# How does the multi-dimensional force sensor calibrate the data?

If you want to measure multi-component force and torque at the same time, you need to use our multi-dimensional force sensor in the ocean, it is inevitable to calibrate (calibrate) before use, otherwise it will not be able to complete the conversion of electrical signal to mechanical value. So how do you calibrate its data? Let's get to know each other.

Multi-dimensional force sensor calibration is generally done with weights, because the weights have very high stability and precision, relying on gravity and vertical downward directionality, this simple standard load is more reliable than many force-applying devices. There are also force generators and high-precision force sensors for automatic loading and measurement, but it is quite difficult to implement, and such a package must still be first calibrated and debugged with a weight.

The signal is obtained by loading, and the load is also known, so that the mathematical relationship between the signal and the load can be obtained. When used, the unknown load can be calculated based on the mathematical relationship obtained by the calibration. Any force sensor needs to be calibrated before use. For multi-dimensional force sensors, calibration is a complex task and data processing methods are varied. The performance of the force sensor is closely related to the calibration equipment and methods.

The core problem that the multi-dimensional force sensor calibration method needs to deal with is how to load (load table design), and how to get the exact mathematical relationship between the component electrical signals and the load (calibration matrix), and also to assess whether the mathematical relationship obtained is accurate enough ( Uncertainty analysis).

A scientific loading load table is usually obtained using the Design Of Experiment (DOE), and a regression relationship between Regression Analysis (RA) is used to obtain a functional relationship between related or independent variables. The final calibration matrix obtained depends largely on the load table and the regression analysis method. Mature dynamometer laboratories have their own set of standards and procedures to obtain and process this data. Sometimes people who are specifically involved in calibration work may not know the data calculation process that occurs behind the calibration process. The DOE method provides less loading. Points get a full, repeatable mathematical model, a statistically based balance calibration method. As early as 1925, this statistically thought-based approach was used in agriculture. This factor design approach needs to consider all the combination factors, but considering the quadratic equation to describe the relationship between the voltage and force of the balance, not all combinations are required. In some cases, it may not be possible to obtain all combined loads, such as a four-degree-of-freedom quasi-body axis calibration system. At this time, the Response Surface Methodology (RSM) (1951) was used to overcome these difficulties and reduce the difficulty of calibration. RSM combines mathematics and statistics and is a method based on polynomial model fitting and considering the limit of loading points.

Common response-surface-based calibration loading designs, such as Central Composite Design (CCD) and Box-Behnken Design (BBD), have been widely used in the aerospace industry. In 2001, NASA adopted an improved central composite design method, Modified Central Composite Design (MCCD), to calibrate the balance in the single vector system Single Vector System (SVS). In this system, the forces and moments are perpendicular to each other. Some people also compared the OFAT and SVS. The results show that the SVS method with stepwise regression takes less time and is more accurate. In 2011, Lynn even considered the effects of wind tunnel pressure and temperature parameters on calibration results.

In order to reduce the nonlinear interference of the calibration system used in the six-component balance, Nouri proposed an improved box line design method Modified Box-Behnken Design (MBBD) in 2015. This method is based on a six-degree-of-freedom calibration system that reduces the nonlinear effects of the calibration system by adding an active factor to the calibration.

Multi-component force sensor calibration is to obtain the correspondence between signal and force. The calibration process can be expressed in the form of a quadratic polynomial. It can be found that this expression is not the same as that in domestic textbooks. We usually put force F to the left of the equal sign. In terms of the calibration process, this expression seems more reasonable, because the signal is given by the application of a certain force.

During the calibration process, the applied load F is known, and the signal Ri is obtained by a high precision data acquisition system, ε being the error term. For a six-component force sensor, there are 36 first-order coefficients and 126 quadratic coefficients. Of course, the acquisition of these coefficients is limited by the calibration equipment, and the magnitude of the calibration error is also highly dependent on the uncertainty of the calibration system.

The calibration mathematical model can be written in a more concise form of vector.

X is called the design matrix and depends on the calibration load table. It plays a key role in the calibration and determines the quality and cost of the calibration. Covariance matrices can be used as an indicator of regression coefficient evaluation. Covariance is a statistic used to measure the relationship between two random variables. Check whether the two variables deviate from the mean at the same time. The covariance matrix is a square matrix obtained by the following formula.

This formula can also be seen why foreign countries attach great importance to the optimization of the calibration load table, because the load load table is designed differently, and different calibration results will be obtained. The same loading load table, using different data processing methods will also have different calibration results.

The above describes some calibration methods for multi-dimensional force sensors. The calibration data processing process is actually more complicated. For detailed operation, you are welcome to call us for Ocean Sensing.