A new simple and fast computation algorithm of the Effective Independence for sensor placement is presented.It is based on downdating of the QR decomposition of the reduced modal matrix.The Effective Independence method

which tries to make the target modes as linearly independent as possible

is significant and influential in the field of sensor placement.Traditional computation of the Effective Independence requires eigenvalue decomposition or inversion of the Fisher Information matrix

and both are costly.By virtue of the connection between the Modal Kinetic Energy and Effective Independence

we can compare the norms of the orthonormal rows after the QR decomposition of the modal matrix to compute the Effective Independence.Moreover

new downdating steps of the QR decomposition based on the combination of modified Gram-Schmidt and Householder transformations are implemented

which further improved its efficiency by eliminating unnecessary expensive QR decompositions in the iterations.Finally

numerical test on the I-40 Bridge shows that the new algorithm computes far more quickly with fewer computation steps

has the advantages of simpleness and clarity in physical significance

and is quite stable.