Statistical Linearization on 2 DOFs Hydropneumatic Suspension with Asymmetric Non-linear Stiffness

Most references on hydropneumatic suspension analysis regard it as harden Duffing spring and take the white noise as the system input, which is quite different from real physical model. It will introduce considerable errors to the analytical result compared with the numerical simulation which makes it impossible to give a good depiction of the hydropneumatic suspension dynamics. In this paper, the dynamic response of the hydropneumatic suspension is worked out using statistical linearization based on 2 DOFs nonlinear suspension model. The damping of the suspension and the tire stiffness are both regarded as linear components and the real road roughness spectrum is used to work out the system input. The explicit analytical equivalent stiffness, dynamic mean value offset from statistic equilibrium position and the sprung acceleration varied with parameters of hydropneumatic spring, road roughness and vehicle velocity are worked out by substituting the nonlinear stiffness of hydropneumatic spring with its first three terms Tyler series at the static equilibrium position using James formula. The comparison of the numerical simulation and analytical result both on statistical parameters and distribution shows the validity of the analysis. The explicit form provides a concise and valid method on hydropneumatic suspension design and optimization.

SEISMIC RANDOM VIBRATION ANALYSIS OF LOCALLY NONLINEAR STRUCTURES

A nonlinear seismic analysis method for complex frame structures subjected to sta- tionary random ground excitations is proposed.The nonlinear elasto-plastic behaviors may take place only on a small part of the structure.The Bouc-Wen differential equation model is used to model the hysteretic characteristics of the nonlinear components.The Pseudo Excitation Method (PEM)is used in solving the linearized random differential equations to replace the solution of the less efficient Lyapunov equation.Numerical results of a real bridge show that the method proposed is effective for practical engineering analysis.

LINEAR SUFFICIENCY IN THE GENERAL GAUSS-MARKOV MODEL

This paper provides further contributions to the theory of linear sufficiency in the general Gauss-Markov model E(y)=Xβ,Var (y)=V.The notion of linear sufficiency introduced by Baksalary and Kala(1981) and Drygas(1983) is extended for any specific estimable function c′β.Some general results with respect to the extended concept are obtained.An essential result concerning the former notion is a direct consequence of this paper.

Time Dependent Gaussian Equivalent Linearization of Duffing Oscillator Using Continuous Wavelet Transform

Evolutionary response analysis of Duffing oscillator using Gaussian equivalent linearization in wavelet based time-frequency frame work is presented here. Cubic （i.e., odd type） non-linearity associated with stiffness and damping is modeled. The goal of this research is to develop the mathematical model of an equivalent linear system which is applicable for different non-stationary input processes （i.e., either summation of amplitude modulated stationary orthogonal processes or digitally simulated non-stationary processes）. The instantaneous parameters of the ELTVS （equivalent linear time varying system） are evaluated by minimizing the error between the displacements of non-linear and equivalent linear systems in wavelet domain. For this purpose, three different basis functions （i.e., Mexican Hat, Morlet and a modified form of Littlewood-Paley） are used. The unknown parameters （i.e., natural frequency and damping） of the ELTVS are optimized in stochastic least square sense. Numerical results are presented for different types of input to show the applicability and accuracy of the proposed wavelet based linearization technique.

Quadrature Kalman particle fitler

In order to resolve the state estimation problem of nonlinear/non-Gaussian systems, a new kind of quadrature Kalman particle filter （QKPF） is proposed. In this new algorithm, quadrature Kalman filter （QKF） is used for generating the impor- tance density function. It linearizes the nonlinear functions using statistical linear regression method through a set of Gaussian- Hermite quadrature points. It need not compute the Jacobian matrix and is easy to be implemented. Moreover, the importantce density function integrates the latest measurements into system state transition density, so the approximation to the system poste- rior density is improved. The theoretical analysis and experimen- tal results show that, compared with the unscented partcle filter （UPF）, the estimation accuracy of the new particle filter is improved almost by 18%, and its calculation cost is decreased a little. So, QKPF is an effective nonlinear filtering algorithm.

Gaussian fluctuation for linear eigenvalue statistics of large dilute Wigner matrices

This paper focuses on the dilute real symmetric Wigner matrix Mn=1/√n（aij）n×n, whose offdiagonal entries aij （1 ≤ em ≠ j ≤ n） have mean zero and unit variance, Eaij4 =θnα （θ 〉 0） and the fifth moments of aij satisfy a Lindeberg type condition. When the dilute parameter 0 〈 α ≤ 1/3 and the test function satisfies some regular conditions, it proves that the centered linear eigenvalue statistics of Mn obey the central limit theorem.

Concordance Between Laboratories Testing Clinical Samples and Its Impact on Vaccine Booster Thresholds

Concordance study between two laboratories testing clinical samples is important to a clinical program to assess the comparability of test results, especially when the two laboratories performed the same test at different locations. Assays that measure immune response should not be compared using the simple linear regression model; instead literature publications recommend an ＂errors-in-variables＂ model that accounts for the variability in these assays （Home, 1998）. In this paper, concordance slope and intercept was estimated using the statistical linear relationship （Tan and Iglewicz, 1999） for various tests between laboratories. The confidence bounds for the concordance line were used to assess the impact on vaccine booster thresholds when a consistent bias was observed between the results generated by two laboratories.

Adaptive Ensemble Kalman Inversion with Statistical Linearization

The ensemble Kalman inversion(EKI),inspired by the well-known ensemble Kalman filter,is a derivative-free and parallelizable method for solving inverse problems.The method is appealing for applications in a variety of fields due to its low computational cost and simple implementation.In this paper,we propose an adaptive ensemble Kalman inversion with statistical linearization(AEKI-SL)method for solving inverse problems from a hierarchical Bayesian perspective.Specifically,by adaptively updating the unknown with an EKI and updating the hyper-parameter in the prior model,the method can improve the accuracy of the solutions to the inverse problem.To avoid semi-convergence,we employ Morozov’s discrepancy principle as a stopping criterion.Furthermore,we extend the method to simultaneous estimation of noise levels in order to reduce the randomness of artificially ensemble noise levels.The convergence of the hyper-parameter in prior model is investigated theoretically.Numerical experiments show that our proposed methods outperform the traditional EKI and EKI with statistical linearization(EKI-SL)methods.

Comparative Analysis of Curing Methods:Natural and Activated Lateritic Concrete

This work was on non-activated and activated lateritic soil used in proportions of 0%to 30%,to replace fine sand by wt.%,in the production of lateritic concrete.A mix of 1:2:4 was used,and the cube samples were cured in four(4)curing media of water,sand,polythene,and sawdust.The aim was to evaluate the effects of these curing methods on the mechanical strengths,and other properties of lateritic concrete.The sensitivity of the generated data was characterized statistically and developing linear regression models for predictions.For the Non-Activated Laterite soil(NALS,control mix(0%)),the design strength of 20 MPa was achieved by all the curing methods(standard and non-standard).However,for other replacement levels,water curing was adequate for 10%and 30%,sand at 10%,and sawdust for 20%and 30%,respectively.On the other hand,for the Activated Laterite soil(ALS),the 20 MPa design strength was met only at 0%replacement for all curing methods.Sawdust medium at 10%also satisfied the 20 MPa strength.

Gaussian limit for determinantal point processes with J-Hermitian kernels

We show that the central limit theorem for linear statistics over determinantal point processes with J-Hermitian kernels holds under fairly general conditions.In particular,we establish the Gaussian limit for linear statistics over determinantal point processes on the union of two copies of Rdwhen the correlation kernels are J-Hermitian translation-invariant.

Fluctuations of deformed Nigner random matrices

Let Xn be a standard real symmetric （complex Hermitian） Wigner matrix, Y1,Y2,...,Yn a sequence of independent real random variables independent of Xn. Consider the deformed Wigner matrix Hn,a = n^（-1/2）Xn ＋ n^（-a/2）diag（y1,...,yn）, where 0 〈 a 〈 1. It is well known that the average spectral distribution is the classical Wigner semicircle law, i.e., the Stieltjes transform mn,a（z） converges in probability to the corresponding Stieltjes transform rn（z）. In this paper, we shall give the asymptotic estimate for the expectation Emn,a （z） and variance Var（mn,a （z））, and establish the central limit theorem for linear statistics with sufficiently regular test function. A basic tool in the study is Stein＇s equation and its generalization which naturally leads to a certain recursive equation.

Estimating the effects of meteorology on PM_(2.5) reduction during the 2008 Summer Olympic Games in Beijing, China

Particulate pollution was a critical challenge to the promise of good air quality during the 2008 Beijing Olympic Games,which took place from August 8th to 24th.To ensure good air quality for the Games,several temporary emission control measures were implemented in Beijing and surrounding areas.Ambient particulate matter concentration decreased significantly during the Olympic period;however,it is difficult to distinguish the effectiveness of those control measures since meteorology also affects ambient PM_(2.5) concentration.In this work,a multiple linear regression model based on continuous field monitoring at a roadside site was conducted to evaluate the effects of meteorology and emission control measures on the reduction of PM_(2.5) during the 2008 Olympic Games.The hourly data set was divided into two time periods,the no control period,June 22nd to July 4th,and the control period,July 28th to August 21st.The response variable was PM_(2.5) and the meteorology covariates used in the model were hourly temperature,dew point temperature,wind speed and precipitation.Wind direction was not a significant predictor of PM_(2.5) levels in either the control or the no control period.Using the meteorologically-based regression coefficients from the two time periods,meteorology was found to contribute to at least a 16%reduction in PM_(2.5) levels in the roadside microenvironment;while the pollution control measures contributed to at least a 43%reduction in PM_(2.5) levels.