Nonlinear Mixed-Effects Models for Repairable Systems Reliability

Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.

Linear mixed-effects model for longitudinal complex data with diversified characteristics

The increasing richness of data encourages a comprehensive understanding of economic and financial activities,where variables of interest may include not only scalar(point-like)indicators,but also functional(curve-like)and compositional(pie-like)ones.In many research topics,the variables are also chronologically collected across individuals,which falls into the paradigm of longitudinal analysis.The complicated nature of data,however,increases the difficulty of modeling these variables under the classic longitudinal frame-work.In this study,we investigate the linear mixed-effects model(LMM)for such complex data.Different types of variables arefirst consistently represented using the corresponding basis expansions so that the classic LMM can then be conducted on them,which gener-alizes the theoretical framework of LMM to complex data analysis.A number of simulation studies indicate the feasibility and effectiveness of the proposed model.We further illustrate its practical utility in a real data study on Chinese stock market and show that the proposed method can enhance the performance and interpretability of the regression for complex data with diversified characteristics.

BLUP Estimation of Linear Mixed-effects Models with Measurement Errors and Its Applications to the Estimation of Small Areas

The linear mixed-effects model （LMM） is a very useful tool for analyzing cluster data. In practice, however, the exact values of the variables are often difficult to observe. In this paper, we consider the LMM with measurement errors in the covariates. The empirical BLUP estimator of the linear combination of the fixed and random effects and its approximate conditional MSE are derived. The application to the estimation of small area is provided. Simulation study shows good performance of the proposed estimators.

Maximum likelihood estimation of nonlinear mixed-effects models with crossed random effects by combining first-order conditional linearization and sequential quadratic programming

Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.

Comparison of isotope-based linear and Bayesian mixing models in determining moisture recycling ratio

Stable water isotopes are natural tracers quantifying the contribution of moisture recycling to local precipitation,i.e.,the moisture recycling ratio,but various isotope-based models usually lead to different results,which affects the accuracy of local moisture recycling.In this study,a total of 18 stations from four typical areas in China were selected to compare the performance of isotope-based linear and Bayesian mixing models and to determine local moisture recycling ratio.Among the three vapor sources including advection,transpiration,and surface evaporation,the advection vapor usually played a dominant role,and the contribution of surface evaporation was less than that of transpiration.When the abnormal values were ignored,the arithmetic averages of differences between isotope-based linear and the Bayesian mixing models were 0.9%for transpiration,0.2%for surface evaporation,and–1.1%for advection,respectively,and the medians were 0.5%,0.2%,and–0.8%,respectively.The importance of transpiration was slightly less for most cases when the Bayesian mixing model was applied,and the contribution of advection was relatively larger.The Bayesian mixing model was found to perform better in determining an efficient solution since linear model sometimes resulted in negative contribution ratios.Sensitivity test with two isotope scenarios indicated that the Bayesian model had a relatively low sensitivity to the changes in isotope input,and it was important to accurately estimate the isotopes in precipitation vapor.Generally,the Bayesian mixing model should be recommended instead of a linear model.The findings are useful for understanding the performance of isotope-based linear and Bayesian mixing models under various climate backgrounds.

Database-oriented storage based on LMDB and linear octree for massive block model

Data organization requires high efficiency for large amount of data applied in the digital mine system. A new method of storing massive data of block model is proposed to meet the characteristics of the database, including ACID-compliant, concurrency support, data sharing, and efficient access. Each block model is organized by linear octree, stored in LMDB（lightning memory-mapped database）. Geological attribute can be queried at any point of 3D space by comparison algorithm of location code and conversion algorithm from address code of geometry space to location code of storage. The performance and robustness of querying geological attribute at 3D spatial region are enhanced greatly by the transformation from 3D to 2D and the method of 2D grid scanning to screen the inner and outer points. Experimental results showed that this method can access the massive data of block model, meeting the database characteristics. The method with LMDB is at least 3 times faster than that with etree, especially when it is used to read. In addition, the larger the amount of data is processed, the more efficient the method would be.

Unified Breakdown Model of SOI RESURF Device with Uniform/Step/Linear Doping Profile

A unified breakdown model of SOI RESURF device with uniform,step,or linear drift region doping profile is firstly proposed.By the model,the electric field distribution and breakdown voltage are researched in detail for the step numbers from 0 to infinity.The critic electric field as the function of the geometry parameters and doping profile is derived.For the thick film device,linear doping profile can be replaced by a single or two steps doping profile in the drift region due to a considerable uniformly lateral electric field,almost ideal breakdown voltage,and simplified design and fabrication.The availability of the proposed model is verified by the good accordance among the analytical results,numerical simulations,and reported experiments.

A New Class of Biased Linear Estimators in Deficient-rank Linear Models

In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.

T-S-fuzzy-model-based quantized control for nonlinear networked control systems

In order to overcome data-quantization, networked-induced delay, network packet dropouts and wrong sequences in the nonlinear networked control system, a novel nonlinear networked control system model is built by the T-S fuzzy method. Two time-varying quantizers are added in the model. The key analysis steps in the method are to construct an improved interval-delay-dependent Lyapunov functional and to introduce the free-weighting matrix. By making use of the parallel distributed compensation technology and the convexity of the matrix function, the improved criteria of the stabilization and stability are obtained. Simulation experiments show that the parameters of the controllers and quantizers satisfying a certain performance can be obtained by solving a set of LMIs. The application of the nonlinear mass-spring system is provided to show that the proposed method is effective.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

A Study on the Multi-Compartment Linear Circulation Pharmacokinetic Model for the Targeting Drug Delivery System

By analyzing the observed phenomena and the data collected in the study, a multi-compartment linear circulation model for targeting drug delivery system was developed and the function formulas of the drug concentration-time in blood and target organ by computing were figured out. The drug concentration-time curve for target organ can be plotted with reference to the data of drug concentration in blood according to the model. The pharmacokinetic parameters of the drug in target organ could also be obtained. The practicability of the model was further checked by the curves of drug concentration-time in blood and target organ(liver) of liver-targeting nanoparticles in animal tests. Based on the liver drug concentration-time curves calculated by the function formula of the drug in target organ, the pharmacokinetic behavior of the drug in target organ(liver) was analyzed by statistical moment, and its pharmacokinetic parameters in liver were obtained. It is suggested that the (relative targeting index( can be used for quantitative evaluation of the targeting drug delivery systems.

Research on a non-linear chaotic prediction model for urban traffic flow

In order to solve serious urban transport problems, according to the proved chaotic characteristic of traffic flow, a non linear chaotic model to analyze the time series of traffic flow is proposed. This model reconstructs the time series of traffic flow in the phase space firstly, and the correlative information in the traffic flow is extracted richly, on the basis of it, a predicted equation for the reconstructed information is established by using chaotic theory, and for the purpose of obtaining the optimal predicted results, recognition and optimization to the model parameters are done by using genetic algorithm. Practical prediction research of urban traffic flow shows that this model has famous predicted precision, and it can provide exact reference for urban traffic programming and control.

Ecoregional height-diameter models for Scots pine in Turkiye

Ecoregion-based height-diameter models were developed in the present study for Scots pine(Pinus sylves-tris L.)stands in Turkiye and included several ecological factors derived from a pre-existing ecoregional classification system.The data were obtained from 2831 sample trees in 292 sample plots.Ten generalized height–diameter models were developed,and the best model(HD10)was selected according to statistical criteria.Then,nonlinear mixed-effects modeling was applied to the best model.The R2 for the generalized height‒diameter model(Richards function)modified by Sharma and Parton is 0.951,and the final model included number of trees,dominant height,and diameter at breast height,with a random parameter associated with each ecoregion attached to the inverse of the mean basal area.The full model predictions using the nonlinear mixed-effects model and the reduced model(HD10)predictions were compared using the nonlinear sum of extra squares test,which revealed significant differences between ecore-gions;ecoregion-based height–diameter models were thus found to be suitable to use.In addition,using these models in appropriate ecoregions was very important for achieving reliable predictions with low prediction errors.

Selection of the Linear Regression Model According to the Parameter Estimation

In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.

Combined model based on optimized multi-variable grey model and multiple linear regression

The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.

The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model

The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition. The results indicate that the valid time period of TLM, during which TLM can be utilized to approximate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double—periodic condition the valid period of the TLM is shorter than that with the rigid—boundary condition. Key words Nonlinear stability and instability - Tangent linear model (TLM) - Validity This work was supported by the National Key Basic Research Project “Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters in China” (No.G1998040910) and the National Natural Science Foundation of China (No.49775262 and No.49823002).

Feedback linearization of the nonlinear model of a small-scale helicopter

In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for hovering control is presented. It is proved that the nonlinear system of the small-scale helicopter can be transformed to a linear system using the dynamic feedback linearization technique. Finally, simulations are carried out to validate the nonlinear controller.

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback linearization, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization problem of the model predictive controller significantly, which, however, is no longer linear in the presence of parameter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.

Contact Analysis and Modeling of Standing Wave Linear Ultrasonic Motor

A contact model for describing the contact mechanics between the stator and slider of the standing wave linear ultrasonic motor was presented. The proposed model starts from the assumption that the vibration characteristics of the stator is not affected by the contact process. A modified friction models was used to analyze the contact problems. Firstly, the dynamic normal contact force, interface friction force, and steady-state characteristics were analyzed. Secondly, the influences of the contact layer material, the dynamic characteristics of the stator, and the pre-load on motor performance were simulated. Finally, to validate the contact model, a linear ultrasonic motor based on in-plane modes was used as an example. The corresponding results show that a set of simulation of motor performances based on the proposed contact mechanism is in good agreement with experimental results. This model is helpful to understanding the operation principle of the standing wave linear motor and thus contributes to the design of these types of motor.

Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control

This paper proposes a new method for model predictive control （MPC） of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion （LDI） and linear matrix inequality （LMI） techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.