| 1. |
- Everitt, Niklas, 1987-, et al.
(författare)
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A Geometric Approach to Variance Analysis of Cascaded Systems
- 2013
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Ingår i: Proceedings of the 52nd Conference On Decision And Control. - : IEEE conference proceedings. - 9781467357173 ; , s. 6496-6501
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Konferensbidrag (refereegranskat)abstract
- Modeling complex and interconnected systems is a key issue in system identification. When estimating individual subsystems of a network of interconnected system, it is of interest to know the improvement of model-accuracy in using different sensors and actuators. In this paper, using a geometric approach, we quantify the accuracy improvement from additional sensors when estimating the first of a set of subsystems connected in a cascade structure. We present results on how the zeros of the first subsystem affect the accuracy of the corresponding model. Additionally we shed some light on how structural properties and experimental conditions determine the accuracy. The results are particularized to FIR systems, for which the results are illustrated by numerical simulations. A surprising special case occurs when the first subsystem contains a zero on the unit circle; as the model orders grows large, thevariance of the frequency function estimate, evaluated at thecorresponding frequency of the unit-circle zero, is shown to be the same as if the other subsystems were completely known.
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| 2. |
- Everitt, Niklas, 1987-
(författare)
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Module identification in dynamic networks: parametric and empirical Bayes methods
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of system identification is to construct mathematical models of dynamical system from experimental data. With the current trend of dynamical systems encountered in engineering growing ever more complex, an important task is to efficiently build models of these systems. Modelling the complete dynamics of these systems is in general not possible or even desired. However, often, these systems can be modelled as simpler linear systems interconnected in a dynamic network. Then, the task of estimating the whole network or a subset of the network can be broken down into subproblems of estimating one simple system, called module, embedded within the dynamic network.The prediction error method (PEM) is a benchmark in parametric system identification. The main advantage with PEM is that for Gaussian noise, it corresponds to the so called maximum likelihood (ML) estimator and is asymptotically efficient. One drawback is that the cost function is in general nonconvex and a gradient based search over the parameters has to be carried out, rendering a good starting point crucial. Therefore, other methods such as subspace or instrumental variable methods are required to initialize the search. In this thesis, an alternative method, called model order reduction Steiglitz-McBride (MORSM) is proposed. As MORSM is also motivated by ML arguments, it may also be used on its own and will in some cases provide asymptotically efficient estimates. The method is computationally attractive since it is composed of a sequence of least squares steps. It also treats the part of the network of no direct interest nonparametrically, simplifying model order selection for the user.A different approach is taken in the second proposed method to identify a module embedded in a dynamic network. Here, the impulse response of the part of the network of no direct interest is modelled as a realization of a Gaussian process. The mean and covariance of the Gaussian process is parameterized by a set of parameters called hyperparameters that needs to be estimated together with the parameters of the module of interest. Using an empirical Bayes approach, all parameters are estimated by maximizing the marginal likelihood of the data. The maximization is carried out by using an iterative expectation/conditional-maximization scheme, which alternates so called expectation steps with a series of conditional-maximization steps. When only the module input and output sensors are used, the expectation step admits an analytical expression. The conditional-maximization steps reduces to solving smaller optimization problems, which either admit a closed form solution, or can be efficiently solved by using gradient descent strategies. Therefore, the overall optimization turns out computationally efficient. Using markov chain monte carlo techniques, the method is extended to incorporate additional sensors.Apart from the choice of identification method, the set of chosen signals to use in the identification will determine the covariance of the estimated modules. To chose these signals, well known expressions for the covariance matrix could, together with signal constraints, be formulated as an optimization problem and solved. However, this approach does neither tell us why a certain choice of signals is optimal nor what will happen if some properties change. The expressions developed in this part of the thesis have a different flavor in that they aim to reformulate the covariance expressions into a form amenable for interpretation. These expressions illustrate how different properties of the identification problem affects the achievable accuracy. In particular, how the power of the input and noise signals, as well as model structure, affect the covariance.
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| 3. |
- Everitt, Niklas, 1987-, et al.
(författare)
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Variance Analysis of Linear SIMO Models with Spatially Correlated Noise
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Substantial improvement in accuracy of identied linear time-invariant single-input multi-output (SIMO) dynamical models ispossible when the disturbances aecting the output measurements are spatially correlated. Using an orthogonal representation for the modules composing the SIMO structure, in this paper we show that the variance of a parameter estimate of a module is dependent on the model structure of the other modules, and the correlation structure of the disturbances. In addition, we quantify the variance-error for the parameter estimates for finite model orders, where the effect of noise correlation structure, model structure and signal spectra are visible. From these results, we derive the noise correlation structure under which the mentioned model parameterization gives the lowest variance, when one module is identied using less parameters than the other modules.
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| 4. |
- Everitt, Niklas, 1987-, et al.
(författare)
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Variance Results for Parallel Cascade Serial Systems
- 2014
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Ingår i: Proceedings of 19th IFAC World Congress. - : Elsevier BV.
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Konferensbidrag (refereegranskat)abstract
- Modelling dynamic networks is important in different fields of science. At present, little is known about how different inputs and sensors contribute to the statistical properties concerning an estimate of a specific dynamic system in a network. We consider two forms of parallel serial structures, one multiple-input-multiple-output structure and one single-input multiple-output structure. The quality of the estimated models is analysed by means of the asymptotic covariance matrix, with respect to input signal characteristics, noise characteristics, sensor locations and previous knowledge about the remaining systems in the network. It is shown that an additive property applies to the information matrix for the considered structures. The impact of input signal selection, sensor locations and incorporation of previous knowledge isillustrated by simple examples.
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| 5. |
- Galrinho, Miguel, et al.
(författare)
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Incorporating noise modeling in dynamic networks using non-parametric models
- 2017
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 50:1, s. 10568-10573
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Tidskriftsartikel (refereegranskat)abstract
- For identification of systems in dynamic networks, two-stage and instrumental variable methods are common time-domain methods. These methods provide consistent estimates of a chosen module of the network without estimating other parts of the network or noise models. However, disregarding noise modeling may come at a cost in estimation error. To capture the noise contribution, we propose the following procedure: first, we estimate a non-parametric model of an appropriate part of the network; second, we estimate the module of interest using signals simulated with the non-parametric model. The simulated signals are derived from an asymptotic maximum likelihood criterion. Preliminary simulations suggest that the propose method is competitive with existing approaches and is particularly beneficial with colored noise.
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| 6. |
- Mårtensson, Jonas, et al.
(författare)
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Variance Analysis in SISO Linear Systems Identification
- 2015
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Ingår i: Automatica. - 0005-1098 .- 1873-2836.
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Tidskriftsartikel (refereegranskat)abstract
- Causal single input single output linear time invariant systems are considered. Expressions for the asymptotic (co)variance of system properties estimated using the prediction error method are derived. These expressions delineate the impacts of model structure, model order, true system dynamics, and experimental conditions. A connection to results on frequency function estimation is established. Also, simple model structure independent upper bounds are derived. Explicit variance expressions and bounds are provided for common system properties such as impulse response coefficients and non-minimum phase zeros. As an illustration of the insights the expressions provide, they are used to derive conditions on the input spectrum which makethe asymptotic variance of non-minimum phase zero estimates independent of the model order and model structure.
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| 7. |
- Valenzuela, Patricio Esteban, et al.
(författare)
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Closed-Loop Identification for Model Predictive Control of HVAC Systems : From Input Design to Controller Synthesis
- 2020
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Ingår i: IEEE Transactions on Control Systems Technology. - : Institute of Electrical and Electronics Engineers (IEEE). - 1063-6536 .- 1558-0865. ; 28:5, s. 1681-1695
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Tidskriftsartikel (refereegranskat)abstract
- Heating, ventilation, and air conditioning (HVAC) systems are responsible for maintaining occupants' thermal comfort and share a large portion of the overall building energy use. Hence, it is of great interest to improve the performance of HVAC control systems and thus the building energy efficiency. Model predictive control (MPC) has been proved to be a promising control strategy to be employed in this field. However, MPC implementation relies on the model of the system, and inaccurate models can deteriorate the control performance, while overly complicated models can lead to the prohibitive computational burden. Because of this, existing models do not usually allow the MPC controller to adjust multiple set points (e.g., both temperature and flow rates) and do not include the dynamics of the heating and ventilation subsystems with their local controllers. In this paper, we address the challenge of developing more reliable HVAC models for MPC controllers based on the experimental data. Data are obtained from an experiment designed using a graph theoretical technique, which guarantees maximum information content in the data. The resulting models are employed to design local controllers of the heating and ventilation subsystems, which are experimentally tested in a real HVAC test bed. A supervisory MPC controller that incorporates the closed-loop models of the heating and ventilation subsystems is then developed. This can lead to a control strategy able to more effectively adapt key HVAC set points based on weather conditions, occupancy, and actual thermal comfort, as shown by a numerical study based on the data from the HVAC test bed.
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