The nonlinearity index of eddy current sensor is a very important index, and the specific meaning of the index has not been understood clearly, especially the specific method of the index calculation formula has not formed a theoretical basis. This causes the following problems:

1, can not really judge the sensor performance.

2, in comparison with other similar manufacturers of sensors, can not really compare.

3, because the index calculation formula of the method of substitution is not clear, may lead to the test method problems.

In view of this, I have sorted out the important indicators of eddy current sensor, so as to form the detection (test) basis, and also facilitate the comparison with other similar products in the future.

One, least square method

The Department of Applied Mathematics, Tongji University, edited the Fifth edition of Advanced Mathematics, Chapter 8, Section 12, explains the least square method in detail.

In a nutshell, the least square method is to find the expression representing the function relationship between two variables from the experimental data of the sum of two variables，The function  at  the smallest deviation from.

calculation method：another，because ofandis known experimental data, so M is regarded as the dependent variable corresponding to the independent variables a and b.

According to the extreme value theorem of functions of several variables. To get the minimum value for M,

Collate and merge, separate out the unknowns a and b, and get

2. Domestic standards for eddy current sensors

At present, there is no standard for eddy current sensor in China. But there are some common or similar standards. As below.

1, "GB/T 7665-2005 General terms for sensors", the standard is only the classification of sensors and basic terms are unified, and does not specify the sensor indicators and calculation methods.

2, "GB/T 18459-2001 sensor main static performance index calculation Method", the standard in detail and scientific specification of the sensor range（）、Full scale output（）、output resolution（）、sensitivity（）、return difference（）、repeatability

（）、degree of linearity（）The definition and calculation method of etc.Especially the reverse deviation（）、repeatability（）、degree of linearity（）,the various algorithms are defined. Domestic manufacturers generally adopt this standard as the basis for their sensor inspection and calibration.

3, "JBT9256-1999 inductance displacement sensor", the standard is too old, does not belong to the national standard, belongs to the mechanical industry standard, the content is not suitable for eddy current displacement sensor.

4, "JB_T13110-2017 Eddy current proximity switch sensor" This standard can only regulate the proximity switch, not the eddy current displacement sensor.

5, "JJG644-2003 vibration displacement sensor verification regulations" the standard has not been adopted by the manufacturers and the industry, there are a lot of content and GB/T 18459-2001 inconsistent, even unscientific. For example, for static sensitivity, for nonlinearity. The most error-prone implementation of this standard is not knowing how to calculate the sensor output at full scale.

Three, linearity

In practice, in order to facilitate the analysis and processing of measurement results, a fitting line is often used to represent the actual characteristic curve approximately. The fitting line is also called the reference line, and the actual characteristic curve refers to the data at the time of measurement. Under specified conditions, the percentage of maximum deviation and full-scale output between the sensor calibration curve and the fitted line is called linearity, as shown in the figure below.Let's call itfor linearity.And

in formula，Is the maximum deviation between the calibration curve and the fitted line；

Full scale output for the sensor，

The total average characteristic value of the sensor at the i-th calibration point. If multiple measurements exist at point i, average is）

传The reference characteristic value of the sensor at the ith calibration point, that is, the value corresponding to the fitting line at the ith calibration point.

It can be seen that linearity is calculated from the fitting line as the reference line. If the reference line is different, the linearity is also different. Therefore, when talking about linearity or nonlinear error, the reference line on which it is based must be explained at the same time.

In "GB/T 18459-2001 Sensor Main static performance Index Calculation Method", the absolute linearity linearity is specified in detail，terminal-based linearity，Translation base linearity，zero based linearity，Front-end base linearity, independent linearity, least square linearity.

Among them, end-base linearityand least square linearity are the two most commonly used linearity.

In Appendix A of GB/T 18459-2001 Calculation Method of Main Static Performance Indicators of Sensors, there is a very detailed calculation process of test data, among which the calculation results of several nonlinear degrees are compared. Usually the end base linearity is the maximum that can be calculated.

4. Foreign standards

1. API STD 670-2014 Vibration, Axial Position and Bearing Temperature Monitoring System, which is a specification for eddy current sensors, is a highly recognized international standard for vibration monitoring and eddy current identification. It is also adopted and promoted by Bently(Bentley) Inc.

The linearity concept is measured by the best linear deviation (DSL) index. (This is specified in (API)670.)

Optimal linear Deviation (DSL) test and calculation method：Within the range（）of the sensor，measure the  sensor output from the start of the range in a  step (usually n=8). The specific reference is as follows.