Identification Of Cascade Systems Research Articles

Synthesis cascade estimation for aircraft system identification

PurposeThe purpose of this paper extends the authors’ previous contributions on aircraft system identification, such as open loop identification or closed loop identification, to cascade system identification. Because the cascade system is one special network system, existing in lots of practical engineers, more unknown systems are needed to identify simultaneously within the statistical environment with the probabilistic noises. Consider this problem of cascade system identification, prediction error method is proposed to identify three unknown systems, which are parameterized by three unknown parameter vectors. Then the cascade system identification is transferred as one parameter identification problem, being solved by the online subgradient descent algorithm. Furthermore, the nonparametric estimation is proposed to consider the general case without any parameterized process. To make up the identification mission, model validation process is given to show the asymptotic interval of the identified parameter. Finally, simulation example confirms the proposed theoretical results.Design/methodology/approachFirstly, aircraft system identification is reviewed through the understanding about system identification and advances in control theory, then cascade system identification is introduced to be one special network system. Secondly, for the problem of cascade system identification, prediction error method and online subgradient decent algorithm are combined together to identify the cascade system with the parameterized systems. Thirdly from the point of more general completeness, another way is proposed to identify the nonparametric estimation, then model validation process is added to complete the whole identification mission.FindingsThis cascade system corresponds to one network system, existing in lots of practice, such as aircraft, ship and robot, so it is necessary to identify this cascade system, paving a way for latter network system identification. Parametric and nonparametric estimations are all studied within the statistical environment. Then research on bounded noise is an ongoing work.Originality/valueTo the best of the authors’ knowledge, research on aircraft system identification only concern on open loop and closed loop system identification, no any identification results about network system identification. This paper considers cascade system identification, being one special case on network system identification, so this paper paves a basic way for latter more advanced system identification and control theory.

Identification of nonlinear block-oriented systems with backlash and saturation

Abstract A new approach to modeling and identification of discrete-time nonlinear dynamic systems with input backlash and output saturation nonlinearities is presented. The proposed three-block cascade mathematical model results from successive applications of the key-term separation principle. This provides special nonlinear model description that is linear in parameters. An iterative technique with internal variable estimation is proposed for estimation of all the model parameters based on measured input/output data and minimizing the least-squares criterion. Illustrative example of cascade system identification with backlash and saturation is included.

Identification of nonlinear dynamic systems with input saturation and output backlash using three-block cascade models

The paper deals with the parameter identification of nonlinear dynamic systems with input saturation and output backlash using three-block cascade models. Multiple application of a decomposition technique provides special formulas for the corresponding nonlinear model description that are linear in parameters. A least-squares-based iterative technique allows estimation of all the model parameters based on measured input/output data. Examples of three-block cascade system identification illustrate the feasibility of proposed method.

Identification of Nonlinear Cascade Systems with Time-Varying Backlash

Identification of Nonlinear Cascade Systems with Time-Varying BacklashRecursive identification of cascade systems with time-varying input backlash and linear dynamic system is presented. A new analytic form of backlash characteristic description is used, hence all the parameters in the cascade model equation are separated and their estimation is solved as a quasi-linear problem using the recursive least squares method with internal variable estimation. Simulation studies are included.

Prediction of Natural History of Neuromuscular Properties After Stroke Using Fugl-Meyer Scores at 1 Month

Background. The link between spasticity and impaired voluntary movement after stroke remains unclear because of the lack of suitable tools characterizing properties of spastic muscles. Describing this relationship early poststroke can potentially help predict the extent and time course of recovery. Objective. To describe the time course of changes in neuromuscular properties after stroke using the upper extremity Fugl-Meyer Assessment (FMA) at 1 month to predict recovery patterns over 1 year. Methods.Using a parallel cascade system identification technique, this study characterized intrinsic and reflex behaviors for different mean elbow joint angles, at specified times poststroke. Then the “growth mixture” model was used to characterize recovery patterns over 1 year. Logistic regression analyses were applied to predict these patterns. The impact of patient characteristics was also investigated. Results. In 21 stroke survivors, 14 had sustained hemorrhage and 7 had thromboses. The study observed several recovery classes, relating intrinsic and reflex stiffness magnitudes with changing elbow angle at different time points. The largest group (48%) showed progressive increase in reflex stiffness over time, but 33% showed declining reflex stiffness over the same period. A third class (19%) showed invariant reflex properties. These differences were linked to the initial reflex magnitudes. The FMA at 1 month showed an inverse relationship with key reflex patterns and proved to be a strong predictor of class membership. Stroke type was also influential. Conclusions. The logistical regression class may enable us to accurately predict reflex responses during the first year, allowing us to apportion impairment between central and peripheral mechanisms.

Identification of cascade systems with backlash

This article deals with identification of cascade dynamic systems including backlash. A new form of backlash description is leading to mathematical models of the cascade system with output backlash and the sandwich system with internal backlash, which have all the model parameters separated. The identification based on these models is solved as a quasi-linear problem using iterative algorithms with internal variable estimation. More illustrative examples are included.

Variance results for identification of cascade systems

The objective of this contribution is to analyze statistical properties of estimated models of cascade systems. Models of such systems are important in for example cascade control applications. The aim is to present and analyze some fundamental limitations in the quality of an identified model of a cascade system under the condition that the true subsystems have certain common dynamics. The model quality is analyzed by studying the asymptotic (large data) covariance matrix of the Prediction Error Method parameter estimate. The analysis will focus on cascade systems with three subsystems. The main result is that if the true transfer functions of the first and second subsystem are identical, the output signal information from the second and third subsystems will not affect the asymptotic variance of the estimated model of the first subsystem. This result implies that for a cascade system with two subsystems, where the dynamics of the first subsystem is a factor of the dynamics of the second one, the output signal information from the second subsystem will not improve the asymptotic quality of the estimate of the first subsystem. The results are illustrated by some simple FIR examples.

On Estimation of Cascade Systems with Common Dynamics

Recent research on identification of cascade systems has revealed some intriguing variance results for the estimated transfer functions of the subsystems. Such structures are common in most engineering applications. Even so, little is known about quality properties for structured estimated models of cascade systems. The objective of this paper is to analyze the underlying mechanism for some non-intuitive variance results when the true subsystems have common dynamics. It turns out that a simple FIR example of two cascaded subsystems can be used to understand the basic issues. The cascade system identification problem for this case corresponds to solving a second order equation in a least squares sense constraining the roots to be real. The difficult case is when the second order equation has double roots (the discriminant Δ zero), which holds when the transfer functions of the subsystems are equal. In this case a more proper statistical analysis should be done conditional on the sign of Δ. If only the second output signal is used for estimation the result is that Δ > 0 gives estimates with poor statistical properties (variance of order O(1/N)), while Δ < 0 will automatically constrains the roots to be real and double and hence this case gives variance of order O (1/N). If both output signals are used for estimation the unconditional variance of the estimate of the first system does not depend, on the average, on the output from the second system. A simulation example shows that the statistical properties also in this case are much better than predicted by average variance analysis if Δ< 0. For this simple example, it is hence possible to monitor the quality of the estimate by studying the sign of Δ. Traditional variance analysis only considers the average effects and hence misses this two mode (good or bad) situation.

On Identification of Cascade Systems

The objective of this contribution is to discuss some aspects of system identification of cascade systems. Models of such systems are important in for example cascade control applications. We will restrict our attention to systems with one input signal and two output signals. First, we will analyze some fundamental limitations regarding the statistical properties of such estimated models and in particular why it can be difficult to identify cascade systems where the sub-transfer functions are close to each other. We will then show how an unstructured SIMO model estimate can be used to find a cascade system model using an indirect prediction error method or balanced model reduction.

Neuromuscular Abnormalities Associated With Spasticity of Upper Extremity Muscles in Hemiparetic Stroke

Our objective was to assess the mechanical changes associated with spasticity in elbow muscles of chronic hemiparetic stroke survivors and to compare these changes with those recorded in the ankle muscles of a similar cohort. We first characterized elbow dynamic stiffness by applying pseudorandom binary positional perturbations to the joints at different initial angles, over the entire range of motion, with subjects relaxed. We separated this stiffness into intrinsic and reflex components using a novel parallel cascade system identification technique. In addition, for controls, we studied the nonparetic limbs of stroke survivors and limbs of age-matched healthy subjects as primary and secondary controls. We found that both reflex and intrinsic stiffnesses were significantly larger in the stroke than in the nonparetic elbow muscles, and the differences increased as the elbow was extended. Reflex stiffness increased monotonically with the elbow angle in both paretic and nonparetic sides. In contrast, the modulation of intrinsic stiffness with elbow position was different in nonparetic limbs; intrinsic stiffness decreased sharply from full- to mid-flexion in both sides, then it increased continuously with the elbow extension in the paretic side. It remained invariant in the nonparetic side. Surprisingly, reflex stiffness was larger in the nonparetic than in the normal control arm, yet intrinsic stiffness was smaller in the nonparetic arm. Finally, we compare the angular dependence of paretic elbow and ankle muscles and show that the modulation of reflex stiffness with position was strikingly different.

Intrinsic and reflex stiffness in normal and spastic, spinal cord injured subjects.

Mechanical changes underlying spastic hypertonia were explored using a parallel cascade system identification technique to evaluate the relative contributions of intrinsic and reflex mechanisms to dynamic ankle stiffness in healthy subjects (controls) and spastic, spinal cord injured (SCI) patients. We examined the modulation of the gain and dynamics of these components with ankle angle for both passive and active conditions. Four main findings emerged. First, intrinsic and reflex stiffness dynamics were qualitatively similar in SCI patients and controls. Intrinsic stiffness dynamics were well modeled by a linear second-order model relating intrinsic torque to joint position, while reflex stiffness dynamics were accurately described by a linear, third-order system relating half-wave rectified velocity to reflex torque. Differences between the two groups were evident in the values of four parameters, the elastic and viscous parameters for intrinsic stiffness and the gain and first-order cut-off frequency for reflex stiffness. Second, reflex stiffness was substantially increased in SCI patients, where it generated as much as 40% of the total torque variance, compared with controls, where reflex contributions never exceeded 7%. Third, differences between SCI patients and controls depended strongly on joint position, becoming larger as the ankle was dorsiflexed. At full plantarflexion, there was no difference between SCI and control subjects; in the mid-range, reflex stiffness was abnormally high in SCI patients; at full dorsiflexion, both reflex and intrinsic stiffness were larger than normal. Fourth, differences between SCI and control subjects were smaller during the active than the passive condition, because intrinsic stiffness increased more in controls than SCI subjects; nevertheless, reflex gain remained abnormally high in SCI patients. These results elucidate the nature and origins of the mechanical abnormalities associated with hypertonia and provide a better understanding of its functional and clinical implications.