Inverse Method Using Finite Strain Measurements to Determine Flight Load Distribution Functions

Abstract

DOI: 10.2514/1.21905 This work seeks to identify in-flight loads based on real-time data provided by strain gauges. Flight loads are identifiedbasedonaninverseinterpolationmethodthatusesresultsfroma finiteelementmodeldevelopedinI-DEAS software. The inverse interpolation is based on minimization of the error between calculated versus measured strains. Finite element strains are used as representative of measured strains for input into the analysis. Strains determinedfromsurfaceloadsofindividual Fourierterms arealsodeterminedfromthe finiteelementmodel.Strain data from the applied unknown load coupled with finite element model data from the Fourier loads allow prediction of the Fourier coefficients of the actual load. Predicted Fourier coefficients are compared to sets of Fourier coefficientsfromadatabasebasedonhistoricalortheoreticalloadsanda“least-squares”minimizationperformedto determine which set of coefficients are most probable. Successful load predictions are made for polynomial surface functions of one andtwo independent variables, using single anddouble Fourier series, respectively. It is shown that the variance of the strain data from individual loads plays a key role in the accuracy of the method. TRUCTURAL health monitoring is becoming increasingly important in military and civilian aerospace applications. Civilian airlines seek to extend the service, safety, and capability of an aging aircraft fleet while military aircraft are subjected to more diverse missions. Combat operations involve an increasing use of autonomous unmanned aircraft. The identification of real-time flight loads may be advantageous in several ways; for example, the information can be used to improve fatigue or critical load damage modelingortoimproveaircrafthandlingorpilotresponsetounusual loads. Autonomous vehicles may use this information to make flight adjustments or to detect and quantify damage while in flight. This type of flight load information will also provide reliable databases, which may be used in a condition based maintenance program. The measurement of real-time flight loads, displacements, and stresses is typically very difficult due to the complexity of load measurement instrumentation. This work proposes the application of an inverse method to develop a database of Fourier coefficients that will enable effective modeling of real-time flight loads. Because loads, stresses, and displacements are determined using experimentally measured structural response, the problem may result in a set of ill-posed governing equations. Hence a finite element based inverse method is chosen to predict the “best” solution. In this method, data obtained from a finite element analysis (FEA) will be used as measured data and analyzed to predict real-time flight loads. The strains could be measuredwitha fiber-opticsensornetwork,microelectromechanical system (MEMS) strain gauges, or typical strain gauges. Several authors have developed various inverse methods to predict loads or displacements based on strain data. Shkarayev et al. [1] developed a finite element based methodology involving an inverseformulationthatemploysmeasuredsurfacestrainstorecover the applied loads, stresses, and displacements in real time. The