System Identification Procedure Research Articles

Objective selection of signals for assessment of cerebral blood flow autoregulation in neonates

A number of different system identification techniques have been proposed to assess dynamic cerebral autoregulation in critically ill patients. From these methods, the response to a standard stepwise change in blood pressure can be estimated. Responses lacking physiological consistency are a common occurrence and could be the consequence of particular system identification procedures or, alternatively, caused by measurements with a poor signal-to-noise ratio. A multi-observer approach was adopted in this paper to classify cerebral blood flow velocity (CBFV) step responses to spontaneous changes in arterial blood pressure in a group of 43 neonates with a mean gestational age of 33.7 weeks (range 24–42 weeks) and a mean birthweight of 1980 g (range 570–3910 g). Three experienced observers independently analysed the estimated step responses in 191 recordings each lasting 100 s; for an autoregressive (ARX) model, 124 (65%) of the step responses were accepted by at least two of the three observers. Two other system identification methods, transfer function analysis and the moving average Wiener–Laguerre model, gave 90 (45%) and 98 (51%) acceptable responses, respectively. Only 54 epochs (28%) were accepted with all three methods. With 88 (46%) responses rejected by at least two methods, it can be concluded that signal quality was the main reason for nonphysiological step responses. To avoid the need for subjective visual selection, an automatic procedure for classifying step responses was implemented leading to sensitivities and specificities in the range 85–90%, with respect to the agreement with subjective evaluations. Objective selection of CBFV step responses is thus feasible and could also be adapted for other physiological measurement techniques relying on system identification methods.

Estimating the transfer function of the cantilever in atomic force microscopy: A system identification approach

Dynamic atomic force microscopy (AFM) offers many opportunities for the characterization and manipulation of matter on the nanometer scale with a high temporal resolution. The analysis of time-dependent forces is basic for a deeper understanding of phenomena such as friction, plastic deformation, and surface wetting. However, the dynamic characteristics of the force sensor used for such investigations are determined by various factors such as material and geometry of the cantilever, detection alignment, and the transfer characteristics of the detector. Thus, for a quantitative investigation of surface properties by dynamic AFM an appropriate system identification procedure is required, characterizing the force sensor beyond the usual parameters spring constant, quality factor, and detection sensitivity. Measurement of the transfer function provides such a characterization that fully accounts for the dynamic properties of the force sensor. Here, we demonstrate the estimation of the transfer function in a bandwidth of 1MHz from experimental data. To this end, we analyze the signal of the vibrations induced by snap-to-contact and snap-off-contact events. For the free cantilever, we determine both a parameter-free estimate [empirical transfer function estimate (ETFE)] and a parametric estimate of the transfer function. For the surface-coupled cantilever the ETFE is obtained. These identification procedures provide an intrinsic calibration as they dispense largely with a priori knowledge about the force sensor.

A bounded-error approach to piecewise affine system identification

This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.

Control Loop Performance Assessment. 2. Hammerstein Model Approach for Stiction Diagnosis

In part 2 of this two-part series, an approach for diagnosis and quantification of stiction using a simple single-parameter model is proposed. The stiction model, in conjunction with an identified process model from routine operating data, is shown to successfully facilitate stiction diagnosis. An optimization approach is used to jointly identify the process model and the stiction parameter. This approach is based on the identification of a Hammerstein model of the system comprising the sticky valve and the process. In this work, a new identification procedure for Hammerstein systems that supports stiction diagnosis is proposed. Industrial and simulation case studies are shown to demonstrate the application of the proposed approach for diagnosing stiction.

High fidelity ground effect model based on DGPS data

A global model approach developed on the X-31 EFM data was recently improved during the experimental aircraft program X-31 VECTOR. The VECTOR program is briefly presented, focusing on extremely precise ESTOL (Extremely Short Take-Off and Landing) manoeuvre following a slow, thrust-vectored approach at high angle of attack. High accuracy navigation and inertial sensor systems enable onboard calculation of the height above runway with sufficient accuracy, which is also required to identify ground effect. System identification procedure utilises a global model to cover the entire flight regime including high lift configuration during power approach and landing. Analysis of specially designed flight tests led to aerodynamic increment tables for supplementary update of the original database. The wind-tunnel and CFD-predicted ground effect was incorporated into the highly accurate identified global model which was then used for conventional landings re-simulation to support the initial ESTOL to the ground flight clearance process. Recently an incremental ground effect model was implemented to supplement the original data set. First identification results from conventional and ESTOL landings show some improvements compared to the predictions at very low height above ground shortly before touch down.

Physical modeling and visualization of soil liquefaction under high confining stress

The mechanisms of seismically-induced liquefaction of granular soils under high confining stresses are still not fully understood. Evaluation of these mechanisms is generally based on extrapolation of observed behavior at, shallow depths. Three centrifuge model tests were conducted at RPI's experimental facility to investigate the effects of confining stresses on the dynamic response of a deep horizontal deposit of saturated sand. Liquefaction was observed at high confining stresses in each of the tests. A system identification procedure was used to estimate the associated shear strain and stress time histories. These histories revealed a response marked by shear strength degradation and dilative patterns. The recorded accelerations and pore pressures were employed to generate visual animations of the models. These visualizations revealed a liquefaction front traveling downward and leading to large shear strains and isolation of upper soil layers.

비선형 동적 시스템의 파라미터 산정을 위한 주파수 영역 볼테라 모델의 이용

비선형 함수로 모델링되는 동적 시스템의 비선형 파라미터를 결정하기 위하여 주파수 영역 볼테라 모델을 적용하는 연구를 수행하였다. 시간영역의 1차, 2차, 3차 전달함수에 해당하는 주파수 영역의 볼테라 핵함수를 비선형 파라미터 산정 과정에 3차 비선형 항까지 포함시켰다. Schetzen의 방법으로 시스템의 비선형 미분방정식에 적합한 볼테라 급수 표현식을 정하고, 이로부터 유도되는 비선형 전달함수를 입력 출력 관계식에 사용하였다. 관찰된 입력을 비선형 주파수 영역 모델에 대입하여 계산한 출력과 관찰된 출력의 차이로 오차를 정의한 후 오차를 최소화 시키는 시스템 파라미터의 값을 구하였다. 예제를 통하여 선형 주파수 구간 뿐만 아니라 2차 혹은 3차 비선형이 지배적인 주파수 범위 대에서 볼테라 모델이 충분한 정확성과 수렴성을 가지며 인식된 파라미터는 실제 값과 잘 일치함을 확인할 수 있었다. Frequency domain Volterra model is applied to nonlinear parameter identification procedure for dynamic systems modeled by nonlinear function. The frequency domain Volterra kernels, which correspond io linear, quadratic, and cubic transfer functions in lime domain, are incorporated in nonlinear parametric identification procedure. The nonlinear transfer functions, which can be derived from the Volterra series representation of the nonlinear differential equation of the system by Schetzen's method(1980), are directly used for modeling input output relation. The error is defined by the difference between the observed output and the estimated output which is calculated by substituting the observed input to nonlinear frequency domain model. The system parameters are searched by minimizing the error. Volterra model guarantees enough accuracy and convergence and the estimated coefficients have a good agreement with their actual values not only in the linear frequency region but also in the legion where the <TEX>$2^{nd}\;or\;3^{rd}$</TEX> order nonlinearity is dominant.

A Technique for Estimating Linear Parameters Using Nonlinear Restoring Force Extraction in the Absence of an Input Measurement

Conventional nonlinear system identification procedures estimate the system parameters in two stages. First, the nominally linear system parameters are estimated by exciting the system at an amplitude (usually low) where the behavior is nominally linear. Second, the nominally linear parameters are used to estimate the nonlinear parameters of the system at other arbitrary amplitudes. This approach is not suitable for many mechanical systems, which are not nominally linear over a broad frequency range for any operating amplitude. A method for nonlinear system identification, in the absence of an input measurement, is presented that uses information about the nonlinear elements of the system to estimate the underlying linear parameters. Restoring force, boundary perturbation, and direct parameter estimation techniques are combined to develop this approach. The approach is applied to experimental tire-vehicle suspension system data.

Nonlinear Model for Sub- and Superharmonic Motions of a MDOF Moored Structure, Part 2—Sensitivity Analysis and Comparison

The nonlinear R-MI/SO system identification procedure and the parameters of the MDOF system identified in Part 1 are examined in detail in this paper. A parametric study is conducted and the results are presented on the sensitivity of the system parameters for two key nonlinear responses—subharmonic and superharmonic resonances. The parameters are compared to determine the appropriateness of using a single set of system parameters for both response regions. A detailed comparison of the MDOF and the corresponding SDOF system results is performed. The knowledge gained from the SDOF and MDOF studies on the applicability of the R-MISO technique for the system identification of MDOF submerged moored structures is discussed. The results show that the MDOF extension of the R-MI/SO nonlinear system identification technique works well; the resulting system parameters are relatively constant and can be applied to the both the sub- and superharmonic regions.

A Frequency Domain Technique for Characterizing Nonlinearities in a Tire-Vehicle Suspension System

Characterization of tire and suspension system nonlinearities in measured data is the first step in developing input-output quarter car models; however, system identification procedures, which require a priori knowledge of all nonlinearities within a system, often receive more attention in the research community. Furthermore, relatively few investigations have focused on nonlinear characterization and identification in the absence of input measurements. A new method for characterizing nonlinearities, in the absence of an input measurement, using transmissibility functions and ordinary coherence functions between response measurement degrees of freedom is discussed here. It is shown that the nonlinear nature of a vehicle system provides information about the nominal linear system when the input is unknown. Nonlinear frequency permutations, which create drops in the ordinary coherence function, serve to characterize the associated nonlinearities. In the absence of input measurements, coherence functions of the response transmissibility between the vehicle spindle and body allow the nonlinearities in the suspension system, but not the tires, to be characterized. Simulation results are discussed and the method is applied to experimental laboratory and operating data to validate the approach.

Human standing posture control system depending on adopted strategies

Control of the standing posture of humans involves at least two distinct modes of operation to restore the body balance in the sagittal plane: the ankle strategy and the hip strategy. The objective of the study was to estimate the contribution of vestibular, visual and somatosensory feedbacks to these distinct strategies. The body dynamics was described as the motion of two linked rigid segments that represented the legs and the rest of the body. The posture controller received the inclination angles of the two body segments as inputs and regulated the moments around the ankle and hip joints. The controller had four feedback paths that were characterised by transfer functions connecting the two inputs and the two outputs. To evoke the distinct strategies, the floor conditions were varied by narrowing the support surface under the feet. A continuous pseudo-random external disturbing force was applied to the waist and the thigh independently. The inclination angles of the body segments and the ground reaction force were measured, and the transfer functions of the controller were estimated with the maximum-likelihood system identification procedure. Six healthy male adult subjects participated in the experiment. When the hip strategy became evident under the narrow support surface conditions, the transfer function relating the leg inclination angle and the ankle joint moment decreased its DC gain (16%), whereas the other three transfer functions increased the gains (20-140%) (ANOVA, p < 0.05). Based on a criterion for simplicity in the modification of the posture controller, these changes suggest a new hypothesis that, when posture control becomes difficult, the central nervous system selectively activates the somatosensory feedback paths from the hip joint angle to the moments around the ankle and hip joints.

VALIDITY OF THE STANDARD CROSS-CORRELATION TEST FOR MODEL STRUCTURE VALIDATION

The standard prediction error framework provides many theoretical results under the assumption that the true system is in the model class. An important example is the expression for the parameter covariance matrix which is used to derive model uncertainty regions. An essential step in a system identification procedure is the (in)validation of this assumption that the model structure is rich enough to contain the true system. The standard test for this purpose is the sample cross-correlation test between the output residuals and the input. It turns out that this standard test itself is valid only under exactly those assumptions it is meant to verify. As a result considerable undermodelling errors can remain undetected. Besides suggesting caution to users of the standard test, methods are presented to adapt the test adequately.

Global Model Approach for X-31 VECTOR System Identification

A global model approach developed on data from the experimental aircraft program X-31 EFM was recently improved during the X-31 VECTOR program. Both programs are briefly presented, focusing on extremely precise ESTOL landings following a slow, thrust-vectored approach at high angle of attack. High-accuracy navigation and inertial sensor systems enable onboard calculation of the height above runway with sufficient accuracy which is also required to identify ground effect. System identification procedure utilizes a global model to cover the entire flight regime including high-lift configuration during power approach and landing. Analysis of specially designed flight test led to aerodynamic increment tables for supplementary update of the original database. The wind-tunnel and computational fluid dynamics (CFD) predicted ground effect was incorporated into the higly accurate identified global model, which was then used for conventional landings resimulation to support the initial extremely short takeoff and landing (ESTOL) to the ground flight clearance process. Recently an incremental ground effect model was implemented to supplement the original data set. First identification results from conventional and ESTOL landings show some improvements compared to the predictions at very low height above ground.

A time and frequency domain approach for identifying nonlinear mechanical system models in the absence of an input measurement

Conventional system identification procedures require that input data or at least an estimate of the input be used in the parameter estimation process. In many ‘real’ mechanical systems inputs are not readily measured, as in automotive road vehicle data in which the input to the tire patch of the tires from the road is neither measurable nor easy to estimate. A new method for nonlinear system identification of mechanical systems, in the absence of an input measurement, using a combination of time and frequency domain techniques is presented here. In the time domain, restoring force plots are used to characterize the frequency and amplitude characteristics of the nonlinearities. These observed nonlinear characteristics are then used in the output-only formulation of the nonlinear identification through feedback of the outputs frequency domain parameter estimation technique to build a model with linear and nonlinear frequency response functions, which can be used to predict the response of the system. The method is applied to experimental tire-vehicle suspension system data.

Input Test Signal Design and Parameter Estimation Method for the Hammerstein−Wiener Processes

We propose a new parameter estimation method for Hammerstein-Wiener-type processes composed of the input-output nonlinear static functions and a linear dynamic subsystem. A special test signal is designed to separate the identification problems of the linear dynamic subsystem and the output nonlinear static function from that of the input nonlinear static function. Then, the system identification procedure can be significantly simplified: the identification problems of the linear dynamic subsystem and the output nonlinear static function can be solved independently without considering the input nonlinear static function, and the model parameters of the input nonlinear static function can also be estimated analytically without any iterative nonlinear optimization. Furthermore, we develop a new estimation algorithm to identify the linear dynamic subsystem and the output nonlinear static function more efficiently. This algorithm does not need to initialize the model parameters of the output nonlinear static function and reduces the searching space in the iterative nonlinear optimization problem, resulting in more robust and faster convergence and easier initialization in the nonlinear optimization compared to previous approaches.

Analysis and performance of the control systems of the NASA 70-meter antennas

The control systems of the NASA 70-m antennas include the antenna control system, the Master Equatorial (ME) control system, and their combinations (called modes). The Master Equatorial is a small telescope mounted on the top of a tower located inside the antenna structure. In the Antenna Encoder mode antenna encoders are used to close the feedback loop. In the Autocollimator mode the Master Equatorial is a master that follows a target, and the antenna is a slave that follows the Master Equatorial. In the Master Equatorial Encoder mode the “master-slave” relationship is reversed. In the paper the analysis begins with the description of the open-loop models of the antenna and of the Master Equatorial. We obtained the models by using field test data and system identification techniques. Next, we analyzed and evaluated the performance of the three modes of the antenna control system. The analysis showed that the Autocollimator and Master Equatorial Encoder tracking modes are feasible for high-rate tracking, and that the latter mode has the smallest tracking error. Finally, we analyzed the switching between antenna modes, necessary while tracking near the keyhold. We showed that switching causes jerks of magnitudes within the acceptable threshold. The contribution of this paper includes the development of the antenna model using field data and system identification procedures, the development of the LQG control algorithm for the 70-meter antenna, the development of two control cooperating systems (antenna and ME), identifying the more appropriate, and analyzing of switching between the two control systems.

A neuro-fuzzy inference system for modeling and prediction of heart rate variability in the neuro-intensive care unit

In the neurological intensive care unit (NICU), prediction of impending changes in patient condition would be highly beneficial. In this paper, we employ a neuro-fuzzy inference system (NFIS) for short-term prediction of heart rate variability in the NICU. An NFIS was selected because it allows for a “gray-box” approach through which a system identification procedure is used in conjunction with fuzzy modeling. The NFIS is described in detail and is compared to an auto-regressive moving average (ARMA) model for its ability to model both simulated and measured data from NICU patients. We found that the NFIS is capable of predicting changes in heart rate to a reasonable extent, and that the NFIS has both advantages and limitations over the ARMA model. The NFIS may therefore be a reasonable technique to consider for more extensive prediction purposes in ICU settings.

Element Level System Identification with Unknown Input with Rayleigh Damping

A novel system identification procedure is proposed for nondestructive damage evaluation of structures. It is a finite element-based time-domain linear system identification technique capable of identifying structures at the element level. The unique features of the algorithm are that it can identify a structure without using any input excitation information and it can consider both viscous and Rayleigh-type proportional damping in the dynamic models. The consideration of proportional damping introduces a source of nonlinearity in the otherwise linear dynamic algorithm. However, it will also reduce the total number of damping coefficients to be identified, reducing the size of the problem. The Taylor series approximation is used to transform a nonlinear set of equations to a linear set of equations. The proposed algorithm, denoted as the modified iterative least square with unknown input algorithm, is verified with several examples considering various types of structures including shear-type building, truss, and beams. The algorithm accurately identified the stiffness of structures at the element level for both viscous (linear) and proportional (nonlinear) damping cases. It is capable of identifying a structure even with noise-contaminated response information. An example shows how the algorithm could be used in detecting the exact location of a defect in a defective element. The algorithm is being developed further and is expected to provide an economical, simple, efficient, and robust system identification technique that can be used as a nondestructive defect detection procedure in the near future.

SYSTEM IDENTIFICATION OF LANDFILL SEISMIC RESPONSE

Assessment of landfill seismic response necessitates the availability of reliable dynamic material properties. During the past decade, geophysical surveys and computational studies have been conducted to investigate the seismic response of the Operating Industries, Inc. (OII) landfill in Southern California. In this paper, a survey and summary of available research results is presented. In addition, a set of Oil input-output seismic records during six earthquakes is thoroughly analysed. Spectral analyses are conducted to shed light on the landfill dynamic response characteristics. A simple shear beam model is found to be useful in modelling the landfill resonant behaviour. System identification techniques are employed to estimate the landfill stiffness and damping properties. These properties are defined by minimising the difference between computed and recorded acceleration response spectra at the landfill top. The identified stiffness properties are found to be near the lower bound of those documented through geophysical measure-ments. Identified damping of about 5% (at resonance) is within the range of earlier investigations. Comparisons of the computed and recorded accelerations show: (I) effectiveness of a linear viscous shear beam model in simulating the landfill dynamic behaviour, for the recorded small to moderate levels of dynamic excitation (up to 0.26 g peak lateral acceleration), and (ii) potential of the employed system identification procedure for analysis of input-output seismic motions.

Pre-Estimation for Better Initial Guesses

Fast, assured convergence of iterative identification methods is important in many on-line applications, including systems that exploit indirect measurements, diagnostics, and model-based control. The transient response of a system can often be mapped directly to an estimate of the system model parameters. This initial estimate, or pre-estimate, can be evaluated in fixed time and may greatly accelerate subsequent iterative system identification procedures. A pre-estimation structure is developed and demonstrated with examples including single-tone frequency estimation and induction motor parameter identification.