Accelerometer Calibration via Rigid Body Motion Decomposition
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Solution Overview
Problem
Current methods for calibrating accelerometer positions and orientations in mechanical structures are time-consuming, prone to errors, and yield sub-optimal solutions due to inaccuracies in sensor calibration and non-convex optimization problems, especially with modern analysis techniques requiring higher precision.
Innovation Solution
A system and method using singular value decomposition (SVD) to process measurements from reference accelerometers, decomposing rigid body motions into infinitesimal translation-rotation pairs, and applying linear recombination to derive accurate orientations and positions, ensuring sufficient excitation and minimizing noise from structural deformations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If manual measurement and documentation of accelerometer orientations and positions is performed, then measurement data can be obtained, but the process becomes time-consuming and error-prone
Solution Approach 1:
The system performs self-calibration by automatically computing accelerometer positions and orientations from the measurement data itself, without requiring manual measurement and documentation. The calibration process is executed autonomously through iterative optimization that uses the recorded acceleration signals to determine sensor geometries
Solution Approach 2:
The patent replaces manual mechanical measurement processes with an automated computational approach. Instead of physically measuring and documenting each accelerometer's position and orientation, the system uses mathematical optimization on the acceleration signals to derive these parameters automatically
2Extent of automation
If nonlinear optimization is used to compute accelerometer positions and orientations from measurement data, then calibration can be automated, but the solution may be sub-optimal due to local minima
Solution Approach 1:
The patent applies preliminary linearization to the optimization problem by formulating it in terms of infinitesimal rotations and translations. This preprocessing step transforms the nonlinear problem into a form that can be solved more reliably using linear algebra techniques, avoiding the pitfalls of direct nonlinear optimization
Solution Approach 2:
The system changes the parameterization of the optimization problem from direct position and orientation parameters to infinitesimal rotation and translation parameters. This transformation linearizes the problem and enables more reliable convergence to the global optimum
3Adaptability or versatility
If excitation encompasses all 6 degrees of freedom to enable self-calibration, then complete calibration is possible, but it is difficult to verify sufficiency and assess data quality
Solution Approach 1:
The patent implements feedback mechanisms that monitor the excitation quality and data quality throughout the calibration process. The system assesses whether all 6 degrees of freedom have been sufficiently excited and provides feedback on the quality of the input data, allowing for iterative improvement of the calibration process
Solution Approach 2:
The system introduces intermediate quality assessment metrics that act as mediators between the raw measurement data and the final calibration results. These metrics provide information about data quality and excitation sufficiency without requiring direct interpretation of the complex measurement signals
Data Source
Figure 1
Figure 2(a)~2(g)
AI summary
The invention relates to a system (SYS) and a method for analyzing the motions of a mechanical structure (STR), comprising: (a) accelerometers (ACC) provided as standard accelerometers (SAC) to measurement-points (MPI) of said mechanical structure (STR), (b) at least three accelerometers (ACC) provided as reference accelerometers (RAC) to measurement-points (MPI) of said mechanical structure (STR), (c) at least one shaker (SHK) being attached to said mechanical structure (STR) for moving the structure (STR) periodically within a first frequency range (FR1), further comprising at least one data processing system (DPS) being prepared to: (d) receiving measurements from said accelerometers (ACC) at the measurement-points when periodically moving the structure (STR) within said first frequency range (FR1) by said at least one shaker (SHK). To enable accurate and quick calibration the invention proposes that said at least one data processing system (DPS) is further prepared to calibrate the accelerometers' (ACC) positions and orientations by the following steps: (e) determining from said measurements of said at least three reference accelerometers (RAC) rigid body motions (RBM), (f) determining positions and orientations of reference accelerometers (ACC) from said rigid body motions (RBM), (g) determining positions and orientations of standard accelerometers (SAC) from said rigid body motions (RBM).