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Linearization of the sensors characteristics: a review

Tarikul Islam
Tarikul Islam
 et 
S. C. Mukhopadhyay
S. C. Mukhopadhyay
   | 23 août 2019
International Journal on Smart Sensing and Intelligent Systems's Cover Image
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Article Category: research-article
Publié en ligne: 23 août 2019
Pages: 1 - 21
Reçu: 29 avr. 2019
DOI: https://doi.org/10.21307/ijssis-2019-007
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© 2019 Tarikul Islam et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1:

Nonlinear impedance response of a ceramic humidity sensor (Islam et al., 2014a).
Nonlinear impedance response of a ceramic humidity sensor (Islam et al., 2014a).

Figure 2:

(A) Symmetrical bridge configuration; (B) its transfer curve (de Graaf and Wolffenbuttel, 2006).
(A) Symmetrical bridge configuration; (B) its transfer curve (de Graaf and Wolffenbuttel, 2006).

Figure 3:

A general block diagram of the linearization unit.
A general block diagram of the linearization unit.

Figure 4:

(A) Inverse response of the humidity sensor; (B) linearization circuit.
(A) Inverse response of the humidity sensor; (B) linearization circuit.

Figure 5:

A mixed signal conditioning circuit for piecewise linearization (Mahaseth et al., 2018).
A mixed signal conditioning circuit for piecewise linearization (Mahaseth et al., 2018).

Figure 6:

Linearization using multilayer perceptron neural network resistance.
Linearization using multilayer perceptron neural network resistance.

Figure 7:

Fuzzy logic-based linearization of the humidity sensor response (4(A)).
Fuzzy logic-based linearization of the humidity sensor response (4(A)).

Analog schemes of linearization of thermistors, thermocouples, and giant magneto resistive sensors (GMR).

Method Range Accuracy (%) Complexity
(Nenova and Nenov, 2009) Timer-based oscillator circuit 0–120 ±1 Low but SPR has low range and low sensitivity
(Stanković and Kyriacou, 2012) Quarter Wheatstone bridge 10–390–100 ±1.5°C Low, limited range
Series parallel resistance (SPR) 0.1°C Low, low sensitivity
(Kaliyugavaradan et al., 1993) Inverting amplifier with thermistor at input 27–113 ±1 Low
(Bandyopadhyay et al., 2016) Timer-based oscillator 23–110 0.2°K High, low reliability
(Fraden, 2003) One-bit sigma–delta modulator na ±0.01 High, but accurate
(Mondal et al., 2009) Op-amp logarithm amplifier T: 0–400°C ±0.1 Simulation results
For TC J: 0–760°C
(Lucaa et al., 2015) CMOS thermal diode with two driving currents 80–1,080 K ±0.6 High not flexible
(Sanyal et al., 2006) Op Amp based log amp 20–48 m/s >±0.1 K Simulation only
(Pappas et al., 2011) Current conveyer NA 0.84 simulation only
(Bera and Marick, 2012) Diodes-based bridge circuit for flow rate 1–10 Kg/min 0.3 Low
(de Graaf and Wolffenbuttel, 2006) Trans impedance amplifier bridge ±20% ±0.2 Low, simulation only
(Maundy and Gift, 2013) Strain gauge amplifier circuits na 0.4 Medium
(Bera et al., 2012) Opto-isolator-based analog circuit na ±1.67 Medium
(Sen et al., 2017) Feedback compensation 0.5–3.5 mT 0.7 Low, GMR inherent nonlinearity
(Jedlicska et al., 2010) Minimizing hysteresis 2.8% 074 High, long time, not accurate
(Munoz et al., 2008) Impedance converter as current source for GMR sensor na na High, more drift
(Li and Dixon, 2016) A close loop feedback analog circuit 0–0.3 mT na Complex circuit, magnetic sensors
(Chavan and Anoop, 2016) Dual slope ADC (digital output) 0.5–3.5 mT 1.5 Precise resistance, large conversion time
(Sen et al., 2018) Feedback circuit na Accuracy not mentioned Low but magnetic sensor
(Ghallab and Badawy, 2006) Current mode Wheatstone bridge consisting three operational floating current convey 0.5–3.5 mT 0.6 Medium
(Azhari and Kaabi, 2000) Operational floating current conveyer na na High
(Farshidi, 2011) Current mode Wheatstone bridge using CMOS transistor

Linearization by direct digital linearization and software-based algorithms.

Method Accuracy/range Complexity Applications
(Eshrat Alahi et al., 2017) Non-linear ADC with piecewise linear input-output characteristics 1%,/30 to 90%RH accuracy depends on pieces Medium Humidity sensor, smart sensors, flash ADC (3 bit and 11-bit ADCs)
(Žorić et al., 2006) Nonlinear ADC for moisture sensor na Medium Humidity sensor
(Islam et al., 2006; Dias Pereira et al., 2009; Rahili et al., 2012) Direct interface to µC for half, full Wheatstone bridge 0.3%/0 to 1), 11-bit resolution (10%) (quarter bridge) Low, lead error, bridge nonlinearity compensation only digital output Resistive sensors, 8-bit AVR ARDUINO board
(Scheiblhofer et al., 2006) Dual slope ADC for direct interface to µC with logarithm amplifier ±0.3°C, 0-120°C Low, digital output Thermistor, implementation by LabVIEW
(Fericean et al., 2009b) Feedback compensation scheme 0.03% (100% range) Low, implementation by analog circuit Nonlinearity of Wheatstone bridge
(Ramadoss and George, 2015) Microcontroller-based direct interface 0.3% low digital output, no ADC Diff. variable inductive sensors
(Nagarajan et al., 2017) Dual slope ADC for direct interface to µC (quarter/half bridge resistive sensors) <0.09%,/100% Digital output, only bridge nonlinearity compensation resistive sensors, LabVIEW and NI ELVIS-II board, Hall effect sensor
(Sreekantan and George, 2014) Dual slope ADC for direct interface to µC converter (diff. third order polynomial <0.7% Low, digital output Differential second- and third-order sensor, tested for inductive sensor
(Islam et al., 2013) Oscillator-based resistance to frequency conversion <1% Medium, quasi digital output, frequency conversion temperature error compensation no sensor nonlinearity compensation Resistive sensors, humidity sensor
(Murmu and Munshi, 2018) Software algorithm for TC ±1.4%, 45-100°C High, costly solution Thermocouple
(Flammini et al., 1997; Flammini et al., 1999; Flammini and Taroni, 1999; Catunda et al., 2003; Erdem, 2010; Islam et al., 2014b) Simple Look-up table for different nonlinear sensors ±1% moisture, accuracy depends on memory size Medium Nonlinear sensors
(Erdem, 2010) Look-up table PWLE for infrared distance sensor. Look-up table_ 0.03% Medium memory than simple Look-up table. Medium, reduced memory. Nonlinear sensor
PWLI for infrared distance sensor 0.032%
(Teodorescu) Look-up table PGA 0.023% Medium, memory Low nonlinear sensor
(Rivera et al., 2009) Progressive polynomial software method (PPC)for sensors <1% (max 36%) Medium, less data points Resistive nonlinear sensor
(Dias Pereira et al., 2009) Adaptive self-calibration algorithm to determine polynomial equation, based on probability density function na Medium, low computation, small memory Smart sensors air flow sensor
(Rahili et al., 2012) Modified PPC: intelligent selection of calibration points to determine polynomial function 0.83% Reduced calibration data, small memory locations Smart sensor nonlinearity for thermistor
(Xinwang et al., 2011) Recursive B-spline least square method 0.01% (6.34%), 0.35% (51% for NTC) High low data points Thermocouple NTC Thermistor
(Optimized Sensor Linearization for Thermocouple, 2015) Thermocouple by software algorithm ±0.02 (−270°C-1372°C) Low memory Thermocouple

Fuzzy rules for sensor linearization.

IF V < V1 (slightly low), then RH is the lowest
IF V1 ⩽ V < V2 (low), then RH is low
IF V2 ⩽ V < V3 (average), then RH is middle
IF V3 ⩽ V < V4 (slightly high), then RH is slightly high
IF V4 ⩽ V (high), then RH is high

Linearization by software-based intelligent methods.

Technique Accuracy Complexity Implementation
(Nenov and Ivanov, 2007) ANN technique for humidity sensor ~1% High, large memory Desktop PC
(Medrano-Marques et al., 2001) MLP for piecewise linearization of thermistor <0.5% High, large memory size depends on data points µC (16-bit ADC) no hardware results
(Islam et al., 2006) Adaptive NN, determine coefficient of polynomial (ADALINE) 2.7% Low, can be more for higher-order polynomial Op-amp based circuit
(Erdem, 2010) ANN for infrared distance 0.017% High, large memory PIC18F452 µC (10-bit ADC) ST52F510 (10-bit resolution)
(Khan et al., 2003) MLP-based inverse ANN model for thermistor <0.5% High, low memoryOptimized data points PIC16F870 µC (10-bit ADC)
(Kumar et al., 2015) Two stages linearization (i) optimizing the parallel form of RNTC and fixed resistance and (ii) MLP ±0.2% High, medium memory µC with AVR studio for coding various sensors with drift compensation
(Patra et al., 2008) Efficient learning machine (ELM) for the pressure sensor with temperature error ±1.5% Medium Xilinx Virtex-II FPGA board (12-bit ADC)
(Patra et al., 2008) Chebyshev neural network pressure sensor ±1% High, computationally efficient basic MLP Only simulation results
(Cotton and Wilamowski, 2011) Fully connected cascade NN <1% High, computationally efficient µC with 8-bit ADC
(Teodorescu) Fuzzy logic 0.07% High, large memory Simulation results for different nonlinearity
(Bouhedda, 2013) Neuro-fuzzy 0.03°C (high) Medium, high memory less hardware than LUT Xilinx Spartan-3A DSP 1800A FPGA board, MAX1132 ADC (16 bit)
(Xiaodong, 2008) software support vector machine humidity sensor <0.05 Better than MLP fuzzy logic MATLAB Neural Network Toolbox
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