Sampled Input Output Data Research Articles

Instrumental variable methods for identifying partial differential equation models

This paper presents a refined instrumental variable method for identifying partial differential equation models of distributed parameter systems directly from discrete-time sampled input–output data. The proposed method is compared with conventional least-squares and other instrumental variable-based techniques. Monte Carlo simulation analysis results are presented to illustrate the effectiveness and superiority of the proposed method in the presence of additive output measurement noise and under different spatio-temporal sampling conditions.

Use of the circle segments visualization technique for neural network feature selection and analysis

In this paper, the circle segments (CS) technique is proposed as a data visualization tool for selecting and analysing the effects of the input features towards the target outputs in constructing neural network models. Specifically, the multi-layer perceptron (MLP) network is employed to tackle function approximation and pattern classification tasks, and CS is used to provide visualization of the correlations between the input features and the target outputs in these tasks. The effectiveness of the proposed approach is evaluated using two benchmark data sets, one for function approximation and another for pattern classification. Performance comparison with the response surface methodology (in function approximation) and with principal component analysis (in pattern classification) is conducted. The results indicate the usefulness of CS in examining the correlations between the input–output data samples, with improved performances. In addition, a real medical diagnosis task is used to evaluate the applicability of the approach. The outcomes, again, demonstrate improvements in accuracy, sensitivity, and specificity with the use of CS for feature selection, even with more than 50% of the input features eliminated.

Identification of continuous-time systems with multiple unknown time delays by global nonlinear least-squares and instrumental variable methods

This paper considers the identification problem of multiple input single output (MISO) continuous-time systems with unknown time delays of the inputs, from sampled input–output data. An iterative global separable nonlinear least-squares (GSEPNLS) method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum, by using the stochastic global-optimization techniques. Furthermore, the GSEPNLS method is modified to a novel global separable nonlinear instrumental variable (GSEPNIV) method to remove the biases of the estimates in the presence of high measurement noise. Simulation results show that the proposed algorithms work quite well.

Interpretability and learning in neuro-fuzzy systems

A methodology for the development of linguistically interpretable fuzzy models from data is presented. The implementation of the model is conducted through the training of a neuro-fuzzy network, i.e., a neural net architecture capable of representing a fuzzy system. In the first phase, the structure of the model is obtained by means of subtractive clustering, which allows the extraction of a set of relevant rules based on a set of representative input–output data samples. In the second phase, the parameters of the model are tuned via the training of a neural network through backpropagation. In order to attain interpretability goals, the method proposed imposes some constraints on the tuning of the parameters and performs membership function merging. In this way, it will be easy to assign linguistic labels to each of the membership functions obtained, after training. Therefore, the model obtained for the system under analysis will be described by a set of linguistic rules, easily interpretable.

Identification of continuous-time systems from samples of input-output data: An introduction

This paper presents an introductory survey of the methods that have been developed for identification of continuous-time systems from samples of input-output data. The two basic approaches may be described as (i) the indirect method, where first a discrete-time model is estimated from the sampled data and then an equivalent continuous-time model is calculated, and (ii) the direct method based on concepts of approximate numerical integration, where a continuous-time model is obtained directly without going through the intermediate step of first determining a discrete-time model.

ACCURATE PREDICTION OF NON-LINEAR WAVE FORCES: PART I (FIXED CYLINDER)

A new equation structure is proposed as an alternative to the Morison equation for the prediction of wave forces. Initially, non-linear, parametric, continuous time differential equation models were estimated from wave force data for a variety of flow situations by adopting a new approach which avoids direct differentiation of the input–output data. The method consists of two stages. The first stage involves the estimation of a discrete time model (polynomial NARMAX) from sampled input–output data and computation of the linear and higher-order frequency response functions. The second stage involves identifying continuous time models by curve fitting to the complex frequency response data using a weighted complex orthogonal estimator. The orthogonal property of the estimator helps in identifying the correct model structure or which terms to include in the model, and the weighting property provides an additional degree of freedom to control the properties of the estimator with respect to the selection of the frequency range and number of data points. Morison equation models were fitted initially to the data but were shown to curve fit to the data without capturing the underlying dynamics. The frequency domain characteristics of the Morison equation models were also analysed and shown to be structurally deficient in representing certain dynamic features of the force. However, it is shown that the new equation structure is capable of emulating all the relevant features of the wave force mechanics. Extensive simulations on the variety of experimental data show that models based on the new structure perform remarkably well compared with the Morison equation. For each flow situation, in addition to the drag and inertia coefficients of the Morison equation, there are two non-dimensional coefficients defining history effects which show some consistency between widely different flow situations.

Identification of Linear Multivariable Time-Invariant Systems from Samples of Input-Output Data

Abstract Two algorithms for the identification of linear multivariable time-invariant systems are proposed for the case when the number of outputs is less than the number of states. The methods do not require a priori knowledge of the structure of the system. Numerical examples are given to test the algorithms.

Identification of Continuous Systems from Noisy Sampled Input-Output Data

The problem of identification of continuous systems is considered when both the discrete input and output measurements are contaminated by white noises. Using a pre-designed digital filter, a discrete-time estimation model is constructed easily without direct approximations of system signal derivatives. If the pass-band of the filter is designed so that it includes the main frequencies of both the system input and output signals in some range, the noise effects are sufficiently reduced, accurate estimates can be obtained by least squares(LS) algorithm in the presence of low measurement noises. Two classes of filters (infinite impulse response(IIR) filter and finite impulse response(FIR) filter) are employed. The former requires less computational burden and memory than the latter while the latter is suitable for the bias compensated least squares(BCLS) method, which compensates the bias of the LS estimate by the estimates of the input-output noise variances and thus yields unbiased estimates in the presence of high noises.

Algorithm for the identification of linear multivariable time-invariant systems from samples of input-output data

Abstract An algorithm for identification of linear multivariable time-invariant systems is proposed for the case when the number of outputs is less than the number of states. The method does not require a priori knowledge of the structure of the system. Two numerical examples are given to test the algorithm.

Identification of continuous systems using digital low-pass filters

Direct methods for recursive identification of continuous systems from sampled input–output data using digital low–pass filters are discussed. The digital low–pass filters are introduced to avoid direct approximations of system signal derivatives from sampled data. Using a pre–designed digital low–pass filter, an approximated discrete–time estimation model is constructed easily. Thus the system parameters can be identified directly by recursive identification algorithms. Numerical results, show that the parameter estimates are not so sensitive to the pass-band of the filter, and if the filter is designed so that its pass-band matches that of the system closely and thus the noise effects are sufficiently reduced, accurate estimates can be obtained by recursive identification algorithms. Two classes of filters (FIR digital filter and IIR digital filter) are considered. It is shown that some other methods can be unified to be either the IIR or the FIR filtering approach.

On the identification of continuous-time multivariable systems from samples of input-output data

A scheme is presented for identifying the parameters of a continuous-time multivariable system from the samples of the input-output data. It utilizes approximate integration of the state equations, assuming that the inputs to the system vary linearly between the sampling instants. From the data first the parameters of an equivalent discrete-time model are determined. These are then transformed to obtain the corresponding continuous-time model. Illustrative examples are included. These demonstrate that, for the general case, this method leads to much better results than obtainable if the input is considered constant between the sampling instants.

Block-pulse function approach to the identification of MIMO-systems and time-delay systems

Several algorithms are presented for identifying linear continuous MIMO systems and systems with time delay from samples of input-output data. The basis of these algorithms is the corresponding difference equation of the continuous systems using block-pulse functions. The recursive algorithms for determining the transfer function matrix in MIMO systems and in systems with known time delay are simpler than other algorithms based on the operational properties of orthogonal functions, and are easy to implement on-line. The algorithms for identifying systems with unknown time delay are also easy to implement owing to the simple and straightforward treatment of input-output data. Illustrative examples show that these algorithms give satisfactory results for certain identification problems.

A new algorithm for single-input single-output system identification via block-pulse functions

A new recursive algorithm via block-pulse functions is presented for estimating the unknown parameters of a linear continuous system from samples of input-output data. Compared with other methods via block-pulse functions, there are no integrals of input-output data to be computed and no initial states or values involved for the purpose of identification. This algorithm is therefore easy to implement and is especially applicable to those estimation problems in which the parameters vary slowly with time in an unknown way. The illustrative examples show that the new algorithm gives satisfactory results for identification problems.

A procedure for determining the optimal sampling interval for system identification using a digital computer

The effect of choosing a very small sampling interval for the identification of continuous-time systems for input-output data samples is illustrated and a method to obtain the optimum sampling interval is proposed. This method allows one to start with an arbitrarily small sampling interval without computational problems and at length converge to the proper sampling interval. Several simulated examples show the usefulness of the method even if the measurements are contaminated with a considerable amount of noise.

Modelling a Robot Arm from Sampled Input-Output Data

Abstract As the performance of an industrial robot becomes more demanding, it is necessary to implement adaptive controllers, since they have the ability to cope with the complex dynamics of the robot. A model of the robot, required for such controllers, may be obtained in several forms. In this paper, the problem of mode ling a robot arm, directly in the continuous time domain, from samples of input-output data is addressed. A brief discussion, on the application of the maximum entropy method for estimating the natural frequencies of a system is also included. Results of modeling an industrial robot are presented

Some system theory applications of block-pulse functions

Discusses the application of block-pulse functions to a number of problems in system theory. These include the numerical solution of state equations, identification of multivariable systems from the samples of input-output data, estimating the states from the samples of the input and output, and analysis and identification of distributed-parameter systems.

A versatile identification method applied to analysis of respiratory mechanics.

A method for the straightforward estimation of the param eters in lumped continuous linear models of respiratory mechanics is presented in this paper. First, a discrete-time model is obtained from the samples of input-output data and then transformed into a conuous-time model.

A direct approach to modeling an industrial robot from samples of input-output data

SUMMARYThe increased demand on the performance and efficiency of industrial robots, has led to the design of sophisticated control systems. Such control systems require an accurate dynamic model of the system. A commonly used method of modeling an industrial robot, involves the description of a set of dynamic equations, relating actuator torques to loads and accelerations. These equations are generally quite complex and inconvenient for implementation on digital computers.Another method often used for identification, is the ‘indirect method’, in which the transfer function is obtained in two steps. The discrete time model is first derived from samples of the input and output measurements, which is then transformed to the continuous-time model. A limitation of this method is that it requires the excitation to be of the ‘persistently exciting’ type, thus precluding the application of simple inputs like the step signal.This paper describes a ‘direct’ method for identification of an ‘industrial robot’ from samples of input and output observations. Results of modeling an industrial robot and two simulations are presented. One of the simulations, and the industrial robot uses the step input as excitation. The other example was excited with an exponential input.

State estimation using block-pulse functions†

An algorithm is presented for estimating the states of an observable linear continuous-time system from the samples of input-output data using the theory of block-pulse functions. The principle of the Luenberger observer is utilized in developing simple algebraic expressions for the estimates of the states. These can be evaluated easily in a recursive manner using a microprocessor. Results of simulation indicate that the proposed method works quite well when the observations are contaminated with a small amount of noise.

Identification of continuous-time state-space model from samples of input-output data

The identification of the parameters of a state-space model for a single-input single-output system from samples of the input-output data is considered. Use of the trapezoidal rule of integration, together with the least-squares algorithm, leads to the continuous-time model directly without assuming that the input is held constant between sampling instants.