A possible approach to meet the increasing performance requirements of lightweight structures in various engineering fields is the application of smart structures. One of the functions, which are required, is the observation of the structures' shape. During operation, however, the monitoring of displacement fields is difficult. This paper discusses the displacement field estimation of a dynamically excited plate using fiber Bragg grating strain sensors. Using a modal approach, it is possible to derive a transformation matrix to estimate the displacement field using only a few strain measurements. To reduce systematic estimation errors due to residual modes, a parameter study was performed and the sensor location optimized using the condition number of the transformation matrix as an objective function. An experiment with an optimized sensor configuration including 16 fiber Bragg grating strain sensors was performed to verify the method and the simulation results..H\ZRUGV shape estimation, fiber Bragg grating (FBG), modal approach, displacement-strain relationship, sensor locations ,1752'8&7,21The observation of structural displacements in smart structures is of great interest in various application fields such as tooling machines (1) , airplane wings (2) , or high-precision-and space-reflectors (3) . Since the displacement field is difficult to be measure in a lot of applications, especially during operation, strain data can be used to estimate the displacement field. Various methods for the shape estimation can be found in literature: calibration methods (4) , the use of transfer functions (5) , least-square-fitting algorithms (6) or a modal approach (7) , which is used here. An advantage of this method is the possibility to estimate the displacement field of a structure using strain data from a few discrete positions. A disadvantage is the systematic estimation error due to the residual modes which introduce temporal aliasing. One of the topics of this study is to minimize this error using an appropriate sensor distribution.In order to achieve an improvement of the estimation quality, a parameter study shall show different relationships between designated estimation variables and the estimation quality. Using the information of the parameter study, the sensor locations will be optimized. The effectiveness of the determined sensor locations will be proven by simulations and an experiment.The strain sensing was enabled by multiplexed fiber Bragg grating strain sensors (FBG). They fit well to the mentioned applications, since they are lightweight themselves, immune to electromagnetic disturbances, easy to integrate into composite structures and enable sensing at many positions using only a single fiber.The displacement of a structure can be expressed by using an infinite number of displacement mode shapesφ and the strain by an infinite number of strain mode shapes ψ . Both can be multiplied with the corresponding weighting factors,