Kalman-type filters for coupled input-state estimation can be used to estimate the full-field dynamic response of structures from only a limited set of vibration measurements. The use of these coupled estimators allows for response prediction to be performed in the absence of any knowledge of both the dynamic evolution and spatial distribution of the excitation forces, where often a set of response-driving equivalent forces is identified from the measurements. In this contribution, a rigorous analysis of the concept of equivalent force based response monitoring is performed, with the aim to clearly establish its limitations and ranges of applicability. It is shown that, unlike commonly assumed, the success of this type of response monitoring cannot be related solely to whether the chosen set of equivalent forces satisfy the controllability requirements, but will depend on the bandwith of the excitation forces in combination with the extent/characteristics of the sensor network. Arguments are instantiated using simple numerical examples where a comparison is made between the theoretical assumptions used to derive the filters and the physical situation. Included in the analyses are situations where (a) the applied and equivalent loads are concentrated and collocated, (b) the applied and equivalent loads are concentrated and non-collocated, (c) modal equivalent loads are used to represent concentrated non-moving forces, and (d) modal equivalent loads are used to represent concentrated moving forces. Results are applicable to any Kalman-type coupled input-state estimator derived using the principles of minimum-variance unbiased estimation.

@en

Kalman-type filters are being increasingly used to estimate the full-field dynamic response of structures from a limited set of vibration measurements. Various coupled input-state and coupled input-state-parameter estimation algorithms have been developed in this context, ranging from an initial formulation for use with linear reduced-order structural systems to alternative filters for dealing with acceleration-only data and recently also nonlinear model descriptions. The use of these algorithms allows for response prediction to be performed in the absence of any knowledge of the excitation forces, where often a set of response-driving equivalent forces is identified from the measurements. Up to now, the success of response estimation based on the identification of equivalent forces has been related only to whether these forces satisfy the so-called controllability requirements. In this contribution, controllability is shown to be an insufficient criterion for guaranteeing the accuracy of response estimates based on equivalent loading. Instead, the need for a new criterion is advocated, which would allow for a proper assessment of the applicability of equivalent force based monitoring to various engineering problems. Concepts are illustrated using simple numerical examples where a comparison is made between the true and assumed noise statistics and the response prediction accuracy for a number of distinct cases. These include situations where (a) the applied and equivalent loads are concentrated and collocated, (b) the applied and equivalent loads are concentrated and non-collocated, and (c) modal equivalent forces are used. Results are applicable to any Kalman-type coupled input-state estimator derived using the principles of minimum-variance unbiased estimation.@en

For the monitoring of large structures where the loading is typically characterized by large uncertainties in temporal and/or spatial evolution, algorithms capable of estimating a set of response driving equivalent forces are strongly desired. In this context, several Kalman-type coupled input-state and coupled input-state-parameter filters have recently been developed, allowing for an estimation of the full-field dynamic response of a structure from only a limited number of vibration measurements. Up to now, the success of response estimation based on the identification of equivalent forces has been related only to whether these forces satisfy the so-called controllability requirements. In this contribution, controllability is shown to be an insufficient criterion for guaranteeing the accuracy of response estimates based on equivalent loading. Instead, the need for a new criterion is advocated, which would allow to assess the applicability of equivalent force based monitoring to various engineering problems. Concepts are illustrated by comparing true and assumed noise statistics as well as the response prediction accuracy for different numerical examples, where a) the applied and equivalent loads are concentrated and collocated, b) the applied and equivalent loads are concentrated and non-collocated, and c) modal equivalent forces are used. Results are applicable to any Kalman-type coupled input-state estimator derived using the principles of minimum-variance unbiased estimation.

@en

For reliable structural health monitoring and possible lifetime extension of offshore wind turbine support structures, accurate predictions of the response of these structures at all critical locations are required. Response predictions in offshore wind applications are, however, affected by large uncertainties on environmental (wind/wave/soil) as well as system parameters (eigenfrequencies/damping). As a first step towards robust health monitoring in the presence of these uncertainties, a methodology for simultaneous estimation of a response equivalent hydrodynamic loading and a system parameter from measured vibration signals is proposed. Use is made of a recently proposed coupled input-state-parameter estimation technique based on the Extended Kalman filter. The identification process is driven by a limited set of artificially generated vibration response data in combination with an approximate reduced-order model of the support structure. The results show that the proposed method is capable of tracking both the response equivalent hydrodynamic loading and a parameter that is related to the stiffness of the substructure.

@en