Blade Tip Timing Analysis Using SVD for Real-Time Displacement
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Solution Overview
Problem
Existing methods for analyzing blade tip displacements in gas turbine engines fail to effectively extract steady-state displacement errors and noise, leading to increased measurement uncertainty and are not suitable for real-time applications, often requiring multiple revolutions and expert intervention.
Innovation Solution
A method that analyzes blade tip displacements by defining asynchronous and synchronous displacements as sums of sinusoidal terms and offset terms, allowing for the calculation of amplitudes, offsets, and residuals without initial data zeroing, using singular value decomposition and iterative best-fitting sine waves, which can be performed in real-time with only two revolutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If known methods are used to extract steady state displacement errors, then measurement uncertainty increases, but the analysis requires many revolutions (30-40) which makes it unsuitable for real-time applications
Solution Approach 1:
The patent applies preliminary action by pre-defining the mathematical model (sum of sinusoidal terms and offset terms) and using singular value decomposition to pre-calculate the transformation matrices. This allows the system to quickly process blade tip displacement data by simply applying the pre-computed model to the measured data, eliminating the need for time-consuming iterative procedures and achieving real-time analysis capability while maintaining measurement precision
Solution Approach 2:
The patent replaces the mechanical iterative procedure (requiring multiple revolutions and manual window definition) with a mathematical computation approach using singular value decomposition. By substituting the mechanical time-consuming process with an efficient mathematical algorithm, the system achieves both high measurement precision and real-time processing capability
2Measurement precision
If expert manual intervention is used to define windows in the data, then measurement precision may improve, but the device complexity and ease of operation deteriorate
Solution Approach 1:
The patent applies self-service by implementing an automated system that performs the entire analysis process without expert manual intervention. The singular value decomposition algorithm automatically identifies the appropriate data windows and extracts displacement errors, eliminating the need for experts to manually define windows while maintaining measurement precision and significantly improving ease of operation
3Measurement precision
If data zeroing is performed to extract steady state displacement errors, then measurement precision may improve, but the process distorts the data by inaccurate definition of windows
Solution Approach 1:
The patent applies the extraction principle by using singular value decomposition to separate and extract the steady-state offset components from the blade tip displacement data. Instead of manually zeroing the data which causes distortion, the mathematical model automatically extracts the offset terms, maintaining both measurement precision and data reliability by avoiding arbitrary window definitions
4Measurement precision
If multiple revolutions (30-40) are used for analysis, then measurement precision improves, but productivity decreases
Solution Approach 1:
The patent applies preliminary action by pre-computing the singular value decomposition matrices and the mathematical model coefficients before actual measurement. This allows the system to achieve high measurement precision using only two revolutions of data, as the heavy computational work has already been done in advance, thereby significantly improving productivity while maintaining precision
Data Source
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AI summary
A method of analysing blade tip displacements (dijk) derived from a rotor (2) having an array of blades (4) that rotate at a rotational speed (ω). The blades (4) are monitored by an array of stationary timing probes (3) for at least two revolutions (j) of the rotor (2). Define asynchronous displacement (dijk_A) as a sum of a sinusoidal term (Va) and an offset per probe term (Oo). Define synchronous displacement (dijk_S) as a sum of a sinusoidal term (Vs) and a common offset term (Cc). Solve the asynchronous displacements (dijk_A) using the blade tip displacements (dijk) to give asynchronous amplitude (|a|), offset per probe (Ok) and asynchronous residuals (rijk_A). Solve the synchronous displacements (dijk_S) using the blade tip displacements (dijk) to give synchronous amplitude (|s|), common offset (cj) and synchronous residuals (rijk_S).