A Kernel-Based Method for Modeling Non-harmonic Periodic Phenomena in Bayesian Dynamic Linear Models

Modeling periodic phenomena with accuracy is a key aspect to detect abnormal behaviour in time series for the context of Structural Health Monitoring. Modeling complex non-harmonic periodic pattern currently requires sophisticated techniques and significant computational resources. To overcome these limitations, this paper proposes a novel approach that combines the existing Bayesian Dynamic Linear Models with a kernel-based method for handling periodic patterns in time series. The approach is applied to model the traffic load on the Tamar Bridge and the piezometric pressure under a dam. The results show that the proposed method succeeds in modeling the stationary and non-stationary periodic patterns for both case-studies. Also, it is computationally efficient, versatile, self-adaptive to changing conditions, and capable of handling observations collected at irregular time intervals.

[1]  J. Mata,et al.  Interpretation of concrete dam behaviour with artificial neural network and multiple linear regression models , 2011 .

[2]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[3]  Ida Kjersem Solhjell.  Bayesian Forecasting and Dynamic Models Applied to Strain Data from the Göta River Bridge , 2009 .

[4]  M.Á. Toledo,et al.  Discussion on “Thermal displacements of concrete dams: Accounting for water temperature in statistical models” , 2015 .

[5]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[6]  Marcin Michalak,et al.  Time Series Prediction with Periodic Kernels , 2011, Computer Recognition Systems 4.

[7]  José Manuel Benítez,et al.  On the use of cross-validation for time series predictor evaluation , 2012, Inf. Sci..

[8]  James M. W. Brownjohn,et al.  Effect of vehicular loading on suspension bridge dynamic properties , 2015 .

[9]  James-A. Goulet,et al.  Structural Health Monitoring with dependence on non-harmonic periodic hidden covariates , 2018, Engineering Structures.

[10]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[11]  G. C. Tiao,et al.  A Course in Time Series Analysis , 2000 .

[12]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[13]  Christopher F. Parmeter,et al.  Applied Nonparametric Econometrics , 2015 .

[14]  James-A. Goulet.  Bayesian dynamic linear models for structural health monitoring , 2017 .

[15]  C. Mann,et al.  A Practical Treatise on Diseases of the Skin , 1889, Atlanta Medical and Surgical Journal (1884).

[16]  Michael Oberguggenberger,et al.  Assessment of long‐term coordinate time series using hydrostatic‐season‐time model for rock‐fill embankment dam , 2017 .

[17]  P. Léger,et al.  Hydrostatic, Temperature, Time-Displacement Model for Concrete Dams , 2007 .

[18]  A. Atiya,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2005, IEEE Transactions on Neural Networks.

[19]  James-A. Goulet,et al.  Empirical Validation of Bayesian Dynamic Linear Models in the Context of Structural Health Monitoring , 2018 .

[20]  Neil D. Lawrence,et al.  Kernels for Vector-Valued Functions: a Review , 2011, Found. Trends Mach. Learn..

[21]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[22]  James-A. Goulet,et al.  Anomaly detection with the Switching Kalman Filter for structural health monitoring , 2018 .

[23]  Michael A. West,et al.  Time Series: Modeling, Computation, and Inference , 2010 .

[24]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[25]  F. Dufour,et al.  Thermal displacements of concrete dams: Accounting for water temperature in statistical models , 2015 .

[26]  David Duvenaud,et al.  Automatic model construction with Gaussian processes , 2014 .

[27]  Neil D. Lawrence,et al.  Kernels for Vector-Valued Functions , 2012 .

[28]  M. Shcherbakov,et al.  A Survey of Forecast Error Measures , 2013 .