Constrained profile estimation for distributed parameter system in one dimension using orthogonal collocation

Seth, Gaurav; Patwardhan, Sachin C.; Bhushan, Mani

doi:10.1016/j.jprocont.2023.103011

Cited by 2 publications

(10 citation statements)

References 37 publications

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“…Here, it is assumed that w a (k) is uncorrelated with the sensor noise v s (k), and S is a (n d × η) cross-correlation matrix. Details of MPM quantification in dynamics and measurement models (evaluating Q a , R a , and S) can be referred from Seth et al 35 The construction of the measurement matrix C m is discussed in Section 4.1. The reduced-dimension model (eqs 16 and 17) along with the measurement model (eq 18) will be used to develop a Bayesian state profile estimator in Section 4.…”

Section: Reduced-dimensional Modeling Of Dpsmentioning

confidence: 99%

“…Further, it is to be noted that the signals w a ( k ) and v a ( k ) are correlated, i.e., state and measurement noise signals are correlated as [ lefttrue boldw a false( k false) v false( k false) ] ∼ scriptN ( bold0 false( n d + η false) × 1 , true[ .25ex2ex Q a boldS S T boldR true] ) Here, it is assumed that w a ( k ) is uncorrelated with the sensor noise v s ( k ), and S is a ( n d × η) cross-correlation matrix. Details of MPM quantification in dynamics and measurement models (evaluating Q a , R a , and S ) can be referred from Seth et al . The construction of the measurement matrix C m is discussed in Section .…”

Section: Preliminariesmentioning

confidence: 99%

“…Further, the MPM arising due to the model order reduction is systematically compensated for while developing the state profile estimator based on the selected reduced-dimension model. In our previous work, 35 the difference between the DPS behavior, i.e., dynamic spatial state profiles predicted by a high dimensional finite difference (FD) model and a reduceddimension OC model was used to select the model order and subsequently quantify the MPM. In particular, for a selected OC model, the following assumption was introduced to account for the MPM associated with it.…”

Section: Reduced-dimensional Modeling Of Dpsmentioning

confidence: 99%

“…However, estimated profiles constructed using Lagrange polynomials may violate the constraints at spatial locations other than the collocation points. Our recent work 35 addressed the issue of profile constraints violation and a modified constrained profile estimation scheme was proposed to ensure the constraints satisfaction by the states throughout the spatial domain. A brief review of the constrained profile estimation scheme is given in Appendix B.…”

Section: Updating States With Profilementioning

confidence: 99%

“…Toward this end, a reduced order DAE model to represent a nonlinear DPS is formulated using the OC method along with the Lagrange interpolating polynomial. A constrained DAE-EKF estimator developed in our previous work 35 is used to estimate states at collocation points, which are subsequently used to reconstruct the state estimates over the entire spatial domain. Use of the OC modeling technique with Lagrange interpolating polynomial also enables us to (i) consider estimation performance throughout the spatial domain in the SPD objective and (ii) allows sensors to be placed anywhere along the spatial domain instead of restricting them at prespecified discrete locations.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Sensor Placement Design for Profile Estimation of Distributed Parameter Systems

Seth,

Bhushan,

Patwardhan

2024

Ind. Eng. Chem. Res.

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This work addresses the problem of sensor placement design (SPD) in distributed parameter systems (DPS), where states evolve both in space and time. Existing approaches, often focused on linear systems and/or steady-state conditions, may not be appropriate for SPD of nonlinear DPS undergoing significant dynamic variations in the operating conditions. Additionally, many existing approaches aim to minimize estimation error properties only at discrete locations, thus leading to inferior profile performance as well as restricting sensor placement choices. In the current work, we propose an SPD approach for nonlinear DPS, considering dynamic variations in operating conditions. Toward this end, utilizing Lagrange polynomials and the orthogonal collocation (OC) method, we propose an objective function for SPD that accounts for estimation error properties across the entire spatial domain over the time period of interest. The approach leads to well-behaved estimates throughout the spatial domain and also enables sensor locations to be continuous variables, thereby eliminating the need for pre-specifying candidate locations. This results in a nonlinear programming optimization problem which does not involve integer variables. Extensive simulations of transport reaction processes described by partial differential equations (PDEs) validate the effectiveness of our SPD approach for state estimation in DPS. Furthermore, we also establish analogies between the optimal sensor placement problem in DPS and the optimal design of experiments problem, providing a conceptual framework for posing various other types of sensor placement objectives.

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Section: Reduced-dimensional Modeling Of Dpsmentioning

confidence: 99%