Physics-informed Machine Learning Method for Forecasting and Uncertainty Quantification of Partially Observed and Unobserved States in Power Grids

We present a physics-informed Gaussian Process Regression (GPR) model to predict the phase angle, angular speed, and wind mechanical power from a limited number of measurements. In the traditional data-driven GPR method, the form of the Gaussian Process auto- and cross-covariance functions is assumed and its parameters are found from measurements. In the physics-informed GPR, we treat unknown variables (including wind speed and mechanical power) as a random process and compute the auto and cross-covariance functions from the resulting stochastic power grid equations. We demonstrate that the physics-informed GPR method is significantly more accurate than the standard data-driven one for immediate forecasting of generators\u27 angular velocity and phase angle. We also show that the physics-informed GPR provides accurate predictions of the unobserved wind mechanical power, phase angle, or angular velocity when measurements from only one of these variables are available. The immediate forecast of observed variables and predictions of unobserved variables can be used for effectively managing power grids (electricity market clearing, regulation actions) and early detection of abnormal behavior and faults. The physics-based GPR forecast time horizon depends on the combination of input (wind power, load, etc.) correlation time and characteristic (relaxation) time of the power grid and can be extended to short and medium-range times

Stochastic modeling of functionally graded double-lap adhesive joints

Perturbation(s) in the adhesive’s properties originating from the manufacturing, glue-line application method and in-service conditions, may lead to poor performance of bonded systems. Herein, the effect of such uncertainties on the adhesive stresses is analyzed via a probabilistic mechanics framework built on a continuum-based theoretical model. Firstly, a generic 2D plane stress/strain linear-elastic model for a composite double-lap joint with a functionally graded adhesive is proposed. The developed model is validated against the results obtained from an analogous finite element model for the cases of bonded joints with metal/composite adherends subjected to mechanical and thermal loadings. Subsequently, the proposed analytical model is reformulated in probabilistic mechanics framework where the elastic modulus of the adhesive is treated as a spatially varying stochastic field for the cases of homogeneous and graded adhesives. The former case represents stochastic nature of conventional joints with a homogeneous bondline while the later case showcases the perturbation in the properties of functionally graded joints. To propagate the uncertainty in the elastic modulus to shear and peel stresses, we use a non-intrusive polynomial chaos approach. For a standard deviation in the elastic modulus, the proposed model is utilized to evaluate the spatial distribution of shear and peel stresses in the adhesive, together with probability and cumulative distribution functions of their peaks. A systematic parametric study is further carried out to evaluate the effect of varying mean value of the adhesive’s Young’s moduli, overlap lengths and adhesive thicknesses on the coefficient of variation/standard deviation in peak stresses due to the presence of a random moduli field. It was observed that the joints with stiffer adhesives and longer bondlengths show smaller coefficient of variation in peak stresses. The findings from this study underscore that the predictive capability of the proposed model would be useful for the stochastic design of adhesively bonded joints