Optimization of training sets for neural-net processing of characteristic patterns from vibrating solids

A method of using an artificial neural network for detecting damage of a vibrating structure, said method comprising the steps of:

• a) recording two time-average holograms of a vibrating structure serving as a training set and each comprised of a first number of pixels;
• b) providing tiles serving as large pixels predetermined from the geometry of the vibrating structure;
• c) sub-sampling each of two time-average holograms of said training set within said large pixels to extract a second number of pixel for each of said two time-average holograms;
• d) subtracting corresponding second pixels of each of said two time-average holograms of said training set to generate a sub-sampled characteristic pattern;
• e) delivering said sub-sampled characteristic pattern of said training set to a folding routine which scales the second pixels comprising said sub-sampled characteristic pattern of said training set in accordance with said second pixels locations in an intensity range and provides a representative output to serve as a training record;
• f) repeating said steps a), b), c), d) and e) until a predetermined number of training set records is obtained;
• g) delivering said predetermined number of training records to train an artificial neural network, said artificial neural network being trained to compare the characteristic patterns comprising said training set records against each other with differences therebetween being indicative of detecting damage of said vibrating structure, said artificial neural network providing a first output representative of the differences between said training set records;
• h) recording two time-average holograms of said vibrating structure serving as a test set and each comprised of a first number of pixels;
• i) providing said tiles serving as large pixels predetermined from the geometry of the vibrating structure;
• j) sub-sampling each of two time-average holograms of said test set within said large pixels to extract a second number of pixel for each of said two time-average holograms;
• k) subtracting corresponding second pixels of each of said two time-average holograms of said test set to generate a sub-sampled characteristic pattern;
• l) delivering said sub-sampled characteristic pattern of said test set to a folding routine which scales the second pixels comprising said sub-sampled characteristic pattern of said test set in accordance with said second pixels locations in an intensity range and provides a representative output to serve as a training record;
• m) repeating said steps h), i), j), k), and 1) until a predetermined number of test set records are obtained;
• n) delivering said test set records to said trained artificial neural network to provide a second representative output from said trained artificial neural network;
• and
• o) said trained artificial neural network comparing said first representative output against said second representative output to determine if a difference of a predetermined amount exists therebetween, said difference representing said detection of damage to said vibrating structure.

A method of training an artificial neural network for detecting damage of a vibrating calculated structure, said method comprising the steps of:

• a) calculating a characteristic pattern of a vibrating structure serving as a training pattern, said training characteristic pattern comprising pixels;
• b) delivering said characteristic pattern to a folding routine which scales the pixels comprising said characteristic pattern in accordance with said pixels locations in an intensity range and provides a representative output to serve as a training record, wherein said folding routine comprises;
• i) determining a first intensity range of said second number of pixels, ii) dividing said determined first intensity range into two or more second intensity ranges;
• and iii) increasing said two or more second intensity ranges to that of the first intensity range;
• and wherein said pixels are comprised of eight bits which represent pixel values from 0 to 255 and which individual pixels satisfy the expression:
• Pixel value=A cos [θ]Jo[2πK·δ]
• where A is a positive random quantity;
• θ is random variable uniformly distributed from 0 to 2π;
• Jo is the Bessel function of the first kind and zero order;
• K is the sensitivity vector;
• and δ is the vibration displacement amplitude measure in wavelengths of light;
• c) repeating said steps a) and b) until a predetermined number of training records is obtained;
• and
• d) delivering said predetermined number of training records to train an artificial neural network thereof, said artificial neural network being trained to compare the characteristic patterns comprising said training records against each other with differences therebetween being indicative of detecting damage of said vibrating calculated structure.

A method of using an artificial neural network for detecting damage of a vibrating structure, said method comprising the steps of:

• a) calculating a characteristic pattern of a vibrating structure serving as training pattern, said training characteristic pattern comprising pixels;
• b) delivering said characteristic pattern to a folding routine which scales the pixels comprising said characteristic pattern in accordance with said pixels locations in an intensity range and provides a representative output to serve as a training record;
• c) repeating said steps a) and b) until a predetermined number of training records is obtained;
• and
• d) delivering said predetermined number of training records to train an artificial neural network said artificial neural network being trained to compare the characteristic patterns comprising said training records against each other with differences therebetween being indicative of detecting damage of said vibrating calculated structure, said artificial neural network providing a first output representative of the difference between said training records;
• e) calculating characteristic patterns of a vibrating structure and serving as test characteristic patterns, said test characteristic patterns comprising pixels;
• f) delivering said test characteristic patterns to a folding routine which scales the pixels comprising said test characteristic patterns in accordance with said pixels locations in an intensity range and provides representative outputs to serve as test set records;
• g) repeating said steps e) and f) until a predetermined number of test set records is obtained;
• h) delivering said test set records to said trained artificial neural network to provide a second representative output from said trained artificial neural network;
• and
• i) said trained artificial neural network comparing said first representative output against said second representative output to determine if a difference of a predetermined amount exists therebetween, said difference representing detection of said damage to said vibrating structure.