Force identification based on the reconstruction of distributed response with an optimized sensor placement

Abstract

The errors of the force identification vary with different spatial locations of the response measurements on machinery. This investigation proposes a method to identify the structural dynamic force with the use of the distributed response. An optimized sensor placement is obtained by using a set of local orthogonal polynomials to approximate the response distribution of the chosen region and choosing the Gaussian quadrature points as the sensor locations. Then the forward model based on the reconstruction of distributed response is established and the dynamic force can be obtained by an appropriate regularization method. Numerical simulations of models with planar and curved surfaces are presented to validate the method. It is found that the proposed method can effectively reduce the influence of noise and improve the precision of the force identification. The method is also validated by an experiment and an accurate recognition of the forces is observed. This paper provides a new perspective on the force identification procedure based on the distributed response.

Keywords

Force identification distributed response sensor placement local orthogonal polynomial Gaussian quadrature point

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References

Hundhausen RJ, Adams DE, Derriso M, et al. Transient loads identification for a standoff metallic thermal protection system panel. In: International Modal Analysis Conference (IMAC XXIII), Orlando, Florida, 31 January-3 February 2005.

Hollandsworth

Busby

. Impact force identification using the general inverse technique. Int J Impact Eng 1989; 8: 315–322.

Janssens K, Gajdatsy P, Gielen L, et al. OPAX: A new transfer path analysis method based on parametric load models. Mechanical Systems & Signal Processing 2011; 25: 1321–1338.

Djamaa

Ouelaa

Pezerat

et al.

Reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering. J Sound Vib 2007; 301: 560–575.

Qiao

Zhang

Wang

et al.

Sparse regularization for force identification using dictionaries. J Sound Vib 2016; 368: 71–86.

Qiao

Chen

Luo

et al.

A novel method for force identification based on the discrete cosine transform. J Vib Acoust 2015; 137: 051012–051012.

Liu

Shepard

. An improved method for the reconstruction of a distributed force acting on a vibrating structure. J Sound Vib 2006; 291: 369–387.

Liu

Han

et al.

A novel approach for distributed dynamic load reconstruction by space–time domain decoupling. J Sound Vib 2015; 348: 137–148.

Thite

Thompson

. The quantification of structure-borne transmission paths by inverse methods. Part 1: Improved singular value rejection methods. J Sound Vib 2003; 264: 411–431.

10.

Choi

Thite

Thompson

. Comparison of methods for parameter selection in Tikhonov regularization with application to inverse force determination. J Sound Vib 2007; 304: 894–917.

11.

Liu

Shepard

. Dynamic force identification based on enhanced least squares and total least-squares schemes in the frequency domain. J Sound Vib 2005; 282: 37–60.

12.

Khoo

Ismail

Kong

et al.

Impact force identification with pseudo-inverse method on a lightweight structure for under-determined, even-determined and over-determined cases. Int J Impact Eng 2014; 63: 52–62.

13.

Lee

Park

. Response selection and dynamic damper application to improve the identification of multiple input forces of narrow frequency band. Mech Syst Signal Process 1994; 8: 649–664.

14.

Thite

Thompson

. Selection of response measurement locations to improve inverse force determination. Appl Acoust 2006; 67: 797–818.

15.

Zheng

Zhou

Lian

et al.

Technical note: coherence analysis of the transfer function for dynamic force identification. Mech Syst Signal Process 2011; 25: 2229–2240.

16.

Kammer

. Sensor placement for on-orbit modal identification and correlation of large space structures. J Guid Control Dynam 1990; 14: 251–259.

17.

Hemez FM and Farhat C. An Energy Based Optimum Sensor Placement Criterion and its application to structural damage detection. In: Proceedings of SPIE – The International Society for Optical Engineering, Honolulu, 1994, pp. 1568–1575.

18.

Heo

Wang

Satpathi

. Optimal transducer placement for health monitoring of long span bridge. Soil Dynam Earthquake Eng 1997; 16: 495–502.

19.

Wang

Law

Yang

. Sensor placement methods for an improved force identification in state space. Mech Sys Signal Process 2013; 41: 254–267.

20.

Liu

Meng

Jiang

et al.

Time–domain Galerkin method for dynamic load identification. Int J Num Meth Eng 2016; 105: 620–640.

21.

Jiang

Zhang

. A mapping relationship based near-field acoustic holography with spherical fundamental solutions for Helmholtz equation. J Sound Vib 2016; 373: 66–88.

22.

Jiang

. Experimental study of the mapping relationship based near-field acoustic holography with spherical fundamental solutions. J Sound Vib 2017; 394: 185–202.

23.

Zhang

et al.

Research on surface texture mapping algorithm. Comput Eng 2005; 31: 216–219.

24.

Tian

Wang

. Research on the properties of orthogonal polynomial kernel functions. Pattern Recog Artificial Intell 2014; 27: 385–393.

25.

Pezerat

. Two inverse methods for localization of external sources exciting a beam. Acta Acustica 1995; 3: 1–10.

26.

Hua

. Theory and application of modal analysis, Shanghai: Shanghai Jiao Tong University Press, 2000.