Identification of marginal and joint CDFs using Bayesian method for RBDO

In RBDO, input uncertainty models such as marginal and joint cumulative distribution functions (CDFs) need to be used. However, only limited data exists in industry applications. Thus, identification of the input uncertainty model is challenging especially when input variables are correlated. Since input random variables, such as fatigue material properties, are correlated in many industrial problems, the joint CDF of correlated input variables needs to be correctly identified from given data. In this paper, a Bayesian method is proposed to identify the marginal and joint CDFs from given data where a copula, which only requires marginal CDFs and correlation parameters, is used to model the joint CDF of input variables. Using simulated data sets, performance of the Bayesian method is tested for different numbers of samples and is compared with the goodness-of-fit (GOF) test. Two examples are used to demonstrate how the Bayesian method is used to identify correct marginal CDFs and copula.     

Fitting marginal accelerated failure time models to clustered survival data with potentially informative cluster size

Methods for analyzing clustered survival data are gaining popularity in biomedical research. Naive attempts to fitting marginal models to such data may lead to biased estimators and misleading inference when the size of a cluster is statistically correlated with some cluster specific latent factors or one or more cluster level covariates. A simple adjustment to correct for potentially informative cluster size is achieved through inverse cluster size reweighting. We give a methodology that incorporates this technique in fitting an accelerated failure time marginal model to clustered survival data. Furthermore, right censoring is handled by inverse probability of censoring reweighting through the use of a flexible model for the censoring hazard. The resulting methodology is examined through a thorough simulation study. Also an illustrative example using a real dataset is provided that examines the effects of age at enrollment and smoking on tooth survival.     

Mixture cure models for multivariate survival data

Mixture cure models (MCMs) have been widely used to analyze survival data with a cure fraction. The MCMs postulate that a fraction of the patients are cured from the disease and that the failure time for the uncured patients follows a proper survival distribution, referred to as latency distribution. The MCMs have been extended to bivariate survival data by modeling the marginal distributions. In this paper, the marginal MCM is extended to multivariate survival data. The new model is applicable to the survival data with varied cluster size and interval censoring. The proposed model allows covariates to be incorporated into both the cure fraction and the latency distribution for the uncured patients. The primary interest is to estimate the marginal parameters in the mean structure, where the correlation structure is treated as nuisance parameters. The marginal parameters are estimated consistently by treating the observations within the cluster as independent. The variances of the parameters are estimated by the one-step jackknife method. The proposed method does not depend on the specification of correlation structure. Simulation studies show that the new method works well when the marginal model is correct. The performance of the MCM is also examined when the clustered survival times share common random effect. The MCM is applied to the data from a smoking cessation study.     

Identification test design for multivariable model-based control: An industrial perspective

The design of plant tests to generate data for identification of dynamic models is critically important for development of model-based process control systems. Multivariable process identification tests in industry continue to rely on uncorrelated input signals, even though investigations have shown the benefits of other input designs which lead to correlated, higher-amplitude input signals. This is partly due to difficulties in formulating and solving computationally tractable problems for identification test design. In this work, related results are summarized and extended. Connections between different designs that target D-optimality or integral controllability are established. Related concepts are illustrated through simulation case studies.     

Development of grey box state estimators for systems subjected to time correlated unmeasured disturbances

Unmeasured disturbances, which arise from uncertainties in the physical input sources, are commonly encountered in a process operation. For the purpose of developing Bayesian state estimators, such disturbances have been traditionally treated as Gaussian white noise processes. In practice, however, such disturbances are often correlated in time and the simplistic white noise assumption may not hold. Thus, to generate accurate estimates of the states, it is essential to obtain a reasonably accurate characterisation of the dynamics associated with the unmeasured disturbances. In this work, a systematic approach has been developed for identifying discrete time stochastic disturbance models, which captures the dynamics associated with such unmeasured disturbances. Under certain simplifying assumptions, the discrete time unmeasured disturbance models are combined with a continuous time mechanistic model to derive a discrete nonlinear grey box model. The grey box model is further used to formulate a nonlinear Bayesian state estimator. A constrained optimisation problem, that maximizes the log likelihood function of the innovation sequence generated by the state estimator, is formulated and solved for estimation of the parameters of the unmeasured disturbance model and the measurement noise covariance from the input–output data. The efficacy of this approach is demonstrated by simulating a benchmark continuous fermenter system and using experimental data obtained from a heater-mixer setup. The simulation studies demonstrate that the proposed approach is able to identify correlated disturbance models that closely match the characteristics of the true unmeasured disturbance models.     

A semiparametric bootstrap approach to correlated data analysis problems

In this note, we outline a simple to use yet powerful bootstrap algorithm for handling correlated outcome variables in terms of either hypothesis testing or confidence intervals using only the marginal models. This new method can handle combinations of continuous and discrete data and can be used in conjunction with other covariates in a model. The procedure is based upon estimating the family-wise error (FWE) rate and then making a Bonferroni-type correction. A simulation study illustrates the accuracy of the algorithm over a variety of correlation structures.     

一种多结构数据的同步拟合方法

计算机视觉领域,多结构模型参数的提取是一个常见任务。传统的提取算法一般先对输入数据集进行分类,然后通过对相关数据类的拟合获得对模型集参数的估计。然而,由于模型集未知,对如何实现数据集的准确划分一直是一个难点。针对这个问题,借鉴免疫系统识别抗原产生抗体的工作机理,提出了一种启发式的鲁棒回归分析方法。该方法将数据集的分类过程设计成一个逐步精确化的逼近过程：先通过随机抽样模型对数据集进行粗略划分,然后利用单模型鲁棒回归方法对各数据类中的优势数据进行尝试建模,以获得更好的模型估计。接着以此模型为基础重新对数据集进行划分,以提高分类的准确性。通过这种“分类”、“提纯”、“再分类”、“再提纯”的反复尝试,逐步逼近准确的数据类划分,同时得到模型集的准确解。仿真结果表明,该方法计算时间少,数据分类准确率高,具有较强的多结构模型参数提取能力。     

Confidence-based reliability assessment considering limited numbers of both input and output test data

Simulation-based methods can be used for accurate uncertainty quantification and prediction of the reliability of a physical system under the following assumptions: (1) accurate input distribution models and (2) accurate simulation models (including accurate surrogate models if utilized). However, in practical engineering applications, often only limited numbers of input test data are available for modeling input distribution models. Thus, estimated input distribution models are uncertain. In addition, the simulation model could be biased due to assumptions and idealizations used in the modeling process. Furthermore, only a limited number of physical output test data is available in the practical engineering applications. As a result, target output distributions, against which the simulation model can be validated, are uncertain and the corresponding reliabilities become uncertain as well. To assess the conservative reliability of the product properly under the uncertainties due to limited numbers of both input and output test data and a biased simulation model, a confidence-based reliability assessment method is developed in this paper. In the developed method, a hierarchical Bayesian model is formulated to obtain the uncertainty distribution of reliability. Then, we can specify a target confidence level. The reliability value at the target confidence level using the uncertainty distribution of reliability is the confidence-based reliability, which is the confidence-based estimation of the true reliability. It has been numerically demonstrated that the proposed method can predict the reliability of a physical system that satisfies the user-specified target confidence level, using limited numbers of input and output test data.     

Comparison between Karhunen–Loève expansion and translation-based simulation of non-Gaussian processes

The Karhunen–Loève (K–L) expansion has been successfully applied to the simulation of highly skewed non-Gaussian processes based on the prescribed covariance and marginal distribution functions. When the stationary random process is indexed over a domain that is much larger than the correlation distance, the K–L expansion will approach the spectral representation. The non-Gaussian K–L technique is applied in the popular spectral representation as a special case to facilitate comparison with translation-based spectral representation. Processes with both incompatible and compatible spectral density and marginal distribution functions are simulated numerically. It is demonstrated that K–L expansion can be used to address the situation with incompatible target functions where the commonly used translation approach may not be applicable. It is therefore a more robust method for simulation of non-Gaussian processes because it can generate different processes satisfying the same target spectral density function and the same target marginal distribution function regardless of their compatibility.     

The analysis of marked point patterns evolving through space and time

A maximum pseudo-likelihood approach has previously been developed for fitting pairwise interaction models to patterns generated by growth-interaction processes that are sampled at fixed time points. This approach is now extended, not only by estimating the parameters of the process through time, but also by employing least squares estimation since likelihood based approaches are much more computationally demanding. First, simple stochastic models are used to demonstrate that least squares methods are as powerful as likelihood-based approaches, as well as being mathematically and computationally simpler. The algorithm generates simulations of the deterministic growth-interaction and stochastic immigration-death process, and through these the parameter estimates are determined. Logistic and linear growth are then combined with (symmetric) disc-interaction and (asymmetric) area-interaction processes, and between them these generate a variety of mark-point spatial structures. A robustness study shows that the procedure works well in that the presence, structure and strength of a growth-interaction process can be determined even when an incorrectly presumed model is employed. Thus, the technique is likely to prove to be very useful in general practical applications where the underlying process generating mechanism is almost certain to be unknown. Finally, the procedure is applied to the analysis of a new Swedish pine forest data set for which tree location and diameter at breast height were recorded in 1985, 1990 and 1996.     

基于独立MMPP业务输入模型的输入／输出排队ATM交换机性能分析方法研究

本文针对现有ATM交换机性能分析中以Poisson或Bernoulli过程作为输入业务流模型的不足,提出了一种基于独立MMPP输入业务流模型的ATM交换机性能分析方法,由于采用了MMPP过程作为输入业务流模型,因此所给出的ATM交换机性能分析方法考虑了输入业务流本身的相关特性和突发特性,从而能够给出与实际情况更接近的ATM交换机性能分析结果。     

Multi-View AAM Fitting and Construction

Active Appearance Models (AAMs) are generative, parametric models that have been successfully used in the past to model deformable objects such as human faces. The original AAMs formulation was 2D, but they have recently been extended to include a 3D shape model. A variety of single-view algorithms exist for fitting and constructing 3D AAMs but one area that has not been studied is multi-view algorithms. In this paper we present multi-view algorithms for both fitting and constructing 3D AAMs. Fitting an AAM to an image consists of minimizing the error between the input image and the closest model instance; i.e. solving a nonlinear optimization problem. In the first part of the paper we describe an algorithm for fitting a single AAM to multiple images, captured simultaneously by cameras with arbitrary locations, rotations, and response functions. This algorithm uses the scaled orthographic imaging model used by previous authors, and in the process of fitting computes, or calibrates, the scaled orthographic camera matrices. In the second part of the paper we describe an extension of this algorithm to calibrate weak perspective (or full perspective) camera models for each of the cameras. In essence, we use the human face as a (non-rigid) calibration grid. We demonstrate that the performance of this algorithm is roughly comparable to a standard algorithm using a calibration grid. In the third part of the paper, we show how camera calibration improves the performance of AAM fitting. A variety of non-rigid structure-from-motion algorithms, both single-view and multi-view, have been proposed that can be used to construct the corresponding 3D non-rigid shape models of a 2D AAM. In the final part of the paper, we show that constructing a 3D face model using non-rigid structure-from-motion suffers from the Bas-Relief ambiguity and may result in a “scaled” (stretched/compressed) model. We outline a robust non-rigid motion-stereo algorithm for calibrated multi-view 3D AAM construction and show how using calibrated multi-view motion-stereo can eliminate the Bas-Relief ambiguity and yield face models with higher 3D fidelity. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Modeling and estimation of discrete-time Gaussian reciprocalprocesses

Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process     

Multi-model multivariate Gaussian process modelling with correlated noises

A composite multiple-model approach based on multivariate Gaussian process regression (MGPR) with correlated noises is proposed in this paper. In complex industrial processes, observation noises of multiple response variables can be correlated with each other and process is nonlinear. In order to model the multivariate nonlinear processes with correlated noises, a dependent multivariate Gaussian process regression (DMGPR) model is developed in this paper. The covariance functions of this DMGPR model are formulated by considering the “between-data” correlation, the “between-output” correlation, and the correlation between noise variables. Further, owing to the complexity of nonlinear systems as well as possible multiple-mode operation of the industrial processes, to improve the performance of the proposed DMGPR model, this paper proposes a composite multiple-model DMGPR approach based on the Gaussian Mixture Model algorithm (GMM-DMGPR). The proposed modelling approach utilizes the weights of all the samples belonging to each sub-DMGPR model which are evaluated by utilizing the GMM algorithm when estimating model parameters through expectation and maximization (EM) algorithm. The effectiveness of the proposed GMM-DMGPR approach is demonstrated by two numerical examples and a three-level drawing process of Carbon fiber production.     

Multi-output process identification

In model based control of multivariate processes, it has been common practice to identify a multi-input single-output (MISO) model for each output separately and then combine the individual models into a final MIMO model. If models for all outputs are independently parameterized then this approach is optimal. However, if there are common or correlated parameters among models for different output variables and/or correlated noise, then performing identification on all outputs simultaneously can lead to better and more robust models. In this paper, theoretical justifications for using multi-output identification for a multivariate process are presented and the potential benefits from using them are investigated via simulations on two process examples: a quality control example and an extractive distillation column. The identification of both the parsimonious transfer function models using multivariate prediction error methods, and of non-parsimonious finite impulse response (FIR) models using multivariate statistical regression methods such as partial least squares (PLS2), canonical correlation regression (CCR) and reduced rank regression (RRR) are considered. The multi-output identification results are compared to traditional single-output identification from several points of view: best predictions, closeness of the model to the true process, the precision of the identified models in frequency domain, stability robustness of the resulting model based control system, and multivariate control performance. The multi-output identification methods are shown to be superior to the single-output methods on the basis of almost all the criteria. Improvements in the prediction of individual outputs and in the closeness of the model to the true process are only marginal. The major benefits are in the stability and performance robustness of controllers based on the identified models. In this sense the multi-output identification methods are more ‘control relevant’.     

一类非线性时滞过程的传感器主动容错控制

通过结合非线性过程的一般模型控制(GMC)、强跟踪预测器(STP)和强跟踪滤波器(STF),本文提出了一类具有输入时滞非线性时变过程的传感器主动容错控制方法.基于强跟踪预测器对未来状态的预测,传统的一般模型控制被扩展到一类具有输入时滞的非线性过程.然后采用强跟踪滤波器估计过程状态及传感器偏差,传感器偏差估计用于驱动一个故障检测逻辑.当某一传感器故障被检测出来时,STF的状态估计值将用于重构过程输出(代替真实输出),此重构输出被STP用于继续进行状态预测,从而确保系统性能.最后,三容水箱系统仿真结果证明该方法的有效性.     

Vega环境中一种自由视点方式的开发

分析了Vega软件环境中的基本视点方式，并阐述了其工作原理。针对视景仿真系统中视点行为可被自由控制的需求，设计了一种自定义的运动模式，通过与视点和鼠标外设关联，实现了基于鼠标控制的自由视点方式，论述了这种视点方式的工作原理和开发方法。应用结果表明：此视点方式灵活、易用，极大增强了视景仿真实验效果，补充完善了Vega的视点功能。     

Flexible multivariate marginal models for analyzing multivariate longitudinal data,with applications in R

Most of the available multivariate statistical models dictate on fitting different parameters for the covariate effects on each multiple responses. This might be unnecessary and inefficient for some cases. In this article, we propose a modelling framework for multivariate marginal models to analyze multivariate longitudinal data which provides flexible model building strategies. We show that the model handles several response families such as binomial, count and continuous. We illustrate the model on the Kenya Morbidity data set. A simulation study is conducted to examine the parameter estimates. An R package mmm2 is proposed to fit the model.     

有色噪声干扰下Hammerstein非线性系统两阶段辨识

针对实际工业过程中普遍存在有色噪声,提出了有色噪声干扰下Hammerstein非线性系统两阶段辨识方法。采用设计的组合式信号实现Hammerstein系统各模块参数辨识分离,简化了辨识过程。在第一阶段,基于可分离信号的输入输出数据,利用相关分析算法估计线性模块参数,减少了有色噪声对辨识的干扰。在第二阶段,基于随机信号的...     

Impact of correlated inputs on the output of the integrate- and-fire model

For the integrate-and-fire model with or without reversal potentials, we consider how correlated inputs affect the variability of cellular output. For both models, the variability of efferent spike trains measured by coefficient of variation (CV) of the interspike interval is a nondecreasing function of input correlation. When the correlation coefficient is greater than 0.09, the CV of the integrate-and-fire model without reversal potentials is always above 0.5, no matter how strong the inhibitory inputs. When the correlation coefficient is greater than 0.05, CV for the integrate-and-fire model with reversal potentials is always above 0. 5, independent of the strength of the inhibitory inputs. Under a given condition on correlation coefficients, we find that correlated Poisson processes can be decomposed into independent Poisson processes. We also develop a novel method to estimate the distribution density of the first passage time of the integrate-and-fire model.