Shape testing in varying coefficient models

We consider varying coefficient models which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (often time). Varying coefficient models have been popular in longitudinal data and panel data studies, and have been applied in fields, such as finance and health sciences. We estimate the coefficient functions by splines. An important question in a varying coefficient model is whether a coefficient function is monotone or convex. We develop consistent testing procedures for monotonicity and convexity. Moreover, we provide procedures to test simultaneously the shapes of certain coefficient functions in a varying coefficient model. The tests use constrained and unconstrained regression splines. The performances of the proposed tests are illustrated on simulated data. We also give a real data application.     

加权非线性随机系数模型异方差性的Score检验

在回归分析中，随机误差的方差齐性的假设往往有助于问题的解决，但方差齐性假设并不总是正确的。在线性和非线性回归中关于异方差的诊断问题已有许多讨论，在韦博成（1995）讨论的加权非线性回归模型的基础上，用随机系数的方法，讨论加权线性随机系统模型中的异方差检验问题，得到了方差齐性检验的Score统计量。     

Modeling of impact toughness of cold formed material by genetic programming

In the paper, an approach completely different from the conventional methods for determination of accurate models for the change of properties of cold formed material, is presented. This approach is genetic programming (GP) method which is based on imitation of natural evolution of living organisms. The main characteristic of GP is its non-deterministic way of computing. No assumptions about the form and size of expressions were made in advance, but they were left to the self organization and intelligence of evolutionary process. First, copper alloy rods were cold drawn under different conditions and then impact toughness of cold drawn specimens was determined by Charpy tests. The values of independent variables (effective strain, coefficient of friction) influence the value of the dependent variable, impact toughness. On the basis of training data, different prediction models for impact toughness were developed by GP. Only the best models, gained by genetic programming were presented in the paper. Accuracy of the best models was proved with the testing data set. The comparison between deviation of genetic model results and regression model results concerning the experimental results has showed that genetic models are more precise and more varied then regression models.     

A new neural network‐based model for hysteretic behavior of materials

Cyclic behavior of materials is complex and difficult to model. A combination of hardening rules in classical plasticity is one possibility for modeling this complex material behavior. Neural network (NN) constitutive models have been shown in the past to have the capability of modeling complex material behavior directly from the results of material tests. In this paper, we propose a novel approach for NN‐based modeling of the cyclic behavior of materials. The proposed NN material model uses new internal variables that facilitate the learning of the hysteretic behavior of materials. The same approach can also be used in modeling of the hysteretic behavior of structural systems or structural components under cyclic loadings. The proposed model is shown to be superior to the earlier versions of NN material models. Although the earlier versions of the NN material models were effective in capturing the multi‐axial material behavior, they were only tested under cyclic uni‐axial state of stress. The proposed NN material model is capable of learning the hysteretic behavior of materials under even non‐uniform stress state in multi‐dimensional stress space. The performance of the proposed model is demonstrated through a series of examples using actual experimental data and simulated testing data. Copyright © 2007 John Wiley & Sons, Ltd.     

单指标模型的异方差检验的渐近性质

在回归分析中,通常假定方差齐性。在参数和非参数回归模型中,关于方差齐性的检验问题都有很多的研究。本文利用P-样条方法,研究了单指标模型的异方差问题、一阶自回归问题,给出了异方差问题、一阶自回归问题Score检验统计量的大样本性质。     

线性相关及回归方程的动态计算模型

本文推证出线性相关的非统计判断的动态模型和与之相适应的回归方程动态计算模型．适合于对相关性数据进行实时处理．     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

Estimation of component failure probability from masked binomial system testing data

The component failure probability estimates from analysis of binomial system testing data are very useful because they reflect the operational failure probability of components in the field which is similar to the test environment. In practice, this type of analysis is often confounded by the problem of data masking: the status of tested components is unknown. Methods in considering this type of uncertainty are usually computationally intensive and not practical to solve the problem for complex systems. In this paper, we consider masked binomial system testing data and develop a probabilistic model to efficiently estimate component failure probabilities. In the model, all system tests are classified into test categories based on component coverage. Component coverage of test categories is modeled by a bipartite graph. Test category failure probabilities conditional on the status of covered components are defined. An EM algorithm to estimate component failure probabilities is developed based on a simple but powerful concept: equivalent failures and tests. By simulation we not only demonstrate the convergence and accuracy of the algorithm but also show that the probabilistic model is capable of analyzing systems in series, parallel and any other user defined structures. A case study illustrates an application in test case prioritization.     

An Analysis of the Factors Influencing the Data Derived from a Plug Type Three-Dimensional Strain Rosette under Compression and Torsion

Abstract:  The embedding of three-dimensional strain rosettes embedded into epoxy models provides an experimental technique for analysing complex structures; however, this technique has been known to produce data that were difficult to explain in terms of their physical significance. To gain a greater insight into the behaviour of a three-dimensional strain rosette used in this way, a three-dimensional strain rosette was embedded into each of two separate prismatic bars of square cross-section and subjected to fundamental tests of compression and torsion in standard commercial testing machines. In initial tests on a bar containing a three-dimensional strain rosette (Bar A) the data derived from the individual gauges sometimes departed from the theoretical values by more that 30  μ e. After critical evaluation of the procedures used for making and testing Bar A, further tests were carried out on Bar B, which led to a reduction in the difference between theoretical and experimental data to 14  μ e, acceptable for most practical purposes. The use of square plugs containing three-dimensional strain rosettes which are embedded into square cavities in the model, and the measurement of the actual direction cosines of the gauges on the square plug prior to embedment is a distinct advantage over the use of cylindrical plugs. In addition, the use of testing machines with a fixed base as opposed to a floating lower platen is recommended.     

Multiple predictor smoothing methods for sensitivity analysis: Example results

The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described in the first part of this presentation: (i) locally weighted regression (LOESS), (ii) additive models, (iii) projection pursuit regression, and (iv) recursive partitioning regression. In this, the second and concluding part of the presentation, the indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present.     

Spin velocimeters for impact debris fragments

An experimental technique for determining the velocity of individual debris fragments from hypervelocity impacts and correlating these velocity data to fragment size is presented. Design trades and experimental results for fragment spin velocimeters based on this technique are also presented. Validation tests were conducted to verify and optimize the performance of these instruments, and they were subsequently used to collect data for four hypervelocity impact tests. Such data are critical to the development of accurate debris environment models and to support safety hazard analyses of flight tests involving impacts. Comparisons with model predictions are presented.     

Bayesian approach to the analysis of fluorescence correlation spectroscopy data I: theory

Fluorescence correlation spectroscopy (FCS) is a powerful tool to infer the physical process of macromolecules including local concentration, binding, and transport from fluorescence intensity measurements. Interpretation of FCS data relies critically on objective multiple hypothesis testing of competing models for complex physical processes that are typically unknown a priori. Here, we propose an objective Bayesian inference procedure for testing multiple competing models to describe FCS data based on temporal autocorrelation functions. We illustrate its performance on simulated temporal autocorrelation functions for which the physical process, noise, and sampling properties can be controlled completely. The procedure enables the systematic and objective evaluation of an arbitrary number of competing, non-nested physical models for FCS data, appropriately penalizing model complexity according to the Principle of Parsimony to prefer simpler models as the signal-to-noise ratio decreases. In addition to eliminating overfitting of FCS data, the procedure dictates when the interpretation of model parameters are not justified by the signal-to-noise ratio of the underlying sampled data. The proposed approach is completely general in its applicability to transport, binding, or other physical processes, as well as spatially resolved FCS from image correlation spectroscopy, providing an important theoretical foundation for the automated application of FCS to the analysis of biological and other complex samples.     

Multiple predictor smoothing methods for sensitivity analysis: Description of techniques

The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described: (i) locally weighted regression (LOESS), (ii) additive models, (iii) projection pursuit regression, and (iv) recursive partitioning regression. Then, in the second and concluding part of this presentation, the indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present.     

Modeling of the material behavior during hot hydroforming

For the purpose of numerically simulating metal forming processes, material data are necessary, determined by testing procedures similar to the particular process. The new technology of hot tube bulge tests has been introduced recently, fulfilling the requirements of material data determination for hot hydroforming. Based on measurement data gained by this technology, selected constitutive relations for approximating the flow stress depending on temperature, strain rate and logarithmic strain were parameterized applying linear regression analysis. Using the material law with the best approximation quality among the regarded equations, a numerical simulation of an exemplary forming process was accomplished. A comparison between the experimentally obtained geometry after a hot hydroforming process and the prediction by numerical analysis is used for evaluating the quality and applicability of the determined material data for this kind of process. Additionally, a process simulation, using extrapolated material data from compression tests is presented to visualize the influence of the testing procedure on the resulting part geometry prediction.     

Flight-by-flight fatigue crack growth life assessment

Conventionally, fatigue crack growth in aircraft structures under flight spectrum loading is often analysed and predicted based on crack growth rates obtained from constant-amplitude crack growth testing with cycle-by-cycle life prediction methods or models. Because the mechanism of fatigue crack growth under spectrum loading is yet to be fully understood, no matter how closely the models are able to account for the load interaction effects, the predictions generally have to be subjected to the validation by fatigue crack growth tests using either representative specimens or real structures under the representative flight spectrum. In view of this fact, it is not difficult to deduce that the predictions should be much more reliable if the predictions are made directly based on the flight spectrum crack growth data. Therefore, a new approach to fatigue crack growth life assessment has been proposed in this paper based on the analysis of flight-by-flight fatigue crack growth data measured by quantitative fractography for several common aircraft structural materials under various fighter aircraft flight spectra. Quantitative fractography was successfully used for titanium coupons to generate crack growth curves under flight spectrum loading. The crack growths were also shown to be exponential. As a demonstration, the flight-by-flight approach was used to determine fatigue crack growth lives of aircraft aft fuselage frames under a fighter aircraft usage.     

Multiple Testing in Regression Models With Applications to Fault Diagnosis in the Big Data Era

Motivated by applications to root-cause identification of faults in multistage manufacturing processes that involve a large number of tools or equipment at each stage, we consider multiple testing in regression models whose outputs represent the quality characteristics of a multistage manufacturing process. Because of the large number of input variables that correspond to the tools or equipments used, this falls in the framework of regression modeling in the modern era of big data. On the other hand, with quick fault detection and diagnosis followed by tool rectification, sparsity can be assumed in the regression model. We introduce a new approach to address the multiple testing problem and demonstrate its advantages over existing methods. We also illustrate its performance in an application to semiconductor wafer fabrication that motivated this development. Supplementary materials for this article are available online.     

Prediction of strength parameters of FRP-confined concrete

This research deals with the prediction of compressive strength and crushing strain of FRP-confined concrete using neural networks and regression models. Basic information on neural networks and the types of neural networks most suitable for the analysis of experimental results are given. A set of experimental data, covering a large range of parameters, for the training and testing of neural networks is used. The prediction models based on neural network are presented. The influence of raw and the non-dimensional group of variables on compressive strength and crushing strain of FRP-confined concrete is studied through sensitivity analysis, which provided a basis for the development of a new regression based model. The neural networks based model gave high prediction accuracy and the results demonstrated that the use of neural networks in assessing the compressive strength and crushing strain of FRP-confined concrete is both practical and beneficial.     

Patient‐Specific Finite Element Modelling and Validation of Porcine Femora in Torsion

The accuracy of biomechanical simulation has been improved by using high‐resolution computed tomography (CT) to define the geometry and material parameters. This technique has been used to assess numerous systems, including the mechanical properties of bone, fixation techniques post‐fracture and the performance of bone microarchitecture. In this study, a semi‐automated process for converting CT data into finite element (FE) models was used to model the mid‐shaft (diaphysis) of porcine femoral samples under sub‐maximal torsional and compressive load. Physical validation was undertaken to investigate if the all‐important geometry and material property mapping functioned correctly. Porcine femoral specimens were imaged using contiguous helical CT, which was converted to FE models using ScanIP from Simpleware, Exeter, UK. The heterogeneous material properties were estimated using density–elasticity relationships proposed in literature for human bone samples. Laboratory testing performed favourably, with a linear strain response validating the use of the array of linear material models used in simulation. The simulation procedure also performed well. Linear regression and mean error calculation demonstrated accurate correlation between predicted (from simulation) and observed (measured within the laboratory) results that offered improvement over the accuracy within comparative testing for human samples. Using FE modelling on a patient‐specific basis offers potential in a number of scenarios, including the determination of injury risk and design of protective equipment. The increased accessibility of animal samples allows large‐scale fracture testing of complex loading mechanisms and the potential to consider younger animal samples (to investigate the behaviour of developing bone). Spiral fractures of long bones have been demonstrated to be an indicator of non‐accidental injury in children. Combining the increased accuracy in torsional simulation in this study with younger sample testing may be employed to attempt to determine the causes of fracture from post fracture scans, aiding in the diagnosis of non‐accidental injury.     

Surface roughness predictive modeling: neural networks versus regression

Surface roughness plays an important role in product quality and manufacturing process planning. This research focuses on developing an empirical model for surface roughness prediction in finish turning. The model considers the following working parameters: work-piece hardness (material), feed, cutter nose radius, spindle speed and depth of cut. Two competing data mining techniques, nonlinear regression analysis and computational neural networks, are applied in developing the empirical models. The values of surface roughness predicted by these models are then compared with those from some of the representative models in the literature. Metal cutting experiments and tests of hypothesis demonstrate that the models developed in this research have a satisfactory goodness of fit. It has also presented a rigorous procedure for model validation and model comparison. In addition, some future research directions are outlined.