Bayesian Dynamic Linear Model Research Articles

An Efficient Decision-Making Approach for Short Term Indoor Room Temperature Forecasting in Smart Environment: Evidence from India

“Smart cities” start with “Smart Buildings” that improve the quality of urban services while ensuring sustainability. The current scenario in India reveals that the corporate and residential building structures are incorporating various self-sustainable techniques. Out of the multiple factors governing the comfort of smart buildings, indoor room temperature is an important one, since it drives the need of cooling or heating through controlling systems. Around one-third of total energy consumption of commercial buildings in India is attributed to Heating, Ventilation and Air Conditioning (HVAC) systems. Accurate prediction of indoor room temperature helps in creating an efficient equilibrium between energy consumption and comfort level of the building, thus providing opportunities for efficient decision making for energy optimization. Considering Indian climatic and geographical conditions, this paper proposes an efficient decision making approach using Bayesian Dynamic Models (BDM) for short-term indoor room temperature forecasting of a corporate building structure. The results obtained from Bayesian Dynamic linear model, using Expectation Maximization (EM) algorithm, have been compared to standard Auto Regressive Integrated Moving Average (ARIMA) model, and have been found to be more accurate. Forecasting of indoor room temperature is a highly nonlinear phenomenon, so to further improve the accuracy of the linear models, a hybrid modeling approach has been proposed. The inclusion of state-of-the-art nonlinear models such as Artificial Neural Networks (ANNs) and Support Vector Regression (SVR) improves the forecasting accuracy of the linear models significantly. Results show that the hybrid model obtained using BDM and ANN is the best fit model.

Data Fusion about Serviceability Reliability Prediction for the Long-Span Bridge Girder Based on MBDLM and Gaussian Copula Technique

This article presented a new data fusion approach for reasonably predicting dynamic serviceability reliability of the long-span bridge girder. Firstly, multivariate Bayesian dynamic linear model (MBDLM) considering dynamic correlation among the multiple variables is provided to predict dynamic extreme deflections; secondly, with the proposed MBDLM, the dynamic correlation coefficients between any two performance functions can be predicted; finally, based on MBDLM and Gaussian copula technique, a new data fusion method is given to predict the serviceability reliability of the long-span bridge girder, and the monitoring extreme deflection data from an actual bridge is provided to illustrated the feasibility and application of the proposed method.

Anomaly detection of structural health monitoring data using the maximum likelihood estimation-based Bayesian dynamic linear model

Enormous data are continuously collected by the structural health monitoring system of civil infrastructures. The structural health monitoring data inevitably involve anomalies caused by sensors, transmission errors, or abnormal structural behaviors. It is important to identify the anomalies and find their origin (e.g. sensor fault or structural damage) to make correct interventions. Moreover, online anomaly identification of the structural health monitoring data is critical for timely structural condition assessment and decision-making. This study proposes an online approach for detecting anomalies of the structural health monitoring data based on the Bayesian dynamic linear model. In particular, Bayesian dynamic linear model, consisting of various components, is implemented to characterize the feature of real-time measurements. Expectation maximization algorithm and Kalman smoother are combined to estimate the Bayesian dynamic linear model parameters and generate log-likelihood functions. The subspace identification method is introduced to overcome the initialization issue of the expectation maximization algorithm. The log-likelihood difference of consecutive time steps is then used to determine thresholds without introducing extra anomaly detectors. The proposed Bayesian dynamic linear model-based approach is first illustrated by the simulation data and then applied to the structural health monitoring data collected from two long-span bridges. The results indicate that the proposed method exhibits good accuracy and high computational efficiency and also allows for reconstructing the strain measurements to replace anomalies.

Dynamic Bayesian temporal modeling and forecasting of short-term wind measurements

Abstract We present a new Bayesian modeling approach for joint analysis of wind components and short-term wind prediction. This approach considers a truncated bivariate matrix Bayesian dynamic linear model (TMDLM) that jointly models the u (zonal) and v (meridional) wind components of observed hourly wind speed and direction data. The TMDLM takes into account calm wind observations and provides joint forecasts of hourly wind speed and direction at a given location. The proposed model is compared to alternative empirically-based time series approaches that are often used for short-term wind prediction, including the persistence method (naive predictor), as well as univariate and bivariate ARIMA models. Model performance is measured predictively in terms of mean squared errors associated to 1-h and 24-h ahead forecasts. We show that our approach generally leads to more accurate short term predictions than these alternative approaches in the context of analysis and forecasting of hourly wind measurements in 3 locations in Northern California for winter and summer months.

Improving the prediction of western North Pacific summer precipitation using a Bayesian dynamic linear model

Seasonal prediction of western North Pacific summer monsoon rainfall (WNPSMR) is in great demand but remains challenging, because the relationships between the Asian monsoon system and precursors are nonstationary and exhibit significant decadal changes. The present study aims to (1) examine decadal variations of the relationships between the WNPSMR and predictors used in previous studies and (2) establish a new prediction model using a Bayesian dynamical linear model (DLM), which is capable of capturing the time-evolving relationships between the predictand and predictors whereas the conventional static linear model cannot. Two predictors were selected previously to predict the WNPSMR. One is the sea level pressure tendency anomalies over the tropical eastern Pacific from late spring to early summer, which represents remote forcing related to ENSO and has a stable effect on WNPSMR throughout the analysis period. The other is the sea surface temperature anomaly difference between the northern Indian Ocean (IO) and the WNP during spring through early summer (called IOWPSST), which denotes local air–sea interaction that affects the WNP subtropical high. Results show that the IOWPSST has strong influence on WNPSMR during 1979–2003 (period 1), while from 2004 to 2017 (period 2) its connection to WNPSMR evidently weakens. This nonstationary relationship is due to the non-persistence of the enhanced WNP subtropical high during period 2, which is associated with the positive-to-negative phase transition of the Interdecadal Pacific Oscillation since ~ 2000. A new prediction model was established using the two predictors with Bayesian DLM. The cross-validation method and a 9-years independent forward-rolling forecast is applied to test the hindcast and actual forecast ability. Results show that the Bayesian DLM has higher hindcast/forecast skill and lower mean square error compared with static linear model, suggesting that the DLM has advantage in predicting WNPSMR and is a promising method for seasonal prediction.

Bayesian dynamic modification of corrosion in a cylindrical rod quantified by guided waves technique

ABSTRACT In this study, both estimation and modification strategies of measurement uncertainty were investigated when using a guided waves (GWs) technique to quantify the corrosion level of a cylindrical rod induced by an accelerated setup, thus providing essential and reliable information for making decisions regarding necessary remedial work. First, the remnant diameters under corrosion were quantified based on the dispersion characteristics of GWs, and the measurement uncertainty derived from time-frequency analysis was specifically considered. After demonstrating the equivalence with the self-adaptive Monte Carlo method, the method in guide to the expression of uncertainty in measurement (GUM) was used as a more efficient approach for carrying out interval estimation of the corrosion level. Furthermore, a designed Bayesian dynamic linear model (BDLM) with a model monitoring mechanism was introduced to modify the measurement sequence. Thus, not only were more credible estimations achieved but discrepant sequences of measurement data could also be identified to avoid a misled judgement.

Time-Varying Price Elasticity in a Service Market with Heterogeneous Customer Valuation

The demand for services such as self-storage varies across locations, over time, as well as across customer segments. Service providers try to leverage these variations and maximize profits by adopting dynamic pricing policies. Implementing dynamic pricing, however, requires accurate estimates of price elasticities at a granular level. Using data from a leading self-storage retailer in Europe, we estimate a Bayesian Dynamic Hierarchical Linear Model (DHLM) to obtain price elasticities across 67 stores, for 21 bi-weeks, and high-valuation vs. low-valuation customer segments. Our estimation procedure accounts for price endogeneity, which is essential when using the estimated price elasticities to set the dynamic pricing policy. We find evidence of different price elasticities between stores and over time, which supports the practice of local dynamic price setting, as well as strong differences between customer segments. Overall, high-valuation customers are more price-sensitive than low-valuation customers. In addition, while the price elasticity of high-valuation customers remains stable, low-valuation customers become less price sensitive over time. This implies that a markup policy should be followed for low-valuation customers, but a more stable pricing regime may suffice for high-valuation customers. Last, we show the benefits of our model compared to a benchmark model with time-invariant price elasticities in determining the pricing policy, and discuss how our model can be applied to other industries that practice revenue management.

Dynamic reliability prediction for the steel box girder based on multivariate Bayesian dynamic Gaussian copula model and SHM extreme stress data

This article presents the dynamic reliability prediction method of the existing steel box girder considering the time-variant nonlinear correlations among the performance functions for the failure modes at the multiple control monitoring points. Firstly, the multivariate Bayesian dynamic linear model (MBDLM) considering the nonlinear correlations among the multiple variables is built to predict the extreme stresses at the different control monitoring points; secondly, based on the predicted covariance matrix of MBDLM, the dynamic correlation coefficients between any two performance functions can be accurately predicted; and finally, multivariate Bayesian dynamic Gaussian copula model through combining MBDLM with Gaussian copula technique is proposed to predict the dynamic reliability of the steel box girder, and the monitoring extreme stress data of an actual bridge are provided to illustrate the feasibility and application of the proposed method. The results show that predicted dynamic reliability of the bridge girder with considering the time-variant nonlinear correlation of failure modes at the multiple control monitoring points is bigger than that without considering the time-dependent nonlinear correlation. It is illustrated that the predicted results without considering the dynamic nonlinear correlation of failure modes at the multiple control monitoring points are more conservative.

Real-time defect detection of high-speed train wheels by using Bayesian forecasting and dynamic model

High-speed rail (HSR) is being developed in Asian and European countries to satisfy the rapidly growing demand for intercity services and to shore up economic growth. The rapid growth of HSR, however, has posed great challenges regarding operation safety, reliability and ride comfort. Irregular wheel defects can induce high-magnitude impact forces hindering safety and ride comfort of HSR and may also cause damage to rail tracks and vehicles. The focus of this study is to develop a real-time defect detection methodology based on Bayesian dynamic linear model (DLM) enabling to detect potentially defective wheels in real time. The proposed methodology embraces logics for (i) prognosis, (ii) potential outlier detection, (iii) identification of change occurrence (change-point detection), and (iv) quantification of damage extent and uncertainty. Relying on the strain monitoring data acquired from high-speed train bogies, the Bayesian DLM for characterizing the actual stress ranges is established, by which one-step forecast distribution is elicited before proceeding to the next observation. The detection of change-point is executed by comparing the routine model (forecast distribution generated by the Bayesian DLM) and an alternative model (the mean value is shifted by a prescribed offset) to determine which better fits the actual observation. If the comparison results are in favor of the alternative model, it is claimed that a potential change has occurred. Whether such an observation is an outlier or the beginning of a genuine change (change-point), three metrics (i.e., Bayes factor, maximum cumulative Bayes factor and run length) are performed for further identification. Once a change-point is confirmed, Bayesian hypothesis testing is conducted for the purpose of damage extent assessment and uncertainty quantification. A severe change, if identified, implies that the quality of train wheels has suffered from a significant alteration due to defects. In the case study, two cases making use of strain monitoring data acquired by fiber Bragg grating (FBG) sensors affixed on bogies are illustrated to verify the performance of the proposed methodology for real-time wheel defect detection of in-service high-speed trains.

Improvement of Bayesian Dynamic Linear Model for Predicting Missing Data of Bridges

The missing data in bridge operation will lead to the decline of the reliability of data analysis results. In this paper, the Bayesian dynamic linear model is improved by changing the parameter matrix of hidden state variables, and the model is optimized under the condition that the predefined variables are unchanged. The frequency of a strain measuring point of the bridge is taken as the observed value, and the collected frequency value of one month is used as the training set (the collection time interval is 30 minutes) to predict the data of the next week. By comparing the predicted result with the observed value, it is found that the absolute error is less than 14.05Hz and the relative error is less than 1.82% when the training frequency value varies from 756 Hz to 773.4 Hz.

Aircraft auxiliary power unit performance assessment and remaining useful life evaluation for predictive maintenance

Modern commercial aircraft are usually configured with aircraft condition monitoring system to collect the operating data of subsystems and components, which can be used for airborne system health monitoring and predictive maintenance. This paper presents a baseline model based aircraft auxiliary power unit performance assessment and remaining useful life prediction method using aircraft condition monitoring system reports data, which can facilitate a cost-effective management of auxiliary power units of aircraft fleet. Firstly, the performance baseline model for auxiliary power unit is established using random forest method. Then a health index characterizing the performance degradation of in-service auxiliary power units is obtained based on the performance baseline model. Finally, the performance degradation trend is predicted using Bayesian dynamic linear model. To improve the prediction accuracy, four performance baseline models are established from the data of auxiliary power units under different operating conditions, among which an optimal model is determined. This data-driven baseline model can be used to quantify the performance degradation of auxiliary power units in service, and can be further used to evaluate the remaining useful life of auxiliary power unit using a Bayesian dynamic model. The developed approach is applied on a real data set from 22 auxiliary power units of a commercial aircraft fleet. The results show that the computed health index can effectively characterize the auxiliary power units performance degradation and the remaining useful life relative prediction errors are less than 4% when auxiliary power unit enters the rapid degradation stage. This would allow operators to accurately assess the performance degradation for the auxiliary power units and further proactively plan future maintenance events based on remaining useful life prediction.

Spatiotemporal changes of drought characteristics and their dynamic drivers in Canada

Abstract There has been a growing concern regarding impacts of global warming on droughts, which can have devastating effects on the environment, society, and economy of nations worldwide. Drought characteristics in terms of duration, frequency, area, and severity are investigated using the Standardized Precipitation Evapotranspiration Index (SPEI) at seasonal (3-month) and annual (12-month) time scales for Canada over 1950–2016 derived from the Climatic Research Unit (CRU) TS4.03 gridded data. Using k-means clustering, Canada is divided into four sub-regions, each with distinct drought characteristics. Next, the influence of climate drivers such as the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) on regional drought variability were examined using a Bayesian Dynamic Linear (BDL) model. The results show that between 1950 and 2016 (1) there has been a prevalent drying trend in southwestern Canada during winter; (2) changes in maximum drought durations have occurred with dipolar patterns, i.e., northern Canada has experienced a longer drought duration than southern Canada; (3) drought frequency, area, and severity have predominantly shown statistically significant decreasing trends, indicating that droughts in Canada have generally become less severe; and (4) the relationships between climate anomalies and drought variability have changed over time. Droughts are generally more negatively correlated to ENSO and PDO after 1970s, but more positively correlated to the Atlantic Multi-decadal Oscillation (AMO) and Arctic Oscillation (AO) after the 1980s. The results provide a better understanding of the characteristics of meteorological droughts in Canada, essential for improving the risk management and mitigation strategies on the impact of droughts.

Bayesian forecasting approach for structure response prediction and load effect separation of a revolving auditorium

A Bayesian dynamic linear model (BDLM) is presented for a data-driven analysis for response prediction and load effect separation of a revolving auditorium structure, where the main loads are self-weight and dead loads, temperature load, and audience load. Analyses are carried out based on the long-term monitoring data for static strains on several key members of the structure. Three improvements are introduced to the ordinary regression BDLM, which are a classificatory regression term to address the temporary audience load effect, improved inference for the variance of observation noise to be updated continuously, and component discount factors for effective load effect separation. The effects of those improvements are evaluated regarding the root mean square errors, standard deviations, and 95% confidence intervals of the predictions. Bayes factors are used for evaluating the probability distributions of the predictions, which are essential to structural condition assessments, such as outlier identification and reliability analysis. The performance of the present BDLM has been successfully verified based on the simulated data and the real data obtained from the structural health monitoring system installed on the revolving structure.

Bayesian Dynamic Linear Model with Adaptive Parameter Estimation for Short-Term Travel Speed Prediction

Bayesian dynamic linear model is a promising method for time series data analysis and short-term forecasting. One research issue concerns how the predictive model adapts to changes in the system, especially when shocks impact system behavior. In this study, we propose an adaptive dynamic linear model to adaptively update model parameters for online system state prediction. The proposed method is an automatic approach based on the feedback of prediction errors at each time slot without the needs of external intervention. The experimental study on short-term travel speed prediction shows that the proposed method can significantly reduce the prediction errors of the traditional dynamic linear model and outperform two state-of-the-art methods in the case of major system behavior changes.

Modeling and forecasting of temperature-induced strain of a long-span bridge using an improved Bayesian dynamic linear model

Temperature-driven baseline is highly responsive to anomalous structural behavior of long-span bridges, which means that the discrepancy between the measured and forecasting temperature-induced strain (TIS) can be examined for anomalies. In this regard, it is important to guarantee the accuracy of the forecasting TIS responses for reliable assessment of structural performance. Bayesian dynamic linear model (BDLM) has shown a promising application in the field of structural health monitoring. Traditionally, BDLM is used to forecast structural responses by utilizing its trend form, seasonal form, regression form, or combination of the three forms. However, different features of time series cannot be totally captured by these forms, which would undermine the accuracy of BDLM. To improve the computational accuracy, an improved BDLM, which considers an autoregressive (AR) component in addition to the trend, seasonal and regression components, is presented in this paper. Specifically, the AR component is able to model the component which cannot be captured by other three components. The real-time monitoring data collected from a long-span cable-stayed bridge is utilized to demonstrate the feasibility of the improved BDLM-based method. In particular, the present BDLM-based method allows for probabilistic forecasts, offering substantial information about the target TIS response, such as mean and confidence interval. Results show that the improved BDLM is capable of capturing the relationship between temperature and TIS. Compared to the AR model, multiple linear regression (MLR) model and BDLM without the AR component, the improved BDLM shows better forecasting performance in modeling and forecasting the TIS of a long-span bridge.

Decadal Shift of NAO-Linked Interannual Sea Level Variability along the U.S. Northeast Coast

Recent studies have linked interannual sea level variability and extreme events along the U.S. northeast coast (NEC) to the North Atlantic Oscillation (NAO), a natural internal climate mode that prevails in the North Atlantic Ocean. The correlation between the NAO index and coastal sea level north of Cape Hatteras was weak from the 1960s to the mid-1980s, but it has markedly increased since around 1987. The causes for the decadal shift remain unknown. Yet understanding the abrupt change is vital for decadal sea level prediction and is essential for risk management. Here we use a robust method, the Bayesian dynamic linear model (DLM), to explore the nonstationary NAO impact on NEC sea level. The results show that a spatial pattern change of NAO-related winds near the NEC is a major cause of the NAO–sea level relationship shift. A new index using regional sea level pressure is developed that is a significantly better predictor of NEC sea level than is the NAO and is strongly linked to the intensity of westerly winds near the NEC. These results point to the vital importance of monitoring regional changes of wind and sea level pressure patterns, rather than the NAO index alone, to achieve more accurate predictions of sea level change along the NEC.

Multi-Decadal Trend and Decadal Variability of the Regional Sea Level over the Indian Ocean since the 1960s: Roles of Climate Modes and External Forcing

Previous studies suggest that anthropogenic warming has affected the multi-decadal trend patterns of sea level over the Indian Ocean (IO). This effect, however, has not been quantified. Using observational datasets combined with large ensemble experiments from two climate models, this paper assesses the effects of natural internal variability versus external forcing on the observed, multi-decadal trend pattern and the decadal sea level anomaly (SLA) of the IO since the 1960s. Because the global mean sea level rise (SLR), which results largely from external forcing, has been removed before the examination, the paper focuses on the regionally uneven distribution of trend and SLA. The impacts of climate modes are quantified using a Bayesian Dynamic Linear Model. For the regional trend pattern of 1958–2005, the effects of internal variability dominate external forcing. Over the Seychelles area where sea-level variations obtain the maximum, internal variability (external forcing) contributes 81% (19 ± 2.4%) of the observed trend. For decadal SLA, internal variability is the predominant cause, with a standard deviation (STD) ratio of externally forced/observed SLA being 18 ± 17% over Seychelles and 17 ± 11% near the Indonesian Throughflow (ITF) area. Climate modes account for most observed SLA during boreal winter, with the total effects of decadal ENSO, Indian Ocean Dipole (IOD), and monsoon accounting for 78–86% of the observed STD near the Seychelles region, ITF area, and coasts of Sumatra and the Bay of Bengal. During summer, climate modes explain 95% of observed STD near the ITF but only 58–67% in other regions. Decadal ENSO dominates the SLA in the south tropical IO for both seasons and near the coasts of Sumatra and the Bay during winter. Decadal IOD and monsoon, however, control the coastal SLA during summer. Remote and local winds over the IO are the main drivers for decadal SLA, while the Pacific influence via the ITF is strong mainly in the southeast basin.

Bayesian Dynamic Linear Regression Analysis of Infant Growth by Weight

The most common anthropometric measurements used to assess physical growth patterns of infant from birth to one year period are body weight and length. Weight gain pattern is dynamic that could not be easily understood. The main objective of this study is to model the biological growth of infants by weight during the first year of their lives using the Bayesian hierarchical and dynamic linear regression model. The data used in this study was from a cohort study for infants born alive and followed from birth to one year period with six visits at Adare General Hospital. There has been a sample of 126 infants under follow-up from birth to 12 months old at Adare General Hospital, Hawassa Ethiopia. A total of 756 weight observations were collected from the following-up of the infants during the one year period. The Bayesian hierarchical and dynamic linear regression model was used to explore weight gain of infants incorporating individual and population level variations observed over time. The mean weight growth of the infants is found to be linearly increasing while variation was declining over the age. Rate of weight change of the infants had two optimum points that might represent inflection points of the growth at around six and eight months. Posterior distributions of the intercept and slope parameters were found to have normal distributions, from which important inferences about the infant’s growth can be derived. The Bayesian hierarchical and dynamic linear model can explain and capable to handle the weight growth patterns of the infants over the short period of time.

Decadal Variability of the Indian and Pacific Walker Cells since the 1960s: Do They Covary on Decadal Time Scales?

Previous studies have investigated the centennial and multidecadal trends of the Pacific and Indian Ocean Walker cells (WCs) during the past century, but have obtained no consensus owing to data uncertainties and weak signals of the long-term trends. This paper focuses on decadal variability (periods of one to few decades) by first documenting the variability of the WCs and warm-pool convection, and their covariability since the 1960s, using in situ and satellite observations and reanalysis products. The causes for the variability and covariability are then explored using a Bayesian dynamic linear model, which can extract nonstationary effects of climate modes. The warm-pool convection exhibits apparent decadal variability, generally covarying with the Indian and Pacific Ocean WCs during winter (November–April) with enhanced convection corresponding to intensified WCs, and the Indian–Pacific WCs covary. During summer (May–October), the warm-pool convection still highly covaries with the Pacific WC but does not covary with the Indian Ocean WC, and the Indian–Pacific WCs are uncorrelated. The wintertime coherent variability results from the vital influence of ENSO decadal variation, which reduces warm-pool convection and weakens the WCs during El Niño–like conditions. During summer, while ENSO decadal variability still dominates the Pacific WC, decadal variations of ENSO, the Indian Ocean dipole, Indian summer monsoon convection, and tropical Indian Ocean SST have comparable effects on the Indian Ocean WC overall, with monsoon convection having the largest effect since the 1990s. The complex causes for the Indian Ocean WC during summer result in its poor covariability with the Pacific WC and warm-pool convection.

Adaptive RTO for handshaking-based MAC protocols in underwater acoustic networks

Underwater acoustic networks (UANs) are attracting interest in recent decades. The unique characteristics of the underwater acoustic channel, such as long propagation delay, delay variance, and high bit error rate, present challenges for the medium access control (MAC) protocol design in UANs. Most existing medium access control protocols ignore the delay variance which prevents the accurate estimation of round trip time (RTT). The expected RTT value can be used to compute the Retransmission Time-Out (RTO) or the waiting time in MAC. The estimation of RTT is also meaningful for Automatic Repeat re-Quest (ARQ) scheme because the system should ensure reliable data transmissions in the presence of high bit error rate in the underwater acoustic channel. By analyzing the impact of RTO on throughput under the effect of delay variance, we conclude that the fixed RTO is inefficient and RTO should be adaptively set to improve the throughput. We present a novel approach of predicting the RTT using a Bayesian dynamic linear model, and then adjust RTO adaptively according to the predicted values. Simulation results show that the predicted values can adapt quickly to the sample RTT values. Under the effect of RTT fluctuations, the Bayesian algorithm offers performance gains in terms of throughput and prediction performance, comparing with Karn’s algorithm. Our study highlights the value of predicting the RTT using Bayesian approach in underwater acoustic networks.