A Novel Method for Uncertainty Inverse Problems and Application to Material Characterization of Composites C. Jiang & G.R. Liu & X. Han Received: 14 February 2007 / Accepted: 31 July 2007 / Published online: 22 August 2007 # Society for Experimental Mechanics 2007 Abstract A novel method is suggested to deal with so- called uncertainty inverse problems (UIPs) which are a class of inverse problems with uncertainty in the system parameters of the forward model. Interval which represents a closed bounded set of real numbers is used to model and characterize the uncertainty in our formulation, and hence only the bounds of the uncertainty of the system parameters are needed. For a specific input vector, the possible values of the outputs form an interval vector because of the uncertainty. An error function is defined using the measured interval vector of the outputs and those computed using a forward model. The UIP is then formulated as an optimization problem which minimizes the error function. To improve the optimization efficiency, an interval forward model is constructed based on the interval analysis method which can calculate very efficiently the bounds of the outputs caused by the uncertainty of the system parameters. The present method is applied to a complex inverse problem, namely material characterization of composite laminates using elastic waves. Uncertainty of load is considered, and the hybrid numerical method (HNM) is used to compute the transient displacement responses. The engineering constants of two kinds of laminates are successfully identified using the simulated measurements of the outputs. Keywords Uncertainty . Inverse problem . Interval . Optimization . Material characterization . Composite laminate Introduction Inverse problems can be defined as problems to estimate input through given output, in contrast with the forward problems concern the determination of output from input. Many problems in science and engineering should and can be formulated as inverse problems, such as identification of cracks and defects, estimation of boundary conditions on inaccessible boundary, and nondestructive evaluation of material property etc. Due to the advances of computer and computational technology, more and more complex design problems are needed to be solved through inverse analysis techniques. Therefore, inverse problems have been widely investigated and a great amount of literatures on this field have been published [e.g. 1–6]. However, most of the existing inverse analysis methods focus on deterministic problems in which all of the concerned parameters can be given in certain values. Thus for a specific input, a deterministic output can be obtained and hence the output can be in turn used to determine the input inversely. In practice, however, uncertainty exists in most of the practical engineering problems such as uncertainties of load, material property and geometrical dimension etc. In such uncertain- Experimental Mechanics (2008) 48:539–548 DOI 10.1007/s11340-007-9081-5 C. Jiang : X. Han State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Automotive Engineering, Hunan University, Changsha 410082, People’ s Republic of China G.R. Liu Centre for Advanced Computations in Engineering Science, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore G.R. Liu (*) Singapore–MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore 117576, Singapore e-mail: mpeliugr@nus.edu.sg