Local calibration of rigid pavement performance models using resampling methods

The performance prediction models in the Pavement-ME design software are nationally calibrated using in-service pavement material properties, pavement structure, climate and truck loadings, and performance data obtained from the Long-Term Pavement Performance programme. The nationally calibrated models may not perform well if the inputs and performance data used to calibrate those do not represent the local design and construction practices. Therefore, before implementing the new M-E design procedure, each state highway agency (SHA) should evaluate how well the nationally calibrated performance models predict the measured field performance. The local calibrations of the Pavement-ME performance models are recommended to improve the performance prediction capabilities to reflect the unique conditions and design practices. During the local calibration process, the traditional calibration techniques (split sampling) may not necessarily provide adequate results when limited number of pavement sections are available. Consequently, there is a need to employ statistical and resampling methodologies that are more efficient and robust for model calibrations given the data related challenges encountered by SHAs. The main objectives of the paper are to demonstrate the local calibration of rigid pavement performance models and compare the calibration results based on different resampling techniques. The bootstrap is a non-parametric and robust resampling technique for estimating standard errors and confidence intervals of a statistic. The main advantage of bootstrapping is that model parameters estimation is possible without making distribution assumptions. This paper presents the use of bootstrapping and jackknifing to locally calibrate the transverse cracking and IRI performance models for newly constructed and rehabilitated rigid pavements. The results of the calibration show that the standard error of estimate and bias are lower compared to the traditional sampling methods. In addition, the validation statistics are similar to that of the locally calibrated model, especially for the IRI model, which indicates robustness of the local model coefficients.     

Engineering-Driven Statistical Adjustment and Calibration

Engineering model development involves several simplifying assumptions for the purpose of mathematical tractability, which are often not realistic in practice. This leads to discrepancies in the model predictions. A commonly used statistical approach to overcome this problem is to build a statistical model for the discrepancies between the engineering model and observed data. In contrast, an engineering approach would be to find the causes of discrepancy and fix the engineering model using first principles. However, the engineering approach is time consuming, whereas the statistical approach is fast. The drawback of the statistical approach is that it treats the engineering model as a black box and therefore, the statistically adjusted models lack physical interpretability. This article proposes a new framework for model calibration and statistical adjustment. It tries to open up the black box using simple main effects analysis and graphical plots and introduces statistical models inside the engineering model. This approach leads to simpler adjustment models that are physically more interpretable. The approach is illustrated using a model for predicting the cutting forces in a laser-assisted mechanical micro-machining process. This article has supplementary material online.     

Influence of temperature on vibrational spectra and consequences for the predictive ability of multivariate models

Temperature, pressure, viscosity, and other process variables fluctuate during an industrial process. When vibrational spectra are measured on- or in-line for process analytical and control purposes, the fluctuations influence the shape of the spectra in a nonlinear manner. The influence of these temperature-induced spectral variations on the predictive ability of multivariate calibration model is assessed. Short-wave NIR spectra of ethanol/water/2-propanol mixtures are taken at different temperatures, and different local and global partial least-squares calibration strategies are applied. The resulting prediction errors and sensitivity vectors of a test set are compared. For data with no temperature variation, the local models perform best with high sensitivity but the knowledge of the temperature for prediction measurements cannot aid in the improvement of local model predictions when temperature variation is introduced. The prediction errors of global models are considerably lower when temperature variation is present in the data set but at the expense of sensitivity. To be able to build temperature-stable calibration models with high sensitivity, a way of explicitly modeling the temperature should be found.     

Development of a robust calibration model for nonlinear in-line process data

A comparative study involving a global linear method (partial least squares), a local linear method (locally weighted regression), and a nonlinear method (neural networks) has been performed in order to implement a calibration model on an industrial process. The models were designed to predict the water content in a reactor during a distillation process, using in-line measurements from a near-infrared analyzer. Curved effects due to changes in temperature and variations between the different batches make the problem particularly challenging. The influence of spectral range selection and data preprocessing has been studied. With each calibration method, specific procedures have been applied to promote model robustness. In particular, the use of a monitoring set with neural networks does not always prevent overfitting. Therefore, we developed a model selection criterion based on the determination of the median of monitoring error over replicate trials. The back-propagation neural network models selected were found to outperform the other methods on independent test data.     

Optimization in locally weighted regression

The application of locally weighted regression (LWR) to nonlinear calibration problems and strongly clustered calibration data often yields more reliable predictions than global linear calibration models. This study compares the performance of LWR that uses PCR and PLS regression, the Euclidean and Mahalanobis distance as a distance measure, and the uniform and cubic weighting of calibration objects in local models. Recommendations are given on how to apply LWR to near-infrared data sets without spending too much time in the optimization phase.     

Real-time inference of stochastic damage in composite materials

This study describes a control system designed for real-time monitoring of damage in materials that employs methods and models that account for uncertainties in experimental data and parameters in continuum damage mechanics models. The methodology involves (1) developing an experimental set-up for direct and indirect measurements of damage in materials; (2) modeling damage mechanics based constitutive equations for continuum models; and (3) implementation of a Bayesian framework for statistical calibration of model with quantification of uncertainties. To provide information for real-time monitoring of damage, indirect measurement of damage is made feasible using an embedded carbon nanotube (CNT) network to perform as sensor for detecting the local damage. A software infrastructure is developed and implemented in order to integrate the various constituents, such as finite element approximation of the continuum damage models, generated experimental data, and Bayesian-based methods for model calibration and validation. The outcomes of the statistical calibration and dynamic validation of damage models are presented. The experimental program designed to provide observational data is discussed.     

An analytical model for B-stage joining and co-curing of carbon fibre epoxy composites

The objective of this paper was to develop cure kinetic models to describe the B-stage curing and co-curing assembly of carbon fibre reinforced thermosetting polymer (CFRP) composites. Starting from the analytical model, temperature cycles and experimental procedures are developed to join a B-stage CFRP part to a reinforcing B-stage CFRP patch for local reinforcement. Our results show that by using the analytical model, one may precisely describe the cure reaction and join the composites without any additional adhesive. The co-cured composites were successfully manufactured with stable fibre volume fractions and glass transition temperatures between the two sub-components. Additionally, merits of the process, such as modifying reinforcing areas locally, or formation of net shape detail are discussed.     

A region-segmentation combining surrogate model based on L-indicator and N-fold cross-validation technique

For complex engineering problems, for which the mathematical models may be linear, low-order nonlinear or even high-order nonlinear, surrogate models which have high adaptability and accuracy are required. This article develops a method for constructing a region-segmentation combining surrogate model. It is based on the idea that in the entire experimental domain, different local regions may present different characteristics (linearity, low-order nonlinearity and high-order nonlinearity), and the entire domain should be divided into several subregions to be approximated by different surrogates so as to achieve high prediction accuracy in local regions. The preferred models in each subregion then constitute a weight-average combining surrogate model. The investigations reveal that the new model not only is more adaptive to analytically unknown functions, but also gives more accurate predictions. The method has been applied to three benchmark problems and a practical engineering problem, and the results maintain validity.     

Multiscale modeling of unsaturated flow of dual-scale fiber preform in liquid composite molding II: Non-isothermal flows

A novel multiscale approach is developed for modeling non-isothermal flows under unsaturated conditions in the dual-scale fabrics of liquid composite molding (LCM). The flow and temperature governing equations at the global or gap or inter-tow (∼m) level and the local or intra-tow (∼mm) levels are based on a previous dual-scale volume averaging method. To solve the coupled equations at two length-scales, a coarse global mesh is used to solve the global flow over the entire domain, and a fine local mesh in form of the unit-cell of periodic fabrics is employed to solve the local tow-impregnation process. (The latter is used to compute sink terms required for solving the former.) A multiscale algorithm based on the hierarchical computational grids is then proposed to solve the dual-scale flow under non-isothermal (but non-reactive) conditions. To test the proposed multiscale model, we first carry out a validation study in which the temperature histories predicted by the multiscale method are compared with experimental data available in a publication for a simple 1-D flow. Despite the lack of information about various model parameters, a reasonably good comparison with the experimental results is achieved. Then, the non-isothermal flow through a simple 1-D flow domain is carried out and the predictions of the multiscale simulation are compared with those of a previously published two-layer model. The multiscale predictions are found to be very similar to the two-layer predictions. A significant difference between the gap and tow temperatures is observed. The ratio of pore volumes in the tow and gap regions, thermal conductivity of the tows, and fiber types are identified as the important parameters for temperature distributions in the gap and tow regions. A further comparison with the single-scale flow simulation highlights significant differences between the conventional single-scale and the proposed dual-scale modeling approaches.     

Exploring the transferability of safety performance functions

Safety performance functions (SPFs), by predicting the number of crashes on roadway facilities, have been a vital tool in the highway safety area. The SPFs are typically applied for identifying hot spots in network screening and evaluating the effectiveness of road safety countermeasures. The Highway Safety Manual (HSM) provides a series of SPFs for several crash types by various roadway facilities. The SPFs, provided in the HSM, were developed using data from multiple states. In regions without local jurisdiction based SPFs it is common practice to adopt national SPFs for crash prediction. There has been little research to examine the viability of such national level models for local jurisdictions. Towards understanding the influence of SPF transferability, we examine the rural divided multilane highway models from Florida, Ohio, and California. Traffic, roadway geometry and crash data from the three states are employed to estimate single-state SPFs, two-state SPFs and three-state SPFs. The SPFs are estimated using the negative binomial model formulation for several crash types and severities. To evaluate transferability of models, we estimate a transfer index that allows us to understand which models transfer adequately to other regions. The results indicate that models from Florida and California seem to be more transferable compared to models from Ohio. More importantly, we observe that the transfer index increases when we used pooled data (from two or three states). Finally, to assist in model transferability, we propose a Modified Empirical Bayes (MEB) measure that provides segment specific calibration factors for transferring SPFs to local jurisdictions. The proposed measure is shown to outperform the HSM calibration factor for transferring SPFs.     

Thermo-mechanical sheet metal forming of aero engine components in Ti-6Al-4V – PART 1: Material characterisation

Ti-6Al-4V is one of the most frequently used titanium alloy in aerospace applications such as for load carrying engine structures, due to their high strength to weight ratio in combination with favourable creep resistance at moderate operating temperatures. In the virtual development process of designing suitable thermo-mechanical forming processes for titanium sheet metal components in aero engine applications numerical finite element (FE) simulations are desirable to perform. The benefit is related to the ability of securing forming concepts with respect to shape deviation, thinning and strain localisation. The reliability of the numerical simulations depends on both models and methods used as well as on the accuracy and applicability of the material input data. The material model and related property data need to be consistent with the conditions of the material in the studied thermo-mechanical forming process. In the present work a set of material tests are performed on Ti-6Al-4V at temperatures ranging from room temperature up to 560°C. The purpose is to study the mechanical properties of the specific batch of alloy but foremost to identify necessary material model requirements and generate experimental reference data for model calibration in order to perform FE-analyses of sheet metal forming at elevated temperatures in Ti-6Al-4V.     

Calibration of adhesion models based on Bayesian inference

The use of composite materials in a myriad of applications fostered the development of reliable procedures to connect components with adhesives. This led to a demand for reliable adhesion models to be used in engineering designs that are based on computer simulations. This paper presents a strategy to be used for calibration of adhesion models. The proposed methodology is built on the formalism of Statistical Inverse Problems. Uncertainties about the unknowns are inferred using Population-Based Markov Chain Monte Carlo and Adaptive Metropolis. It is proposed to perform model assessments based on the analysis of a validation metric. Realizations of the validation metric are computed with the posterior densities of model parameters that are provided by the calibration process. The analysis of the validation metric allows for model selection to be performed. Some numerical experiments are presented with noise-contaminated data. The calibration strategy proved effective when dealing with both the nonlinearity and nondifferentiability of the adhesion constitutive equation.     

一种热线式MAF传感器分段块联模型辨识

采用静态非线性函数与动态线性环节的块连接模型来描述热线式空气质量流量（MAF）传感器的动态特性,非线性环节用多项式表示,动态线性环节采用OE模型结构．基于静、动态标定实验数据,分别建立了热线式MAF传感器在正、负阶跃激励下各校准点的Hammerstein模型,并利用非建模数据对其进行了相互验证．通过合理选择分段区间,确定出热线式MAF传感器各工作区域的最佳局部动态数学模型．模型检验结果表明：基于Hammerstein模型的分段模型比由任意一组动态数据所建模型具有更高的预测精度．     

Development,characterization and analysis of auxetic structures from braided composites and study the influence of material and structural parameters

Auxetic materials are gaining special interest in technical sectors due to their attractive mechanical behaviour. This paper reports a systematic investigation on missing rib design based auxetic structures produced from braided composites for civil engineering applications. The influence of various structural and material parameters on auxetic and mechanical properties was thoroughly investigated. The basic structures were also modified with straight longitudinal rods to enhance their strengthening potential in structural elements. Additionally, a new analytical model was proposed to predict Poisson’s ratio through a semi empirical approach. Auxetic and tensile behaviours were also predicted using finite element analysis. The auxetic and tensile behaviours were observed to be more strongly dependent on their structural parameters than the material parameters. The developed analytical models could well predict the auxetic behaviour of these structures except at very low or high strains. Good agreement was also observed between the experimental results and numerical analysis.     

尖头弹侵彻延性金属靶板弹道极限的解析模型

现有的尖头弹侵彻金属靶板的弹道极限计算模型往往需要大量的试验数据和靶板材料的动态性能参数,且没有考虑侵彻速度对侵彻效果的影响,这给工程应用带来了很大的不便和误差。基于这一问题,考虑速度效应和靶板材料参数对侵彻的影响,结合流体动力学原理与动态空穴膨胀理论,分别提出了双模式和单模式侵彻模型。双模式侵彻模型的侵彻过程可分为两个阶段：流体动力变形阶段和塑性变形阶段,当侵彻速度小于靶材产生流体动力变形的临界速度时,侵彻进入塑性变形阶段,根据功能原理,建立了计算弹道极限的解析模型;单模式侵彻模型仅考虑塑性变形阶段。解析模型计算的弹道极限与弹道试验结果吻合的较好,且模型中不涉及弹道试验数据和靶板材料的动态性能参数,易于迅速求解,便于工程应用,可用于对延性金属靶板抗尖头弹侵彻能力的评估。     

Implicit constitutive modelling for viscoplasticity using neural networks

Up to now, a number of models have been proposed and discussed to describe a wide range of inelastic behaviours of materials. The fatal problem of using such models is however the existence of model errors, and the problem remains inevitably as far as a material model is written explicitly. In this paper, the authors define the implicit constitutive model and propose an implicit viscoplastic constitutive model using neural networks. In their modelling, inelastic material behaviours are generalized in a state-space representation and the state-space form is constructed by a neural network using input–output data sets. A technique to extract the input–output data from experimental data is also described. The proposed model was first generated from pseudo-experimental data created by one of the widely used constitutive models and was found to replace the model well. Then, having been tested with the actual experimental data, the proposed model resulted in a negligible amount of model errors indicating its superiority to all the existing explicit models in accuracy. © 1998 John Wiley & Sons, Ltd.     

Simulation of germanium detector calibration using the Monte Carlo method: comparison between point and surface source models

Simulation of detector calibration using the Monte Carlo method is very convenient. The computational calibration procedure using the MCNP code was validated by comparing results of the simulation with laboratory measurements. The standard source used for this validation was a disc-shaped filter where fission and activation products were deposited. Some discrepancies between the MCNP results and laboratory measurements were attributed to the point source model adopted. In this paper, the standard source has been simulated using both point and surface source models. Results from both models are compared with each other as well as with experimental measurements. Two variables, namely, the collimator diameter and detector-source distance have been considered in the comparison analysis. The disc model is seen to be a better model as expected. However, the point source model is good for large collimator diameter and also when the distance from detector to source increases, although for smaller sizes of the collimator and lower distances a surface source model is necessary.     

Development of regression equations for local calibration of rutting and IRI as predicted by the MEPDG models for flexible pavements using Ontario's long-term PMS data

Local calibration is an important step before a transportation agency adopts the American Association of State Highway and Transportation Officials' (AASHTO) mechanistic-empirical pavement design guide (MEPDG). This paper presents the challenges of and findings from the local calibration of flexible pavements in provincial highways under the jurisdiction of the Ministry of Transportation of Ontario (MTO). A calibration database was developed that involved a hierarchical framework of the input parameters required for AASHTOWare Pavement ME (the MEPDG software) and the historical field performance data based on the MTO's second-generation pavement management system. A regression analysis is carried out for preliminary calibration of rutting and international roughness index (IRI) models by comparing the predicted distress to observed distress. The analysis suggested that whereas the MEPDG provided fairly unbiased prediction of the IRI value, it often over-predicted the total rutting. Calibrated predicted IRI and rut depth are found for Ontario's local conditions from MEPDG distress prediction models. A further clustering analysis based on Functional Class and geographical zone for the rutting and IRI, respectively, improved the precision of the locally calibrated models.     

Bayesian uncertainty analysis with applications to turbulence modeling

In this paper, we apply Bayesian uncertainty quantification techniques to the processes of calibrating complex mathematical models and predicting quantities of interest (QoI's) with such models. These techniques also enable the systematic comparison of competing model classes. The processes of calibration and comparison constitute the building blocks of a larger validation process, the goal of which is to accept or reject a given mathematical model for the prediction of a particular QoI for a particular scenario. In this work, we take the first step in this process by applying the methodology to the analysis of the Spalart-Allmaras turbulence model in the context of incompressible, boundary layer flows. Three competing model classes based on the Spalart-Allmaras model are formulated, calibrated against experimental data, and used to issue a prediction with quantified uncertainty. The model classes are compared in terms of their posterior probabilities and their prediction of QoI's. The model posterior probability represents the relative plausibility of a model class given the data. Thus, it incorporates the model's ability to fit experimental observations. Alternatively, comparing models using the predicted QoI connects the process to the needs of decision makers that use the results of the model. We show that by using both the model plausibility and predicted QoI, one has the opportunity to reject some model classes after calibration, before subjecting the remaining classes to additional validation challenges.     

Simulated stiffness determination from simple compression tests on a thick laminate

A set of experimental compression tests were simulated with a 3D finite element (FE) model to evaluate a technique for determination of engineering constants (Young’s moduli and Poisson’s ratios). During the experiments prism specimens of E-glass UD weave/PET were compressed between parallel platens. The prisms were equipped with four 0°/90° strain gauges. The simulations include friction between prism and platens and measured specimen misalignment. The simulated stress/strain and strain/strain responses are in good agreement with the linear part of the experimental response. The simulations confirm that good estimates of engineering constants can be obtained by proper strain averaging and extrapolation of the non-oscillating last part of the differentiated stress/strain and strain/strain curves.