Identification of distributed-parameter systems from sparse measurements

Abstract

In this paper, a method for the identification of distributed-parameter systems is proposed, based on finite-difference discretization on a grid in space and time. The method is suitable for the case when the partial differential equation describing the system is not known. The sensor locations are given and fixed, but not all grid points contain sensors. Per grid point, a model is constructed by means of lumped-parameter system identification, using measurements at neighboring grid points as inputs. As the resulting model might become overly complex due to the involvement of neighboring measurements along with their time lags, the Lasso method is used to select the most relevant measurements and so to simplify the model. Two examples are reported to illustrate the effectiveness of the method, a simulated two-dimensional heat conduction process and the construction of a greenhouse climate model from real measurements.

Subspace Identification of Temperature Dynamics

“…• Method B: Model selection on the basis of the openloop simulation of ( 9)-( 10). This method is based on the simulation of the Kalman innovation representation ( 9)- (10). Similarly to the Method A, using the state-space model ( 9)-( 10) we form a least-squares problem and estimate the initial state.…”

“…• Method C: Model selection on the basis of the closedloop simulation of ( 9)- (10). The initial state is estimated using the procedure used to estimate the initial state in Method B.…”

“…Figure (10) shows the residual test results. The results are obtained for the parameters giving the smallest value of the relative error.…”

“…To develop methods and actuators to counteract these thermally induced deformations, it is of paramount importance that the temperature dynamics of optical elements is accurately modeled and controlled [2]- [8]. Besides this, modeling and control of temperature dynamics are important for temperature estimation and health monitoring of lithium-ion batteries [9], as well as for temperature control of greenhouses [10], [11], buildings [12]- [14], and for proper operation of a number of industrial processes and systems [15], [16].…”

Parameter estimation of partial differential equations using artificial neural network

“…The direct method utilizes the infinite-dimensional system model to obtain the parameters. The reduction-based method, which is also known as time-space separation, involves spatial discretisation in order to reduce the PDEs into a set of ODEs in time to which estimation methods for LPS can be applied (Hidayat et al, 2017). A number of other related works exist in literature including statistical methods (Banks and Kunisch, 1989;Fitzpatrick, 1991;Xun et al, 2013), Laguerre-polynomial approach (Ranganathan et al, 1984), general orthogonal polynomials (Lee and Chang, 1986), Fourier series method (Mohan and Datta, 1989), singular value decomposition (Gay and Ray, 1995), artificial neural networks coupled with traditional numerical discretisation techniques (Gonzalez-Garcia et al, 1998), and extended multiple shooting method (eMSM) (Muller and Timmer, 2002).…”