Xiaomo Jiang

Bayesian risk-based decision method for model validation under uncertainty

This paper develops a decision-making methodology for computational model validation, considering the risk of using the current model, data support for the current model, and cost of acquiring new information to improve the model. A Bayesian decision theory-based method is developed for this purpose, using a likelihood ratio as the validation metric for model assessment. An expected risk or cost function is defined as a function of the decision costs, and the likelihood and prior of each hypothesis. The risk is minimized through correctly assigning experimental data to two decision regions based on the comparison of the likelihood ratio with a decision threshold. A Bayesian validation metric is derived based on the risk minimization criterion. Two types of validation tests are considered: pass/fail tests and system response value measurement tests. The methodology is illustrated for the validation of reliability prediction models in a tension bar and an engine blade subjected to high cycle fatigue. The proposed method can effectively integrate optimal experimental design into model validation to simultaneously reduce the cost and improve the accuracy of reliability model assessment.

Bayesian validation assessment of multivariate computational models

Abstract Multivariate model validation is a complex decision-making problem involving comparison of multiple correlated quantities, based upon the available information and prior knowledge. This paper presents a Bayesian risk-based decision method for validation assessment of multivariate predictive models under uncertainty. A generalized likelihood ratio is derived as a quantitative validation metric based on Bayes’ theorem and Gaussian distribution assumption of errors between validation data and model prediction. The multivariate model is then assessed based on the comparison of the likelihood ratio with a Bayesian decision threshold, a function of the decision costs and prior of each hypothesis. The probability density function of the likelihood ratio is constructed using the statistics of multiple response quantities and Monte Carlo simulation. The proposed methodology is implemented in the validation of a transient heat conduction model, using a multivariate data set from experiments. The Bayesian methodology provides a quantitative approach to facilitate rational decisions in multivariate model assessment under uncertainty.

Bayesian structural equation modeling method for hierarchical model validation

A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.

Bayesian inference method for model validation and confidence extrapolation

This paper presents a Bayesian-hypothesis-testing-based methodology for model validation and confidence extrapolation under uncertainty, using limited test data. An explicit expression of the Bayes factor is derived for the interval hypothesis testing. The interval method is compared with the Bayesian point null hypothesis testing approach. The Bayesian network with Markov Chain Monte Carlo simulation and Gibbs sampling is explored for extrapolating the inference from the validated domain at the component level to the untested domain at the system level. The effect of the number of experiments on the confidence in the model validation decision is investigated. The probabilities of Type I and Type II errors in decision-making during the model validation and confidence extrapolation are quantified. The proposed methodologies are applied to a structural mechanics problem. Numerical results demonstrate that the Bayesian methodology provides a quantitative approach to facilitate rational decisions in model validation and confidence extrapolation under uncertainty.

Bayesian inference method for stochastic damage accumulation modeling

Abstract Damage accumulation based reliability model plays an increasingly important role in successful realization of condition based maintenance for complicated engineering systems. This paper developed a Bayesian framework to establish stochastic damage accumulation model from historical inspection data, considering data uncertainty. Proportional hazards modeling technique is developed to model the nonlinear effect of multiple influencing factors on system reliability. Different from other hazard modeling techniques such as normal linear regression model, the approach does not require any distribution assumption for the hazard model, and can be applied for a wide variety of distribution models. A Bayesian network is created to represent the nonlinear proportional hazards models and to estimate model parameters by Bayesian inference with Markov Chain Monte Carlo simulation. Both qualitative and quantitative approaches are developed to assess the validity of the established damage accumulation model. Anderson–Darling goodness-of-fit test is employed to perform the normality test, and Box–Cox transformation approach is utilized to convert the non-normality data into normal distribution for hypothesis testing in quantitative model validation. The methodology is illustrated with the seepage data collected from real-world subway tunnels.

Bayesian Wavelet Methodology for Damage Detection of Thermal Protection System Panels

This paper presents an intelligent computational methodology for loose-bolt detection in thermal protection panels, considering uncertainties in sensed data. The proposed methodology is based on the integration of a dynamic artificial neural network, wavelet signal analysis, and Bayesian probabilistic assessment. A dynamic fuzzy wavelet neural-network model is employed to perform the multiple-input/multiple-output nonparametric system identification of the panel using time-series data obtained from the panel under a healthy condition. The trained model is used to predict dynamic responses of the structural system under unknown conditions. Both predicted and sensed-time-history data are decomposed into multiple time-frequency resolutions using a discrete wavelet-packet transform method. The wavelet-packet component energy is computed in terms of the decomposed coefficients and used as a signal feature to detect loose bolts. The effectiveness of the selected features is assessed using both cross-correlation and cross-coherence metrics. The multivariate comparison in damage detection is handled by an interval-based Bayesian hypothesis-testing approach. The methodology is implemented to detect one loose bolt of a prototype thermal protection system panel with four mechanically bolted joints using experimental data collected at the U.S. Air Force Research Laboratory from seven different sensor configurations.

Tunnel waterproofing practices in China

Abstract Water ingress in transportation tunnels not only will shorten the durability of concrete lining and reduce the function of establishments in the tunnel, but also will worsen the tunnel surrounding so much that the traffic will be greatly affected. In this situation, therefore, high maintenance costs are compulsory. In many cases, a perfect appearance is strongly recommended to take measures in order to prevent leakage. However, in China, tunnel waterproof requirements and standards for various special uses are considerably different, such that the basis which engineers apply to design in water-control is insufficient. Especially in montanic region, unpleasant geological condition confines engineers in working out more reasonable methods to stop water seepage, even leakage. In this paper, the current waterproofing requirements and measures in different special tunnels adopted in China are reviewed. The limitations of the popular methods in several practical cases applied to prevent water leakage, such as watertight lining, drainage system, as well as grouting, are analyzed at length. Then, some available measures, regarding concrete lining, watertight layer, drainage establishments as well as casting watertight concrete, are proposed, which we think indispensable for tunnel engineering to efficiently control water seepage and even completely prevent water leakage. In the end, to analyze the seepage field in montanic tunnels, the finite element and boundary element coupling analysis method is presented. As an example, the seepage field in Zhenwushan tunnel of Chongqing is simulated. The calculation results coincide with the in-situ data well, and provide credible evidence for the waterproof measures which will be taken in that tunnel project. The method presented in this paper will save expenditures for surveying measures and will enable more reasonable and reliable waterproofing measures to be taken.

An investigation of Bayesian inference approach to model validation with non-normal data

Quantitative model validation is playing an increasingly important role in performance and reliability assessment of a complex system whenever computer modelling and simulation are involved. The foci of this paper are to pursue a Bayesian probabilistic approach to quantitative model validation with non-normality data, considering data uncertainty and to investigate the impact of normality assumption on validation accuracy. The Box–Cox transformation method is employed to convert the non-normality data, with the purpose of facilitating the overall validation assessment of computational models with higher accuracy. Explicit expressions for the interval hypothesis testing-based Bayes factor are derived for the transformed data in the context of univariate and multivariate cases. Bayesian confidence measure is presented based on the Bayes factor metric. A generalized procedure is proposed to implement the proposed probabilistic methodology for model validation of complicated systems. Classic hypothesis testing method is employed to conduct a comparison study. The impact of data normality assumption and decision threshold variation on model assessment accuracy is investigated by using both classical and Bayesian approaches. The proposed methodology and procedure are demonstrated with a univariate stochastic damage accumulation model, a multivariate heat conduction problem and a multivariate dynamic system.

Discussion of “A Wavelet Network Model for Short-Term Traffic Volume Forecasting”by Yuanchang Xie and Yunlong Zhang

This paper presents a Wavelet Network (WN) model for forecasting short-term traffic flow. The Levenberg-Marquardt learning algorithm is employed to train the WN model. Earlier, Jiang and Adeli (2005a) demonstrated that the Wavelet Neural Network (WNN) model outperformed the conventional neural network in traffic flow forecasting and elucidated several important issues regarding the WNN structure and wavelet type. First, the advantages of developing the WNN model for traffic flow forecasting need to be clarified. It is well known that the simple backpropagation neural network model has its inherent shortcomings such as lack of an efficient constructive model, slow convergence rate resulting in excessive computation time, and entrapment in a local minimum (Adeli, 2001). In contrast, the WNN model uses a wavelet function with a spatial-spectral zooming property, which influences the output of the model only in the finite range of input data. This property has two advantages for traffic flow forecasting: (1) it reduces the undesirable interaction effects among the nodes of the neural network, thus in general improving the accuracy of traffic forecasting, and (2) it accelerates the neural network training process, thus improving its computational efficiency in traffic forecasting. Second, it is necessary to clarify how to construct the WNN model. When wavelet transformation is integrated into the neural network to create a WNN model, three important issues need to be considered as follows:

Maintenance strategies optimisation of metro tunnels in soft soil

Abstract This paper proposes a quantitative approach for selecting effective maintenance strategies for metro tunnels in order to reduce maintenance cost and ensure tunnel safety in the presence of structural degradation during the service life. A non-stationary gamma process is used to simulate the tunnel gradual degradation and to investigate the effects of different maintenance measures on the life cycle maintenance cost of metro tunnels in soft soil. Two commonly applied reinforcement methods, Aramid Fibre Reinforced Polymer and bonded steel plate reinforcement, are investigated in this study. The feasibility of the proposed methodology is demonstrated with maintenance strategies based on periodic and aperiodic inspection policies. Numerical results show that the optimisation of maintenance strategy can reduce the life cycle maintenance cost of metro tunnels in soft soil while ensuring sufficient level of structural safety, and the maintenance strategy with aperiodic inspection policy produces lower maintenance cost.