Optical Tracking Alias Protection via Wavelet Filtering
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Solution Overview
Problem
High-speed digital image correlation techniques face challenges in accurately measuring dynamic quantities such as Shock Response Spectrum and velocity/acceleration time history due to temporal aliasing and noise amplification, leading to unreliable data and invalid conclusions.
Innovation Solution
The implementation of a system using two sensors within the Region of Interest (ROI) of a DIC system, one analog low-pass filtered and one non-filtered, combined with wavelet de-noising filters to differentiate and filter DIC displacement signals, allowing for alias protection and comparison to determine reliable dynamic quantities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If temporal differentiation is applied to DIC displacement signals to obtain dynamic quantities of interest, then the ability to measure dynamic quantities such as Shock Response Spectrum and velocity/acceleration time history is improved, but noise amplification and error amplification occur severely
Solution Approach 1:
The patent applies wavelet filtering to the DIC displacement signals before performing temporal differentiation. This preliminary filtering action removes noise and high-frequency artifacts that would otherwise be amplified during differentiation, thereby maintaining data reliability while still obtaining accurate dynamic quantities.
Solution Approach 2:
The wavelet transform acts as an intermediary between the raw DIC displacement data and the final dynamic quantities. It provides an intermediate filtered representation that preserves the essential dynamic information while eliminating noise, allowing safe differentiation without direct amplification of errors.
2Reliability
If digital low-pass filtering techniques are applied to DIC data to guard against temporal aliasing, then aliasing protection is improved, but the frequency-rich signals encountered and Analog/Digital conversion limitations make it impossible to digitally filter data after aliasing has occurred
Solution Approach 1:
The patent applies wavelet filtering before the Analog/Digital conversion process. This preliminary action removes high-frequency components that would cause aliasing during sampling, ensuring that only frequencies within the Nyquist limit are converted to digital form. This prevents aliasing from occurring in the first place rather than attempting to correct it afterward.
Solution Approach 2:
The patent replaces traditional analog low-pass filtering with wavelet-based digital filtering applied to the displacement signals. This substitution allows for more flexible and effective filtering that adapts to the specific frequency content of the signals while maintaining the ability to capture frequency-rich characteristics.
3Ease of manufacture
If Fourier filtering techniques are used to process DIC-derived data products, then periodic signal processing is improved, but periodicity is a poor assumption for most high speed DIC applications due to the inherent non-periodic nature of phenomena
Solution Approach 1:
The patent replaces Fourier filtering techniques with wavelet filtering techniques. Wavelet transforms are specifically designed to handle non-periodic and transient signals effectively, providing time-frequency analysis that adapts to the instantaneous characteristics of the signal. This substitution allows accurate processing of non-periodic phenomena while maintaining ease of implementation through standardized wavelet algorithms.
Solution Approach 2:
The patent changes the filtering approach from frequency-domain (Fourier) to time-frequency domain (wavelet). This parameter change allows the filtering to adapt to the time-varying characteristics of non-periodic signals, providing better measurement precision for transient and non-repeating phenomena while still offering systematic processing through wavelet decomposition levels.
4Ease of operation
If central difference method is used to compute temporal derivatives from raw DIC data, then computational simplicity is improved, but errors due to noise or uncertainly are severely amplified at each differentiation step
Solution Approach 1:
The patent applies wavelet filtering to the raw DIC displacement data before computing temporal derivatives using the central difference method. This preliminary filtering action reduces the noise content in the data, thereby minimizing the amplification of errors during differentiation while maintaining the computational simplicity of the central difference approach.
Solution Approach 2:
The wavelet filtering acts as a cushioning mechanism that anticipates and mitigates the error amplification that will occur during differentiation. By removing high-frequency noise components before differentiation, the system prepares the data in advance to withstand the error amplification inherent in numerical differentiation operations.
Data Source
AI summary
Systems and methods for realizing practical applications of high speed digital image correlation (DIC) for dynamic quantities of interest are provided. In particular, a series of images are captured for a component of interest in which a non-filtered sensor and an analog low-pass filtered sensor are included within the region of interest for the series of images. Displacement signals are obtained for the component of interest, the non-filtered sensor, and the analog low-pass filtered sensor by applying digital image correlation processing to the series of images, which may also be wavelet filtered. Dynamic quantities of interest may be generated and derived from the displacement signals after having been wavelet filtered. Such dynamic quantities of interest based on the wavelet filtered DIC-derived displacement signal may be compared to sensor-derived dynamic quantities of interest to determine if aliasing is or is likely to be present.