Statistical Measures of Parameter Estimates from Models Fit to Respiratory Impedance Data: Emphasis on Joint Vanabilities

To describe respiratory mechanical impedance data, many investigators have proposed electromechanical models and then fit them to data using formal parameter estimation techniques. This approach has resulted in confusion as to how to interpret the resulting estimated values, and hence as to which model is most appropriate. A key cause of this confusion is that most studies rely on the quality of fit between the model and the data as the only measure of model validity rather than performing adequate statistical analysis of the parameter estimates themselves. This paper describes several statistical measures that should be applied to parameter estimates obtained from forced oscillation data. Specifically, we describe standard errors of the parameter estimates, confidence intervals for each parameter estimate, and the joint confidence region for the parameters. Much emphasis is placed on the joint confidence region which, unlike the interval, allows for simultaneous variations in parameters. The measures are applied to an often used six-element model for respiratory impedance data of dogs from 4 to 64 Hz. This application indicated that even when fitting data over this frequency range, parameter estimates are not well defined and the parameter estimated with least accuracy is airway resistance.     

Partitioning of respiratory mechanical impedance by absolute and differential body plethysmography

We have recently demonstrated the feasibility of partitioning total respiratory impedance (Zrs) into its airway (Zaw) and tissular (Zti) components by measuring alveolar gas compression (Vpl) plethysmographically during pressure oscillations at the airway opening (Peslin et al.). The aim of this study was to comparatively evaluate an alternative approach: the measurement of Zrs and of the transfer function (FTF) between airway flow and body surface flow obtained by absolute body plethysmography. The two approaches are theoretically equivalent, provided thermal and other artifacts are properly eliminated. Zrs and Vpl (method 1) and Zrs and FTF (method 2) were measured in 11 healthy subjects from 4 to 29 Hz, using a pressure-type and a flow-type plethysmograph, respectively. Inspired gas was conditioned to body temperature and pressure, saturated with water vapor in both instances to minimize thermal factors. Zaw and Zti spectra computed from both sets of data were quite similar in shape. Neither airway resistance nor tissue compliance differed significantly; tissue resistance, however, was about 14% lower with method 1, which may be due to imperfect gas conditioning. The reproducibility of the data was similar with the two approaches. We conclude that absolute body plethysmography is as reliable as differential body plethysmography to partition Zrs.     

大口径压电快摆镜机构迟滞非线性补偿与控制

为了提高空间天文望远镜精密稳像系统中大口径压电快摆镜机构（Fast Steering Mirror,FSM）的控制精度,采用迟滞前馈补偿和最优PID控制算法相结合的复合控制策略。针对基于广义Play算子的Prandtl-Ishlinskii（PI）模型可逆性受约束条件限制以及求逆过程中模型参数估计误差累加的问题,提出了一种基于广义Stop算子的PI逆模型进行压电执行器（Piezoelectric Actuator,PZT）迟滞补偿。针对逆迟滞模型的不确定性和直接前馈控制抗干扰能力差的问题,在控制系统中加入最优PID闭环控制器。采用自适应差分进化算法（Adaptive Differential Evolution,ADE）对迟滞逆模型参数和PID控制器参数进行寻优并引入混沌搜索机制来提高ADE算法的性能。实验结果表明:与传统PI模型解析求逆方法相比,基于广义Stop算子的PI逆模型能够更好描述逆迟滞曲线,拟合频率为1 Hz的迟滞曲线,拟合精度提高78.04%;实时跟踪频率分别为1、10、20 Hz的大口径快摆机构目标摆动位移,复合控制策略的跟踪精度相比于直接前馈控制分别提高了38.56%,22.92%和13.5%。     

Confidence bounds on respiratory mechanical properties estimatedfrom transfer versus input impedance in humans versus dogs

Using parameters typical of a dog, we have shown that estimates for the parameters in the six-element model of Dubois et al. would be very unreliable if either input (Z(in)) or transfer (Ztr) data from only 2-32 Hz were fit. It has subsequently been shown that this model is not appropriate for human Z(in) from 2-320 Hz. However, several studies have continued to apply the model to human Ztr data from only 2-32 Hz. In this study a sensitivity analysis is used to determine whether and why the six-element model could be applicable to lower frequency (less than 64 Hz) Ztr data in humans, but not Z(in) data over any frequency range. We first predicted the joint parameter uncertainty bounds assuming a fit to either 2-32 Hz Z(in) or Ztr data created from literature based mean parameter values. Consistent with previous studies, we predicted that the estimates will be very unreliable if obtained from Z(in) data for humans or dogs, or from Ztr data from dogs. Surprisingly, however, the reliability of several parameter estimates from human Ztr data from only 2-32 Hz are reasonable. We next evaluated the variability in 2-64 Hz based Ztr parameter estimates by comparing experimental variability in two healthy human subjects (over 10 and 13 trials) to theoretical and Monte Carlo numerical predictions based on a single trial. Again, the Ztr parameters were reliable. A simulation study was used to describe the reasons for enhanced reliability when using human Ztr data. It is shown that this reliability is largely dependent on alveolar gas compressibility, Cg.(ABSTRACT TRUNCATED AT 250 WORDS)     

A new model for step-stress testing

The mathematical intractability of the Weibull cumulative exposure model (CE-M) has impeded the development of statistical procedures for step-stress accelerated life tests. Our new model (KH-M) is based on a time transformation of the exponential CE-M. The time-transformation enables the reliability engineer to use known results for multiple-step, multiple-stress models that have been developed for the exponential step-stress model. KH-M has a realistically appealing proportional-hazard property. It is as flexible as the Weibull CE-M for fitting data, but its mathematical form makes it easier to obtain parameter estimates and standard deviations. Maximum likelihood estimates are given for test plans with unknown shape parameter. The mathematical similarity to the constant-stress Weibull model is shown. Chi-square goodness of fit tests are performed on simulated data to compare the fit of the models     

Parameter Estipiates in a Five-Element Respiratory Mechanical Model

Using four sets of forced random noise impedance data from each of five normal subjects and five patients with obstructuve lung disease, we computed parameter estimates for a three-element series model and a five-element parallel compartment model. For normal subjects, the five-element model provided no better fit to the impedance data than did the simple series model. Estimates obtained from normal subjects using this three-element model were reasonable and reproducible within 25 percent. For all subjects with lung disease, the five-element model provided a significantly (p 0.05) better fit than the three-element model. Estimates for parameters representing central inertance and resistance, airway compliance, and peripheral resistance were reasonable and reproducible-within 18 percent. However, estimates for the compliance of the lung and chest wall were more variable since measured impedance appeared to be insensitive to this parameter in the frequency range used.     

基于小波变换的话务量预测

本文将小波变换应用到话务量的预测中,利用小波分解法将非平稳时间序列的GSM话音话务量分解为多个细节信号分量和逼近信号分量。对细节信号采用AR模型或者余弦逼近进行拟合建模,对逼近信号采用多项式拟合和AR模型相结合的方式建模。利用某运营商2009年1月~2013年7月每月的博彩日话音话务作为检验序列集,前50个月的数据用来建模拟合,最后5个月数据作为预测比较,发现拟合相关度为0.991,预测平均绝对误差为0.029,预测结果比单纯使用曲线拟合要好。     

Improving the ability of a distributed feedback lasertransfer-matrix model to fit to spectra from distributed-feedback lasers

Fitting distributed-feedback (DFB) laser models to data is a difficult process that is time consuming and often inaccurate. Having a good initial estimate of the facet parameters greatly reduces the time required by a fitting routine. If the general effects of laser parameters are well known, fitting routines do not have to be overly complicated to obtain a best fit. It is also very important to fit to spectra from both facets simultaneously and over a wide bandwidth for quick, accurate, and nondegenerate results     

基于瞬时相位拟合的LFM信号参数估计算法

针对传统线性调频（LFM）信号参数估计算法中复杂的搜索和计算问题,提出了一种不需要参数搜索的快速LFM信号参数估计算法。该算法先用希尔伯特变换估计LFM信号瞬时相位,再用二次相位函数拟合LFM信号瞬时相位从而得到初始频率和调频斜率的估计。仿真验证了本文算法的有效性,说明该算法能够给出满意的参数估计结果。     

Importance of low-frequency impedance data for reliably quantifying parallel inhomogeneities of respiratory mechanics

The ability to reliably measure total respiratory input impedance Z/sup rs/ from 0.25 to 4 Hz has only recently been reported and only in healthy subjects. The real part of Z/sup rs/ decreased substantially with frequency. One explanation is provided by the Otis model, which contains parallel resistance-compliance time-constant inhomogeneities. Several investigators have suggested the use of this model at the level of estimating its parameters by fitting the model to data. Such an approach would permit quantification of the functional inhomogeneity of an individual's respiratory system and may be useful diagnostically. In this study, experimental data and a sensitivity analysis are combined to specify the requirements and limitations associated with estimating the parameters. The data acquisition technique was improved to acquire Z/sup rs/ as low as 0.125 Hz in seven healthy subjects. The Otis model provided an excellent fit to the data with reasonably low intra- and intersubject variability.<>     

Generating High-Accuracy Simulation Models Using Problem-Tailored Orthogonal Polynomials Basis

The problem of computing high-accuracy simulation models for systems described by tabulated frequency data is of paramount importance in the modeling arena. Standard algorithms for this task involve generating rational function approximations to the data. However, for complicated data sets, high-order approximations are required. Unfortunately, numerical conditioning problems arise when attempting to fit high-order rational approximations to the data, effectively limiting the accuracy of the models that can be generated. While robust fitting schemes based on orthogonal polynomial exist, they usually pose strict constraints on the data points, which are either hard or even impossible to guarantee. Furthermore, the approximation must still be translated such that it can directly be used inside a simulator. In this paper, we present an algorithm for robustly generating such a model using only the data given. The model is supported on a problem-tailored orthogonal polynomial basis. We also present a method for directly generating a state-space model associated with a rational function described in terms of such polynomials, effectively making the model amenable for simulation. An extension to the MIMO case is described and it is shown that the method is easily included with existing passivity enforcing procedures. Finally, we demonstrate the proposed technique by constructing approximations to several real-world data sets     

逆F类功放数字预失真改进算法

针对逆F类射频功率放大器高效率实现带来的严重的非线性失真,提出基于幅度索引的查找表(LUT)模型数字预失真改进算法,以获得具有高线性和高效率的逆F类射频放大系统。由于逆F类功放复杂的特性曲线,传统LUT数字预失真算法已经不能很好地拟合功放模型,为此采用非均匀取点拟合,并且结合多项式、EWMA和平滑等曲线拟合方法。实验结果表明:运用该方法,使3载波WCDMA信号施加到中心频率为930 MHz的逆F类功率放大器后的非线性失真现象明显改善。     

A two-dimensional Prony's method for spectral estimation

The problem of estimating the parameters of a model for bidimensional data made up by a linear combination of damped two-dimensional sinusoids is considered. Frequencies, amplitudes, phases, and damping factors are estimated by applying a generalization of the monodimensional Prony's method to spatial data. This procedure finds the desired quantities after an autoregressive model fitting to the data, a polynomial rooting, and a least-squares problem solution. The autoregressive models involved have a particular nature that simplifies the analysis. In fact, their characteristic polynomial factors into two parts so that many of their properties can be easily determined. Quick estimates of the parameters computed are found by using standard one-dimensional autoregressive estimation methods. An iterative procedure for refining the autoregressive parameters estimates which gives rise to better frequency estimates is also discussed. Some simulation results are reported     

Nonlinear blind source separation algorithm based on spline interpolation and artificial bee colony optimization

A post-nonlinear blind source separation algorithm based on spline interpolation fitting and artificial bee colony optimization was proposed for the more complicated nonlinear mixture situations.The separation model was constructed by using the spline interpolation to fit the inverse nonlinear distortion function and using entropy as the separation criterion.The spline interpolation node parameters were solved by the modified artificial bee colony optimization algorithm.The correlation constraint was added into the objective function for limiting the solution space and the outliers wuld be restricted in the separation process.The results of speech sounds separation experiment show that the proposed algorithm can effectively realize the signal separation for the nonlinear mixture.Compared with the traditional separation algorithm based on odd polynomial fitting,the proposed algorithm has higher separation accuracy.     

A nonstatistical approach to estimating confidence intervals aboutmodel parameters: application to respiratory mechanics

Estimates of parameters obtained by fitting models to physiologic data are of little use unless accompanied by confidence intervals. The standard methods for estimating confidence intervals are statistical, and make the assumption that the fitted model accounts for all the deterministic variation in the data while the residuals between the fitted model and the data reflect only stochastic noise. In practice, this is frequently not the case, as one often finds the residuals to be systematically distributed about zero. In this paper, we develop an approach for assessing confidence in a parameter estimate when the order of the model is clearly less than that of the system being modeled. Our approach does not require a parameter to have a single value located within a region of confidence. Instead, we let the parameter value vary over the data set in such a way as to provide a good fit to the entire data set. We apply our approach to the estimation of the resistance of the respiratory system in which a simple model is fitted to measurements of tracheal pressure and flow by recursive multiple linear regression. The values of resistance required to achieve a good fit are represented as a modified histogram in which the contribution of a particular resistance value to the histogram is weighted by the amount of information used in its determination. Our approach provides parameter frequency distribution functions that convey the degree of confidence one may have in the parameter, while not being based on erroneous statistical assumptions.     

Array response kernels for EEG and MEG in multilayer ellipsoidal geometry

We present forward modeling solutions in the form of array response kernels for electroencephalography (EEG) and magnetoencephalography (MEG), assuming that a multilayer ellipsoidal geometry approximates the anatomy of the head and a dipole current models the source. The use of an ellipsoidal geometry is useful in cases for which incorporating the anisotropy of the head is important but a better model cannot be defined. The structure of our forward solutions facilitates the analysis of the inverse problem by factoring the lead field into a product of the current dipole source and a kernel containing the information corresponding to the head geometry and location of the source and sensors. This factorization allows the inverse problem to be approached as an explicit function of just the location parameters, which reduces the complexity of the estimation solution search. Our forward solutions have the potential of facilitating the solution of the inverse problem, as they provide algebraic representations suitable for numerical implementation. The applicability of our models is illustrated with numerical examples on real EEG/MEG data of N20 responses. Our results show that the residual data after modeling the N20 response using a dipole for the source and an ellipsoidal geometry for the head is in average lower than the residual remaining when a spherical geometry is used for the same estimated dipole.     

Experimental comparison of integer/fractional-order electrical models of plant

In this paper, different integer and fractional-order models are studied from electrical point of view, these models are used to fit the measured impedance data for different types of fruits and vegetables. Experimental work is done on eight different models for six types of fruits to verify the best fitting model. Electric impedance is measured in the range of frequencies (200 mHz–200 Khz) using a non-destructive method, where the tissues are not damaged by electrode insertion. Moreover, two integer order models have been extended to the fractional order domain where data analysis and fitting are applied. The extra degrees of freedom of the fractional order models have enhanced the fitting parameters showing better accuracy. The double Cole Model has been found to be the best fit among different integer and fractional models based on root mean square error (RMSE).     

Endothelial cell electrical impedance parameter artifacts produced by a gold electrode and phase sensitive detection

Frequency dependent cellular micro-impedance estimates obtained from a gold two-electrode configuration using phase sensitive detection have become increasingly used to evaluate cellular barrier model parameters. The results of this study show that cellular barrier function parameter estimates optimized using measurements obtained from this biosensor are highly susceptible to both time dependent and systematic instrumental artifacts. Based on a power spectral analysis of experimentally measured microelectrode voltages, synchronous, 60 Hz, and white Gaussian noise were identified as the most significant time dependent instrumental artifacts. The reduction of these artifacts using digital filtering produced a corresponding reduction in the optimized model parameter fluctuations. Using a series of instrumental circuit models, this study also shows that electrode impedance voltage divider effects and circuit capacitances can produce systematic deviations in cellular barrier function parameter estimates. Although the implementation of an active current source reduced the voltage divider effects, artifacts produced by coaxial cable and other circuit capacitive elements at frequencies exceeding 1 kHz still remained. Reducing time dependent instrumental fluctuations and systematic errors produced a significant reduction in cellular model barrier parameter errors and improved the model fit to experimental data.     

Simultaneous EEG Source and Forward Model Reconstruction (SOFOMORE) Using a Hierarchical Bayesian Approach

We present an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model representation is motivated by the many random contributions to the path from sources to measurements including the tissue conductivity distribution, the geometry of the cortical surface, and electrode positions. We first present a hierarchical Bayesian framework for EEG source localization that jointly performs source and forward model reconstruction (SOFOMORE). Secondly, we evaluate the SOFOMORE approach by comparison with source reconstruction methods that use fixed forward models. Analysis of simulated and real EEG data provide evidence that reconstruction of the forward model leads to improved source estimates.     

Real time frequency domain fiberoptic temperature sensor

The excited state phosphorescence lifetime of alexandrite crystals is used to monitor temperature in the physiological range from 15-45°C with precision and accuracy of 0.2°C. A 500-μm cubic alexandrite crystal bounded to the distal end of an optical fiber of similar core dimensions is excited with pulsed Ne-He laser light. This apparatus uses a sampler for data acquisition and frequency domain methods for data fitting. The instrument amplifies the AC components of the detector output and band limits the signal to 12.5 kHz. The fundamental frequency of the excitation is set to 195.13 Hz to obtain 64 harmonics. This band limited signal is sampled and averaged over few hundred cycles in the time domain. The frequency domain representation of the data is obtained by employing fast Fourier transform algorithms. The phase delay and the modulation ratio of each sampled harmonic are then computed. Five to 50 values of the phase and modulations are averaged before computing the sensor lifetime. The instrument is capable of measuring precise and accurate excited state lifetimes from subpicowatt luminescent signals in plastic optical fibers. A least squares fit yields the lifetimes of single exponentials. A component of zero lifetime is introduced to account for the backscatter excitation seen by the photodetector leaking through optical interference filters. The phosphorescence lifetimes measured reproducibly to about three parts in a thousand are used to monitor physiological temperature. Temperatures are computed employing empirical polynomials. The system drift is negligible over 15 h of continuous operation. The instrumentation and methods allow 1.3-s update times and 30-s full response times