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-2016355278-A1
Application number	US-201514731255-A
Country	US
Kind code	A1
Filing date	Jun 4, 2015
Priority date	Jun 4, 2015
Publication date	Dec 8, 2016
Grant date	—

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 computer-implemented method for system identification using a closed form shape fit, comprising:
receiving a set of data obtained from a plurality of sensors; selecting a particular sensor from the plurality of sensors; gathering data from the set of data for the particular sensor for a group of excitations; formulating a linear least squares problem for the particular sensor for the group of excitations; solving the linear least squares problem for the particular sensor for the group of excitations; and extracting one or more mode shape terms to obtain mode shape information from the set of data for the particular sensor for the group of excitations.

2 . The method of claim 1 , wherein formulating the linear least squares problem for the particular sensor for the group of excitations comprises selecting a portion of a fit equation relevant to just the particular sensor and the group of excitations such that the selected portion of the fit equation corresponds to a non-zero block of a block diagonal matrix.

3 . The method of claim 1 , wherein formulating the linear least squares problem comprises performing a variable substitution that places a fit equation into a form of a simple linear equation for which a least squares closed-form optimization can be performed to find optimal values for the mode shape terms.

4 . The method of claim 1 , wherein solving the linear least squares problem comprises solving a set of equations resulting from a substitution of variables for mode shape terms and excitation terms in a fit equation.

5 . The method of claim 1 , wherein extracting one or more mode shape terms comprises inverting a substitution of variables for mode shape terms and excitation terms in a fit equation to obtain one or more mode shape terms and excitation terms for the fit equation.

6 . The method of claim 1 , wherein each sensor of the plurality of sensors is selected in turn and the method is repeated to obtain mode shape information from the set of data for each sensor of the plurality of sensors and the group of excitations.

7 . The method of claim 1 , wherein receiving the set of data comprises receiving flutter time history data in the form of sensor response and time pairs indexed by sensor, excitation event, and time points.

8 . The method of claim 1 , further comprising performing a non-linear optimization wherein solving the linear least squares problem for the particular sensor for the group of excitations 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.

9 . The method of claim 1 , further comprising:
performing a non-linear optimization for a first set of the plurality of sensors; and solving the linear least squares problem for a second set of the plurality of sensors, wherein the second set includes and is larger than the first set.

10 . The method of claim 1 , further comprising:
loading parameters into a fit equation; using the mode shape information obtained from solving the linear least squares problem to determine a fit equation offset and a mode shape amplitude and phase; and computing one or more residuals of the fit equation.

11 . A system comprising:
a plurality of sensors configured to provide a flutter test data from a 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 computer processor configured to receive the machine-readable time history data and to execute a process, the process including: performing one or more fits of a series of damped sine curves to the time history data; computing a Fast Fourier Transform (FFT) of a fit error of a first fit of the one or more fits of the series of damped sine curves to the time history data; estimating a next damped sine curve to include in the series of damped sine curves; performing one or more iterations of a closed form shape fit to optimize one or more mode shape terms and a first non-linear fit to optimize one or more frequency and damping and excitation level terms for the series of damped sine curves; perform a second nonlinear fit of the series of damped sine curves, using the optimized frequency and damping and excitation level and mode shape terms, to the time history data; and output the results of the nonlinear fit.

12 . The system of claim 11 , further comprising an aircraft fitted with the plurality of sensors for acquiring the flutter test data during flight.

13 . The system of claim 11 , wherein performing the closed form shape fit further comprises:
formulating a linear least squares problem for a particular sensor of the plurality of sensors and for a group of the one or more excitation events; solving the linear least squares problem for the particular sensor for the group of one or more excitation events; and extracting one or more mode shape terms to obtain mode shape information from the set of data for the particular sensor for the group of one or more excitation events; and repeating the formulating, solving and extracting for each of the plurality of sensors.

14 . The system of claim 11 , wherein performing the closed form shape fit further comprises formulating a linear least squares problem for a particular sensor for a group of one or more excitation events, including selecting a portion of a fit equation relevant to just the particular sensor and the group of one or more excitation events such that the selected portion of the fit equation is solved by a non-zero block of a block diagonal Jacobian matrix corresponding to the entire fit equation.

15 . The system of claim 11 , wherein performing the closed form shape fit further comprises formulating a linear least squares problem, including performing a variable substitution that places a fit equation into a form of a simple linear equation for which a least squares closed-form optimization can be performed to find optimal values for the mode shape terms.

16 . The system of claim 11 , wherein performing the closed form shape fit further comprises solving a linear least squares problem in equations resulting from a substitution of variables for mode shape terms and excitation terms in a fit equation.

17 . The system of claim 11 , wherein performing the closed form shape fit further comprises extracting one or more mode shape terms resulting from solving a linear least squares problem in equations resulting from a substitution of variables for mode shape terms and excitation terms in a 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.

18 . The system of claim 11 , wherein the computer processor is further configured to perform a non-linear optimization for a first set of the plurality of sensors; and solve a linear least squares problem using a closed form shape fit for a second set of the plurality of sensors, wherein the second set includes and is larger than the first set.

19 . The system of claim 11 , wherein the computer processor is further configured to load one or more parameters from the series of damped sine curves into a fit equation; use a mode shape information obtained from using a closed form shape fit to solve a linear least squares problem to determine a fit equation offset and a mode shape amplitude an

Assignees

• Boeing Co

Inventors

• Goodman Charles E

Classifications

• B64D45/00

  Aircraft indicators or protectors not otherwise provided for · CPC title

• 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