# US 2018/0024016 A1 · Method for analyzing stress in an object

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2018/0024016 A1
- Document ID: US20180024016A1
- Status: Published application
- Kind: A1
- Application number: 15/653,855
- Filed: 2017-07-19
- Published: 2018-01-25
- Earliest claimed: 2016-07-22
- Assignees: National Tsing Hua University
- Applicants: National Tsing Hua University
- Inventors: Wei-Chung WANG; Po-Chi SUNG; Yu-An CHIANG; Te-Heng HUNG
- Web page: https://patentgrep.com/patent/US20180024016A1

## CPC

- G01L 1/241: {by photoelastic stress analysis}
- G01B 11/18: {using photoelastic elements}
- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G01B 11/168: {by means of polarisation}
- G06F 17/12: Simultaneous equations {, e.g. systems of linear equations}
- G06F 17/13: Differential equations (using digital differential analysers G06F7/64)
- G06F 17/147: {Discrete orthonormal transforms, e.g. discrete cosine transform, discrete sine transform, and variations therefrom, e.g. modified discrete cosine transform, integer transforms approximating the discrete cosine transform (G06F17/145 takes precedence)}
- G06F 17/17: Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method ({G06F17/18 takes precedence } ; interpolation for numerical control G05B19/18)
- G06F 2111/10: Numerical modelling
- G01L: MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE (weighing G01G)
- G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method for analyzing stress in an object according to spectrum data is provided. The spectrum data is obtained from an interference fringe pattern of the object that results from performing photoelasticity. The method includes: analyzing the spectrum data to obtain three sets of intensity data related respectively to different wavelengths of light used in photoelasticity; calculating wrapped phases according to the three sets of intensity data, respectively; calculating preliminary stress values according to the wrapped phases, respectively; determining a system of stress equations according to a relation among the preliminary stress values; and calculating an estimated stress value using the system of stress equations.

## Claims

### Claim 1

A method for analyzing stress in an object according to spectrum data, the spectrum data being obtained from an interference fringe pattern (IFP) of the object that results from performing photoelasticity, the method comprising the steps of:
a) analyzing the spectrum data to obtain three sets of intensity data that are related respectively to different wavelengths of light used in photoelasticity;
b) calculating three wrapped phases according to the three sets of intensity data, respectively;
c) calculating three preliminary stress values according to the wrapped phases, respectively, wherein each of the preliminary stress values is directly proportional to a product of a corresponding one of the wrapped phases and a linear function of a corresponding one of the wavelengths;
d) determining a system of stress equations according to a relation among the preliminary stress values; and
e) calculating an estimated stress value based on the preliminary stress values using the system of stress equations determined in step d).

### Claim 2 (depends on 1)

The method of claim 1, wherein, in step b) each of the wrapped phases is calculated by substituting a corresponding one of the sets of intensity data into one of the inverse sine function, the inverse cosine function and the inverse tangent function.

### Claim 3 (depends on 1)

The method of claim 1, wherein, in step c), the preliminary stress values are calculated based on
S
w
=
A


λ
+
B
π

δ
w
,
where Sw denotes the preliminary stress values, λ denotes a corresponding one of the wavelengths, A and B are known parameters related to characteristics of material of the object, and δw denotes a corresponding one of the wrapped phases.

### Claim 4 (depends on 3)

The method of claim 3, wherein step d) includes the sub-steps of:
d10) determining whether the relation among the preliminary stress values satisfies Swλ1 =Swλ2=Swλ3, where Swλ1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ1 of the wavelengths, Swλ2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ2 of the wavelengths, Swλ3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ3 of the wavelengths, and λ1>λ2>λ3; and
d11) when the determination made in sub-step d10) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+Swλ2,
S=2i1(Aλ3+B)+Swλ3
where S denotes the estimated stress value, and i1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ1.

### Claim 5 (depends on 3)

The method of claim 3, wherein step d) includes the following sub-steps of:
d20) determining whether the relation among the preliminary stress values satisfies Swλ1=Swλ2≠Swλ3, where Swλ1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ1 of the wavelengths, Swλ2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ2 of the wavelengths, Swλ3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ3 of the wavelengths, and λ1>λ2>λ3;
d21) when the determination made in sub-step d20) is affirmative, determining whether the relation between the second and third preliminary stress values Swλ2, Swλ3 satisfies Swλ2>Swλ3; and
d22) when the determination made in sub-step d21) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)−S″wλ2,
S=2i1(Aλ3+B)−S″wλ3
where S denotes the estimated stress value, and i1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ1.

### Claim 6 (depends on 5)

The method of claim 5, wherein step d) further includes the sub-steps of:
d23) when the determination made in sub-step d21) is affirmative, determining whether the relation between the second and third preliminary stress values Swλ2, Swλ3 satisfies Swλλ2=S′wλ3=2(Aλ3+B)−Swλ3; and
d24) when the determination made in sub-step d23) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+Swλ2.
S=2i1(Aλ3+B)+S′wλ3

### Claim 7 (depends on 6)

The method of claim 6, wherein step d) further includes the sub-step of:
d25) when the determination made in sub-step d23) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+S′wλ2,
S=2i1(Aλ3+B)+S′wλ3
where S′wλ2=2(Aλ2+B)−Swλ2.

### Claim 8 (depends on 3)

The method of claim 3, wherein step d) includes the following sub-steps of:
d30) determining whether the relation among the preliminary stress values satisfies Swλ1≠Swλ2=Swλ3, where Swλ1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ1 of the wavelengths, Swλ2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ2 of the wavelengths, Swλ3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ3 of the wavelengths, and λ1>λ2>λ3;
d31) when the determination made in sub-step d30) is affirmative, determining whether the relation between the first and second preliminary stress values Swλ1, Swλ2 satisfies Swλ1>Swλ2; and
d32) when the determination made in sub-step d31) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)−Swλ2,
S=2i1(Aλ3+B)+Swλ3
where S denotes the estimated stress value, and i1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ1.

### Claim 9 (depends on 8)

The method of claim 8, wherein step d) further includes the sub-step of:
d33) when the determination made in sub-step d31) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+Swλ2,
S=2i1(Aλ3+B)+S′wλ3
where S′wλ3=2(Aλ3+B)−Swλ3.

### Claim 10 (depends on 3)

The method of claim 3, wherein step d) includes the sub-steps of:
d400) determining whether the relation among the preliminary stress values satisfies
Swλ1≠Swλ2
Swλ2≠Swλ3,
Swλ3≠Swλ1
where Swλ1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ1 of the wavelengths, Swλ2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ2 of the wavelengths, Swλ3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ3 of the wavelengths, and λ1>λ2>λ3;
d401) when the determination made in sub-step d400) is affirmative, determining whether the relation among the first, second and third preliminary stress values Swλ1, Swλ2, Swλ3 satisfies
S
w


λ
1
-
S
w


λ
2
S
w


λ
2
-
S
w


λ
3
=
λ
1
-
λ
2
λ
2
-
λ
3
;
d402) when the determination made in sub-step d401) is affirmative, determining whether the relation among the first and second preliminary stress values Swλ1, Swλ2 satisfies Swλ1>Swλ2; and
d403) when the determination made in sub-step d402) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)−Swλ2,
S=2i1(Aλ3+B)−Swλ3
where S denotes the estimated stress value, and i1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ1.

### Claim 11 (depends on 10)

The method of claim 10, wherein step d) further includes the sub-step of:
d404) when the determination made in sub-step d402) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+Swλ2.
S=2i1(Aλ3+B)+Swλ3

### Claim 12 (depends on 10)

The method of claim 10, wherein step d) further includes the sub-steps of:
d405) when the determination made in sub-step d401) is negative, determining whether the relation between the first and second preliminary stress values Swλ1, Swλ2 satisfies Swλ1>Swλ2;
d406) when the determination made in sub-step d405) is affirmative, determining whether the relation between the second and third preliminary stress values Swλ2, Swλ3 satisfies Swλ2>Swλ3;
d407) when the determination made in sub-step d406) is affirmative, determining whether the relation among the first, second and third preliminary stress values Swλ1, Swλ2, Swλ3 satisfies
S
w


λ
1
-
S
w


λ
2
′
S
w


λ
2
′
-
S
w


λ
3
′
=
λ
1
-
λ
2
λ
2
-
λ
3
,
where
S′wλ2=2(Aλ2+B)−Swλ3, and S′wλ3=2(Aλ3+B)−Swλ3; and
d408) when the determination made in sub-step d407) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+S′wλ2.
S=2i1(Aλ3+B)+S′wλ3

### Claim 13 (depends on 12)

The method of claim 12, wherein step d) further includes the sub-step of:
d409) when the determination made in sub-step d407) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)−Swλ2.
S=2i1(Aλ3+B)+Swλ3

### Claim 14 (depends on 12)

The method of claim 12, wherein step d) further includes the sub-steps of:
d410) when the determination made in sub-step d406) is negative, determining whether the relation among the first, second and third preliminary stress values Swλ1, Swλ2, Swλ3 satisfies
S
w


λ
1
-
S
w


λ
2
S
w


λ
2
+
S
w


λ
3
=
λ
1
-
λ
2
λ
2
-
λ
3
;
and
d411) when the determination made in sub-step d410) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)−Swλ2.
S=2i1(Aλ3+B)+Swλ3

### Claim 15 (depends on 14)

The method of claim 14, wherein step d) further includes the sub-step of:
d412) when the determination made in sub-step d410) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)+Swλ2.
S=2i1(Aλ3+B)+Swλ3

### Claim 16 (depends on 12)

The method of claim 12, wherein step d) further includes the sub-steps of:
d413), when the determination made in sub-step d405) is negative, determining whether the relation among the second and third preliminary stress values Swλ2, Swλ3 satisfies Swλ2>Swλ3;
d414) when the determination made in sub-step d413) is affirmative, determining whether the relation among the first, second and third preliminary stress values Swλ1, Swλ2, Swλ3 satisfies
S
w


λ
1
-
S
w


λ
2
S
w


λ
2
-
S
w


λ
3
′
=
λ
1
-
λ
2
λ
2
-
λ
3
;
and
d415) when the determination made in sub-step d414) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+Swλ2.
S=2i1(Aλ3+B)+S′wλ3

### Claim 17 (depends on 16)

The method of claim 16, wherein step d) further includes the sub-step of:
d416) when the determination made in sub-step d414) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+S′wλ2.
S=2i1(Aλ3+B)+S′wλ3

### Claim 18 (depends on 16)

The method of claim 16, wherein step d) further includes the sub-steps of:
d417) when the determination made in sub-step d413) is negative, determining whether the relation among the first, second and third preliminary stress values Swλ1, Swλ2, Swλ3 satisfies
S
w


λ
1
+
S
w


λ
2
-
S
w


λ
2
+
S
w


λ
3
=
λ
1
-
λ
2
λ
2
-
λ
3
;
and
d418) when the determination made in sub-step d417) is affirmative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)−Swλ1
S=2i1(Aλ2+B)+Swλ2.
S=2i1(Aλ3+B)+Swλ3

### Claim 19 (depends on 18)

The method of claim 18, wherein step d) further includes the sub-step of:
d419) when the determination made in sub-step d417) is negative, making the following system of candidate equations the system of stress equations
S=2i1(Aλ1+B)+Swλ1
S=2i1(Aλ2+B)+Swλ2.
S=2i1(Aλ3+B)+S′wλ3

### Claim 20 (depends on 1)

The method of claim 1, further comprising, between steps c) and d), the steps of normalizing the preliminary stress values, and filtering out high-frequency noise from the preliminary stress values.

### Claim 21 (depends on 1)

The method of claim 1, further comprising, after step e), the step of smoothing the estimated stress value.

### Claim 22 (depends on 1)

The method of claim 1, wherein, in the step e), the estimated stress value is calculated by fitting the system of stress equations us ing the least square method.