“…The displacement d s ∈ R m d , velocity v s ∈ R m v , and acceleration a s ∈ R m a in the measurement direction and at the sensor location can be expressed in terms of the node displacementd ∈ R n d , node velocityv ∈ R n d , and node accelerationâ ∈ R n d in the GCS. Moreover, the displacement, velocity, and acceleration can also be expressed in terms of the eigenvector φ i ∈ R n d and the generalized coordinates q di , q vi , q ai ∈ R for the displacement, velocity, and acceleration of the model, as shown in Equations ( 16)- (18). In addition, the mode shapes φ dsi ∈ R m d , φ vsi ∈ R m v , and φ asi ∈ R m a for the displacement, velocity, and acceleration at the measurement location corresponding to eigenvector φ i can be defined in terms of the transformation matrices N d , N v , and N a , as shown in Equations ( 19)-(21).…”