Signal Evaluation for Natural Frequency Determination
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Solution Overview
Problem
Existing methods for determining the natural frequency of devices using sensor signals are not precise enough, leading to errors in further evaluations such as mass determination.
Innovation Solution
An evaluation method that involves bandpass filtering of signal curves to isolate specific frequency ranges, followed by regression analysis to determine the natural frequency with high precision, using a parameterized form of damped harmonic oscillation and optimization criteria.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional evaluation methods are used to determine natural frequency from sensor signals, then the evaluation process is simple, but the measurement precision is insufficient leading to errors in mass determination
Solution Approach 1:
The signal evaluation process is segmented into distinct stages: bandpass filtering to isolate specific frequency components, followed by regression analysis on the filtered signal. This segmentation allows each stage to focus on a specific task, improving overall measurement precision while keeping individual stages manageable in complexity
Solution Approach 2:
Bandpass filtering is applied as a preliminary action before regression analysis. By pre-processing the signal to isolate the frequency range containing the natural frequency, the subsequent regression analysis operates on cleaner, more targeted data, significantly improving measurement accuracy without requiring complex algorithms
2Measurement precision
If the evaluation period is extended to improve frequency determination accuracy, then the measurement precision increases, but the loss of time increases
Solution Approach 1:
Instead of using the entire detection period for evaluation, only a specific evaluation period containing the most relevant signal characteristics is used. This partial action approach achieves high measurement precision by focusing on the most informative portion of the signal, reducing the time loss compared to using the full detection period
Solution Approach 2:
The bandpass filter parameters (frequency range) are optimized to capture the natural frequency components within a specific bandwidth. By changing the frequency domain parameters through filtering, the effective signal-to-noise ratio is improved, allowing accurate frequency determination in shorter evaluation periods
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach achieves an accuracy at least one order of magnitude better than prior art, often two orders of magnitude, allowing for precise determination of natural frequencies and subsequent properties like mass or spring characteristics.
Implementation Method 1
subjects the signal curve of the evaluation period to bandpass filtering with a lower and an upper limit frequency and thus determines a filtered signal curve
Implementation Method 2
sets a parameterized form of a damped harmonic oscillation, determines the frequency of the damped harmonic oscillation by means of a regression of the filtered signal curve according to an optimization criterion
Data Source
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AI summary
An evaluation unit (3) continuously receives and stores a signal (ax, ay, az) from a number of sensors (2) connected to a device (1) during a recording period (T), so that the evaluation unit (3) generates a signal waveform for the signal (ax, ay, az). The signals (ax, ay, az) are characteristic of a path traveled by the device (1) at the location of the respective sensor (2) in a respective direction (x, y, z) or of a time derivative of this path. The evaluation unit (3) defines a period within the recording period (T') as the evaluation period (T) and subjects the signal waveform of the evaluation period to bandpass filtering with a lower and an upper cutoff frequency (fmin, fmax), thus determining a filtered signal waveform.The evaluation unit (3) applies a parameterized form of a damped harmonic oscillation and determines the frequency (f) of the damped harmonic oscillation by means of a regression of the filtered signal waveform according to an optimization criterion. The evaluation unit (3) defines the frequency (f) thus determined as a natural frequency (EFi) of the device (1). Using the natural frequencies (EFi) determined for the signals (ax, ay, az) of the sensors (2), the evaluation unit (3) determines a property (m, m1, m2, k) of the device (1).