| 1. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(author)
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Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎
- 2018
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In: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 784-789
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Journal article (peer-reviewed)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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| 2. |
- Abdalmoaty, Mohamed R. H., 1986-, et al.
(author)
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Identification of Non-Linear Differential-Algebraic Equation Models with Process Disturbances
- 2021
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In: 2021 60th IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781665436595 - 9781665436588 - 9781665436601 ; , s. 2300-2305
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Conference paper (peer-reviewed)abstract
- Differential-algebraic equations (DAEs) arise naturally as a result of equation-based object-oriented modeling. In many cases, these models contain unknown parameters that have to be estimated using experimental data. However, often the system is subject to unknown disturbances which, if not taken into account in the estimation, can severely affect the model's accuracy. For non-linear state-space models, particle filter methods have been developed to tackle this issue. Unfortunately, applying such methods to non-linear DAEs requires a transformation into a state-space form, which is particularly difficult to obtain for models with process disturbances. In this paper, we propose a simulation-based prediction error method that can be used for non-linear DAEs where disturbances are modeled as continuous-time stochastic processes. To the authors' best knowledge, there are no general methods successfully dealing with parameter estimation for this type of model. One of the challenges in particle filtering methods are random variations in the minimized cost function due to the nature of the algorithm. In our approach, a similar phenomenon occurs and we explicitly consider how to sample the underlying continuous process to mitigate this problem. The method is illustrated numerically on a pendulum example. The results suggest that the method is able to deliver consistent estimates.
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| 3. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(author)
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Identification of a Class of Nonlinear Dynamical Networks⁎
- 2018
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In: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873
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Journal article (peer-reviewed)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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| 4. |
- Bereza-Jarocinski, Robert, et al.
(author)
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Stochastic Approximation for Identification of Non-Linear Differential-Algebraic Equations with Process Disturbances
- 2022
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In: 2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781665467612 - 9781665467605 - 9781665467629 ; , s. 6712-6717
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Conference paper (peer-reviewed)abstract
- Differential-algebraic equations, commonly used to model physical systems, are the basis for many equation-based object-oriented modeling languages. When systems described by such equations are influenced by unknown process disturbances, estimating unknown parameters from experimental data becomes difficult. This is because of problems with the existence of well-defined solutions and the computational tractability of estimators. In this paper, we propose a way to minimize a cost function-whose minimizer is a consistent estimator of the true parameters-using stochastic gradient descent. This approach scales significantly better with the number of unknown parameters than other currently available methods for the same type of problem. The performance of the method is demonstrated through a simulation study with three unknown parameters. The experiments show a significantly reduced variance of the estimator, compared to an output error method neglecting the influence of process disturbances, as well as an ability to reduce the estimation bias of parameters that the output error method particularly struggles with.
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