Kalman filter technique for estimating encountered wave profiles and unmeasured ship responses using measurement data in short-crested irregular waves

• The Kalman filter (KF) technique accurately estimates wave profiles encountered by a ship from measured responses in short-crested irregular waves. • Using only ship motions or stresses as input reduces estimation accuracy for wave directions; combining both inputs enhances performance. • Accurate estimation of wave profiles is achieved by integrating ship motions and stresses, leading to sufficient accuracy in wave direction estimates. • The time series of unmeasured ship responses can be accurately estimated using wave coefficients and transfer functions, particularly when correlated responses are utilized. • Wave profile estimation improves by assuming long-crested waves when the transfer functions at the main wave direction closely resemble those of the adjacent wave directions. Understanding the condition of a ship during operation is crucial for ensuring hull safety. This can be achieved either by directly monitoring the ship's hull or by using response estimation models when the wave field is known. Developing a method for real-time estimation of wave profiles and subsequent ship responses, especially in short-crested irregular waves that closely resemble real sea conditions, is essential. This study aims to develop and validate a Kalman Filter (KF) technique to estimate wave profiles encountered by a ship and unmeasured ship responses from measured response signals in short-crested irregular waves. A tank testing with a scaled model is performed in short-crested irregular waves to validate the method. The wave profiles are represented as a linear superposition of elementary waves, assuming linearity in both the waves and ship responses. The wave amplitudes of these elementary waves are modeled as state variables and estimated in real-time using the KF technique. The results demonstrate that unmeasured ship responses can also be predicted with good accuracy by combining the estimated wave profiles with transfer functions. This research extends the authors’ previous work, which applied the KF technique to long-crested irregular waves. In this study, short-crested irregular waves are modeled using a double-summation method, and a new method for calculating wave directional spectra is proposed. This method accounts for interference among waves of the same frequency but different wave encounter angles.