Kalman Filter Estimation Using First-Order Lag Elements
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Solution Overview
Problem
In dynamic systems like gas turbine engines, the number of performance parameters that can be estimated is limited by the number of sensors, making it difficult to detect and specify aged deteriorations and faults in engine elements that are not observable externally.
Innovation Solution
A dynamic system estimation device and method that uses a Kalman filter with first-order lag elements to estimate performance parameters beyond the number of sensors, by introducing these elements to describe temporal changes in performance parameters, allowing for the estimation of a larger number of performance parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of sensors is increased to estimate more performance parameters, then the estimation capability is improved, but the device complexity and cost increase
Solution Approach 1:
The patent transforms performance parameters from constant values to time-varying parameters by introducing first-order lag elements. This parameter change allows the Kalman filter to estimate temporal variations of performance parameters using the same sensor data, effectively increasing estimation capability without adding sensors. The dynamic model incorporates these lag elements to represent aging and fault developments over time.
Solution Approach 2:
The patent introduces first-order lag elements as intermediary components between the sensors and the performance parameters. These lag elements act as mediators that transform static sensor measurements into dynamic parameter estimates by modeling the temporal evolution of performance degradation. This intermediary mechanism enables estimation of more parameters than the number of physical sensors.
2Reliability
If the number of performance parameters to be estimated is increased beyond the number of sensors, then the detection of aged deteriorations and faults is improved, but the mathematical solvability of the estimation problem deteriorates
Solution Approach 1:
The patent applies dynamics by transforming the estimation problem from a static algebraic system to a dynamic system. By introducing first-order lag elements with time constants, the performance parameters become dynamic state variables that evolve over time. This dynamic formulation allows the Kalman filter to solve the estimation problem using temporal information from sensor measurements, making it possible to estimate more parameters than sensors by utilizing the time dimension.
Solution Approach 2:
The patent adds the time dimension to the estimation problem by modeling performance parameters as time-varying quantities. This dimensional transformation converts a potentially unsolvable algebraic problem (more parameters than sensors) into a solvable dynamic problem where temporal evolution provides additional information. The first-order lag elements introduce time constants that enable the system to utilize historical data for current parameter estimation.
Data Source
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AI summary
A dynamic system estimation device and method, whereby estimation for more performance parameters than there are sensors can be performed, the estimation taking temporal changes into account. The dynamic system estimation device includes: a prescribed number of sensors that detect prescribed observation values from a gas turbine engine; and a Kalman filter that uses a dynamic model of the gas turbine engine and estimates the state of the gas turbine engine, on the basis of the observation values detected by the sensors. The gas turbine engine includes an element having changes in temporal performance recorded by performance parameters. The Kalman filter enables more than the prescribed number of performance parameters to be estimated, as a result of introducing a first-order lag element in place of the element.