Unbalance identification using the least angle regression technique

Abstract The present investigation proposes a robust procedure for unbalance identification using the equivalent load method based on sparse vibration measurements. The procedure is demonstrated and benchmarked on an example rotor at constant speed. Since the number of measuring positions is much smaller than the number of possible fault locations, performing unbalance identification leads to an ill-posed problem. This problem was tried to be overcome previously with modal expansion in the time domain and with several linear regressions in the frequency domain. However, since the solution to the problem is a sparse equivalent force vector, these methods cannot provide a robust identification procedure. A robust identification can only be achieved by providing a-priori information on the number of unbalances to be identified. The presently proposed procedure achieves more precise unbalance identification without the need of a-priori information by incorporating a regularization technique. A well-known technique for producing sparse solutions is the Least Absolute Shrinkage and Selection Operator (LASSO). The proposed procedure is based on the generalized technique Least Angle Regression (LAR) which finds all the solutions of LASSO. A comparison of the time-domain approach, the frequency-domain approach and the proposed technique is made and the superiority of the latter technique in identifying the number of possible fault locations is highlighted. The selection of the threshold of the convergence algorithm of LAR as well as the selection of the value of the Lagrangian multiplier is discussed in some detail.