis function trained by genetic algorithm (AL4), radial basis function trained by particle swarm optimization (AL5), and radial basis function trained by firefly algorithm (AL6).^41–50

ANN training is done first by assuming only one hidden layer, and the resulting MSE and R values are recorded. Training is then repeated by increasing the number of hidden layers to two, and this process is repeated up to four hidden layers. MSE and R are recorded in all cases, these results are provided in Table 1. A mesh plot of MSE and R values corresponding to different algorithms and numbers of hidden layers are shown in Figures 10–11. From Table 1, Table 2, Figure 10, and Figure 11, it is evident that back propagation trained by ant ACO results in the most optimized network when taking MSE as the threshold. back propagation trained by and colony optimization with two hidden layers is considered the most optimized ANN for the desired accuracy. Details of the optimized ANN are summarized in Table 3.

Figure 10. Variation of Mean square error (MSE) with the number of hidden layers and algorithm (AL).

AL1 - back propagation trained with particle swarm optimization, AL2 - radial basis function trained by ant colony optimization, AL3 - radial basis function trained by artificial bee colony, AL4 - radial basis function trained by genetic algorithm, AL5 - radial basis function trained by particle swarm optimization, AL6 - radial basis function trained by firefly algorithm.

Figure 11. Variation of regression (R) with the number of hidden layers and algorithm (AL).

AL1 - back propagation trained with particle swarm optimization, AL2 - radial basis function trained by ant colony optimization, AL3 - radial basis function trained by artificial bee colony, AL4 - radial basis function trained by genetic algorithm, AL5 - radial basis function trained by particle swarm optimization, AL6 - radial basis function trained by firefly algorithm.

4. Results and analysis

The optimized ANN is trained, validated, and tested with simulated data using equation 1, 2 and 3. It is subjected to various test inputs corresponding to thermistors with different reference resistances and temperature coefficients, all within the specified range. The temperatures measured by a practical set up along with the output of the data conversion unit are recorded for (i) R₀ = 800 Ω and β = 5000 K and (ii) R₀ = 5000 Ω and β = 5000 K, and (iii) R₀ = 10000 Ω and β = 8000 K. These data are listed in columns 1 and 2 of Table 4.⁵¹

The output of the data conversion unit, and R₀ and β, are used as inputs to the trained, optimized ANN. The corresponding ANN outputs and the temperature measured by the proposed technique are noted in columns 3 and 4 of Table 4. The results shown in Table 4 suggest that the proposed system has measured the temperature with very high accuracy. It is evident from Table 4 that the proposed measurement technique has gained intelligence and increased the linearity range.

Next, the output is made to adapt to variations in reference resistance and temperature coefficient. The calibration process need not be repeated if the thermistor is changed to another with different R₀ and β. The signals are fed online to the proposed system through LabVIEW DAQ Assistant, and the output corresponding to various inputs is provided in Table 4. Figure 12 is a picture of the experimental setup used to carry out the proposed work.

Figure 12. Output characteristics of proposed calibration technique with different thermistors.

Figure 12 plots the input–output characteristics obtained by the proposed calibration technique. It is seen that the output obtained is linear and is adaptive to different thermistors. The output value does not vary with thermistor type. Figure 13 shows a plot of the measurement errors. The proposed measurement technique can achieve an accuracy of 1.8% and a maximum 2°C temperature deviation in monitoring even when using different sensors.

Figure 13. Error variation for testing of different thermistors.

5. Conclusions

Thermistors are the most widely used temperature sensors because of their economic feasibility and higher sensitivity, although they are highly nonlinear and have longer response times. Several calibration techniques were studied, and a broad literature survey indicated around 30 reported works in the last decade on thermistor-based temperature sensing. Existing works^1–32 have investigated various techniques for temperature measurement calibration using thermistors. A few have also reported on sensor design to obtain better characteristics.

However, the literature has not discussed systems adaptive to reference resistance and temperature coefficient variations. Hence, any change in reference resistance and temperature coefficient of a thermistor requires repeated calibration. Furthermore, most reported works have not utilized the full-scale measurement range. In all the above-referenced literature, neural networks were selected without any justification when used.

In contrast to the existing literature,^1–32 linear input output characteristics for the entire input temperature range have been achieved with the measurement technique proposed in this study. These objectives have been fulfilled using an optimized ANN. Training, validation, and testing were conducted employing different schemes and algorithms. The desired MSE and R (near one) with two hidden layers were attained using the radial basis function trained by the firefly algorithm, in contrast to arbitrary ANNs used in most reported studies. The neural network model data are further validated with practical data online in a real-time environment. The results show that the proposed technique can be used to design an adaptive calibration technique.

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