| 1. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Linear Prediction Error Methods for Stochastic Nonlinear Models
- 2019
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 105, s. 49-63
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Tidskriftsartikel (refereegranskat)abstract
- The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear identification methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem.
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| 2. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 784-789
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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.
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| 3. |
- Abdalmoaty, Mohamed Rasheed, 1986-, et al.
(författare)
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Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors
- 2018
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Ingår i: 2018 IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781538613955 - 9781538613948 - 9781538613962 ; , s. 3842-3847
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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.
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| 4. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Identification of a Class of Nonlinear Dynamical Networks⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873
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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.
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| 5. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models
- 2017
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Ingår i: The 20th IFAC World Congress. - : Elsevier. ; 50:1, s. 14058-14063
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Konferensbidrag (refereegranskat)abstract
- Nonlinear stochastic parametric models are widely used in various fields. However, for these models, the problem of maximum likelihood identification is very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the analytically intractable likelihood function and compute either the maximum likelihood or a Bayesian estimator. These methods, albeit asymptotically optimal, are computationally expensive. In this contribution, we present a simulation-based pseudo likelihood estimator for nonlinear stochastic models. It relies only on the first two moments of the model, which are easy to approximate using Monte-Carlo simulations on the model. The resulting estimator is consistent and asymptotically normal. We show that the pseudo maximum likelihood estimator, based on a multivariate normal family, solves a prediction error minimization problem using a parameterized norm and an implicit linear predictor. In the light of this interpretation, we compare with the predictor defined by an ensemble Kalman filter. Although not identical, simulations indicate a close relationship. The performance of the simulated pseudo maximum likelihood method is illustrated in three examples. They include a challenging state-space model of dimension 100 with one output and 2 unknown parameters, as well as an application-motivated model with 5 states, 2 outputs and 5 unknown parameters.
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| 6. |
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| 7. |
- Bombois, Xavier, et al.
(författare)
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Optimal identification experiment design for the interconnection of locally controlled systems
- 2018
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 89, s. 169-179
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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.
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| 8. |
- Bottegal, Giulio, et al.
(författare)
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A new kernel-based approach to system identification with quantized output data
- 2017
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 85, s. 145-152
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data. (C) 2017 Elsevier Ltd. All rights reserved.
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| 9. |
- Bottegal, Giulio, et al.
(författare)
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Outlier robust kernel-based system identification using l1-Laplace techniques
- 2015
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Ingår i: 2015 54th IEEE Conference on Decision and Control. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 2109-2114
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Konferensbidrag (refereegranskat)abstract
- Regularized kernel-based methods for system identification have gained popularity in recent years. However, current formulations are not robust with respect to outliers. In this paper, we study possible solutions to robustify kernel-based methods that rely on modeling noise using the Laplacian probability density function (pdf). The contribution of this paper is two-fold. First, we introduce a new outlier robust kernel-based system identification method. It exploits the representation of Laplacian pdfs as scale mixture of Gaussians. The hyperparameters characterizing the problem are chosen using a new maximum a posteriori estimator whose solution is computed using a novel iterative scheme based on the expectation-maximization method. The second contribution of the paper is the review of two other robust kernel-based methods. The three methods are compared by means of numerical experiments, which show that all of them give substantial performance improvements compared to standard kernel-based methods for linear system identification.
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| 10. |
- Ebadat, Afrooz, et al.
(författare)
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Blind identification strategies for room occupancy estimation
- 2015
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Ingår i: 2015 European Control Conference (ECC). - Piscataway, NJ : IEEE Communications Society. - 9783952426937 ; , s. 1315-1320
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Konferensbidrag (refereegranskat)abstract
- We propose and test on real data a two-tier estimation strategy for inferring occupancy levels from measurements of CO2 concentration and temperature levels. The first tier is a blind identification step, based either on a frequentist Maximum Likelihood method, implemented using non-linear optimization, or on a Bayesian marginal likelihood method, implemented using a dedicated Expectation-Maximization algorithm. The second tier resolves the ambiguity of the unknown multiplicative factor, and returns the final estimate of the occupancy levels. The overall procedure addresses some practical issues of existing occupancy estimation strategies. More specifically, first it does not require the installation of special hardware, since it uses measurements that are typically available in many buildings. Second, it does not require apriori knowledge on the physical parameters of the building, since it performs system identification steps. Third, it does not require pilot data containing measured real occupancy patterns (i.e., physically counting people for some periods, a typically expensive and time consuming step), since the identification steps are blind.
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