3D Convolution Decomposition for Aircraft Engine Density Measurement
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for measuring the volume density of a specific phase in materials, such as porosity, in large tomographic images are computationally intensive due to algorithmic complexity dependent on the product of image and reference volume sizes, leading to excessively long calculation times, making them unsuitable for production controls.
Innovation Solution
A method that decomposes 3D convolution into three 1D convolutions, allowing for parallelization of operations and using an averaging kernel corresponding to a parallelepipedal reference volume, significantly reducing the number of calculation steps and independent of image content, thereby accelerating processing time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the conventional algorithm for calculating volumetric porosity ratio is used, then the measurement precision is maintained, but the calculation time becomes excessively long
Solution Approach 1:
The patent applies segmentation by dividing the 3D convolution operation into three separate 1D convolution operations along different spatial dimensions. This decomposition transforms a single complex N×L calculation into three simpler operations, each processing one dimension independently, thereby reducing overall computational complexity and calculation time while maintaining measurement precision.
Solution Approach 2:
The patent utilizes dimensionality change by transitioning from a direct 3D volumetric calculation to a series of 1D linear operations. By processing data along individual dimensions (x, y, z axes) separately and combining results, the method converts a computationally intensive 3D problem into manageable 1D problems, significantly accelerating processing while preserving accuracy.
2Measurement precision
If the algorithm processes large tomographic images with large reference volumes, then the measurement accuracy is improved, but the algorithmic complexity increases to O(NL)
Solution Approach 1:
The patent segments the complex 3D convolution algorithm into three independent 1D convolution operations. Each 1D operation processes one spatial dimension with linear complexity O(N), and the combined complexity of three sequential operations remains O(N) rather than O(NL). This segmentation maintains measurement accuracy by preserving the full 3D reference volume information while eliminating the quadratic complexity of the original approach.
Solution Approach 2:
The patent changes the computational parameters by transforming the operation from a 3D volumetric convolution (requiring N×L operations) into three 1D convolutions. This parameter transformation maintains the effective reference volume size for accurate measurement while reducing the computational operations from product-scale to linear-scale complexity.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
The invention concerns a method and a system for non-intrusively measuring the volume density of a specific phase in a part, comprising: - processing means (9) for producing a three-dimensional image (17) of said part (11), said image being formed by a three-dimensional grid of voxels of which the values indicate the arrangement of said specific phase in said part, - processing means (9) for associating a binary coefficient with each voxel of said three-dimensional image, thus constructing an initial three-dimensional matrix representation of binary coefficients, said binary coefficients being representative of a presence or absence of said specific phase in areas of said part corresponding to the voxels, - processing means (9) for convolving said initial matrix representation with a matrix convolution kernel corresponding to a predefined reference volume, said convolution being performed by implementing a composition of three (successive) one-dimensional convolutions in three separate directions, thus forming a resulting matrix representation of which each resulting coefficient represents a volume level (density) of said specific phase in said reference volume.