Fixed Design Points Research Articles

Shape Optimization of the Diffuser Blade of an Axial Blood Pump by Computational Fluid Dynamics

Computational fluid dynamics (CFD) has been a viable and effective way to predict hydraulic performance, flow field, and shear stress distribution within a blood pump. We developed an axial blood pump with CFD and carried out a CFD-based shape optimization of the diffuser blade to enhance pressure output and diminish backflow in the impeller-diffuser connecting region at a fixed design point. Our optimization combined a computer-aided design package, a mesh generator, and a CFD solver in an automation environment with process integration and optimization software. A genetic optimization algorithm was employed to find the pareto-optimal designs from which we could make trade-off decisions. Finally, a set of representative designs was analyzed and compared on the basis of the energy equation. The role of the inlet angle of the diffuser blade was analyzed, accompanied by its relationship with pressure output and backflow in the impeller-diffuser connecting region.

Moment consistency of estimators in partially linear models under NA samples

Consider the heteroscedastic regression model Y (j)(x in , t in ) = t in β + g(x in ) + σ in e (j)(x in ), 1 ≤ j ≤ m, 1 ≤ i ≤ n, where $${\sigma_{in}^{2}=f(u_{in})}$$ , (x in , t in , u in ) are fixed design points, β is an unknown parameter, g(·) and f(·) are unknown functions, and the errors {e (j)(x in )} are mean zero NA random variables. The moment consistency for least-squares estimators and weighted least-squares estimators of β is studied. In addition, the moment consistency for estimators of g(·) and f(·) is investigated.

Fixed design regression for negatively associated random fields

Data collected on the surface of the earth at different sites often have two- or three-dimensional coordinates associated with it. We assume a simple setting where these sites are integer lattice points, say, 𝒵 N , N ≥ 1, in the N-dimensional Euclidean space R N . Denote n = (n 1, …, n N )∈𝒵 N and I n = {i: i∈𝒵 N , 1 ≤ i k ≤n k , k = 1, …, N}. Consider a simple regression model where the design points x ni 's and the responses Y ni 's are related as follows: Y ni = g(x ni )+ϵ ni , i∈I n , where x ni 's are fixed design points taking values in a compact subset of R d and where g is a bounded real-valued function defined on R d and ϵ ni are negatively associated random disturbances with zero means and finite variances. The function g(x) is estimated by a general linear smoother g n (x). The asymptotic normality of the estimate g n (x) is established under weak conditions, and general conditions under which the bias g n (x) tends to zero are also determined.

Importance sampling for elasto-plastic systems using adapted process with deterministic control

A new importance sampling method is presented for computing the first passage probability of elasto-plastic systems under white noise excitations. The importance sampling distribution corresponds to shifting the mean of the excitation to an ‘adapted’ stochastic process whose future is determined based on information only up to the present. This causal property is responsible for maintaining the theoretical rigor of the resulting importance sampling procedure. It opens up great possibilities in the design of adapted process for variance reduction using importance sampling. In this work the adapted process is designed using concepts of deterministic optimal control. Numerical results show that the use of adapted process is particularly useful for hysteretic systems where hysteretic effects undermine the effectiveness of conventional importance sampling method based on fixed design points.

A BERRY-ESSEEN TYPE BOUND OF REGRESSION ESTIMATOR BASED ON LINEAR PROCESS ERRORS

Consider the nonparametric regression model <TEX>$Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}$</TEX> (<TEX>$1\;{\leq}\;i\;{\leq}\;n$</TEX>), where g(<TEX>$\cdot$</TEX>) is an unknown regression function, <TEX>$x_{ni}$</TEX> are known fixed design points, and the correlated errors {<TEX>${\epsilon}_{ni}$</TEX>, <TEX>$1\;{\leq}\;i\;{\leq}\;n$</TEX>} have the same distribution as {<TEX>$V_i$</TEX>, <TEX>$1\;{\leq}\;i\;{\leq}\;n$</TEX>}, here <TEX>$V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}$</TEX> with <TEX>${\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|$</TEX> < <TEX>$\infty$</TEX> and {<TEX>$e_t$</TEX>} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g(<TEX>$\cdot$</TEX>). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O(<TEX>$n^{-1/4}({\log}\;n)^{3/4}$</TEX>).

First passage probability of elasto-plastic systems by importance sampling with adapted process

A new importance sampling method is presented for computing the first passage probability of elasto-plastic systems under white noise excitations. The importance sampling distribution corresponds to shifting the mean of the excitation to an ‘adapted’ (‘predictable’) stochastic process whose future is determined based on information only up to the present. Choosing the adapted process involves designing an adaptive control force algorithm in a stochastic environment that targets to drive the response to first passage failure based on information up to the present. Algorithms for single-degree-of-freedom linear and elasto-plastic systems are proposed and their resulting computational efficiency investigated. Numerical results show that the use of adapted process is particularly useful for nonlinear hysteretic systems where hysteretic effects undermine the effectiveness of conventional importance sampling method based on fixed design points.

Wavelet Estimation in Heteroscedastic Model Under Censored Samples

Consider the heteroscedastic regression model Yi = g(xi) + σiei, 1 ≤ i ≤ n, where \( \sigma ^{2}_{i} = f{\left( {u_{i} } \right)} \), here (xi, ui) being fixed design points, g and f being unknown functions defined on [0, 1], ei being independent random errors with mean zero. Assuming that Yi are censored randomly and the censored distribution function is known or unknown, we discuss the rates of strong uniformly convergence for wavelet estimators of g and f, respectively. Also, the asymptotic normality for the wavelet estimators of g is investigated.

ASYMPTOTIC NORMALITY OF ESTIMATOR IN NON-PARAMETRIC MODEL UNDER CENSORED SAMPLES

Consider the regression model Yi = g(xi)+ei for i = 1, 2, . . . , n, where: (1) xi are fixed design points, (2) ei are independent random errors with mean zero, (3) g(·) is unknown regression function defined on [0, 1]. Under Yi are censored randomly, we discuss the asymptotic normality of the weighted kernel estimators of g when the censored distribution function is known or unknown.

Asymptotics of estimators in semi-parametric model under NA samples

This paper is concerned with the heteroscedastic semi-parametric regression model y i = x i β + g ( t i ) + σ i e i , 1 ⩽ i ⩽ n , where σ i 2 = f ( u i ) , ( x i , t i , u i ) are fixed design points, g and f are unknown functions, and random errors e i are negatively associated (NA) random variables. The strong consistency and asymptotic normality for least-squares estimators and weighted least-squares estimators of β are studied. In addition, the strong consistency for the estimators of f ( · ) and g ( · ) is investigated. Some results on independent random error settings are extended.

Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

Consider the nonparametric regression model Y ni = g ( x ni ) + ε ni for i = 1 , … , n , where g is unknown, x ni are fixed design points, and ε ni are negatively associated random errors. Nonparametric estimator g n ( x ) of g ( x ) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of g n ( x ) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).

Fixed design regression quantiles for time series

This paper studies nonparametric estimation of regression quantiles under the fixed design model. We suppose that the error random variables are coming from a strictly stationary stochastic process satisfying the strong mixing condition. The joint asymptotic normality for the estimators of several quantiles is given. The same property is established for the regression quantile estimator at different fixed design points.

PARAMETER ESTIMATION IN A PARTLY LINEAR REGRESSION MODEL WITH RANDOM COEFFICIENT AUTOREGRESSIVE ERRORS

ABSTRACT Consider a partly linear regression model where Yi 's are responses, and are fixed design points, is an unknown parameter vector, is an unknown bounded real-valued function defined on a compact subset of the real line , and are unobservable random errors. We study the above model when is a first-order random coefficient autoregressive process, i.e., a stationary solution of , where {zi } and {ei } are zero mean independent processes each consisting of i.i.d. random variables with finite second moments and respectively. Various estimators of β, θ and are investigated and their limit distributions established. Consistent estimators of the covariance matrices of the various estimators of β are also proposed.

Bootstrap approximation in a partially linear regression model

Abstract Consider the semiparametric regression model Y i =X i T β+g(T i )+e i (i=1,…,n), where ( X i , T i ) are known and fixed design points, β is a p -dimensional unknown parameter, g (·) is an unknown function on [0,1], and e i are i.i.d. random errors with mean 0 and variance σ 2 . In this paper, we first construct bootstrap statistics β n ∗ and σ n 2 ∗ by resampling. Then we prove that for the estimators β n and σ n 2 of the parameters β and σ 2 , n (β n ∗ −β n ) and n (β n −β), n (σ n 2 ∗ −σ n 2 ) and n (σ n 2 −σ 2 ) have the same limit distributions, respectively. The advantage of the bootstrap approximation is explained. The feasibility of this approach is also shown in a simulation study.

Aerodynamic benefits of adaptive wing technology

Especially in the case of large transonic transport aircraft, flight conditions change considerably during a typical mission. This is accounted for by multiple but fixed design points which compromise aircraft performance. Employing adaptive wing technology where the wing geometry, or other means of flow control, adjusts the flow development to the changing freestream and load conditions allows us to explore fully the flow potential at each point of the flight envelope. Various means of flow control by geometric adaptation and by direct boundary layer control have been investigated within the German national program ADIF and the EU-project EUROSHOCK II and their potential explored. Here, corresponding results are presented and discussed, indicating the applicability and benefits of the adaptive control methods considered. It is also demonstrated that, generally, flow control must be adaptive to work in real aeronautical conditions since these conditions change within the mission flight envelope.

Second Order Asymptotic Risks of Smoothed Linear Estimators in Nonparametric Regression Models

We consider experiments with fixed design points and replicated observations at these points, and investigate smoothed linear estimators of the mean vector of these observations. We propose some methods to choose the degree of smoothing in a data-dependent way. To assess the performance of such estimators we approximate the mean square error by second order power series in n −1 and σ 2, respectively, where n is the sample size and σ 2 is the common variance of the observations. At least for special cases we see that the adaptive smoothed estimator can improve the least squares estimator asymptotically. Furthermore, we show the second order equivalence of the proposed adaptive estimators.

Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case

Consider the nonparametric regression model Y i ( n) = g( x i ( n) ) + ε i ( n) , i = 1, …, n, where g is an unknown regression function and assumed to be bounded and real valued on A ⊂ R p , x i ( n) 's are known and fixed design points and ε i ( n) 's are assumed to be both dependent and non-identically distributed random variables. This paper investigates the asymptotic properties of the general nonparametric regression estimator g n ( x) = Σ i = 1 n W ni ( x) Y i ( n) , where the weight function W ni ( x) is of the form W ni ( x) = W ni ( x; x 1 ( n) , x 2 ( n) , …, x n ( n) . The estimator g n ( x) is shown to be weak, mean square error, and universal consistent under very general conditions on the temporal dependence and heterogeneity of ε i ( n) 's. Asymptotic distribution of the estimator is also considered.

Trigonometric series regression estimators with an application to partially linear models

Let μ be a function defined on an interval [ a, b] of finite length. Suppose that y 1, …, y n are uncorrelated observations satisfying E( y j ) = μ( t j ) and var( y j ) = σ 2, j = 1, …, n, where the t j 's are fixed design points. Asymptotic (as n → ∞) approximations of the integrated mean squared error and the partial integrated mean squared error of trigonometric series type estimators of μ are obtained. Our integrated squared bias approximations closely parallel those of Hall in the setting of density estimation. Estimators that utilize only cosines are shown to be competitive with the so-called cut-and-normalized kernel estimators. Our results for the cosine series estimator are applied to the problem of estimating the linear part of a partially linear model. An efficient estimator of the regression coefficient in this model is derived without undersmoothing the estimate of the nonparametric component. This differs from the result of Rice whose nonparametric estimator was a partial spline.

Consistent regression estimation with fixed design points under dependence conditions

For n = 1, 2,… and i integer between 1 and n, let x ni be fixed design points in a compact subset S of R p , p⩾ 1 , and let Y ni be observations taken at these points through g, an unknown continuous real-valued function defined on R p , and subject to errors ε ni ; that is, Y ni = g( x ni ) + ε ni . For any x in R p , g(x) is estimated by g n( x; x n ) = Σ n i = 1 w ni ( x; x n ) Y ni , where x n = ( x n1 ,…, x nn ) and w ni (·;·) are suitable weights. If the errors ε ni are centered at their expectations, the proposed estimate is asymptotically unbiased. It is also consistent in quadratic mean and strongly consistent, if, in addition and for each n, the random variables ε ni , i ⩾ 1, are coming from a strictly stationary sequence obeying any one of the four standard modes of mixing.

Convolution type estimators for nonparametric regression

Convolution type kernel estimators such as the Priestley-Chao estimator have been discussed by several authors in the fixed design regression model Y i = g( t i )+ ε i , where ε i are uncorrelated random errors, t i are fixed design points where measurements are made, and g is the function to be estimated from the noisy measurements Y i . Using properties of order statistics and concomitants, we derive the asymptotic mean squared error of these estimators in the random design case where given i.i.d. bivariate observations ( X i , Y i ), i = 1,..., n, the aim is to estimate the regression function m( x) = E( Y/ X = x). The comparison with the well-known quotient type Nadaraya-Watson kernel estimators shows that convolution type estimators have a bias behavior which corresponds to that in the fixed design case. This makes possible the straightforward extension to the estimation of derivatives.

On the Selection of an Optimum Design Point for Phase-Coherent Receivers Employing Bandpass Limiters

In the design of phase-coherent receivers employing bandpass limiters, it is customary to specify system performance relative to its value at a fixed design point. For a given design point, it is well known that an optimum tradeoff can be found between the power allocated to the carrier and sideband signals. This paper describes an attempt to further improve the performance of such coherent carrier systems by optimizing the design point based upon a given practical optimization criterion. The single-channel system is treated in detail and a brief discussion is given on how to extend the optimization technique to a two-channel system.