5,692 research outputs found
On the interpretation and identification of dynamic Takagi-Sugenofuzzy models
Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples
Fitting stochastic predator-prey models using both population density and kill rate data
Most mechanistic predator-prey modelling has involved either parameterization
from process rate data or inverse modelling. Here, we take a median road: we
aim at identifying the potential benefits of combining datasets, when both
population growth and predation processes are viewed as stochastic. We fit a
discrete-time, stochastic predator-prey model of the Leslie type to simulated
time series of densities and kill rate data. Our model has both environmental
stochasticity in the growth rates and interaction stochasticity, i.e., a
stochastic functional response. We examine what the kill rate data brings to
the quality of the estimates, and whether estimation is possible (for various
time series lengths) solely with time series of population counts or biomass
data. Both Bayesian and frequentist estimation are performed, providing
multiple ways to check model identifiability. The Fisher Information Matrix
suggests that models with and without kill rate data are all identifiable,
although correlations remain between parameters that belong to the same
functional form. However, our results show that if the attractor is a fixed
point in the absence of stochasticity, identifying parameters in practice
requires kill rate data as a complement to the time series of population
densities, due to the relatively flat likelihood. Only noisy limit cycle
attractors can be identified directly from population count data (as in inverse
modelling), although even in this case, adding kill rate data - including in
small amounts - can make the estimates much more precise. Overall, we show that
under process stochasticity in interaction rates, interaction data might be
essential to obtain identifiable dynamical models for multiple species. These
results may extend to other biotic interactions than predation, for which
similar models combining interaction rates and population counts could be
developed
A study of parameter identification
A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix
emgr - The Empirical Gramian Framework
System Gramian matrices are a well-known encoding for properties of
input-output systems such as controllability, observability or minimality.
These so-called system Gramians were developed in linear system theory for
applications such as model order reduction of control systems. Empirical
Gramian are an extension to the system Gramians for parametric and nonlinear
systems as well as a data-driven method of computation. The empirical Gramian
framework - emgr - implements the empirical Gramians in a uniform and
configurable manner, with applications such as Gramian-based (nonlinear) model
reduction, decentralized control, sensitivity analysis, parameter
identification and combined state and parameter reduction
The Parameter Houlihan: a solution to high-throughput identifiability indeterminacy for brutally ill-posed problems
One way to interject knowledge into clinically impactful forecasting is to
use data assimilation, a nonlinear regression that projects data onto a
mechanistic physiologic model, instead of a set of functions, such as neural
networks. Such regressions have an advantage of being useful with particularly
sparse, non-stationary clinical data. However, physiological models are often
nonlinear and can have many parameters, leading to potential problems with
parameter identifiability, or the ability to find a unique set of parameters
that minimize forecasting error. The identifiability problems can be minimized
or eliminated by reducing the number of parameters estimated, but reducing the
number of estimated parameters also reduces the flexibility of the model and
hence increases forecasting error. We propose a method, the parameter Houlihan,
that combines traditional machine learning techniques with data assimilation,
to select the right set of model parameters to minimize forecasting error while
reducing identifiability problems. The method worked well: the data
assimilation-based glucose forecasts and estimates for our cohort using the
Houlihan-selected parameter sets generally also minimize forecasting errors
compared to other parameter selection methods such as by-hand parameter
selection. Nevertheless, the forecast with the lowest forecast error does not
always accurately represent physiology, but further advancements of the
algorithm provide a path for improving physiologic fidelity as well. Our hope
is that this methodology represents a first step toward combining machine
learning with data assimilation and provides a lower-threshold entry point for
using data assimilation with clinical data by helping select the right
parameters to estimate
Stochastic control system parameter identifiability
The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters
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