A Novel Method for Load Bounds Identification for Uncertain Structures in Frequency Domain

2018 ◽  
Vol 15 (06) ◽  
pp. 1850051 ◽  
Author(s):  
Z. C. He ◽  
X. Y. Lin ◽  
Eric Li
Keyword(s):  
Least Squares ◽  
Frequency Domain ◽  
Interval Uncertainty ◽  
Uncertain Parameters ◽  
Interval Extension ◽  
Uncertain Structure ◽  
Novel Method ◽  
Uncertain Structures ◽  
Derivatives Of ◽  
Least Squares Approach

A novel method for load bounds identification for uncertain structures is proposed in the frequency domain. The uncertain parameters are assumed to locate in their intervals and only their bounds rather than their precise information are needed. To quantitatively describe the effect of the interval uncertainty on the load identification in the frequency ranges, the interval extension is then introduced in the frequency response function (FRF)-based least squares approach. Therefore, the load bounds are determined through the summation of the two separate parts including the midpoint part and the perturbed part of the load. The midpoint part is computed by using the Moore–Penrose pseudo-inversion and the perturbed part is transformed into the first derivatives of the midpoint load with respect to the uncertain parameters by applying the truncated total least squares (TTLS). Two numerical examples are investigated to validate that the proposed method is very effective to predict the load bounds for the uncertain structure in frequency domain.

DYNAMIC LOAD IDENTIFICATION FOR UNCERTAIN STRUCTURES BASED ON INTERVAL ANALYSIS AND REGULARIZATION METHOD

2011 ◽  
Vol 08 (04) ◽  
pp. 667-683 ◽  
Author(s):  
J. LIU ◽  
X. HAN ◽  
C. JIANG ◽  
H. M. NING ◽  
Y. C. BAI
Keyword(s):  
Interval Analysis ◽  
Dynamic Load ◽  
Inverse Method ◽  
Stable Solution ◽  
Uncertain Parameters ◽  
The Finite Element Method ◽  
Lower And Upper Bounds ◽  
Interval Extension ◽  
Uncertain Structures ◽  
Measured Response

In this paper, an inverse method that combines the interval analysis with regularization is presented to stably identify the bounds of dynamic load acting on the uncertain structures. The uncertain parameters of the structure are treated as intervals and hence only their bounds are needed. Using the first-order Taylor expansion, the identified load can be approximated as a linear function of the uncertain parameters. In this function, it is assumed that the load at the midpoint of the uncertain parameters can be expressed as a series of impulse kernels. The finite element method (FEM) is used to obtain the response function of the impulse kernel and the response to the midpoint load is expressed in a form of convolution. In order to deal with the ill-posedness arising from the deconvolution, two regularization methods are adopted to provide the numerically efficient and stable solution of the desired unknown midpoint load. Then, a sensitivity analysis is suggested to calculate the first derivative of the identified load with respect to each uncertain parameter. Applying the interval extension in interval mathematics, the lower and upper bounds of identified load caused by the uncertainty can be finally determined. Numerical simulation demonstrates that the present method is effective and robust to stably determine the range of the load on the uncertain structures from the noisy measured response in time domain.

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