Evaluation of Kriging-NARX Modeling for Uncertainty Quantification of Nonlinear SDOF Systems with Degradation

2021 ◽  
pp. 2150060
Author(s):  
Xiaoshu Gao ◽  
Hetao Hou ◽  
Liang Huang ◽  
Guangquan Yu ◽  
Cheng Chen
Keyword(s):  
Uncertainty Quantification ◽  
Performance Indicator ◽  
Kriging Model ◽  
Least Angle Regression ◽  
Ground Motion Model ◽  
Narx Models ◽  
Form Model ◽  
Input Form ◽  
Nonlinear Autoregressive ◽  
Narx Model

Structural assessment for collapse is commonly approached by observing the failure or collapse of systems fully incorporating degradation. Challenges however exist in the performance indicator or damage measure due to compound impacts of uncertainties of external (seismic excitation) and internal (structural properties) characteristics with degradation behavior. To account for the impacts of uncertainties, the state-of-the-art kriging nonlinear autoregressive with exogenous (NARX) model is explored in this study to replicate the response of nonlinear single-degree-of-freedom systems. The generalized hysteretic Bouc-Wen model with internal uncertainties is selected to emulate the stiffness and strength degradation. A probabilistic stochastic ground motion model is introduced to represent the external uncertainties. The global terms of NARX model are selected by least-angle regression algorithm and the kriging model is utilized to surrogate uncertain parameters into corresponding NARX model coefficients. The predictions of kriging NARX models are further compared with that of the polynomial chaos nonlinear autoregressive with exogenous input form model as well as Monte Carlo simulation. The comparisons show that kriging NARX model presents an effective and efficient meta-model technique for uncertainty quantification of systems with degradation.

NARX Neural Networks Model for Forecasting Daily Patient Arrivals in the Emergency Department

2020 ◽  
pp. 1-18
Author(s):  
Melih Yucesan ◽  
Suleyman Mete ◽  
Faruk Serin ◽  
Erkan Celik ◽  
Muhammet Gul
Keyword(s):  
Emergency Department ◽  
Network Architecture ◽  
Waiting Times ◽  
Bayesian Regularization ◽  
Mean Square ◽  
Data Set ◽  
Levenberg Marquardt ◽  
Narx Models ◽  
Nonlinear Autoregressive ◽  
Narx Model

Regarding measuring of service quality at the emergency departments (ED), essential parameters are length of stay (LOS) and waiting times. Patient arrivals, which is related to LOS and waiting times, is hard to forecast and is affected by many parameters. Therefore, authors employed a Nonlinear Autoregressive Exogenous (NARX) model for forecasting of ED arrivals. NARX models are used extensively in many applications that show non-linear and dynamic behavior, but as far as authors know, the NARX method has not yet been used in the forecast of ED arrivals before. In this study, calendar and climatic variables are defined as input parameters. Patient Arrivals is defined as output parameter. A commercial software, MATLAB, was used to train and test the data set. To find the best network architecture Levenberg-Marquardt (LM) and Bayesian Regularization (BR) algorithms, different lags, and number of neurons were tested. R-squared and mean square error (MSE) are used to evaluate the accuracy of the tested networks.

Application of nonlinear autoregressive neural network to estimation of global solar radiation over Nigeria

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Olusola Samuel Ojo ◽  
Babatunde Adeyemi
Keyword(s):  
Neural Network ◽  
Solar Radiation ◽  
Global Solar Radiation ◽  
Surface Data ◽  
Narx Models ◽  
Sahel Region ◽  
Nonlinear Autoregressive ◽  
Narx Model ◽  
Mlr Model ◽  
Autoregressive Neural Network

In this paper, surface data meteorological were used as input variables to create, train and validate the network in which global solar radiation serves as a target. These surface data were obtained from the archives of the European centre for Medium-Range weather forecast for a span of 36 years (1980-2015) over Nigeria. The research aims to evaluate the predictive ability of the nonlinear autoregressive neural network with exogenous input (NARX) model compared with the multivariate linear regression (MLR) model using the statistical metrics. Model selection analysis using the index of agreement (dr) metric showed that the MLR and NARX models have values of 0.710 and 0.853 in the Sahel, 0.748 and 0.849 in the Guinea Savannah, 0.664 and 0.791 in the Derived Savannah, 0.634 and 0.824 in the Coastal regions, and 0.771 and 0.806 in entire Nigeria respectively. Meanwhile, error analyses of the models using root mean square errors (RMSE) showed the values of 1.720 W/m2 and 1.417 in the Sahel region, 2.329 W/m2 and 1.985 W/m2 in the Guinea Savannah region, 2.459 W/m2 and 2.272 W/m2 in the Derived Savannah region, 2.397 W/m2 and 2.261 W/m2 in the Coastal region and 1.691 W/m2 and 1.600 W/m2 in entire Nigeria for MLR and NARX models respectively. These showed that the NARX model has higher dr values and lower RMSE values over all the climatic regions and entire Nigeria than the MLR model. Finally, it can be inferred from these metrics that the NARX model gives a better prediction of global solar radiation than the traditional common MLR models in all the zones in Nigeria.

scholarly journals Improved Rainfall Prediction through Nonlinear Autoregressive Network with Exogenous Variables: A Case Study in Andes High Mountain Region

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Mario Peña ◽  
Angel Vázquez-Patiño ◽  
Darío Zhiña ◽  
Martin Montenegro ◽  
Alex Avilés
Keyword(s):  
Linear Models ◽  
Hydrological Cycle ◽  
Decision Makers ◽  
Support Vector ◽  
High Mountain ◽  
Suitable Model ◽  
Exogenous Variables ◽  
Extreme Precipitation Events ◽  
Nonlinear Autoregressive ◽  
Narx Model

Precipitation is the most relevant element in the hydrological cycle and vital for the biosphere. However, when extreme precipitation events occur, the consequences could be devastating for humans (droughts or floods). An accurate prediction of precipitation helps decision-makers to develop adequate mitigation plans. In this study, linear and nonlinear models with lagged predictors and the implementation of a nonlinear autoregressive model with exogenous variables (NARX) network were used to predict monthly rainfall in Labrado and Chirimachay meteorological stations. To define a suitable model, ridge regression, lasso, random forest (RF), support vector machine (SVM), and NARX network were used. Although the results were “unsatisfactory” with the linear models, the specific direct influences of variables such as Niño 1 + 2, Sahel rainfall, hurricane activity, North Pacific Oscillation, and the same delayed rainfall signal were identified. RF and SVM also demonstrated poor performance. However, RF had a better fit than linear models, and SVM has a better fit than RF models. Instead, the NARX model was trained using several architectures to identify an optimal one for the best prediction twelve months ahead. As an overall evaluation, the NARX model showed “good” results for Labrado and “satisfactory” results for Chirimachay. The predictions yielded by NARX models, for the first six months ahead, were entirely accurate. This study highlighted the strengths of NARX networks in the prediction of chaotic and nonlinear signals such as rainfall in regions that obey complex processes. The results would serve to make short-term plans and give support to decision-makers in the management of water resources.

scholarly journals Enhanced Prediction of Solar Radiation Using NARX Models with Corrected Input Vectors

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2576 ◽  
Author(s):  
Eduardo Rangel ◽  
Erasmo Cadenas ◽  
Rafael Campos-Amezcua ◽  
Jorge L. Tena
Keyword(s):  
Wind Speed ◽  
Relative Humidity ◽  
Solar Radiation ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Relevant Information ◽  
Causality Tests ◽  
Narx Models ◽  
Persistence Model ◽  
Narx Model

The main objective of this work is to analyze and configure appropriately the input vectors to enhance the performance of NARX models to forecast solar radiation one hour ahead. For this study, Engle–Granger causality tests were implemented. Additionally, collinearity among the meteorological variables of the databases was examined. Different databases were used to test the contribution of these analyses in the improvement of the input vectors. For that, databases from three cities of Mexico with different climates were obtained, namely: Chihuahua, Temixco, and Zacatecas. These databases consisted of hourly measurements of the following variables: solar radiation (SR), wind speed (WS), relative humidity (RH), pressure (P), and temperature (T). Results showed that, in all three cases, proper NARX models were produced even when using input vectors formed only with solar radiation and temperature data. Consequently, it was inferred that pressure, wind speed, and relative humidity could be excluded from the input vectors of the forecasting models since, according to the causality tests, they did not provide relevant information to improve the solar radiation forecast in the studied cases. Conversely, these variables could generate spurious results. Forecasting results obtained with the NARX model were compared to the smart persistence model, commonly used to validate SR prediction. Error measures, such as mean absolute error (MAE) and root mean squared error (RMSE), were used to compare prediction results obtained from different models. In all cases, results obtained from the enhanced NARX model surpassed the results of the smart persistence, namely: in Chihuahua up to 11.5 % , in Temixco up to 15.7 % , and in Zacatecas up to 27.2 % .

scholarly journals Rainfall Prediction with AMSR-E Soil Moisture Products Using SM2RAIN and Nonlinear Autoregressive Networks with Exogenous Input (NARX) for Poorly Gauged Basins: Application to the Karkheh River Basin, Iran

2018 ◽  
Author(s):  
Majid Fereidoon ◽  
Manfred Koch
Keyword(s):  
Soil Moisture ◽  
River Basin ◽  
Land Surface ◽  
Daily Rainfall ◽  
Rainfall Data ◽  
Rainfall Prediction ◽  
Nonlinear Autoregressive ◽  
Karkheh River Basin ◽  
The Karkheh River ◽  
Narx Model

Accurate estimates of daily rainfall are essential for understanding and modeling the physical processes involved in the interaction between the land surface and the atmosphere. In this study, daily satellite soil moisture observations from the Advanced Microwave Scanning Radiometer - Earth Observing System (AMSR-E) generated by implementing the standard NASA- algorithm are employed for estimating rainfall, firstly, through the use of recently developed approach, SM2RAIN (Brocca et al., 2013) and, secondly, the nonlinear autoregressive network with exogenous inputs (NARX) neural modelling at five climate stations in the Karkheh river basin (KRB), located in southwest Iran. In the SM2RAIN method, the period 1 January 2003 to 31 December 2005 is used for the calibration of algorithm and the remaining 9 months from 1 January 2006 to 30 September 2006 is used for the validation of the rainfall estimates. In the NARX model, the full study period is split into a training (1 January 2003 to 31 September 2005) and a testing (1 September 2005 to 30 September 2006) stage. For the prediction of the rainfall as the desired target (output), relative soil moisture changes from AMSR-E and measured air temperature time series are chosen as exogenous (external) inputs in NARX. The quality of the estimated rainfall data is evaluated by comparing it with observed rainfall data at the five rain gauges in terms of the correlation coefficient R, the RMSE and the statistical bias. For the SM2RAIN method, R ranges between 0.44 and 0.9 for all stations, whereas for the NARX- model the values are generally slightly lower. Moreover, the values of the bias for each station indicate that although SM2RAIN is likely to underestimate large rainfall intensities, due to the known effect of soil moisture saturation, its biases are somewhat lower than those of NARX. In conclusion, the results of the present study show that with the use of AMSR-E soil moisture products in the physically based SM2RAIN- algorithm as well as in the NARX neural network, rainfall for poorly gauged regions can be fairly predicted.

scholarly journals Realized Volatility Forecasting with Neural Networks

2020 ◽  
Vol 18 (3) ◽  
pp. 502-531
Author(s):  
Andrea Bucci
Keyword(s):  
Neural Networks ◽  
Short Term Memory ◽  
Predictive Performance ◽  
Econometric Methods ◽  
Forecasting Method ◽  
Data Generating Process ◽  
Narx Models ◽  
Lstm Network ◽  
Nonlinear Behaviors ◽  
Nonlinear Autoregressive

Abstract In the last few decades, a broad strand of literature in finance has implemented artificial neural networks as a forecasting method. The major advantage of this approach is the possibility to approximate any linear and nonlinear behaviors without knowing the structure of the data generating process. This makes it suitable for forecasting time series which exhibit long-memory and nonlinear dependencies, like conditional volatility. In this article, the predictive performance of feed-forward and recurrent neural networks (RNNs) was compared, particularly focusing on the recently developed long short-term memory (LSTM) network and nonlinear autoregressive model process with eXogenous input (NARX) network, with traditional econometric approaches. The results show that RNNs are able to outperform all the traditional econometric methods. Additionally, capturing long-range dependence through LSTM and NARX models seems to improve the forecasting accuracy also in a highly volatile period.

Adaptive Kriging Method for Uncertainty Quantification of the Photoelectron Sheath and Dust Levitation on the Lunar Surface

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Xinpeng Wei ◽  
Jianxun Zhao ◽  
Xiaoming He ◽  
Zhen Hu ◽  
Xiaoping Du ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Lunar Surface ◽  
Kriging Model ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
Kriging Method ◽  
Photoelectron Sheath ◽  
The One ◽  
Adaptive Kriging ◽  
Dust Levitation

Abstract This paper presents an adaptive Kriging based method to perform uncertainty quantification (UQ) of the photoelectron sheath and dust levitation on the lunar surface. The objective of this study is to identify the upper and lower bounds of the electric potential and that of dust levitation height, given the intervals of model parameters in the one-dimensional (1D) photoelectron sheath model. To improve the calculation efficiency, we employ the widely used adaptive Kriging method (AKM). A task-oriented learning function and a stopping criterion are developed to train the Kriging model and customize the AKM. Experiment analysis shows that the proposed AKM is both accurate and efficient.

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