A dynamic network approach to identification of physical systems

System identification problems utilizing a prediction error approach are typically considered in an input/output setting, where a directional cause-effect relationship is presumed and transfer functions are used to estimate the causal relationships. In more complex interconnection structures, as e.g. appearing in dynamic networks, the cause-effect relationships can be encoded by a directed graph. Physical dynamic networks are most commonly described by diffusive couplings between node signals, implying that cause-effect relationships between node signals are symmetric and therefore can be represented by an undirected graph. This paper shows how (prediction error) identification methods developed for linear dynamic networks can be configured to identify components in (undirected) physical networks with known topology

Closed-loop identification of multivariable processes with part of the inputs controlled

\u3cp\u3eIn many multivariable industrial processes a subset of the available input signals is being controlled. In this paper it is analysed in which sense the resulting partial closed-loop identification problem is actually a full closed-loop problem, or whether one can benefit from the presence of non-controlled inputs to simplify the identification problem. The analysis focuses on the bias properties of the plant estimate when applying the direct method of prediction error identification, and the possibilities to identify (parts of) the plant model without the need of simultaneously estimating full-order noise models.\u3c/p\u3

Detecting nonlinear modules in a dynamic network:a step-by-step procedure\u3csup\u3e⁎\u3c/sup\u3e

\u3cp\u3eAdopting a dynamic network viewpoint allows one to analyze and identify subsystems of a complex interconnected system. When studying a network of dynamic systems, it is important to know if significant nonlinear behavior is present in a dynamic network under study and where the nonlinearity is located in the network. This work extends the Best Linear Approximation framework from the closed-loop to the networked setting. The framework is illustrated using a practical step-by-step estimation and analysis procedure. It is shown how nonlinear behavior can be quantified and located in a dynamic network using this framework.\u3c/p\u3

A local direct method for module identification in dynamic networks with correlated noise

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is a set of algorithms that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. Three algorithms are presented that differ in their approach of selecting measured node signals. Either a maximum or a minimum number of measured node signals can be considered, as well as a preselected set of measured nodes

Some asymptotic properties of multivariable models identified by equation error techniques

\u3cp\u3eSome interesting properties are derived for simple equation-error-identification techniques - least squares and basic instrumental variable methods - applied to a class of linear, time-invariant, time-discrete multivariable models. The system at hand is not supposed to be contained in the chosen model set. Assuming that the input is unit variance white noise, it is shown that the Markov parameters of the system are estimated asymptotically unbiased over a certain interval around t equals 0.\u3c/p\u3

Some asymptotic properties of multivariable models identified by equation error techniques

\u3cp\u3eSome interesting properties are derived for simple equation error identification techniques, least squares and basic instrumental variable methods, applied to a class of linear time-invariant time-discrete multivariable models. The system at hand is not supposed to be contained in the chosen model set. Assuming that the input is unit-variance white noise, it is shown that the Markov parameters of the system are estimated asymptotically unbiased over a certain interval around t equals 0.\u3c/p\u3

Locating nonlinearity in mechanical systems: a dynamic network perspective

Though it is a crucial step for most identification methods in nonlinear structural dynamics, nonlinearity location is a sparsely addressed topic in the literature. In fact, locating nonlinearities in mechanical systems turns out to be a challenging problem when treated nonparametrically, that is, without fitting a model. The present contribution takes a new look at this problem by exploiting some recent developments in the identification of dynamic networks, originating from the systems and control community

Allocation of excitation signals for generic identifiability of dynamic networks

\u3cp\u3eThis paper studies generic identifiability of dynamic networks, in which the edges connecting the vertex signals are described by proper transfer functions, and partial vertices are excited by designed external signals. We assume that the topology of the underlying graph is known, and all the vertex signals are measured. We show that generic identifiability of a directed network is related to the existence of a set of disjoint directed pseudo-trees that cover all the edges of the underlying graph, based on which, an excitation allocation problem is studied, aiming to select the minimal number excitation signals to achieve the generic identifiability of the whole network. An algorithmic procedure thereby is devised for selecting locations of the external signals such that all the edges can be consistently estimated.\u3c/p\u3

Bayesian topology identification of linear dynamic networks

\u3cp\u3eIn networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying the connectivity of networks of transfer functions, without the need to estimate the dynamics. The algorithm employs a Bayesian measure and a forward-backward search algorithm. To obtain the Bayesian measure, the impulse responses of network modules are modeled as Gaussian processes and the hyperparameters are estimated by marginal likelihood maximization using the expectation-maximization algorithm. Numerical results demonstrate the effectiveness of this method.\u3c/p\u3

Experiment design for batch-to-batch model-based learning control

\u3cp\u3eAn Experiment Design framework for dynamical systems which execute multiple batches is presented in this paper. After each batch, a model of the system dynamics is refined using the measured data. This model is used to synthesize the controller that will be applied in the next batch. Excitation signals may be injected into the system during each batch. From one hand, perturbing the system worsens the control performance during the current batch. On the other hand, the more informative data set will lead to a better identified model for the following batches. The role of Experiment Design is to choose the proper excitation signals in order to optimize a certain performance criterion defined on the set of batches that is scheduled. A total cost is defined in terms of the excitation and the application cost altogether. The excitation signals are designed by minimizing the total cost in a worst case sense. The Experiment Design is formulated as a Convex Optimization problem which can be solved efficiently using standard algorithms. The applicability of the method is demonstrated in a simulation study.\u3c/p\u3