Principal Component Analysis Assisted Surrogate Modeling (PCA-SM) of Correlated Loads for Uncertainty Analysis of Design Load Envelopes

Abstract

Target design load setting is one of the critical aspects in preliminary design phase of aircraft design process. Overestimation or underestimation of design loads lead to the aircraft’s performance and reliability implications, risk of costly re-desisgn, and specific design lead time. Selection of reliable design loads under uncertainties require a large number of analyses to evaluate loads for numerous flight conditions like maneuver loads, gust loads, ground loads, time dependent response under control deflection and so on leading to huge computational burden. To overcome this issue, Principal Component Analysis assisted Surrogate Modeling (PCA-SM) is developed in the current work for rapid reconstruction of correlated loads with relatively smaller number of analyses using Design of Experiments (DoE). The advantages of PCA-SM method over other surrogate modeling techniques have been discussed and demonstrated on a twin-aisle commercial transport aircraft case. Nomenclature λi i th eigenvalue of Σ Lg Data matrix of gust load data Lm Data matrix of static maneuver load data Λ Diagonal matrix containing eigenvalues of Σ φi i th eigenvectors of Σ Φ Matrix containing all the eigenvectors of Σ Φk Matrix containing k eigenvectors of Σ with largest k eigenvalues F Flight condition lm , lg Load vector for static maneuver and gust load respectively U Uncertain variable w Vector of weight or scores of x associated with eigenvectors stored in Φ X Data matrix consisting of all obeservation of x x Random vector Σ Correlation Matrix of X θ Polar angles Cg Convex hull for gust loads Cm Convex hull for static maneuver loads Fx, Fy, Fz Shear forces along x, y and z axis ∗PhD Candidate, School of Aerospace Engineering, Aerospace Systems Design Laboratory, Student Member. †Boeing Regents Professor of Advanced Aerospace Systems Analysis, School of Aerospace Engineering, AIAA Fellow ‡Loads technical skill leader for uncertainty management 1 of 15 American Institute of Aeronautics and Astronautics IQs Interesting quantities k Dimension of lower dimensional data representation Mx,My,Mz Moments about x, y and z axis p Dimension of random variable or load vector Si Sample covariance of i th descriptor xi of data t time xc, yc Centroid of all convex hull vertices zi Z-score of i th descriptor xi of data

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