Bridge structure deformation prediction based on GNSS data using Kalman-ARIMA-GARCH model

Bridges are an essential part of the ground transportation system. Health monitoring is fundamentally important for the safety and service life of bridges. A large amount of structural information is obtained from various sensors using sensing technology, and the data processing has become a challenging issue. To improve the prediction accuracy of bridge structure deformation based on data mining and to accurately evaluate the time-varying characteristics of bridge structure performance evolution, this paper proposes a new method for bridge structure deformation prediction, which integrates the Kalman filter, autoregressive integrated moving average model (ARIMA), and generalized autoregressive conditional heteroskedasticity (GARCH). Firstly, the raw deformation data is directly pre-processed using the Kalman filter to reduce the noise. After that, the linear recursive ARIMA model is established to analyze and predict the structure deformation. Finally, the nonlinear recursive GARCH model is introduced to further improve the accuracy of the prediction. Simulation results based on measured sensor data from the Global Navigation Satellite System (GNSS) deformation monitoring system demonstrated that: (1) the Kalman filter is capable of denoising the bridge deformation monitoring data; (2) the prediction accuracy of the proposed Kalman-ARIMA-GARCH model is satisfactory, where the mean absolute error increases only from 3.402 mm to 5.847 mm with the increment of the prediction step; and (3) in comparision to the Kalman-ARIMA model, the Kalman-ARIMA-GARCH model results in superior prediction accuracy as it includes partial nonlinear characteristics (heteroscedasticity); the mean absolute error of five-step prediction using the proposed model is improved by 10.12%. This paper provides a new way for structural behavior prediction based on data processing, which can lay a foundation for the early warning of bridge health monitoring system based on sensor data using sensing technolog

Linear regression models with autoregressive integrated moving average errors for measurements from real time kinematics-global navigation satellite system during dynamic test

The autoregressive integrated moving average (ARIMA) method has been used to model global navigation satellite systems (GNSS) measurement errors. Most ARIMA error models describe time series data of static GNSS receivers. Its application for modeling of GNSS under dynamic tests is not evident. In this paper, we aim to describe real time kinematic-GNSS (RTK-GNSS) errors during dynamic tests using linear regression with ARIMA errors to establish a proof of concept via simulation that measurement errors along a trajectory logged by the RTK-GNSS can be “filtered”, which will result in improved positioning accuracy. Three sets of trajectory data of an RTK-GNSS logged in a multipath location were collected. Preliminary analysis on the data reveals the inability of the RTK-GNSS to achieve fixed integer solution most of the time, along with the presence of correlated noise in the error residuals. The best linear regression models with ARIMA errors for each data set were identified using the Akaike information criterion (AIC). The models were implemented via simulations to predict improved coordinate points. Evaluation on model residuals using autocorrelation, partial correlation, scatter plot, quantile-quantile (QQ) plot and histogram indicated that the models fitted the data well. Mean absolute errors were improved by up to 57.35% using the developed models

Study on the sensitive factors of structural nonlinear damage based on the innovation series

Constructing a damage-sensitive factor (DSF) is one of the key steps in structural damage detection. In this paper, innovation series extracted from the auto-regressive conditional heteroscedasticity (ARCH) model are proposed to construct a DSF, which is defined as the standard deviation of innovation (SDI). A three-story shear building structure is used to demonstrate and verify the performance of the proposed method, and the results are compared with the standard deviation of the residuals (SDR) based on an auto-regressive (AR) model. In the proposed method, the AR model is established using the acceleration responses obtained from the reference and test states. The residual series are then extracted for fitting the SDR. Subsequently, the ARCH model is constructed based on the residual series from the AR model, and a new DSF of SDI is defined. This study focuses on analyzing the accuracy of fitting AR model and ARCH model to vibration response data via the normal probability distribution, and identifying the characteristics of the residual and innovation series. The mean squared error (MSE) is used as the loss function to calculate the loss on residual and innovation series from the AR model and ARCH model, respectively. The results demonstrate that the SDR can be used for nonlinear damage detection. However, the proposed SDI can provide more accurate nonlinear damage identification and is robust to varying environmental condition and small damages. Thus, the innovation series developed based on ARCH model are promising for expressing and constructing nonlinear DSFs.Liujie Chen, Yahui Mei, Jiyang Fu, Ching Tai Ng and Zhen Cu

Enhancing Prediction Method of Ionosphere for Space Weather Monitoring Using Machine Learning Approaches: A Review

This paper studies the machine learning techniques that can be used to enhance the prediction method of the ionosphere for space weather monitoring. Previously, the empirical model is used. However, there is a large deviation of the total electron content of ionosphere data for the areas located in the equatorial and low-latitude regions due to the lack of observation data contributed by these areas during the development of the empirical model. The machine learning technique is an alternative method used to develop the predictive model. Thus, in this study, the machine learning techniques that can be applied are investigated. The aim is to improve the predictive model in terms of reducing the total electron content deviation, increasing the accuracy and minimizing the error. In this review, the techniques used in previous works will be compared. The artificial neural network is found to be a suitable technique and the most favorable from the review conducted. Also, this technique can provide an accurate model for time series data and fewer errors compared to other techniques. However, due to the size and complexity of the data, the deep neural network technique that is an improved artificial neural network technique is suggested. By using this technique, an accurate ionosphere predictive model in equatorial and low region area is expected. In the future, this study will analyze further by using computing tools and real-time data

Data Normalization and Anomaly Detection in a Steel Plate-Girder Bridge Using LSTM

Modal properties are recognized as indicators reflecting structural condition in structural health monitoring (SHM). However, changing environmental and operational variables (EOVs) cause variability in the identified modal parameters and subsequently obscure damage effects. To address the issue caused by EOV-related variability, this study investigated the variability of modal frequencies in long-term SHM of a steel plate-girder bridge. A Bayesian fast Fourier transform (FFT) method was used for operational modal analysis in a probabilistic viewpoint. Bayesian linear regression (BLR) and Gaussian process regression (GPR) models were utilized to capture the variability in the identified most probable values (MPVs) of modal frequencies as temperature-driven models, and the limitation of these models for data normalization with latent EOVs is discussed. To overcome the interference of latent EOVs indirectly, a long short-term memory (LSTM) network was established to trace the variability as an autocorrelated process, with a traditional seasonal autoregressive integrated moving average (SARIMA) model as a benchmark. Finally, an anomaly detection method based on residuals of one-step-ahead predictions by LSTM was proposed associating with the Mann-Whitney U-test

Bayesian Prediction of Pre-Stressed Concrete Bridge Deflection Using Finite Element Analysis

Vertical deflection has been emphasized as an important safety indicator in the management of railway bridges. Therefore, various standards and studies have suggested physics-based models for predicting the time-dependent deflection of railway bridges. However, these approaches may be limited by model errors caused by uncertainties in various factors, such as material properties, creep coefficient, and temperature. This study proposes a new Bayesian method that employs both a finite element model and actual measurement data. To overcome the limitations of an imperfect finite element model and a shortage of data, Gaussian process regression is introduced and modified to consider both, the finite element analysis results and actual measurement data. In addition, the probabilistic prediction model can be updated whenever additional measurement data is available. In this manner, a probabilistic prediction model, that is customized to a target bridge, can be obtained. The proposed method is applied to a pre-stressed concrete railway bridge in the construction stage in the Republic of Korea, as an example of a bridge for which accurate time-dependent deflection is difficult to predict, and measurement data are insufficient. Probabilistic prediction models are successfully derived by applying the proposed method, and the corresponding prediction results agree with the actual measurements, even though the bridge experienced large downward deflections during the construction stage. In addition, the practical uses of the prediction models are discussed

On Nonlinear Cointegration Methods for Structural Health Monitoring

Structural health monitoring (SHM) is emerging as a crucial technology for the assessment and management of important assets in various industries. Thanks to the rapid developments of sensing technology and computing machines, large amounts of sensor data are now becoming much easier and cheaper to obtain from monitored structures, which consequently has enabled data-driven methods to become the main work forces for real world SHM systems. However, SHM practitioners soon discover a major problem for in-service SHM systems; that is the effect of environmental and operational variations (EOVs). Most assets (bridges, aircraft engines, wind turbines) are so important that they are too costly to be isolated for testing and examination purposes. Often, their structural properties are heavily in uenced by ambient environmental and operational conditions, or EOVs. So, the most important question raised for an effective SHM system is, how one could tell whether an alarm signal comes from structural damage or from EOVs? Cointegration, a method originating from econometric time series analysis, has proven to be one of the most promising approaches to address the above question. Cointegration is a property of nonstationary time series, it models the long-run relationship among multiple nonstationary time series. The idea of employing the cointegration method in the SHM context relies on the fact that this long-run relationship is immune to the changes caused by EOVs, but when damage occurs, this relationship no longer stands. The work in this thesis aims to further strengthen and extend conventional linear cointegration methods to a nonlinear context, by hybridising cointegration with machine learning and time series models. There are three contributions presented in this thesis: The first part is about a nonlinear cointegration method based on Gaussian process (GP) regression. Instead of using a linear regression, this part attempts to establish a nonlinear cointegrating regression with a GP. GP regression is a powerful Bayesian machine learning approach that can produce probabilistic predictions and avoid overfitting. The proposed method is tested with one simulated case study and with the Z24 Bridge SHM data. The second part concerns developing a regime-switching cointegration approach. Instead of modelling nonlinear cointegration as a smooth function, this part sees cointegration as a piecewise-linear function, which is triggered by some external variable. The model is trained with the aid of the augmented Dickey-Fuller (ADF) test statistics. Two case studies are presented in this part, one simulated mulitidegree-of-freedom system, and also the Z24 Bridge data. The third part of this work introduces a cointegration method for heteroscedastic data. Heteroscedasticity, or time-dependent noise is often observed in SHM data, normally caused by seasonal variations. In order to address this issue, the TBATS (an acronym for key features of the model: Trigonometric, Box-Cox transformation, ARMA error, Trend, Seasonal components) model is employed to decompose the seasonal-corrupted time series, followed by conventional cointegration analysis. A simulated cantilever beam and real measurement data from the NPL Bridge are used to validate the proposed method