The identification of nonlinear biological systems: Volterra kernel approaches

Representation, identification, and modeling are investigated for nonlinear biomedical systems. We begin by considering the conditions under which a nonlinear system can be represented or accurately approximated by a Volterra series (or functional expansion). Next, we examine system identification through estimating the kernels in a Volterra functional expansion approximation for the system. A recent kernel estimation technique that has proved to be effective in a number of biomedical applications is investigated as to running time and demonstrated on both clean and noisy data records, then it is used to illustrate identification of cascades of alternating dynamic linear and static nonlinear systems, both single-input single-output and multivariable cascades. During the presentation, we critically examine some interesting biological applications of kernel estimation techniques.     

The identification of nonlinear biological systems: Volterra kernel approaches

Representation, identification, and modeling are investigated for nonlinear biomedical systems. We begin by considering the conditions under which a nonlinear system can be represented or accurately approximated by a Volterra series (or functional expansion). Next, we examine system identification through estimating the kernels in a Volterra functional expansion approximation for the system. A recent kernel estimation technique that has proved to be effective in a number of biomedical applications is investigated as to running time and demonstrated on both clean and noisy data records, then it is used to illustrate identification of cascades of alternating dynamic linear and static nonlinear systems, both single-input single-output and multivariable cascades. During the presentation, we critically examine some interesting biological applications of kernel estimation techniques.     

Spectral Approach to Equivalent Statistical Quadratization and Cubicization Methods for Nonlinear Oscillators

Random vibrations of nonlinear systems subjected to Gaussian input are investigated by a technique based on statistical quadratization, and cubicization. In this context, and depending on the nature of the given nonlinearity, statistics of the stationary response are obtained via an equivalent system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method. The Volterra series response is expanded in a trigonometric Fourier series over an adequately long interval T, and exact expressions are derived for the Fourier coefficients of the second- and third-order response in terms of the Fourier coefficients of the first-order, Gaussian response. By using these expressions, statistics of the response are determined using the statistics of the Fourier coefficients of the first-order response, which can be readily computed since these coefficients are independent zero-mean Gaussian variables. In this manner, a significant reduction of the computational cost is achieved, as compared to alternative formulations of quadratization and cubicization methods where rather prohibitive multifold integrals in the frequency domain must be determined. Illustrative examples demonstrate the reliability of the proposed technique by comparison with data from pertinent Monte Carlo simulations.     

基于连续反演算法的时滞补偿控制综述

在实际系统的工作过程中,时滞现象普遍存在,如控制信号的采集与传输、控制器的构建与实施、事件的决策与处理等。考虑并有效处理时滞特性的影响有助于提升系统的性能。基于连续反演算法的时滞补偿控制策略是一种有效的控制方法且取得很多研究成果。该时滞补偿控制的主要思路是将具有时滞特性的常微分方程或偏微分方程变换为不具有时滞特性的常微分方程?偏微分方程/常微分方程?偏微分方程(ODE?PDE/PDE?PDE)级联系统。进一步地,基于变换的级联系统,结合连续反演算法提出相应的控制策略。该方法具有系统的稳定性证明简单,鲁棒性强,易于求取闭环系统精确解等优点。详细论述了连续反演算法的基本原理,并针对基于连续反演算法的时滞补偿控制算法在处理输入、输出、状态等类型时滞特性的最新研究进展做简单的阐述和总结。最后,开放式地论述了时滞系统的未来研究方向。      

Sensitivity analysis of kernel estimates: implications in nonlinear physiological system identification

Many techniques have been developed for the estimation of the Volterra/Wiener kernels of nonlinear systems, and have found extensive application in the study of various physiological systems. To date, however, we are not aware of methods for estimating the reliability of these kernels from single data records. In this study, we develop a formal analysis of variance for least-squares based nonlinear system identification algorithms. Expressions are developed for the variance of the estimated kernel coefficients and are used to place confidence bounds around both kernel estimates and output predictions. Specific bounds are developed for two such identification algorithms: Korenberg's fast orthogonal algorithm and the Laguerre expansion technique. Simulations, employing a model representative of the peripheral auditory system, are used to validate the theoretical derivations, and to explore their sensitivity to assumptions regarding the system and data. The simulations show excellent agreement between the variances of kernel coefficients and output predictions as estimated from the results of a single trial compared to the same quantities computed from an ensemble of 1000 Monte Carlo runs. These techniques were validated with white and nonwhite Gaussian inputs and with white Gaussian and nonwhite non-Gaussian measurement noise on the output, provided that the output noise source was independent of the test input.     

Dynamic Load Simulator: Actuation Strategies and Applications

The development of a multiple-actuator dynamic load simulator (DLS), for the simulation of correlated dynamic loads on small-scale structural components and substructures, or on bench-scale system assemblage is presented in this paper. Conceptually, the DLS employs actuators to simulate a desired dynamic loading environment due to wind, waves, or earthquakes, which in special cases may serve as a replacement for conventional facilities such as wind tunnels, wave tanks and shaking tables. The actuation strategy of the DLS is based on force-control rather than the customary motion control (displacement/velocity) scheme. The load simulator is ideal for structural components and for systems that can be idealized as lumped mass systems. An actuation strategy for the DLS based on an innovative scheme that utilizes the coupled control system is developed. For implementation of this scheme, the nonlinear control system toolbox in MATLAB is used. In this scheme, the tuning of control parameters in the time domain is carried out by solving a constrained optimization problem. A suite of loading protocols that includes sinusoidal, two-point correlated fluctuations in wind loading, earthquake induced loading and loads characterized by strong non-Gaussian features is simulated by employing the control scheme introduced here. The load simulation examples presented here demonstrate that the loading time histories generated by utilizing the DLS matched the target values with high fidelity.     

Stochastic Response and Stability of a Nonintegrable System

For determining the stochastic response and stability of a strongly nonlinear single-degree-of-freedom system using the stochastic averaging technique, the size of excitations should be small such that the response of the system converges weakly to a Markov process. This condition is not often met with practical problems, and therefore, application of this method for obtaining their responses becomes difficult. Further, for systems with nonlinearities that cannot be integrated in closed form, stability analysis by examining the conditions of the two boundaries of the problem is not possible. A semianalytical method along with a weighted residual technique is presented here to circumvent these difficulties and to determine the response and stability of a strongly nonlinear system subjected to sizable stochastic excitation. The weighted residual technique is employed to correct the errors in averaged drift and diffusion coefficients resulting due to the size of the stochastic excitation. Two example problems are solved as illustrations of the method.     

Quick Seismic Response Estimation of Prestressed Concrete Bridges Using Artificial Neural Networks

Seismic early warning has been very important and has become feasible in Taiwan. Perhaps because of the lack of quick and reliable estimations of the induced structural response, however, the triggering criteria of almost all of the existing earthquake protection or early warning systems in the world are merely based on the collected or estimated data of the ground motion, without any information regarding the structural response. This paper presents a methodology of generating quick seismic response estimations of a prestressed concrete (PC) bridge using artificial neural networks (ANNs), which may be incorporated in a seismic early warning system for the bridge. In the methodology ANNs were applied to model the critical structural response of a PC bridge subjected to earthquake excitation of various magnitudes along various directions. The objective was to implement a well-trained network that is capable of providing a quick prediction for the critical response of the target bridge. The well-known multilayer perception (MLP) networks with back propagation algorithm were employed. A simple augmented form of MLP that can be quantitatively determined was proposed. These networks were trained and tested based on the analytical data obtained from the nonlinear dynamic finite fiber element analyses of the target PC bridge. The augmented MLPs were found to be much more efficient than the MLPs in modeling the critical bending moments of the piers and girder of the PC bridge.     

Analysis of Class of Nonlinear System under Deterministic and Stochastic Excitations

In this paper, some analysis techniques of nonlinear dynamics are applied to physical systems which may be modeled by the Duffing nonlinear differential equation. The response of the Duffing oscillator to both deterministic sinusoidal and stochastic loadings is investigated and distinct regimes of the response motion are discerned and discussed. The stochastic input to the system is low-pass Gaussian white noise. The efficacy of studying the variation in time of the probability density of one or more of the system output states to determine the type of motion of the system is examined. Attractors in phase space are defined via Poincaré mapping and bounds on motion which serve as signatures for particular types of motion (e.g., chaotic, periodic) are identified by a hypervolume measurement technique. An accepted method for adapting one measured output state into a higher dimensional space by using time-delayed coordinates is used in conjunction with correlation dimension calculation to supply a lower-bound estimate of the fractal dimension and insight into the character of the motion of a nonlinear dynamic system.     

Identification of Parametric Variations of Structures Based on Least Squares Estimation and Adaptive Tracking Technique

An important objective of health monitoring systems for civil infrastructures is to identify the state of the structure and to detect the damage when it occurs. System identification and damage detection, based on measured vibration data, have received considerable attention recently. Frequently, the damage of a structure may be reflected by a change of some parameters in structural elements, such as a degradation of the stiffness. Hence it is important to develop data analysis techniques that are capable of detecting the parametric changes of structural elements during a severe event, such as the earthquake. In this paper, we propose a new adaptive tracking technique, based on the least-squares estimation approach, to identify the time-varying structural parameters. In particular, the new technique proposed is capable of tracking the abrupt changes of system parameters from which the event and the severity of the structural damage may be detected. The proposed technique is applied to linear structures, including the Phase I ASCE structural health monitoring benchmark building, and a nonlinear elastic structure to demonstrate its performance and advantages. Simulation results demonstrate that the proposed technique is capable of tracking the parametric change of structures due to damages.     

Real-Time Substructure Tests Using Hydraulic Actuator

A new real-time substructure method for testing systems under dynamic loading is described. The method separates a complex system into a physical, possibly nonlinear, subsystem (to be tested experimentally at large scale) and a surrounding linear system, modeled numerically. The two subsystems interact in real time allowing realistic time-dependent nonlinear behavior to take place. This behavior may be impossible to model computationally, and the method overcomes problems associated with scaling and time-dependent effects associated with current shaking table and pseudodynamic test methods. Dynamic forces are applied to the numerical model, and the resulting displacements at the interface between the two subsystems are applied to the physical system using servohydraulic actuators. The restoring forces are then measured and fed back to the numerical model, so that the response for the next time step can be calculated. The technique can be applied to a wide range of complex, linear∕nonlinear systems such as structures with localized plastic deformation, soil-structure interaction, or vehicle-suspension interaction. The method is demonstrated for both single and multi-degree-of-freedom systems, using a single actuator to apply displacements to a physical specimen. Comparisons between experimental and theoretical results show excellent agreement.     

Evaluation of clothing systems to determine heat strain

This article describes the basic evaluation process and test methodology employed when temperature extremes for clothing systems must be considered as part of the U.S. Army's Health Hazard Assessment for material in the development and acquisition process. The goals of the evaluation are to select clothing systems that minimize the hazards of heat strain and to predict the heat strain for persons wearing such clothing. Clothing evaluations begin with biophysical assessments that determine the thermal characteristics (vapor permeability and insulation) for textiles via guarded hot plate tests and for clothing systems via thermal manikin tests. The results from biophysical tests can be used to select the textile and/or clothing with the best thermal characteristics. The data from manikin evaluations also can be used in prediction modeling. Human physiological testing is best done in a controlled laboratory environment, although for realism and user acceptability field trials may also be conducted. Proven test and measurement methods must be employed, and tests must control for confounding variables; subjects serve as their own controls, and test environment and procedures are consistent between trials. The process and test methodology described can be applied to the evaluation of civilian clothing systems as well as to the military systems for which they were developed.     

In vitro evolution of molecular cooperation in CATCH, a cooperatively coupled amplification system

BACKGROUND: One of the key issues in the investigation of evolution is how complex systems evolved from simple chemical replicators. Theoretical work proposed several models in which complex replicating systems are kinetically stabilized. The development of powerful isothermal amplification technique allows complex nucleic acid based evolving in vitro systems to be set up, which may then serve to verify experimentally current theories of evolution. Recently such a system based on the 3SR (self-sustained sequence replication) reaction has been established to investigate the evolution of cooperation: the trans-cooperatively coupled CATCH (cooperative amplification by cross hybridization). RESULTS: Over four rounds of serial transfer, the cooperatively coupled two species CATCH system evolved into a more complex cooperative four species system, which then was overgrown by CATCH-derived RNA-Z-like hairpin species. In contrast to the classical RNA-Z species, these molecules have complementary loop sequences and self-amplify using a dual mechanism that includes concentration-dependent phases of noncooperative and cooperative amplification. CONCLUSIONS: The evolution of a cooperative system, under conditions that were alternately unfavorable and favorable for cooperative amplification, led to a system showing facultative cooperation. This principle of facultative cooperation preserves the complexity of the system investigated and could have general implications for the evolution and stabilization of cooperation under oscillating reaction conditions.     

Deterministic Excitation Forces for Simulation and Identification of Nonlinear Hysteretic SDOF Systems

This paper investigates how to design deterministic excitation forces in studying nonlinear single-degree-of-freedom systems, especially those with rate and path dependency and strength and stiffness degradation. One frequency-modulated periodic excitation and its amplitude-modulated counterpart are proposed as a solution, and a series of numerical exercises are carried out to show that these forces can be designed for sufficient forcing functions to study the complex nonlinear hysteresis. To rapidly reveal the underlying characteristics of the system and also to further lead to an effective system identification, four evaluation tools are proposed to be utilized together with the proposed excitation forces. These tools include the response curves, force-state map, intercycle drift, and intercycle pattern change, based on which some distinctive “patterns” are obtained to reveal the existence of nonlinearities, types of nonlinearities, existence of memory, and degradation. By using both Bouc-Wen and Bouc-Wen-Baber-Noori models for the system in all the simulations, the writers compare the commonly used forces with the proposed excitation forces to further demonstrate the advantages of the proposed excitation forces and evaluation tools. The writers also explore challenges in terms of implementing the proposed excitation forces. The results of this study are expected to benefit both physical testing and numerical simulation of complex nonlinear hysteretic systems in a time- and cost-effective manner, as well as leading to efficient schemes for system identification.     

Riemann Solvers with Runge–Kutta Discontinuous Galerkin Schemes for the 1D Shallow Water Equations

The spectrum of this survey turns on the evaluation of some eminent Riemann solvers (or the so-called solver), for the shallow water equations, when employed with high-order Runge–Kutta discontinuous Galerkin (RKDG) methods. Based on the assumption that: The higher is the accuracy order of a numerical method, the less crucial is the choice of Riemann solver; actual literature rather use the Lax-Friedrich solver as it is easy and less costly, whereas many others could be also applied such as the Godunov, Roe, Osher, HLL, HLLC, and HLLE. In practical applications, the flow can be dominated by geometry, and friction effects have to be taken into consideration. With the intention of obtaining a suitable choice of the Riemann solver function for high-order RKDG methods, a one-dimensional numerical investigation was performed. Three traditional hydraulic problems were computed by this collection of solvers cooperated with high-order RKDG methods. A comparison of the performance of the solvers was carried out discussing the issue of L1-errors magnitude, CPU time cost, discontinuity resolution and source term effects.     

Parametric Analysis of Water-Hammer Effects in Small Hydro Schemes

In small hydro schemes, when equipped with small inertia turbines, the parameterization of water-hammer effects might allow a better characterization of the dynamic behavior of these turbomachines, assisting in the choice of the most appropriate solution. This is particularly important when there is a lack of turbine characteristic curves. A novel technique, based on a dynamic orifice concept, is presented herein. This technique enables the simulation of the turbine operation during both steady-state and transient conditions, which allows a reliable evaluation of various scenarios with different characteristics, essential for design purposes. This type of analysis establishes the interaction between the powerhouse and the hydraulic circuit by means of the characteristic parameters of each component. The most severe hydrotransients occur during extreme operating conditions, such as full-load rejection and turbine stoppages, particularly when the small hydro is installed in hydraulic systems with high head or long pipeline length.     

Image feature based automatic correction of low-frequency spatial intensity variations in MR images

An automatic method of compensating for low-frequency variations in magnetic resonance images is presented. Small variations within a tissue type are modelled and a correction function is generated. The method is based completely on image features and does not need a phantom or user interaction to generate the compensation function. This image correction simplifies digital image analysis and may enhance clinical evaluation. As a result, the correction technique reduces inhomogeneity and improves contrast. Our results show that the radiofrequency response variation of coils can be reduced. The segmentation process, even with a simple threshold method, produces more reliable results when corrected images are used. The presented method is most useful for images acquired in the sagital and coronal planes with circular local coils, or using surface coils, e.g., spine coils.     

Sensitivity-Based External Calibration of Multiaxial Loading System

Due to the nonlinear nature of coordinate transformations, evaluation and calibration of multiaxial loading systems in global Cartesian coordinates are challenging problems. This study proposes a systematic calibration method for multiaxial loading systems in global coordinates using an external measurement system. Global coordinate measurement for a multiaxial loading system is usually obtained from a geometric transformation based on internal actuator measurements. However, any misrepresentation of initial actuator configuration (e.g., origin, pin locations, etc.) introduces errors and cross-talk in the global Cartesian coordinates. Such errors and cross-talk cannot be observed or eliminated based on internal measurements. The method proposed in this paper is based on the sensitivity of the global coordinates with respect to the initial actuator length. To validate the proposed method, calibration is performed using the state-of-the-art Load and Boundary Condition Box at University of Illinois at Urbana-Champaign as the multiaxial loading system and the Krypton Dynamic Measurement Machine as the external measurement system. Experimental results demonstrate that the proposed sensitivity-based external calibration method is effective for improving control accuracy and reducing cross-talk of multiaxial loading systems in global Cartesian coordinates.     

Resource-saving direct alloying of steel

The development of the alloying and modification of steel by oxides, including natural materials, is very promising. Potential materials include barium–strontium carbonate ores, nickel concentrates, and vanadium converter slag, which may be used to produce steel with improved properties, without the expensive process of producing ferroalloys and intermediate alloys. Considerable research is required to improve steel-making processes. Thermodynamic modeling may be used for that purpose. In the present work, thermodynamic modeling is used for elementary systems involved in the extraction of barium, strontium, vanadium, and nickel from their oxides by means of different reducing agents. The results indicate that microalloying and modification of steel by inexpensive materials is possible; and permit the determination of the type of reducing agent and the optimal quantities employed. The Terra software used in thermodynamic modeling permits the determination of the equilibrium composition of the multicomponent heterogeneous system for high-temperature conditions, on the basis of the maximum-entropy principle. The reducing agents considered are carbon, silicon, and aluminum. The influence of the temperature and reducing-agent consumption on the reduction processes is investigated. The results regarding the reduction of barium and strontium show that silicon or aluminum is the best reducing agent when barium-bearing oxide materials are employed. The optimal reducing-agent consumption corresponding to maximum reduction of the barium and strontium is determined. The possibility of reducing nickel by carbon is confirmed. It is found that vanadium may be reduced by silicon or carbon or a complex process in which carbon is the predominant reducing agent. The results permit the development of a resource-saving technology based on oxides for the alloying, microalloying, and modification of Fe–C systems.     

On the recovery and recrystallization which attend static softening in hot-deformed copper and aluminum

The fundamental nature of the static restoration processes which result in static softening after a hot deformation has been studied in copper and aluminum. The kinetics of static softening were determined using the double-hit technique applied to hot compression while the microstructural changes were characterized by the quantitative metallography of quenched specimens. A static softening parameter based on the area under the compression flow curve was used to describe the static softening kinetics. The static softening curves exhibited a simple sigmoidal shape showing no inflection. The relative softening occurring prior to the initiation of recrystallization was found to be small when compared with that occurring after the onset of recrystallization, and was dependent on deformation temperature, amount of deformation, purity and stacking fault energy. The static softening was related to the fractional recrystallization in a nonlinear manner; the degree of nonlinearity was dependent on the occurrence of recovery and dynamic recrystallization. The recrystallization process in Al was of the classical type with the nucleation stage being either the boundary bulge or subgrain growth mechanism. In Cu twinning appeared to be the major nucleation mechanism for recrystallization. When the applied prestrain was greater than the critical strain for dynamic recrystallization, recrystallization was observed to be completed before the completion of static softening. In this case, the remaining softening occurred by the operation of multiple recrystallization where high-order twins formed in the already twinned regions.