Defect identification signal analysis method
First Claim
1. A method of characterizing defects in a part, the method comprising:
- a) identifying a numerically quantifiable physical property that provides good part array Ai of n numerical values given by equation 1 that characterize a first reference part without a defect and defect array Bi of n values as provided by equation 2 that characterize a second reference part with a known defect;
Aiε
(A1, A2, . . . An)
1;
Biε
(B1, B2, . . . Bn)
2;
wherein, n is an integer, and array Ai and array Bi are ordered by an independent parameter pi that is associated with the values in array Ai and array Bi through the functional relationship Ai=fa(pi) and Bi=fb(pi);
b) creating good part vector A of n dimensions as provided by equation 3 whose components are the n numerical values in good part array Ai;
A=<
A1, A2, . . . An>
3;
c) creating defect vector B of n dimensions as provided by equation 4 whose components are the n values in defect array Bi;
B=<
B1, B2, . . . Bn>
4;
d) identifying vector R by selecting a vector from the group consisting of vector B, vector C, vector D, and vector E;
wherein, vector C is created by taking the difference between good part vector A and defect vector B as provided in equation 5;
C=A−
B
5; and
vector D is formed by;
1) creating difference vector C of n dimensions as provided by equation 5 which is the difference between good part vector A and defect vector B;
C=A−
B
5;
2) identifying m components of vector C as provided by equation 6 having the largest magnitudes;
C′
iε
(C′
1, C′
2, . . . C′
m)
6;
3) creating vector D of m dimensions as provided by equation 7 whose components are the n values in array C′
i and vector E is formed by;
1) creating difference vector C of n dimensions as provided by equation 5 which is the difference between good part vector A and defect vector B;
C=A−
B
5;
2) identifying m components of vector C as provided by equation 6 having the largest magnitudes;
C′
iε
(C′
1, C′
2, . . . C′
m)
6;
3) creating vector D of m dimensions as provided by equation 7 whose components are the n values in array 7; and
5) normalizing vector D to form vector E as provided in equation 9;
E=D/|D|
8;
e) determining array Fi of n numerical values as provided by equation 9 that characterize a test part that may have an unknown defect using the numerically quantifiable physical property;
Fiε
(F1, F2, . . . Fn)
9;
f) creating vector F of n dimensions as provided by equation 10 whose components are the n values in array Fi;
F<
F1, F2, . . . Fn>
10;
9) identifying vector S by selecting a vector selected from the group consisting of vector F, vector G, vector H, and vector I, wherein, vector G is formed by taking the difference between vector A and vector F as provided in equation 11;
G=A−
F
11; and
vector H is formed by;
1) creating vector G as provided by equation 11 which is the difference between vector A and vector F;
G=A−
F
11;
2) identifying m components of vector G as provided by equation 12 which correspond to the same values for pi as the m components selected in step d for vector F;
G′
iε
(G′
1, G′
2, . . . G′
m)
12;
3) creating vector H as provided in equation 13 of dimension m having as components only the m components of step 2;
4) normalizing vector H to create vector I as provided in equation 14;
I=H/|H|
14; and
vector I is formed by;
1) creating vector G as provided by equation 11 which is the difference between-vector A and vector F;
G=A−
F
11;
2) identifying m components of vector G as provided by equation 12 which correspond to the same values for pi as the m components selected in step d for vector F;
G′
iε
(G′
1, G′
2, . . . G′
m)
12;
3) creating vector H as provided in equation 13 of dimension m having as components only the m components of step 2;
4) normalizing vector H to create vector I as provided in equation 14;
I=H/|H|
14; and
h) forming dot product DP as provided in equation 15;
DP=R·
S
15;
wherein the dot product provides a number related to the probability that the test part that may have an unknown defect has the known defect in the second reference part with the proviso that when vector B is selected in step d vector F is selected in step g, vector C is selected in step d vector G is selected in step g, vector D is selected in step d vector H is selected in step g, and vector E is selected in step d vector I is selected in step g.
1 Assignment
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Accused Products
Abstract
The present invention provides a method of identifying a defect in a part by forming a dot product between a vector related to a part with a known defect and a vector related to a part with an unknown defect. The magnitude of the dot product has been found to increase as the likelihood that unknown defect is the know defect increases. The components of each of these vectors determined from a quantifiable physical property capable of discriminating between parts with and without defects. The most useful quantifiable physical property for the method of the invention is the magnitudes of vibrations in an operating part. Frequency spectrum generated with this property are easily analyzed and defects identified. The present invention provides another method of identifying defects that is readily applicable to time domain spectra also uses dot product but shifts the vector to maximize the dot product.
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Citations
28 Claims
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1. A method of characterizing defects in a part, the method comprising:
-
a) identifying a numerically quantifiable physical property that provides good part array Ai of n numerical values given by equation 1 that characterize a first reference part without a defect and defect array Bi of n values as provided by equation 2 that characterize a second reference part with a known defect;
Aiε
(A1, A2, . . . An)
1;
Biε
(B1, B2, . . . Bn)
2;
wherein, n is an integer, and array Ai and array Bi are ordered by an independent parameter pi that is associated with the values in array Ai and array Bi through the functional relationship Ai=fa(pi) and Bi=fb(pi);
b) creating good part vector A of n dimensions as provided by equation 3 whose components are the n numerical values in good part array Ai;
A=<
A1, A2, . . . An>
3;
c) creating defect vector B of n dimensions as provided by equation 4 whose components are the n values in defect array Bi;
B=<
B1, B2, . . . Bn>
4;
d) identifying vector R by selecting a vector from the group consisting of vector B, vector C, vector D, and vector E;
wherein, vector C is created by taking the difference between good part vector A and defect vector B as provided in equation 5;
C=A−
B
5; and
vector D is formed by;
1) creating difference vector C of n dimensions as provided by equation 5 which is the difference between good part vector A and defect vector B;
C=A−
B
5;
2) identifying m components of vector C as provided by equation 6 having the largest magnitudes;
C′
iε
(C′
1, C′
2, . . . C′
m)
6;
3) creating vector D of m dimensions as provided by equation 7 whose components are the n values in array C′
iand vector E is formed by;
1) creating difference vector C of n dimensions as provided by equation 5 which is the difference between good part vector A and defect vector B;
C=A−
B
5;
2) identifying m components of vector C as provided by equation 6 having the largest magnitudes;
C′
iε
(C′
1, C′
2, . . . C′
m)
6;
3) creating vector D of m dimensions as provided by equation 7 whose components are the n values in array 7; and
5) normalizing vector D to form vector E as provided in equation 9;
E=D/|D|
8;
e) determining array Fi of n numerical values as provided by equation 9 that characterize a test part that may have an unknown defect using the numerically quantifiable physical property;
Fiε
(F1, F2, . . . Fn)
9;
f) creating vector F of n dimensions as provided by equation 10 whose components are the n values in array Fi;
F<
F1, F2, . . . Fn>
10;
9) identifying vector S by selecting a vector selected from the group consisting of vector F, vector G, vector H, and vector I, wherein, vector G is formed by taking the difference between vector A and vector F as provided in equation 11;
G=A−
F
11; and
vector H is formed by;
1) creating vector G as provided by equation 11 which is the difference between vector A and vector F;
G=A−
F
11;
2) identifying m components of vector G as provided by equation 12 which correspond to the same values for pi as the m components selected in step d for vector F;
G′
iε
(G′
1, G′
2, . . . G′
m)
12;
3) creating vector H as provided in equation 13 of dimension m having as components only the m components of step 2;
4) normalizing vector H to create vector I as provided in equation 14;
I=H/|H|
14; and
vector I is formed by;
1) creating vector G as provided by equation 11 which is the difference between-vector A and vector F;
G=A−
F
11;
2) identifying m components of vector G as provided by equation 12 which correspond to the same values for pi as the m components selected in step d for vector F;
G′
iε
(G′
1, G′
2, . . . G′
m)
12;
3) creating vector H as provided in equation 13 of dimension m having as components only the m components of step 2;
4) normalizing vector H to create vector I as provided in equation 14;
I=H/|H|
14; and
h) forming dot product DP as provided in equation 15;
DP=R·
S
15;
wherein the dot product provides a number related to the probability that the test part that may have an unknown defect has the known defect in the second reference part with the proviso that when vector B is selected in step d vector F is selected in step g, vector C is selected in step d vector G is selected in step g, vector D is selected in step d vector H is selected in step g, and vector E is selected in step d vector I is selected in step g. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. A method of characterizing defects in a part, the method comprising:
-
a) providing a first collection of reference parts wherein each part in the set has a known defect;
b) identifying a numerically quantifiable physical property that provides good part array Ai of n values given in equation 1 that characterizes a part without a defect and provides a collection Bji of arrays given by equation 17 that characterize each part in the collection of reference parts, each member of the second collection of arrays corresponds to one member of the collection of reference parts and has n dimensions;
Aiε
(A1, A2, . . . An)
1;
Bjiε
(Bj1, Bj2, . . . Bjn)
16;
wherein, n is an integer, and array Ai and array Bji are ordered by the same independent parameter pi that is associated with the values in array Ai and array Bji through the functional relationship Ai=fa(pi) and Bji=fjb(pi);
c) creating good part vector A of n dimensions given by equation 3 whose components are the n numerical values in good part array Ai
A=<
A1, A2, . . . An>
3;
d) creating collection Bj of defect vectors of n dimensions as given in equation 17, the components of each defect vector in the third collection being the n numerical values of each array in the second collection of arrays;
Bj=<
Bj1, Bj2, . . . . Bjn>
17;
e) creating a set of difference vectors Cj each of n dimensions given by equation 18, the components of each difference vector Cj in the fourth collection being the difference between good part vector A and each defect vector Bj;
Cj=A−
Bj
18;
f) identifying m components of vector Cj as provided by equation 19 having the largest magnitudes;
Cj′
iε
(Cj′
1, Cj′
2, . . . Cj′
m)
19;
wherein the m components are expressable as array Cj′
i, the largest magnitudes are identified independently for each vector Cj, and each component of the Cj′
i correspond to a value of the parameter pi;
g) creating vector Dj of m dimensions as provided by equation 20 whose components are the n values in array Cj′
ih) normalizing vector Dj to form vector Ej as provided in equation 21;
Ej=Dj/|Dj|
21;
i) determining array Fi of n numerical values as provided by equation 22 using the numerically quantifiable physical property that characterize a test part that may have an unknown defect
Fiε
(F1, F2, . . . Fn)
22;
j) creating vector F of n dimensions as provided by equation 23 whose components are the n values in array Fi
F=<
F1, F2, . . . Fn>
23;
k) forming a vector G as provided by equation 24 which is the difference between vector A and vector F;
G=A−
F
24;
l) identifying m components of vector G as provided by equation 25 which correspond to the same values for pi as the m components selected in step g;
G′
iε
(G′
1, G′
2, . . . G′
m)
25;
m) creating vector H as provided in equation 26 of dimension m having as components only the m components of step m;
n) optionally normalizing vector H to create vector I as provided in equation 27;
I=H/|H|
27; and
o) creating a set of dot products DPi as provided in equation 28;
DPi=Ej·
I
28;
wherein each dot product DPi provides a number related to the probability that the test part that may have an unknown defect has the known defect in the second reference part with the largest dot product corresponds to the most likely defect in the product with an unknown defect. - View Dependent Claims (15, 16, 17, 18, 19, 20, 21, 22)
-
-
23. A method of characterizing defects in a part, the method comprising:
-
a) identifying a numerically quantifiable physical property that provides good part array Ai of n numerical values given by equation 1 that characterize a first reference part without a defect and defect array Bi of n values as provided by equation 2 that characterize a second reference part with a known defect;
Aiε
(A1, A2, . . . An)
1;
Biε
(B1, B2, . . . Bn)
2;
wherein, n is an integer, and array Ai and array Bi are ordered by an independent parameter pi that is associated with the values in array Ai and array Bi through the functional relationship Ai=fa(pi) and Bi=fb(pi);
b) creating good part vector A of n dimensions as provided by equation 3 whose components are the n numerical values in good part array Ai;
A=<
A1, A2, . . . An>
3;
c) creating defect vector B of n dimensions as provided by equation 4 whose components are the n values in defect array Bi;
B=<
B1, B2, . . . Bn>
4;
d) forming vector E by the method comprising;
1) creating difference vector C of n dimensions as provided by equation 5 which is the difference between good part vector A and defect vector B;
C=A−
B
5;
2) identifying m components of vector C as provided by equation 6 having the largest magnitudes;
C′
iε
(C′
1, C′
2, . . . C′
m)
6;
3) creating vector D of m dimensions as provided by equation 7 whose components are the n values in array C′
iand 5) normalizing vector D to form vector E as provided in equation 9;
E=D/|D|
8;
e) determining array Fi of n numerical values as provided by equation 9 that characterize a test part that may have an unknown defect using the numerically quantifiable physical property;
Fiε
(F1, F2, . . . Fn)
9;
f) creating vector F of n dimensions as provided by equation 10 whose components are the n values in array Fi;
F=<
F1, F2, . . . Fn>
10;
g) forming vector I by the method comprising;
1) creating vector G as provided by equation 11 which is the difference between vector A and vector F;
G=A−
F
11;
2) identifying m components of vector G as provided by equation 12 which correspond to the same values for pi as the m components selected in step d for vector F;
G′
iε
(G′
1, G′
2, . . . G′
m)
12;
3) creating vector H as provided in equation 13 of dimension m having as components only the m components of step 2;
4) normalizing vector H to create vector I as provided in equation 14;
I=H/|H|
14; and
h) forming dot product DP as provided in equation 15′
;
DP=E·
I
15′
;
wherein the dot product provides a number related to the probability that the test part that may have an unknown defect has the known defect in the second reference part.
-
-
24. A method of characterizing defects in a part, the method comprising:
-
a) identifying a numerically quantifiable physical property that provides good part array Ai of n numerical values given by equation 1 that characterize a first reference part without a defect and defect array Bi of n values as provided by equation 2 that characterize a second reference part with a known defect;
Aiε
(A1, A2, . . . An)
1;
Biε
(B1, B2, . . . Bn)
2;
wherein, n is an integer, and array Ai and array Bi are ordered by an independent parameter pi that is associated with the values in array Ai and array Bi through the functional relationship Ai=fa(pi) and Bi=fb(pi);
b) creating good part vector A of n dimensions as provided by equation 3 whose components are the n numerical values in good part array Ai;
A=<
A1, A2, . . . An>
3;
c) creating defect vector B of n dimensions as provided by equation 4 whose components are the n values in defect array Bi;
B=<
B1, B2, . . . Bn>
4;
e) determining array Fi of n numerical values as provided by equation 9 that characterize a test part that may have an unknown defect using the numerically quantifiable physical property;
Fiε
(F1, F2, . . . Fn)
9;
f) creating vector F of n dimensions as provided by equation 10 whose components are the n values in array Fi;
F=<
F1, F2, . . . Fn>
10; and
h) forming dot product DP as provided in equation 15;
DP=B·
F
15;
wherein the dot product provides a number related to the probability that the test part that may have an unknown defect has the known defect in the second reference part. - View Dependent Claims (26, 27, 28)
-
-
25. A method of characterizing defects in a part, the method comprising:
-
a) identifying a numerically quantifiable physical property in a part which is expressible as a measured dependant variable Ydi as a function of an independent variable Xi for a first reference part that has a known defect and wherein the measured dependant variable is determined at discrete intervals of the independent variable given by equation 31;
Xi+1=Xi+c
31;
wherein c is a constant;
b) providing a test pattern for the numerically quantifiable physical property such that dependant variable Yni is expressed as a function of an independent variable Xi wherein values of Yni are given at discrete intervals of the independent variable given by equation 32;
X′
i+1=X′
i+c
32;
wherein X′
0=X0+d and d is adjustable offset; and
c) forming the dot product sum DP given by equation 27;
DP=Σ
YdiYui
33;
wherein d is adjusted to provide the maximum value for P.
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Specification