In this paper, a new approach to guided wave ray tomography for temperature-robust damage detection with time-of-flight (TOF) temperature compensation is developed. Based on the linear relationship between the TOF of a guided wave and temperature, analyses show that the TOF of the baseline signal can be compensated by the temperature measurement of the inspected materials without estimating the temperature compensation parameters. The inversion is based on the optimization of the TOF misfit function between the inspected and compensated baseline TOFs of the guided waves, and is applied by the elastic net penalty approach to perform thickness change mapping in a structural health monitoring (SHM) application. Experiments that are conducted in isotropic plates by piezoelectric sensors demonstrate the effectiveness of the proposed method. According to the results, our approach not only eliminates the artefacts that are caused by a temperature variation from 25 °C to 70 °C but also provides more accurate and clearer imaging of damage than conventional ray tomography methods.

The PARAFAC decomposition is known as one of the most commonly used tools in tensor signal/data processing. Unfortunately, its classical algorithms barely take the potential statistical and/or deterministic prior information of the decomposed tensor into consideration, while the modern ones are usually problem oriented, which limits their applications. To fill in this gap, the PARAFAC decomposition of a tensor is brought into the framework of Bayesian inference in this paper. By introducing transition models for the loading/factor matrices of a tensor, the PARAFAC decomposition can be formulated as an alternating Bayesian filter. By means of the flexibility of the Bayesian filter, the proposed filtering decomposition approach illustrated can cover two commonly used priors – parametric and time transition ones. Under the linear Gaussian assumption, the proposed filter can be implemented as an Alternating (Matrix) Kalman Filter. Analyses show that the performance of the proposed filter is similar to the reported ALS based algorithms when priors are unavailable. The results of numerical simulations show that our Bayesian approach outperforms the reported PARAFAC decomposition algorithms in literature, especially for the cases where the statistical and/or deterministic priors are offered such as the target tracking application of a bistatic ULA MIMO radar system.

Alternating Least Squares (ALS) and its variations are the most commonly used algorithms for the PARAFAC decomposition of a tensor. However, it is still troubled for one how to accelerate the ALS algorithm with the reduced computational complexity. In this paper, a new acceleration method for the ALS with a Matrix Polynomial Predictive Model (MPPM) is proposed. In the MPPM, a matrix-valued function is first approximated by a matrix polynomial. It is shown that the future value of the function can be predicted by an FIR filter with the coefficients determined offline. By viewing each factor matrix of a tensor as a matrix-valued function, a new ALS algorithm, the ALS-MPPM algorithm, is then given. Analyses show that our ALS-MPPM algorithm is of a low computational complexity and a close relation with the existing ALS algorithms. Moreover, to further accelerate the convergence of the proposed algorithm, a new technique called the Multi-Model (MM) prediction is also introduced. While the analytical results are verified by the numerical simulations, it is also show that our ALS-MPPM outperforms the existing ALS-based algorithms in terms of the rate of convergence.