Life Prediction of TMR Current Sensor under Accelerated Degradation Test

Sensors are an important component of smart grids. This paper proposes an accelerated degradation test plan for magnetoresistive sensors and establishes a life prediction model based on performance degradation trajectories. Firstly, the structure and working principle of tunneling magnetoresistance (TMR) current sensor are explained, and the performance degradation parameter is selected. Secondly, the Arrhenius model and basic concepts of accelerated degradation testing are introduced. Then, taking a certain model of the TMR current sensor as an example, the experiment is designed and the platform is constructed to obtain the performance degradation trajectory, and thus the life prediction is carried out.


Introduction
Sensors and their measurement technology are the foundation for realizing monitoring, control, analysis, and decision-making in smart grids, and they are also key to the development of smart grids.The weak currents detected in the power grid mainly include leakage currents [1] of cables and substation equipment, grounding currents, etc., with amplitudes ranging from several hundred microamps to hundreds of milliamps.Sometimes there is a phenomenon of mixing AC and DC currents in certain scenarios [2].Compared with traditional current transformers, shunts and other devices, magnetoresistive current sensors have the advantages of being able to measure alternating currents, direct currents and impulse currents, which can meet the current measurement needs in different application scenarios, and have good sensitivity to weak current signals, making them suitable for monitoring weak current signals in the power grid.
In practical application scenarios, magnetoresistive current sensors work for a long time in complex environments and are affected by environmental stress, which gradually degrades their performance, reduces measurement accuracy and reliability, and ultimately fails to meet measurement requirements.Studying the regularity of the performance of the current sensor over time and predicting its life is beneficial to ensure that the sensor operates with high reliability This paper focuses on TMR current sensors and predicts their life using accelerated degradation tests.Firstly, the working principle of TMR current sensors is introduced, and the degradation parameter is determined.Then, the Arrhenius model and accelerated degradation testing are introduced.Next, the experiment is designed and the platform is constructed.Finally, the obtained performance degradation trajectory is processed to obtain a life prediction model under high temperatures.By generalizing it to the operating temperature range, the pseudo-failure life at that temperature is predicted.

Magneto resistive current sensor
2.1.Working principle TMR current sensors are based on the tunneling magnetoresistance effect, and measure the current by inducing a magnetic field generated by the measured current.The basic structure of the TMR element is shown in Figure 1.The key part of the TMR element is the magnetic tunnel junction (MTJ), which consists of a ferromagnetic layer-insulating layer-ferromagnetic layer structure [3].The ferromagnetic layer with lower coercive force is the free layer, and the direction of the magnetic domain arrangement changes with the external magnetic field.The ferromagnetic layer with higher coercive force is the pinned layer, and the direction of the magnetic domain arrangement is fixed.When the external magnetic field changes, the relative magnetization direction between the two ferromagnetic layers changes, and the probability of electrons passing through the insulating layer also changes, which results in a macroscopic change in the resistance value of the element.When the temperature changes, the random thermal movement of the magnetic domains is enhanced or weakened accordingly, and the arrangement of the magnetic domains will also change accordingly, resulting in a change in magnetoresistance.At this time, the measurement performance of the TMR current sensor changes, and the accuracy and reliability of the sensor are seriously affected.Figure 2 is a structural diagram of a closed-loop TMR current sensor.The TMR element is fixed in the gap of the magnetic core, and the magnetic field generated by the measured current is opposite to the magnetic field generated by the feedback current.The TMR element senses the magnetic field intensity at the gap and outputs a voltage signal to adjust the magnitude of the feedback current, ultimately making the magnetic flux at the gap of the magnetic core equal to zero.Through subsequent circuit processing, the output voltage signal of the current sensor can be used to infer the size of the measured current.

Selection of performance degradation parameters
According to the analysis of the working principle of the TMR current sensor, it can be understood that the degradation of its measurement performance mainly manifests in the change of the ratio of output voltage to input current, i.e., the change of the calibration factor.As the operating time of the TMR current sensor increases, the corresponding calibration factor can be obtained by measuring the output voltage under the same input current, which is used to characterize the change in the sensor performance and for subsequent life prediction.

Arrhenius Model
Arrhenius model is the most typical acceleration model used in temperature stress testing and has been widely used in accelerated degradation tests of electronic products.
In the equation, K represents the reaction rate or degradation rate, A is a constant, E represents the activation energy of the degradation mechanism, k represents the Boltzmann constant, and T represents the absolute temperature.
The Arrhenius model indicates that the degradation rate of product performance indicators increases exponentially with the increase in temperature.

Accelerated degradation test [4]
The accelerated degradation test is suitable for devices with high reliability and long life [5], such as TMR current sensors, performance degradation is slow under normal operating conditions.To evaluate their life, accelerated degradation tests can be used to obtain performance degradation data at high stress levels, and then obtain the life at different stress levels [6].
Accelerated degradation testing is the process of increasing stress levels to reach a predetermined failure threshold in a shorter time while keeping the failure mechanism unchanged.Based on the performance degradation trajectory and life distribution under accelerated stress, an Arrhenius model is established, and extrapolation is conducted to obtain the pseudo-failure life at a specific stress level [7].The following basic assumptions are made for accelerated degradation testing [8]: 1) Consistency assumption The failure mechanism of the product remains unchanged under different stress levels.

2) Distribution homogeneity assumption
The life of the product under different stress levels follows the same type of distribution.

3) Nelson assumption
The remaining life of the product depends only on the accumulated failure and the current stress level, regardless of the accumulation method [9] This model is used to estimate the life expectancy of a product or system.The method involves four steps:

Degradation Trajectory Method
1) Plotting the performance degradation trajectory [10] by selecting appropriate parameters and plotting their curves over time.
2) Fitting and extrapolating the degradation trajectory using a suitable model to determine the pseudo-failure life corresponding to the intersection point between the fitted curve and the failure threshold.
3) Estimating the probability density function by using the Weibull distribution or normal distribution model to estimate the pseudo-failure life of multiple test objects under the same experimental conditions.

Construction of test platform and case study
According to stress classification, there are three types of accelerated degradation tests: constant stress test, step stress test, and sequential stress test.Since constant stress is relatively simple, this study conducted accelerated degradation tests on a certain model of TMR current sensor (with a maximum operating temperature of 105°C) under constant stresses of 90°C and 100°C, respectively.Since the calibration factor error of the sensor is ±1.6%, it can be used as a criterion for failure.
As shown in Figure 3, the AC/DC voltage source, protective resistor, and shunt are placed outside the temperature chamber and connected by wires to form the measurement loop.Some of the wires enter the TMR sensor and extend into the temperature chamber.The sensor monitors the induced magnetic field and outputs a voltage signal to a digital multimeter, which displays the measurement results through Labview.In addition, the output signal of the shunt is used as the true value of the measurement.Figure 4 shows part of the physical test platform: the temperature and humidity chamber, the digital multimeter, Labview (computer), and the AC/DC power supply.Based on this test platform, first, the output signals of the shunt and sensor were measured at 20℃ with direct and alternating currents of 0.1 A, 0.2 A, and 0.3 A to obtain the calibration factor under this condition, and this was used as a baseline for subsequent changes in the calibration factor at high temperatures.Then, the same operation was repeated every 3-5 hours at 90℃ and 100℃ to calculate the calibration factor and its relative error with respect to the reference value at 20℃, from which the performance degradation trajectory can be obtained.

Specific Examples 4.2.1. Fitting and extrapolation of performance degradation trajectory
The relative error of the calibration factor as a function of time constitutes the performance degradation trajectory.Taking 90℃ and a direct current of 0.1 A as an example, since its trajectory approximately shows linearity, a first-order linear polynomial can be used for fitting, as shown in Figure 5. Combined with the threshold, the pseudo-failure life of the sensor can be obtained.As shown in Figure 6, for the pseudo-failure life, Weibull analysis is used to estimate that the pseudofailure life is approximately linear.Therefore, it can be assumed that the pseudo-failure life follows a Weibull distribution.Weibull estimation was performed on the pseudo-failure life at 90℃ and 100℃.

Life prediction model
Taking the logarithm of both sides of Equation ( 1 In the equation, t is the pseudo-failure life at temperature T. Based on this equation, the pseudofailure life of the TMR current sensor at 20℃ can be predicted to be 13.86 years.

Conclusions
As a new type of measurement device, TMR sensors have attracted increasing attention from researchers due to their good economy and convenience.However, research on their reliability is still in its infancy.In this study, accelerated degradation testing was used to explore the performance of the sensor at high temperatures and generalize it to low temperatures, thus obtaining the pseudo-failure life at different temperatures.This provides a valuable reference for the promotion of TMR sensors in power systems.However, it should be noted that the actual operating environment is complex and can affect the sensor performance.Therefore, it is necessary to study the effect of various stress types on the sensor's mechanism.In addition, data collected during actual operation should be used to better verify the conclusions obtained in this study.

Figure 1 .
Figure 1.The basic structure of the TMR chip.

4 )
Fitting the Arrhenius model to the estimated parameters and corresponding temperatures obtained from the probability density estimation.This enables further extrapolation of the pseudo-failure life at other temperatures.

Figure 5 .Figure 6 .
Figure 5.The degradation trajectory of scaling factor.4.2.2.Probability density estimation of pseudo-failure life ), we obtain the following equation:In the equation, a=ln A，b=-E/k.Fitting m and η yields the life model at any temperature: