| 1. |
- Andersson, Torbjörn, et al.
(författare)
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Estimation of Residence Time in Continuous Flow Systems with Dynamics
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. ; , s. 401-406
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Konferensbidrag (refereegranskat)abstract
- A method for estimation of residence time in continuous flow systems with varying dynamics is presented. By resampling, i.e., choosing time instants different from the given sampling instants, and interpolation between measured data points, we obtain a continuous flow system with constant residence time expressed in the new resampled time vector. We assume the flow patterns in the systems are invariant. The new data set is then used for identification of parameters in a chosen model structure. From the identified model, the residence time is readily calculated and a procedure for that is briefly described. The presented method is readily extended to enable use in recursive identification. In that case, however, as an improvement of tracking ability of an ordinary recursive routine.
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| 2. |
- Andersson, Torbjörn, et al.
(författare)
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Estimation of Residence Time in Continuous Flow Systems with Dynamics
- 1995
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Ingår i: Journal of Process Control. - : Elsevier BV. - 0959-1524 .- 1873-2771. ; 5:1, s. 9-17
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Tidskriftsartikel (refereegranskat)abstract
- A method for estimation of residence time in continuous flow systems with varying dynamics is presented. By resampling, i.e., choosing time instants different from the given sampling instants, and interpolation between measured data points, we obtain a continuous flow system with constant residence time expressed in the new resampled time vector. We assume the flow patterns in the systems are invariant. The new data set is then used for identification of parameters in a chosen model structure. From the identified model, the residence time is readily calculated and a procedure for that is briefly described. The presented method is readily extended to enable use in recursive identification. In that case, however, as an improvement of tracking ability of an ordinary recursive routine. Keywords : System identification, residence time estimation, time-varying systems, variable flow and/or volume, continuous flow systems, recursive identification.
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| 3. |
- Andersson, Torbjörn, et al.
(författare)
-
Estimation of Residence Time in Continuous Flow Systems with Varying Flow and Volume
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A method for estimation of residence time in continuous flow vessels with variable flow and volume is presented. By resampling, i.e., choosing time instants different from the given sampling instants, and interpolation of measured data points, we obtain a continuous flow system with constant residence time expressed in the new resampled time vector, assuming the flow patterns in the vessels and tanks are invariant. The new data set is then used for identification of parameters in a chosen model structure. From the identified model the residence time is easily calculated and a procedure for that is briefly described. The presented method is easily extended to enable use in recursive identification but then as an improvement of tracking ability of an ordinary recursive routine.
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| 4. |
- Andersson, Torbjörn, et al.
(författare)
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Identification Aspects of Inter-Sample Input Behavior
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 137-142
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Konferensbidrag (refereegranskat)abstract
- In this contribution aspects of inter-sample input signal behavior are examined. The starting point is that parametric identification always is performed on basis of discrete-time data. This is valid for identification of discrete-time models as well as continuous-time models. The usual assumptions on the input signal are; i) it is band-limited, ii) it is piecewise constant or iii) it is piecewise linear. One point made in this paper is that if a discrete-time model is used, the best possible (in the model structure) adjustment to data is made. This is independent of the assumption on the input signal. However, a transformation of the obtained discrete model to a continuous one is not possible without additional assumptions on the input signal. The other point made is that the frequency functions of the discrete models very well coincides with the frequency functions of the discretized continuous time models and the continuous time transfer function fitted in the frequency domain.
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| 5. |
- Andersson, Torbjörn, et al.
(författare)
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Identifying Models using Piecewise Linear Approximation of Input Signals
- 1992
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Very often in system identification problems it is assumed that the input signal is piecewise constant but in many practical cases this is not the fact. In such cases when the input signal is continuous it shows that a piecewise linear approximation of the input signal leads to a better model. In this report it is shown how to handle system identification problems using state space descriptions and the assumption of piecewise linear input signals with MathWork's system identification software.
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| 6. |
- Niu, Steve S., et al.
(författare)
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Hinging Hyperplanes for Non-Linear Identification
- 1995
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The hinging hyperplane method is an elegant and efficient way of identifying piecewise linear models based on the data collected from an unknown linear or nonlinear system. This approach provides "a powerful and efficient alternative to neural networks with computing times several orders of magnitude less than fitting neural networks with a comparable number of parameters", as stated in [3]. In this report, the hinging hyperplane approach is discussed from the system identification viewpoint. The bottleneck of this approach, namely, the hinge finding scheme, is investigated. The behavior of the hinge finding algorithm is very dependent on the initial values provided. Several methods for analyzing low dimensional cases are suggested. Although not general, these methods provide some interesting insights into the mechanisms of the hinge finding algorithm. Information from linear models produced by the multiple model least-squares is used to facilitate implementation. The possibility of using binary-tree structured models is also discussed. In addition, an extension of the hinging hyperplane idea leads to a hinge smoothing method in which the hinging hyperplanes are smoothed at the hinge. As a result a neural net like basis function is obtained. Finally, the hinging hyperplane method is used for modeling three real systems.
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| 7. |
- Pucar, Predrag
(författare)
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Modeling and Segmentation using Multiple Models
- 1995
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- An established area within the system identification field is identification of linear models. In practice, sometimes the performance of such models is not satisfactory and non-linear models are needed. This thesis is devoted to modeling and identification of systems by means of multiple models. The models used in a bank of models are simple models, often linear, that combined manage to well describe an input-output relationship of a more complex system.The material is presented in two parts. The parts differ by the assumption on availability of information. In Part I it is assumed that the switching between the models in the model bank is guided by an unobserved stochastic process. We have chosen to model the switching by a Markov chain. The task is to model the output of a "jumping" system and estimate parameters in the models. That task is not difficult to solve if the points where the models switch are known. Since they are not, the complexity of the task increases severely. In the first part of the thesis we extend known solutions for the one-dimensional case to two dimensions. The resulting methods are sub-optimal. Sub-optimality iis the price payed for avoiding an otherwise overwhelming computational complexity of the estimation algorithms. The methods are applied to data from a laser range system. As a spin-off the problem of estimation of the number of hidden states of the Markov chain, given output data only, is investigated.The second part treats the case when the choice of a model from a model bank is governed by the input to the system considered. We are, thus, in a framework of function approximation, since an input-output relation can be viewed as a function mapping from the input of the system to the output. A recently introduced model class, the hinging hyperplane models, is presented. It turns out to be related to other model classes such as neural network models, regression trees, etc. A number of issues related to the new model class is discussed, e.g., parameterization, conditioning, etc. Finally, as a last contribution, a variant of hinging hyperplane models, so called smooth hinging hyperplane models, is presented.
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| 8. |
- Pucar, Predrag, et al.
(författare)
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On the Hinge Finding Algorithm for Hinging Hyperplanes
- 1995
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper concerns the estimation algorithm for hinging hyperplane HH models a nonlinear black box model structure suggested in The estimation algorithm is analysed and it is shown that it is a special case of a Newton algorithm applied on a quadratic criterion This insight is then used to suggest possible improvements of the algorithm so that convergence can be guaranteed In addition the way of updating the parameters in the HH model is discussed In a stepwise updating procedure is proposed In this paper we stress that simultaneous updating of the model parameters can be preferable in some cases
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| 9. |
- Pucar, Predrag, et al.
(författare)
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On the Hinge Finding Algorithm for Hinging Hyperplanes
- 1996
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 32:6
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Tidskriftsartikel (refereegranskat)abstract
- This correspondence concerns the estimation algorithm for hinging hyperplane (HH) models, a piecewise-linear model for approximating functions of several variables, suggested in Breiman (1993). The estimation algorithm is analyzed and it is shown that it is a special case of a Newton algorithm applied to a sum of squared error criterion. This insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed. In addition, the way of updating the parameters in the HH model is discussed. In Breiman, a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step. This connects closely to some previously suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters.
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| 10. |
- Pucar, Predrag, et al.
(författare)
-
On the Hinge Finding Algorithm for Hinging Hyperplanes - Revised Version
- 1995
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This correspondence concerns the estimation algorithm for hinging hyperplane (HH) models, a piecewise-linear model for approximating functions of several variables, suggested in Breiman (1993). The estimation algorithm is analyzed and it is shown that it is a special case of a Newton algorithm applied to a sum of squared error criterion. This insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed. In addition, the way of updating the parameters in the HH model is discussed. In Breiman, a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step. This connects closely to some previously suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters.
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