Inference in dynamic error‐in‐variable‐measurement problems

Abstract

Efficient algorithms were developed for estimating model parameters from measured data, even in the presence of gross errors. In addition to point estimates of parameters, however, assessments of uncertainty are needed. Linear approximations provide standard errors, but they can be misleading when applied to models that are substantially nonlinear. To overcome this difficulg, profiling methods were developed for the case in which the regressor variables are error-free. These methods provide accurate nonlinear confidence regions, but become expensive for a large number of parameters. These profiling methods are modified to error-in-variable-measurement models with many incidental parameters. Laplace S method is used to integrate out the incidental parameters associated with the measurement errors, and then profiling methods are applied to obtain approximate confidence contours for the parameters. This approach is computa-tional& efficient, requires few function evaluations, and can be applied to large-scale problems, It is useful when certain measurement errors (such as input variables) are relatively small, but not so small that they can be ignored.We illustrate the effect of increasing input noise on approximation (Eq. 29) in a very simple situation. Consider a problem with only one state variable x, one incidental parameter u, and one parameter 0 where the measurements are given by

Fluid Catalytic Cracking (FCC) Process Modeling, Simulation, and Control

“…After minimization of the plant–model mismatch, this model is used for process optimization using an economic objective function. Because essentially the same detailed model can be used for data reconciliation and parameter estimation (and later process optimization), various authors advocate that these two tasks should be considered simultaneously through the solution of a large online optimization problem, using a global errors-in-variables approach, for which decomposition strategies are available to speed its solution. , A number of industrial reports reinforce the importance of the parameter estimation task to the success of developing adequate models for the application of model-based supervision strategies to FCC units. − …”

Online Data Reconciliation with Poor Redundancy Systems

“…Interactive software, hardware, and information technology systems are qualitatively represented in Figure . Certain reconciled datasets are acquired from the historical server of the DCS and used to initialize the so-called “Error-In-Variable” method − (EVM, described later), which is an optimization problem aimed at estimating the adaptive parameters and, hence, adapting the detailed process simulation to the current plant operating conditions. The adaptive parameters are used to simulate the process and reproduce a reliable and coherent picture of the operating conditions; in this case, the data used to initialize the process simulation are the fresh data coming from the field (not yet reconciled).…”

“…The second problem to be solved is the so-called “Error-in-Variable” method (EVM), originally proposed by Biegler, to whom one could refer for more details. ,, Briefly, it is formulated as follows: min boldx i , normalθ nobreak.25em normalΦ = ∑ i = 1 SSC ( m i − x i ) T Q − 1 false( boldm i − boldx i false) subject to f false( boldx i , boldθ false) = 0 where Φ is the is the objective function; x and m are the vectors of reconciled and measured values, respectively; Q is the positive definite diagonal matrix of weights; g ( x ) = 0 and h ( x ) ≤ 0 are equality and inequality constraints, respectively, to which the minimization problem is subjected. The key point of EVM is its large-size dimension, with respect to the data reconciliation, since its degrees of freedom are the adaptive parameters θ and the reconciled vectors of each steady-state condition (SSC) acquired by the historical server of the DCS.…”

“…The second problem to be solved is the so-called "Error-in-Variable" method (EVM), originally proposed by Biegler, to whom one could refer for more details. 16,17,32 Briefly, it is formulated as follows:…”

Sulfur Recovery Units: Adaptive Simulation and Model Validation on an Industrial Plant

“…Data reconciliation has been largely studied, and several approaches and techniques have been proposed in the literature, but from a process and chemical point of view, its applications have been mainly reduced to solve daily/weekly production accounting as well as approximate performance monitoring issues. Moreover, facing the most recent promising approaches such as dynamic reconciliation, − model-based performance monitoring, , etc., only the simplest methods have been used to practically tackle the aforementioned problems.…”