Identification of systems with unknown inputs using indirect input measurements

Linder, Jonas; Enqvist, Martin

doi:10.1080/00207179.2016.1222557

Cited by 37 publications

(34 citation statements)

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“…We will now formulate and analyze an abstraction algorithm for dynamic networks that generalizes the procedure of immersion Dankers et al (2016) and the indirect inputs method Linder and Enqvist (2017a). It starts by dividing the network nodes into a set of nodes w S that are retained after abstraction and a set of nodes w Z that will be removed.…”

Section: Abstraction Of Networkmentioning

confidence: 99%

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Abstractions of linear dynamic networks for input selection in local module identification

et al. 2020

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In abstractions of linear dynamic networks, selected node signals are removed from the network, while keeping the remaining node signals invariant. The topology and link dynamics, or modules, of an abstracted network will generally be changed compared to the original network. Abstractions of dynamic networks can be used to select an appropriate set of node signals that are to be measured, on the basis of which a particular local module can be estimated. A method is introduced for network abstraction that generalizes previously introduced algorithms, as e.g. immersion and the method of indirect inputs. For this abstraction method it is shown under which conditions on the selected signals a particular module will remain invariant. This leads to sets of conditions on selected measured node variables that allow identification of the target module.

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Section: Abstraction Of Networkmentioning

confidence: 99%

“…This alternative method of eliminating node variable w 4 is referred to as the indirect inputs method introduced in (Linder and Enqvist, 2017a). The principle idea is that the out-neighbor of a node that needs to be abstracted contains information about that node.…”

Section: Abstraction Applied To An Example Networkmentioning

confidence: 99%

Abstractions of linear dynamic networks for input selection in local module identification

et al. 2020

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“…These properties are important to consider in the choice of parameter estimation method and certain methods might be better suited than others (Linder and Enqvist, 2016).…”

Section: Properties Of the Indirect Modelmentioning

confidence: 99%

“…If the additional nodes w A contain information about all the unobservable nodes, an alternative solution is to use these measurements to form an indirect model (Linder and Enqvist, 2016). If we assume that G AU has full column-rank and that there exists a filter f UA such that…”

Section: Indirect Node Observationsmentioning

confidence: 99%

Identification and Prediction in Dynamic Networks with Unobservable Nodes

Linder

Enqvist

2017

IFAC-PapersOnLine

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The interest for system identification in dynamic networks has increased recently with a wide variety of applications. In many cases, it is intractable or undesirable to observe all nodes in a network and thus, to estimate the complete dynamics. If the complete dynamics is not desired, it might even be challenging to estimate a subset of the network if key nodes are unobservable due to correlation between the nodes. In this contribution, we will discuss an approach to treat this problem. The approach relies on additional measurements that are dependent on the unobservable nodes and thus indirectly contain information about them. These measurements are used to form an alternative indirect model that is only dependent on observed nodes. The purpose of estimating this indirect model can be either to recover information about modules in the original network or to make accurate predictions of variables in the network. Examples are provided for both recovery of the original modules and prediction of nodes.Keywords: Dynamic networks, closed-loop identification, identifiability, system identification Identification and Prediction in DynamicNetworks with Unobservable Nodes Jonas Linder and Martin EnqvistDivision of Automatic Control, Linköping University. 2017-01-24 AbstractThe interest for system identification in dynamic networks has increased recently with a wide variety of applications. In many cases, it is intractable or undesirable to observe all nodes in a network and thus, to estimate the complete dynamics. If the complete dynamics is not desired, it might even be challenging to estimate a subset of the network if key nodes are unobservable due to correlation between the nodes. In this contribution, we will discuss an approach to treat this problem. The approach relies on additional measurements that are dependent on the unobservable nodes and thus indirectly contain information about them. These measurements are used to form an alternative indirect model that is only dependent on observed nodes. The purpose of estimating this indirect model can be either to recover information about modules in the original network or to make accurate predictions of variables in the network. Examples are provided for both recovery of the original modules and prediction of nodes.

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“…The first one is based on the simulation study presented in Linder et al (2014b) and the second one is based on data from a modified inverted pendulum process presented in Linder et al (2014a) and Linder and Enqvist (2016a). The goals of the first simulation study are to show the impact of measurement noise and to verify the applicability of the proposed method.…”

Section: Experimental Verificationmentioning

confidence: 99%

Indirect System Identification for Unknown Input Problems: With Applications to Ships

Linder¹

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System identification is used in engineering sciences to build mathematical models from data. A common issue in system identification problems is that the true inputs to the system are not fully known. In this thesis, existing approaches to unknown input problems are classified and some of their properties are analyzed.A new indirect framework is proposed to treat system identification problems with unknown inputs. The effects of the unknown inputs are assumed to be measured through possibly unknown dynamics. Furthermore, the measurements may also be dependent on other known or measured inputs and can in these cases be called indirect input measurements. Typically, these indirect input measurements can arise when a subsystem of a larger system is of interest and only a limited set of sensors is available. Two examples are when it is desired to estimate parts of a mechanical system or parts of a dynamic network without full knowledge of the signals in the system. The input measurements can be used to eliminate the unknown inputs from a mathematical model of the system through algebraic manipulations. The resulting indirect model structure only depends on known and measured signals and can be used to estimate the desired dynamics or properties. The effects of using the input measurements are analyzed in terms of identifiability, consistency and variance properties. It is shown that cancelation of shared dynamics can occur and that the resulting estimation problem is similar to errors-in-variables and closed-loop estimation problems because of the noisy inputs used in the model. In fact, the indirect framework unifies a number of already existing system identification problems that are contained as special cases.For completeness, an instrumental variable method is proposed as one possibility for estimating the indirect model. It is shown that multiple datasets can be used to overcome certain identifiability issues and two approaches, the multi-stage and the joint identification approach, are suggested to utilize multiple datasets for estimation of models. Furthermore, the benefits of using the indirect model in filtering and for control synthesis are briefly discussed.To show the applicability, the framework is applied to the roll dynamics of a ship for tracking of the loading conditions. The roll dynamics is very sensitive to changes in these conditions and a worst-case scenario is that the ship will capsize. It is assumed that only motion measurements from an inertial measurement unit (IMU) together with measurements of the rudder angle are available. The true inputs are thus not available, but the measurements from the IMU can be used to form an indirect model from a well-established ship model. It is shown that only a subset of the unknown parameters can be estimated simultaneously. Data was collected in experiments with a scale ship model in a basin and the joint identification approach was selected for this application due to the properties of the model. The approach was applied to the collected data ...

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Identification of systems with unknown inputs using indirect input measurements

Cited by 37 publications

References 32 publications

Abstractions of linear dynamic networks for input selection in local module identification

Abstractions of linear dynamic networks for input selection in local module identification

Identification and Prediction in Dynamic Networks with Unobservable Nodes

Indirect System Identification for Unknown Input Problems: With Applications to Ships

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