Inverse Finite Element Shape Estimation Using Interpolated Mesh Grids
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Solution Overview
Problem
Existing structural damage detection systems for downhole structures in boreholes face challenges in accurately determining the shape of the structure due to limitations in the number and placement of strain sensors, leading to potential inaccuracies in deformation measurement.
Innovation Solution
The method involves using a plurality of strain sensors to measure strains, creating a mesh grid with nodes corresponding to sensor locations, and employing an inverse finite element method to estimate the shape, with additional nodes and strain values interpolated from adjacent nodes to enhance accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of strain sensors is increased to improve measurement accuracy, then the measurement precision improves, but the device complexity and cost increase
Solution Approach 1:
The patent applies preliminary action by creating additional mesh grid nodes and interpolating strain values before performing the inverse finite element analysis. This preprocessing step fills in missing data points and creates a more complete strain distribution map, allowing accurate deformation measurement without requiring a proportional increase in physical sensor数量
Solution Approach 2:
The patent uses an intermediary approach by introducing a mesh grid system that interpolates strain values between actual sensor locations. This intermediary computational model acts as a bridge between limited discrete sensor measurements and the continuous strain field required for accurate shape estimation, enabling high measurement precision without directly increasing sensor count
2Device complexity
If strain sensors are sparsely distributed to reduce device complexity, then the device complexity decreases, but the measurement precision deteriorates
Solution Approach 1:
The patent performs preliminary interpolation of strain values at additional mesh grid nodes before the inverse finite element analysis. This advance preparation creates a complete strain distribution map from sparse sensor data, ensuring measurement precision is maintained even with minimal physical sensors
Solution Approach 2:
The patent changes the parameter distribution by interpolating strain values at computational mesh nodes that differ from physical sensor locations. This parameter transformation allows the system to work effectively with sparse sensor input by redistributing and refining the strain data across the entire structure surface
3Device complexity
If traditional algorithms are used with limited sensor data, then the device complexity remains low, but the reliability of shape estimation deteriorates due to non-convergence
Solution Approach 1:
The patent applies preliminary action by creating a complete mesh grid with interpolated strain values at all nodes before performing inverse finite element analysis. This preprocessing ensures that the algorithm receives complete input data, preventing non-convergence issues and improving reliability without requiring complex adaptive algorithms
Solution Approach 2:
The patent uses beforehand cushioning by interpolating strain values at additional mesh grid nodes prior to analysis. This preparatory step cushions against potential algorithmic failures due to insufficient data, ensuring the inverse finite element method can converge reliably even when physical sensors are sparse
Data Source
AI summary
A method for estimating a shape, the method including: selecting a structure comprising a plurality of strain sensors inoperable communication with the structure, each strain sensor configured to provide a strain measurement; placing the structure in a borehole; receiving the strain measurements from the plurality of strain sensors; creating a mesh grid having nodes, each node related to a location of one strain sensor and assigned a strain value measured by the one strain sensor; creating an additional node for the mesh grid wherein a strain value assigned to the additional node is derived from the strain value corresponding to at least one adjacent node; and performing an inverse finite method using the mesh grid with the assigned strain values to estimate the shape.