Flowmeter Transducer Calibration via Polynomial Nonlinearity
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Solution Overview
Problem
Flowmeters face challenges in accurately predicting and compensating for intermodulation distortion and transducer nonlinearity, particularly in modeling and calibrating transducer strength, which affects the accuracy of flow measurements due to variability in transducer strength and manufacturing processes.
Innovation Solution
A method and apparatus for calibrating flowmeter transducers using a polynomial model of system nonlinearity, allowing for real-time electrical measurement-based calibration and compensation for transducer strength, enabling accurate prediction of output tones and phases from input tones, and accommodating variability in transducer strength through collocated drivers and pickoff sensors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If transducer strength is treated as a constant gain, then the system is simple to model, but measurement precision deteriorates due to transducer variability and nonlinearity
Solution Approach 1:
The patent transforms the transducer model from a constant gain parameter to a position-dependent polynomial model. The transducer output is expressed as a polynomial function of position (y = P_n*x^n + P_n-1*x^ n-1 + ... + P_1*x + P_0), where coefficients are determined through calibration. This allows the model to adapt to actual transducer behavior while maintaining mathematical tractability for flow calculation.
Solution Approach 2:
The patent implements a calibration procedure performed before normal operation to determine the polynomial coefficients and transducer strength. During calibration, the transducer is positioned at multiple known locations and the relationship between position and output is characterized. These pre-determined parameters are then stored and used during flow measurement, eliminating the need for complex real-time modeling while improving accuracy.
2Measurement precision
If polynomial nonlinearity modeling is implemented, then measurement precision improves by accounting for transducer variability, but device complexity increases due to additional calibration and computation
Solution Approach 1:
The patent creates a mathematical copy of the transducer's input-output relationship through the polynomial model. Instead of physically modifying the transducer or using complex hardware, the system creates a software-based representation (polynomial coefficients) that replicates the transducer's nonlinear behavior. This mathematical copy can be evaluated efficiently during flow measurement without requiring additional physical components.
Solution Approach 2:
The system performs self-calibration by using its own measurement capabilities to characterize its own transducers. The calibration procedure uses the flowmeter's internal position sensing and transducer output measurement to automatically determine the polynomial coefficients, eliminating the need for external specialized equipment or manual adjustment procedures.
3Adaptability or versatility
If transducer position is restricted to a particular range, then the polynomial model remains accurate, but adaptability deteriorates when observing IM distortion effects across broader ranges
Solution Approach 1:
The patent makes the polynomial model dynamic by allowing the determination of coefficients at different operating conditions. The calibration can be performed at multiple position points across the expected range of motion, and the polynomial can be adjusted or recalibrated if the transducer operates outside the original range. This dynamic approach allows the model to adapt to different input frequencies and amplitudes while maintaining accuracy within each calibrated range.
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 allows for precise calibration and compensation of transducer strength, improving the accuracy of flow measurements by accounting for transducer variability, enabling on-demand recalibration, and reducing the need for specialized equipment.
Implementation Method 1
a velocity transducer, such as a voice coil transducer suitable for a flowmeter, may have an output described as: y=k*x_dot
Implementation Method 2
due to the varying engagement of the permanent magnet with respect to the coil, the transducer gain is actually a function of position
Data Source
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Figure 3A
AI summary
A method for calibrating a flowmeter (5) transducer is provided comprising the steps of exciting a vibration mode of a flowmeter (5) flow tube (130, 130') and ceasing to excite the vibration mode, wherein a free decay response of the flow tube (130, 130') is measured. Amplitudes and phases of the free decay response at a drive frequency are extracted, and a strength of the transducer is calculated.