Limitations of the potential step technique to impedance measurements using discrete time Fourier transform

Recently, a new method of measuring impedance of electrochemical systems was proposed in the literature by Yoo and Park (Yoo, J.-S.; Park, S.-M. Anal. Chem. 2000, 72, 2035). It is based on the analysis of system response to a potential step. Differentiation of the applied potential step and the current response in the time domain followed by applying Fourier transform to both signals allows for determination of the system's impedance. It has been proposed that the measurements carried out in a short time period permit the determination of the system's impedance in the whole frequency range. The aim of the present work was to verify the validity of the impedance spectra obtained using this method, as well as to establish the conditions for which the method may be used. This method was tested using simulated data for a simple ideally polarized electrode and a simple one-electron redox system in the solution. The results show that the reliable impedance spectra may be obtained only for frequencies between 1/(NDeltat) and 1/(2Deltat), where Deltat denotes the sampling time and N is the number of points acquired during the experiment. However, the artifacts are generated when the experimental data are extrapolated to lower frequencies.     

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito–Taylor’s discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations.     

Accuracy of one‐step integration schemes for damped/forced linear structural dynamics

This paper proposes an energy‐based measure for the evaluation of the local truncation error of two‐level one‐step integration schemes. The measure applies to multiple degree of freedom systems and does not necessarily require modal reduction to a scalar model; it naturally handles the structural damping and external forcing terms that are generally and mistakenly neglected in error analyses, and it segregates the error associated with the free and forced response components of the problem. To illustrate the approach, two examples associated with the application of the trapezoidal scheme and of a high‐order scheme proposed in the literature are analyzed. The latter reveals the shortcomings of the standard approach that is based on the undamped/unforced linear oscillator and therefore highlights the need for the proposed framework. Indeed, the scheme order of accuracy is below expectation when structural damping or external forcing is considered, in the numerically dissipative setting. Developments on the basis of the time discontinuous Galerkin (TDG) method are then proposed to recover the scheme high‐order accuracy. Additionally, they show the similarity that exists between schemes related to the TDG method and the ones obtained by integration by parts of the equation of motion. Copyright © 2014 John Wiley & Sons, Ltd.     

MIMO线性系统输入输出信号统计特征的双谱评定方法

基于高阶统计量具备处理随机信号的特性,提出了一种利用三阶谱(双谱)评定MIMO线性系统时域输入输出信号统计特征的新方法。通过建立线性系统双谱数学模型,根据系统响应、所测得的频响函数以及离散信号的双谱数值估计算法,经逆运算获得系统的双谱驱动信号,随后利用高阶谱对高斯随机信号的盲性判定其输入信号的高斯性。将上述方法与采用传统相位随机化法(对功率谱添加随机相位)所获得的驱动信号分别应用于一悬臂梁模拟控制系统中,通过对输入信号的分析及控制结果的比较,发现基于双谱所生成的时域随机驱动信号呈现出较强的非高斯性且收敛速度更快。对于输出信号统计特征的评定,提出从输入信号与系统频带接近的程度入手,再次利用高阶统计量对高斯随机信号的盲性进行定性判定,对于无法判别满足何种非高斯统计分布特征的,不管是对于输入信号还是输出信号,一律采用绘制信号的概率分布特征曲线进行定量评定。     

An energy‐momentum‐conserving temporal discretization scheme for adhesive contact problems

Numerical solution of dynamic problems requires accurate temporal discretization schemes. So far, to the best of the authors’ knowledge, none have been proposed for adhesive contact problems. In this work, an energy‐momentum‐conserving temporal discretization scheme for adhesive contact problems is proposed. A contact criterion is also proposed to distinguish between adhesion‐dominated and impact‐dominated contact behaviors. An adhesion formulation is considered, which is suitable to describe a large class of interaction mechanisms including van der Waals adhesion and cohesive zone modeling. The current formulation is frictionless, and no dissipation is considered. Performance of the proposed scheme is compared with other schemes. The proposed scheme involves very little extra computational overhead. It is shown that the proposed new temporal discretization scheme leads to major accuracy gains both for single‐degree‐of‐freedom and multi‐degree‐of‐freedom systems. The single‐degree‐of‐freedom system is critically analyzed for various parameters affecting the response. For the multi‐degree‐of‐freedom system, the effect of the time step and mesh discretization on the solution is also studied using the proposed scheme. It is further shown that a temporal discretization scheme based on the principle of energy conservation is not sufficient to obtain a convergent solution. Results with higher order contact finite elements for discretizing the contact area are also discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive Exponentially Weighted Moving Average Schemes Using a Kalrnan Filter

Two adaptive exponentially weighted moving average control schemes are proposed. The weighting coefficient is updated using a Kalman filter algorithm. The two test statistics incorporate an integral error term. Simulated average run lengths indicate the proposed schemes are sensitive to small process shifts, but do tend to ring false alarms when there is no process change. For medium and large process changes and trends their performance is comparable to that, of Lucas's combined Shewhart-CUSUM control scheme. Some application of the proposed schemes to correlated data indicate robust performance. Conclusions are drawn that the Kalman filter used to model a process together with a detection mechanism applied to the residuals closely resembles the work done in control theory.     

Axial wave propagation in viscoelastic bars using a new finite-element-based method

A new solution for the finite-element implementation of the axial vibration of viscoelastic bars is proposed. The effect of viscoelasticity on the dynamic response is accounted for by a convolution integral, avoiding the difficulties associated with the high-order time derivatives used in conventional models for viscoelasticity. A convenient but excellent numerical approximation for the obtained convolution integral is proposed. This numerical approximation allows easy implementation of the finite-element procedure in the time domain as it only introduces additional terms to the mass matrix and the force vector. The additional terms are calculated from quantities obtained in the previous time step. To validate the proposed numerical procedure, a few simple examples are presented and solved by the existing direct methods as well as the new alternative method. The examples include the computation of the dynamic axial response of a viscoelastic bar fixed at one end and subject to a step or sinusoidally varying load at the other end. It is concluded that the new method is valid and works satisfactorily.     

Free vibration of laminated composite conical shells with random material properties

In the present study, the sensitivity of randomness in material parameters on linear free vibration response of conical shells is presented. Higher order shear deformation theory is used to model system behavior and uncertain lamina material properties are modeled as basic random variables. A finite element method is successfully combined with first-order perturbation technique to obtain the response statistics of the structure. The solution methodology is validated with the results available in the literature and an independent Monte Carlo simulation. Typical numerical results for second-order statistics of linear free vibration response of simply supported laminated composite conical shells are obtained for different lamination schemes and thickness to radius ratios.     

The bipenalty method for arbitrary multipoint constraints

In finite element (FE) analysis, traditional penalty methods impose constraints by adding virtual stiffness to the FE system. In dynamics, this can decrease the critical time step of the system when conditionally stable time integration schemes are used by introducing spurious modes with high eigenfrequencies. Recent studies have shown that using mass penalties alongside traditional stiffness penalties can mitigate this effect for systems with a one single‐point constraint. In the present work, we extend this finding to include systems with an arbitrary set of multipoint constraints. By analysing the generalised eigenvalue problem, we show that the values of spurious eigenfrequencies may be controlled by the choice of stiffness and mass penalty parameters. The method is demonstrated using numerical examples, including a one‐dimensional contact–impact formulation and a two‐dimensional crack propagation analysis. The results show that constraint imposition using the bipenalty method can be employed such that the critical time step of an analysis is unaffected, whereas also displaying superiority over the mass penalty method in terms of accuracy and versatility. Copyright © 2012 John Wiley & Sons, Ltd.     

A physical approach to structural stochastic optimal controls

The generalized density evolution equation proposed in recent years profoundly reveals the intrinsic connection between deterministic systems and stochastic systems by introducing physical relationships into stochastic systems. On this basis, a physical stochastic optimal control scheme of structures is developed in this paper, which extends the classical stochastic optimal control methods, and can govern the evolution details of system performance, while the classical stochastic optimal control schemes, such as the LQG control, essentially hold the system statistics since there is still a lack of efficient methods to solve the response process of the stochastic systems with strong nonlinearities in the context of classical random mechanics. It is practically useful to general nonlinear systems driven by non-stationary and non-Gaussian stochastic processes. The celebrated Pontryagin’s maximum principles is employed to conduct the physical solutions of the state vector and the control force vector of stochastic optimal controls of closed-loop systems by synthesizing deterministic optimal control solutions of a collection of representative excitation driven systems using the generalized density evolution equation. Further, the selection strategy of weighting matrices of stochastic optimal controls is discussed to construct optimal control policies based on a control criterion of system second-order statistics assessment. The stochastic optimal control of an active tension control system is investigated, subjected to the random ground motion represented by a physical stochastic earthquake model. The investigation reveals that the structural seismic performance is significantly improved when the optimal control strategy is applied. A comparative study, meanwhile, between the advocated method and the LQG control is carried out, indicating that the LQG control using nominal Gaussian white noise as the external excitation cannot be used to design a reasonable control system for civil engineering structures, while the advocated method can reach the desirable objective performance. The optimal control strategy is then further employed in the investigation of the stochastic optimal control of an eight-storey shear frame. Numerical examples elucidate the validity and applicability of the developed physical stochastic optimal control methodology.     

复合随机振动系统的动力可靠度分析

建议了一类新的复合随机振动系统动力可靠度分析方法。基于复合随机振动系统反应分析的密度演化方法,根据首次超越破坏准则,对密度演化方程施加相应的边界条件,进而求解密度演化方程,在安全域内积分给出结构的动力可靠度。结合精细时程积分方法与具有TVD性质的差分格式,研究了基于密度演化方法求解结构动力可靠度问题的数值方法。以受到随机地震作用、具有随机参数的八层层间剪切型结构为例,进行了结构动力可靠度分析并与随机模拟结果进行了比较。研究表明,建议的方法具有较高的精度和效率。     

Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration

This paper presents a new module towards the development of efficient computational stochastic mechanics. Specifically, the possibility of an adaptive polynomial chaos expansion is investigated. Adaptivity in this context refers to retaining, through an iterative procedure, only those terms in a representation of the solution process that are significant to the numerical evaluation of the solution. The technique can be applied to the calculation of statistics of extremes for nongaussian processes. The only assumption involved is that these processes be the response of a nonlinear oscillator excited by a general stochastic process. The proposed technique is an extension of a technique developed by the second author for the solution of general nonlinear random vibration problems. Accordingly, the response process is represented using its Karhunen-Loeve expansion. This expansion allows for the optimal encapsulation of the information contained in the stochastic process into a set of discrete random variables. The response process is then expanded using the polynomial chaos basis, which is a complete orthogonal set in the space of second-order random variables. The time dependent coefficients in this expansion are then computed by using a Galerkin projection scheme which minimizes the approximation error involved in using a finite-dimensional subspace. These coefficients completely characterize the solution process, and the accuracy of the approximation can be assessed by comparing the contribution of successive coefficients. A significant contribution of this paper is the development and implimentation of adaptive schemes for the polynomial chaos expansion. These schemes permit the inclusion of only those terms in the expansion that have a significant contribution.     

Chemical sensing systems using xerogel-based sensor elements and CMOS photodetectors

We present the first example of an integrated complementary metal-oxide-semiconductor (CMOS) photodetector coupled with a solid-state xerogel-based thin-film sensor to produce a compact chemical sensor system. We compare results using two different CMOS-based detector systems to results obtained by using a standard photomultiplier tube (PMT) or charge-coupled device (CCD) detector. Because the chemical sensor elements are governed by a Stern-Volmer relationship, the Stern-Volmer quenching constant is used as the primary comparator between the different detectors. All of the systems yielded Stern-Volmer constants from 0.042 to 0.049 O/sub 2/%/sup -1/. The results show that the CMOS detector system yields analytical data that are comparable to the CCD- and PMT-based systems. The disparity between the data obtained from each detector is primarily associated with the difference in how the signals are obtained by each detector as they presently exist. We have also observed satisfactory reversibility in the operation of the sensor system. The CMOS-based system exhibits a response time that is faster than the chemical sensor element's intrinsic response time, making the CMOS suitable for time-dependent measurements. The CMOS array detector also uses less than 0.1% the power in comparison to a standard PMT or CCD. The combined xerogel/CMOS system represents an important step toward the development of a portable, efficient sensor system.     

Optimum load time history for non-linear analysis using dynamic relaxation

A modification of the dynamic relaxation method is proposed which facilitates static analysis of non-linear problems. Continuous loading in time is adopted instead of the ordinary step function of time. Inertia and damping forces arising during the loading process are kept at a minimum using an optimum load time history. This results from the stationary condition of an appropriate functional. The equation of motion is included as a subsidiary condition. Continuous load—deflection curves can be obtained. An incremental solution is avoided. Application of the method is extremely simple. Existing programs based on explicit time integration schemes can be easily adapted for it. Sample solutions are presented.     

A combined method using modified routh stability array and MSE criterion for the reduction of discrete‐time systems

Abstract

A new mixed method using modified stability array and mean‐square error (MSE) criterion is proposed for deriving reduced‐order 2‐transfer functions for discrete‐time systems. More precisely, the modified Routh stability array is used to obtain the reduced‐order denominator, thus ensuring stability preservation, while the numerator is obtained by minimizing the mean‐square error between the unit step responses of the original system and reduced model. The main feature of the method is that it does not actually evaluate the system and model responses in the step of minimizing mean‐square error.     

A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

As multibody systems often involve unilateral constraints, nonsmooth phenomena, such as impacts and friction, are common in engineering. Therefore, a valid nonsmooth dynamics method is highly important for multibody systems. An accuracy representation of multibody systems is an important performance indicator of numerical algorithms, and the energy balance can be used efficiently evaluate the performance of nonsmooth dynamics methods. In this article, differential algebraic equations (DAEs) of a multibody system are constructed using the D'Alembert's principle, and a novel nonsmooth dynamics method based on symplectic discrete format is proposed. The symplectic discrete format can maintain the energy conservation of a conservative system; this property is expected to extend to nonconservative systems with nonsmooth phenomena in this article. To evaluate the properties of the proposed method, several numerical examples are considered, and the results of the proposed method are compared with those of Moreau's midpoint rule. The results demonstrate that the solutions obtained using the proposed method, which is based on the symplectic discrete format, can realize a higher solution accuracy and lower numerical energy dissipation, even under a large time step.     

基于Trnsys的复合式地板辐射供冷控制系统的仿真

采用人工神经网络模型设计某大空间建筑控制系统,联合Tmsys与Matlab建立复合式地板辐射供冷控制系统的仿真模型,对比分析不同控制时间步长下室内温度变化情况。结果显示针对该复合式地板辐射供冷控制系统,控制时间步长宜为15min,并提出一种既能避免控制器频繁运作又能减小系统响应时间的控制策略。     

Self‐regularized pseudo time‐marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non‐linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least‐square solution is through a regularized Gauss–Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo‐dynamical GNM (PD‐GNM) update equation addresses the major numerical difficulty associated with the near‐zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo‐dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo‐dynamic ensemble Kalman filter (PD‐EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of the PD‐EnKF by proposing an inner iteration within every time step. Results using the pseudo‐dynamic strategy obtained through PD‐EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD‐EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright © 2009 John Wiley & Sons, Ltd.     

Control of dead-time systems using derivative free local search guided population based incremental learning algorithms

This paper introduces two improved forms of population based incremental learning (PBIL) algorithm applied to proportional integral derivative (PID) controller and Smith predictor design. Derivative free optimization methods, namely simplex derivative pattern search (SDPS) and implicit filtering (IMF) are used to intensify search mechanism in PBIL algorithm with improved convergence than that of the original PBIL. Although the idea of combining local methods and global methods is not new, this paper focuses application of hybrid heuristics to the vast field of control design especially, control of systems having dead-time. The effectiveness of the controller schemes arrived using the developed algorithms namely simplex derivative pattern search guided population based incremental learning (SDPS-PBIL) and implicit filtering guided population based incremental learning (IMF-PBIL) are demonstrated using unit step set point response for a class of dead-time systems. The results are compared with some existing methods of controller tuning.