Identification of electric circuits described by ill-conditioned mathematical models

This paper treats the problem of identification of a linear electric circuit described by an ill-conditioned mathematical model. The identification problem is considered as the problem of model parameters determination by means of processing experimental data measured for the objective circuit. Topological singularities (low-admittance cutsets and low-impedance loops) in a circuit are found to be origins of ill-conditionality of a circuit model. For more in-depth investigation the classification of electric circuits is made in respect to singularities position. It is shown that the first set of experimental data obtained for an ill-conditioned model is useless for getting the required solution of the identification problem. In this case a solution error amounts to a huge value that exponentially increases with growth in condition number of a model matrix. It is found that linear relations between model parameters can be determined in an ill-conditioned problem. Accuracy of these relations does not depend on condition number, but is defined only by measurement precision. An approach named as repeat measurements principle (RMP) and based on linear relations is suggested to solve an ill-conditioned identification problem. A new RMP-based algorithm of linear circuit identification is developed. The algorithm shows a high efficiency and allows us to determine model parameters accurate to measurement precision as applied to any type of reciprocal and nonreciprocal linear circuits.     

Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines

A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles.     

A Dyadic Green's Function Based Method for the Transient Analysis of Lossy and Dispersive Multiconductor Transmission Lines

This paper describes a new algorithm for the analysis of multiconductor transmission lines characterized by frequency-dependent per-unit-length parameters. The proposed model is based on studying telegrapher's equations as a Sturm-Liouville problem. The open-end impedance matrix is expressed in a series form as an infinite sum of matrices of rational functions, derived from the series form of the dyadic Green's function. The rational form of the open-end impedance matrix allows an easy identification of poles and residues and, thus, the development of a reduced-order system of the interconnect. The pole-residue representation can be synthesized in an equivalent circuit or converted into a state-space model, which can be easily embedded into conventional nonlinear circuit SPICE-like solvers. The numerical results confirm the validity of the proposed modeling technique.     

Test Generation Algorithm for Linear Systems Based on Genetic Algorithm

This paper proposes a test generation algorithm combining genetic algorithm for fault diagnosis on linear systems. Most test generation algorithms just used a single value fault model. This test generation algorithm is based on a continuous fault model. This algorithm can improve the treatment of the tolerance problem, including the tolerances of both normal and fault parameters, and enhance the fault coverage rate. The genetic algorithm can be used to choose the characteristic values. The genetic algorithm can enhance precision of test generation algorithm especially for complex fitness functions derived from complex systems under test. The genetic algorithm can also further improve the fault coverage rate by reducing the loop number of divisions of the initial fault range. The experiments are carried out to show this test generation algorithm with a linear system and an integrated circuit.     

Linear bispectrum of signals and identification of nonminimum phaseFIR systems driven by colored input

The identification of non-minimum-phase finite-impulse-response (FIR) systems driven by third-order stationary colored signals that are not linear processes is addressed. Modeling the linear part of the bispectrum of a signal is discussed. The bispectrum of a signal is decomposed into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white-noise-driven linear shift-invariant (LSI) system. The linear bispectrum of the output of the unknown LSI system is represented using an ARMA (autoregressive moving average) model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. An algorithm for identifying the MA and AR parameters is given. How the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output is discussed. The method is applied to blur identification     

FIR Filtering for Discrete-Time Markov Jump Linear Systems

This paper is concerned with finite impulse response (FIR) filtering problem for discrete-time linear system which possesses stochastically jumping parameters described by a finite-state Markov process. An FIR filter processes the measured inputs and outputs on a finite receding horizon linearly and the filter gain is obtained by minimizing variance of the error between real state and estimated one. According to inverse computation, system matrix is always assumed to be non-singular. In terms of engineering application, we must have complete access to the current time jump mode. The FIR filter is presented in batch form and recursive form, respectively, and Kalman filter is also addressed for comparison. Finally, a numerical example is given to illustrate the design procedure and their effectiveness.     

线性时滞系统可辨识性的探讨

可辨识性分析法是为具有时滞状态，可控输入和可观测输出的线性时滞系统开发的，该系统具有有限数量的集总延迟。文中阐述了提供充分不平稳输入信号时，线性时滞系统传递函数的在线辨识性，可控输入的不连续性对系统的马尔科夫参数可辨识性的决定性，系统传递函数的在线辨识性和系统的马尔科夫参数可辨识性的关系，分析了系统可辨识的条件和必需的输入信号特性，用一个例子说明了系统可辨识性理论的应用。     

Modeling and Optimization of Compact Microwave Bandpass Filters

This paper presents the modeling and optimization of compact microwave bandpass filters whose compactness leads to complex and strong stray coupling paths, thereby making the identification of a simple and sparse coupling topology difficult and even impossible. The strong coupling coefficients needed for a broadband response can also cause an ambiguity in identifying the spatial extent of local resonances. An equivalent circuit, which is extracted directly from Maxwell's equations, is used in optimizing these filters. The filter is represented by its global resonances instead of individual resonators. The extraction of the parameters of the equivalent circuit is carried out in the physical frequency and not in the normalized frequency in order to preserve the physicality of the equivalent circuit, especially for asymmetric responses. The technique is successfully applied to the optimization of second-order suspended stripline bandpass filters with one transmission zero either below or above the passband, as well as fourth-order filters with three transmission zeros. A fourth-order filter with three transmission zeros is fabricated and measured.     

Optimized method for obtaining permittivity and conductivityprofiles of microwave materials

An iterative method for obtaining the distribution of the relative permittivity ϵ_r(z) or electrical conductivity σ(z) of microwave semiconducting materials is presented. The semiconducting material is fitted in a rectangular waveguide which is terminated by a variable short circuit. The reflection coefficients of the system are measured at a single frequency and at different positions of the moving short. The measured coefficients are used in the iterative process of solving the inverse problem by obtaining the functional gradient. The method takes into account continuous and discontinuous profiles     

An efficient algorithm for the extraction of parameters with high confidence from nonlinear models

Analytical models with parameters numerically extracted from I-V data have been used in simulation of MOS circuits. The equations are quasi-physical and the extracted parameters do not normally relate to any single identifiable physical mechanism. We have developed an extraction system that can provide a measure of the level of confidence in the extracted parameters; hence, these parameters may be reliably used in circuit simulation as well as process control. The algorithm described is model independent and can be used for any nonlinear least-squares parameter extraction problem.     

Computer-Aided Filter Alignment and Diagnosis

The cavity resonant frequencies and coupling values of a wide range of bandpass filters, band-reject filters, and equalizers have been determined in situ by computer-adjusting analytic models to fit the scattering parameters measured on an automatic network analyzer. A higher order mode elliptic filter, a dual-mode quasi-elliptic filter, and a dual-mode band-reject filter are presented as examples. The general relationships between mechanical dimensions and circuit parameters are discussed. The circuit adjustment procedure is outlined, and equations for the sensitivity coefficients of several element types are tabulated.     

基于模糊逻辑的两级运算放大器宏模型

运算放大器是最常用的模拟集成电路功能块,本文提出了一种基于模糊逻辑建立的运算放大器宏模型。基于运放电路结构分解的模糊逻辑建模方法利用了电路内部的结构特点与工作特性等先验知识。根据电路的结构知识确定模型整体结构;根据电路的工作特性确定模糊逻辑模型的规则（包括条数、前提与结论函数的形式）及初始参数。这就大大简化了模型构造过程,使一开始构造出来的初始模型就有较好的逼近精度,后续模型参数的学习训练只需经过少量的迭代,相对于传统的系统辨识方法具有很大的优势。     

语言辨识系统中最佳线性融合技术的研究

本文利用不同参数提取方法对语言辨识系统中的线性融合技术进行了研究。融合系数的获取通过三个准则进行实现,CFM准则、MSE准则和CE准则。实验系统采用了区分性高斯混合模型,利用OGI-TS多语种电话语音语料库,对决策级融合性能进行了评估。实验表明,利用决策级融合技术,选择最佳融合系数,可以很好地改善语言辨识率。     

低副瓣直线阵的最坏情况容差最优化方法研究

本文以激励系数为设计参量,讨论了直线阵的最坏情况容差最优化问题,给出了直线阵的最坏情况问题,固定容差问题和可变容差问题,研究了它们的新求解方法。固定容差问题将采用正多面体方法来求解,可变容差问题由一个双层迭代算法求解。可变容差问题以实际与理想方向图在容差域中的最大偏差为基准,协调阵列方向图的副(?)电平和激励系数的容差,使阵列方向图的副(?)电平满足所希望的指标要求,同时尽可能地放宽激励系数的容差,文中最后给出了6元和16元直线阵的最坏情况容差最优化的模拟计算结果。     

On the Parameter Estimation of 2-D Moving Average Random Fields

The problem of estimating the parameters of 2-D homogeneous moving average (MA) random fields only from output measurements is addressed. A novel computationally efficient algorithm for the estimation of the parameters of a minimum-phase 2-D MA model with a nonsymmetric half-plane (NSHP) region of support (ROS) is proposed. Using the 2-D spectral factorization, relationship between the NSHP MA model parameters and the cepstral coefficients of a 2-D MA random field is considered. Based on this relation, recursive equations are derived so as to estimate the NSHP MA model parameters. It is noteworthy that the proposed algorithm is practical, i.e., it does not require computationally complex processes namely fitting to a high-order autoregressive model, any initial estimates, nor matrix inversion. Performance analysis of the derived algorithm together with an existing method is given for comparison purposes. Index     

An optimization approach to the frequency-domain inverse problemfor a nonuniform LCRG transmission line

The inverse problem for a nonuniform LCRG transmission line is considered in the frequency domain. Imbedding equations for the reflection and transmission coefficients are derived through the concept of wave-splitting. An optimization approach is applied to reconstruct the line parameters as functions of the position using band-limited reflection and/or transmission data. Exact and explicit expressions for the gradients are derived, and the reconstruction algorithm (based upon a conjugate gradient method) is tested with both clean and noisy data, The problem of the nonuniqueness is also discussed     

一种基于预测开路电压估算SOC初值的方法

为解决电动汽车动力电池 SOC初值估算问题,文章以锂离子动力电池为对象,进行了脉冲放电实验,拟合了锂离子动力电池开路电压与 SOC函数关系式。对七阶Thevenin等效电池模型进行了参数辨识,预测了锂离子电池开路电压,将预测的开路电压代入开路电压与 SOC函数关系式进行了 SOC初值的估计。通过仿真实验,得出 SOC 初值估计误差为0.1321%。文中 SOC初值估算精度优于市场上通用的电池容量检测仪精度,验证了预测开路电压估算 SOC初值方法的可行性。     

Discretization Error Analysis and Adaptive Meshing Algorithms for Fluorescence Diffuse Optical Tomography: Part I

For imaging problems in which numerical solutions need to be computed for both the inverse and the underlying forward problems, discretization can be a major factor that determines the accuracy of imaging. In this work, we analyze the effect of discretization on the accuracy of fluorescence diffuse optical tomography. We model the forward problem by a pair of diffusion equations at the excitation and emission wavelengths and consider a finite element discretization method for the numerical solution of the forward problem. For the inverse problem, we use an optimization framework which allows incorporation of a priori information in the form of zeroth- and first-order Tikhonov regularization terms. Next, we convert the inverse problem into a variational problem and use Galerkin projection to discretize the inverse problem. Following the discretization, we analyze the error in reconstructed images due to the discretization of the forward and inverse problems and present two theorems which point out the factors that may lead to high error such as the mutual dependence of the forward and inverse problems, the number of sources and detectors, their configuration and their positions with respect to fluorophore concentration, and the formulation of the inverse problem. Finally, we demonstrate the results and implications of our error analysis by numerical experiments. In the second part of the paper, we apply our results to design novel adaptive discretization algorithms.      

Recursive parameter identification of constrained systems: anapplication to electrically stimulated muscle

In the application of real-time identification methods for diagnosis or adaptive control of biomedical systems, there is often known model information that is ignored. Constraints on the allowable values of parameters, which may be based on physical considerations, are often neglected because the information does "fit" easily into commonly used parameter-identification algorithms. In this paper a method of incorporating constraints on model parameters is developed. This method is applicable to most recursive parameter-identification algorithms. It enforces linear equality constraints on identified parameters. The use of this method for the real-time identification of autoregressive moving-average-type time series models, subject to parameter constraints, is described in detail. These constraints may be time varying. At each time step, the parameter estimate obtained by a recursive least squares estimator is orthogonally projected onto the constraint surface. This simple idea, when appropriately executed, enhances the output prediction accuracy of estimated parameters. Using constraint information in this way is important when we do not wish to destroy a "natural" parameterization of the model (by an initial projection to incorporate equality constraints), or when we cannot use a single initial model simplification (because the constraints are time varying or involve inputs and outputs). Because it improves output prediction at future times, this method is advantageous for use in predictive adaptive controllers. The use of this algorithm is demonstrated in the identification of electrically stimulated quadriceps muscles in paraplegic human subjects, using percutaneous intramuscular electrodes. The nonlinear steady-state force versus pulsewidth recruitment characteristic of the electrode-muscle system is identified simultaneously with the input-output muscle response dynamics, using a Hammerstein-type model. Knowledge of the recruitment curve's shape is translated into constraints on the identified parameters. This information improves the experimental predictive quality of the identified model.     

Cumulant-based deconvolutionand identification: several new families of linear equations

This paper presents several new families of cumulant-based linear equations with respect to the inverse filter coefficients for deconvolution (equalisation) and identification of nonminimum phase systems. Based on noncausal autoregressive (AR) modeling of the output signals and three theorems, these equations are derived for the cases of 2nd-, 3rd and 4th-order cumulants, respectively, and can be expressed as identical or similar forms. The algorithms constructed from these equations are simpler in form, but can offer more accurate results than the existing methods. Since the inverse filter coefficients are simply the solution of a set of linear equations, their uniqueness can normally be guaranteed. Simulations are presented for the cases of skewed series, unskewed continuous series and unskewed discrete series. The results of these simulations confirm the feasibility and efficiency of the algorithms.