| 1. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
-
Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎
- 2018
-
Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 784-789
-
Tidskriftsartikel (refereegranskat)abstract
- The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presented and discussed.
|
|
| 2. |
- Abdalmoaty, Mohamed Rasheed, 1986-, et al.
(författare)
-
Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors
- 2018
-
Ingår i: 2018 IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781538613955 - 9781538613948 - 9781538613962 ; , s. 3842-3847
-
Konferensbidrag (refereegranskat)abstract
- We consider a parameter estimation problem in a general class of stochastic multiple-inputs multiple-outputs Wiener models, where the likelihood function is, in general, analytically intractable. When the output signal is a scalar independent stochastic process, the likelihood function of the parameters is given by a product of scalar integrals. In this case, numerical integration may be efficiently used to approximately solve the maximum likelihood problem. Otherwise, the likelihood function is given by a challenging multidimensional integral. In this contribution, we argue that by ignoring the temporal and spatial dependence of the stochastic disturbances, a computationally attractive estimator based on a suboptimal predictor can be constructed by evaluating scalar integrals regardless of the number of outputs. Under some conditions, the convergence of the resulting estimators can be established and consistency is achieved under certain identifiability hypothesis. We highlight the relationship between the resulting estimators and a recently proposed prediction error method estimator. We also remark that the method can be used for a wider class of stochastic nonlinear models. The performance of the method is demonstrated by a numerical simulation example using a 2-inputs 2-outputs model with 9 parameters.
|
|
| 3. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
-
Identification of a Class of Nonlinear Dynamical Networks⁎
- 2018
-
Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873
-
Tidskriftsartikel (refereegranskat)abstract
- Identification of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example.
|
|
| 4. |
- Bombois, Xavier, et al.
(författare)
-
Optimal identification experiment design for the interconnection of locally controlled systems
- 2018
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 89, s. 169-179
-
Tidskriftsartikel (refereegranskat)abstract
- This paper considers the identification of the modules of a network of locally controlled systems (multi-agent systems). Its main contribution is to determine the least perturbing identification experiment that will nevertheless lead to sufficiently accurate models of each module for the global performance of the network to be improved by a redesign of the decentralized controllers. Another contribution is to determine the experimental conditions under which sufficiently informative data (i.e. data leading to a consistent estimate) can be collected for the identification of any module in such a network.
|
|
| 5. |
- Everitt, Niklas, et al.
(författare)
-
An empirical Bayes approach to identification of modules in dynamic networks
- 2018
-
Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 91, s. 144-151
-
Tidskriftsartikel (refereegranskat)abstract
- We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods.
|
|
| 6. |
- Everitt, Niklas, et al.
(författare)
-
Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method
- 2018
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 89, s. 221-234
-
Tidskriftsartikel (refereegranskat)abstract
- In system identification, it is often difficult to use a physical intuition when choosing a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, the model orders must be chosen according to the true system. However, if only the plant estimates are of interest and the experiment is performed in open loop, the noise model can be over-parameterized without affecting the asymptotic properties of the plant. The limitation is that, as PEM suffers in general from non-convexity, estimating an unnecessarily large number of parameters will increase the risk of getting trapped in local minima. Here, we consider the following alternative approach. First, estimate a high-order ARX model with least squares, providing non-parametric estimates of the plant and noise model. Second, reduce the high-order model to obtain a parametric model of the plant only. We review existing methods to do this, pointing out limitations and connections between them. Then, we propose a method that connects favorable properties from the previously reviewed approaches. We show that the proposed method provides asymptotically efficient estimates of the plant with open-loop data. Finally, we perform a simulation study suggesting that the proposed method is competitive with state-of-the-art methods.
|
|
| 7. |
- Ferizbegovic, Mina, et al.
(författare)
-
Nonlinear FIR Identification with Model Order Reduction Steiglitz-McBride⁎
- 2018
-
Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 646-651
-
Tidskriftsartikel (refereegranskat)abstract
- In system identification, many structures and approaches have been proposed to deal with systems with non-linear behavior. When applicable, the prediction error method, analogously to the linear case, requires minimizing a cost function that is non-convex in general. The issue with non-convexity is more problematic for non-linear models, not only due to the increased complexity of the model, but also because methods to provide consistent initialization points may not be available for many model structures. In this paper, we consider a non-linear rational finite impulse response model. We observe how the prediction error method requires minimizing a non-convex cost function, and propose a three-step least-squares algorithm as an alternative procedure. This procedure is an extension of the Model Order Reduction Steiglitz-McBride method, which is asymptotically efficient in open loop for linear models. We perform a simulation study to illustrate the applicability and performance of the method, which suggests that it is asymptotically efficient.
|
|
| 8. |
- Ferizbegovic, Mina, et al.
(författare)
-
Weighted Null-Space Fitting for Cascade Networks with Arbitrary Location of Sensors and Excitation Signals
- 2018
-
Ingår i: 57th IEEE Conference on Decision and Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781538613955 ; , s. 4707-4712
-
Konferensbidrag (refereegranskat)abstract
- Identification of a complete dynamic network affected by sensor noise using the prediction error method is often too complex. One of the reasons for this complexity is the requirement to minimize a non-convex cost function, which becomes more difficult with more complex networks. In this paper, we consider serial cascade networks affected by sensor noise. Recently, the Weighted Null-Space Fitting method has been shown to be appropriate for this setting, providing asymptotically efficient estimates without suffering from non-convexity; however, applicability of the method was subject to some conditions on the locations of sensors and excitation signals. In this paper, we drop such conditions, proposing an extension of the method that is applicable to general serial cascade networks. We formulate an algorithm that describes application of the method in a general setting, and perform a simulation study to illustrate the performance of the method, which suggests that this extension is still asymptotically efficient.
|
|
| 9. |
- Galrinho, Miguel
(författare)
-
System Identification with Multi-Step Least-Squares Methods
- 2018
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of system identification is to build mathematical models for dynam-ical systems from experimental data. With the current increase in complexity of engineering systems, an important challenge is to develop accurate and computa-tionally simple algorithms, which can be applied in a large variety of settings.With the correct model structure, maximum likelihood (ML) and the predictionerror method (PEM) can be used to obtain (under adequate assumptions) asymp-totically efficient estimates. A disadvantage is that these methods typically requireminimizing a non-convex cost function. Alternative methods are then needed toprovide initialization points for the optimization.In this thesis, we consider multi-step least-squares methods for identificationof dynamical systems. These methods have a long history for estimation of timeseries. Typically, a non-parametric model is estimated in an intermediate step, andits residuals are used as estimates of the innovations of the parametric model ofinterest. With innovations assumed known, it is possible to estimate the parametricmodel with afinite number of least-squares steps. When applied with an appropriateweighting orfiltering, these methods can provide asymptotically efficient estimates.The thesis is divided in two parts. In thefirst part, we propose two methods:model order reduction Steiglitz-McBride (MORSM) and weighted null-spacefitting(WNSF). MORSM uses the non-parametric model estimate to create a simulateddata set, which is then used with the Steiglitz-McBride algorithm. WNSF is a moregeneral approach, which motivates the parametric model estimate by relating thecoefficients of the non-parametric and parametric models.In settings where different multi-step least-squares methods can be applied, weshow that their algorithms are essentially the same, whether the estimates are basedon estimated innovations, simulated data, or direct relations between the modelcoefficients. However, their range of applicability may differ, with WNSF allowing usto establish a framework for multi-step least-squares methods that is quiteflexible inparametrization. This is specially relevant in the multivariate case, for which WNSFis applicable to a large variety of model structures, including both matrix-fractionand element-wise descriptions of the transfer matrices.We conduct a rigorous statistical analysis of the asymptotic properties of WNSF,where the main challenge is to keep track of the errors introduced by truncationof the non-parametric model, whose order must tend to infinity as function of thesample size for consistency and asymptotic efficiency to be attained. Moreover, weperform simulation studies that show promising results compared with state-of-the-art methods.In the second part, we consider extensions of the developed methods for appli-cability in other settings. These include unstable systems, recursive identification,dynamic networks, and cascaded systems.
|
|
| 10. |
- Galrinho, Miguel, et al.
(författare)
-
Weighted Null-Space Fitting for Identification of Cascade Networks⁎
- 2018
-
Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 856-861
-
Tidskriftsartikel (refereegranskat)abstract
- For identification of systems embedded in dynamic networks, the prediction error method (PEM) with a correct parametrization of the complete network provides asymptotically efficient estimates. However, the network complexity often hinders a successful application of PEM, which requires minimizing a non-convex cost function that can become more intricate for more complex networks. For this reason, identification in dynamic networks often focuses in obtaining consistent estimates of modules of interest. A downside of these approaches is that splitting the network in several modules for identification often costs asymptotic efficiency. In this paper, we consider dynamic networks with the modules connected in serial cascade, with measurements affected by sensor noise. We propose an algorithm that estimates all the modules in the network simultaneously without requiring the minimization of a non-convex cost function. This algorithm is an extension of Weighted Null-Space Fitting (WNSF), a weighted least-squares method that provides asymptotically efficient estimates for single-input single-output systems. We illustrate the performance of the algorithm with simulation studies, which suggest that a network WNSF method may also be asymptotically efficient when applied to cascade structures. Finally, we discuss the possibility of extension to more general networks affected by sensor noise.
|
|
