Systems and methods for analyzing flutter test data using damped sine curve fitting with the closed form shape fit

Patent metadata

Field	Value
Publication number	US-10634580-B2
Application number	US-201514731255-A
Country	US
Kind code	B2
Filing date	Jun 4, 2015
Priority date	Jun 4, 2015
Publication date	Apr 28, 2020
Grant date	Apr 28, 2020

Abstract

System identification from free response time decay history data of a dynamic system employs a new closed form shape fit for solving the dynamic system free response decay equation. The closed form shape fit allows for the treatment of the mode shapes as linear coefficients and allows the mode shapes for each sensor to be computed independently, thereby reducing computation time. The closed form shape fit efficiently provides mode shapes for a large set of sensors based on a fit from a small set of sensors. The closed form shape fit combined with a non-linear fit of frequency and damping characteristics efficiently estimates the optimal solution, thereby reducing the time to completion of non-linear optimization. A nonlinear optimization can incorporate the closed form shape fit into determining the Jacobian matrix of sensitivities and evaluating the residuals, thereby reducing the number of parameters and reducing the time to completion of the non-linear optimization.

First claim

What is claimed is:

1. A method for system identification, the method comprising:
(1) receiving a set of flutter test data, the flutter test data being associated with sensor data obtained from a plurality of sensors coupled to a structure;
(2) fitting curves to the flutter test data, wherein said curve-fitting comprises:
(2A) identifying a set of fit equations, each fit equation corresponding to exactly one sensor, each sensor corresponding to one or more fit equations, wherein each fit equation comprises a first set of one or more first parameters, and comprises a second set of one or more second parameters for the corresponding sensor, wherein:
each first parameter is present in fit equations corresponding to at least two sensors, and the first set depends on a frequency and a damping parameter of each vibrational mode in a set of one or more modes present in the fit equations for the at least two sensors; and
each fit equation comprises one or more second parameters for the corresponding sensor and for no other sensor;

(2B) determining a first parameter value for each first parameter;
(2C) separately for each sensor, with each first parameter being fixed at the corresponding first parameter value, and each second parameter being treated as unknown, optimizing each fit equation corresponding to the sensor, to determine a second parameter value of each corresponding second parameter corresponding to the sensor;
(2D) with each second parameter being fixed at the corresponding second parameter value, and each first parameter being treated as unknown, optimizing a fit error that combines residuals of all the fit equations for all the sensors, to determine a new first parameter value for each first parameter.

2. The method of claim 1 , wherein:
the sensor data was obtained from the structure subject to excitation events;
for each sensor, each corresponding fit equation corresponds to exactly one excitation events;
for at least one sensor, for each mode and each excitation, the corresponding second set comprises a corresponding mode shape amplitude parameter, a corresponding mode shape phase parameter, and a corresponding offset parameter;
in operation (2C), for each sensor, each fit equation is optimized by linear optimization;
in operation (2D), the fit error is optimized by non-linear optimization; and

the method further comprises:
extracting one or more mode shape terms to obtain mode shape information from the set of flutter test data for the group of excitations; and
outputting the mode shape information.

3. The method of claim 2 , wherein in operation (2C), optimizing each fit equation comprises performing a variable substitution that places the fit equation into a form of a linear equation, and preforming a least squares closed-form optimization of the linear equation.

4. The method of claim 1 , wherein the flutter test data comprises first set further comprises data obtained in a plurality of excitations; wherein the first set comprises an excitation level amplitude parameter and a phase parameter for each mode and each excitation.

5. The method of claim 1 , wherein in operation (2C), optimizing each fit equation comprises inverting a substitution of variables for one or more second parameters to obtain the second parameter value for each second parameter.

6. The method of claim 1 , wherein receiving the set of flutter test data comprises receiving flutter time history data in the form of sensor response and time pairs indexed by sensor, excitation event, and time points, the operation (2) is performed for a subset of the sensors, and the method further comprises using the parameters to provide mode shape information for a plurality of sensors outside the subset of sensors based on a fit of a subset of the sensors.

7. The method of claim 2 , wherein formulating and solving the linear least squares problem provides an optimization of one or more frequency and damping and mode shape terms that reduces an amount of computation steps for solving the non-linear optimization.

8. The method of claim 1 , wherein operation (2) is performed for a first set of a plurality of sensors; and
the method further comprises performing operation (2C) for a second set of the plurality of sensors using the new first parameter values determined for the first set of the plurality of sensors, wherein the second set includes and is larger than the first set.

9. The method of claim 2 , wherein step (2C) comprises evaluating residuals and using partial derivatives.

10. A system configured to perform the method of claim 1 , the system comprising:
The plurality of sensors configured to provide the flutter test data from the structure subject to one or more excitation events, the flutter test data comprising machine-readable time history data corresponding to physical measurements taken by the sensors; and
a processor configured to receive the machine readable time history data and preform the operation (2) to determine mode shape information about the structure, and
output results of the operation (2).

11. The system of claim 10 , wherein the structure is an aircraft fitted with the plurality of sensors for acquiring the flutter test data during flight.

12. The system of claim 10 , wherein the process if further configured to preform the operation (2) repeatedly to obtain a sequence of iterations of operation (2), wherein each subsequent iteration comprises a new set of fit equations with more modes than in the immediately preceding iteration, wherein in operation (2B) in each subsequent iteration, at least one first parameter value for at least one new mode is obtained based on the optimized fit error in the immediately preceding iteration;
wherein in each iteration, in operation (2C), each fit equation is optimized using a closed from shape fit.

13. The system of claim 10 , wherein the processor is further configured to perform the closed form shape fit to formulate the linear least squares problem, including perform a variable substitution that places a fit equation into a form of a simple linear equation for which a least squares can be performed to find optimal values of the mode shape terms.

14. The system of claim 10 , wherein the processor is further configured to perform the closed form shape fit to solve the linear squares problem in equations resulting from a substitution of variables for mode shape terms and excitation terms in a fit equation.

15. The system of claim 10 , wherein the processor is further configured to perform the closed form shape fit to extract one or more mode shape terms resulting from solving the linear least squares problem in equations resulting from a substitution of variables for mode shape terms and excitation terms in the fit equation, including inverting the substitution of variables for mode shape terms and excitation terms to obtain one or more mode shape terms and excitation terms for the fit equation.

16. The method of claim 1 , wherein the processor is configured to perform the operation (2) for a first set of the plurality of sensors; and
is further configured to perform operation (2C) for the second set of the plurality of sensors using the first parameter values determined in the operation (2D) for the first set of the plurality of sensors, wherein the second set includes and is larger than the first set.

17. The system of claim 10 , wherein the processor is further configured to:
load one or more parameters from the series of damped sine curves into the fit equation;
use the mode shape information obtained from using the

Assignees

• Boeing Co

Inventors

• Goodman Charles E

Classifications

• G01M5/0041

  by determining deflection or stress · CPC title

• B64D2045/0085

  Devices for aircraft health monitoring, e.g. monitoring flutter or vibration · CPC title

• B64F5/60

  Testing or inspecting aircraft components or systems · CPC title

• G01M5/0016 Primary

  of aircraft wings or blades · CPC title

• B64D45/00

  Aircraft indicators or protectors not otherwise provided for · CPC title