Diagnosis of a Continous Stirred Tank Reactor Using Kalman Filter

Hsoumi, Aicha; Harabi, Rafika El; Ali, Saloua Bel Hadj; Abdelkrim, Mohamed Naceur

doi:10.1109/cssim.2009.22

Cited by 10 publications

(9 citation statements)

References 9 publications

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“…The residual of a particular measurement at any instant is given by

r_{k} = {\overset{y}{true}}_{k} = y_{k} - {\overset{y}{true}}_{k | k - 1}

where

y_{k}

is the measured vector at a particular instant, and

\overset{y}{true}

contains the corresponding predicted values. Among various methods for residual generation, the Kalman‐filter‐based residual generation method was employed to calculate the residuals . The Kalman filter is an optimal state estimator for a linear system in the presence of Gaussian noise.…”

Section: Fault Detection and Diagnosismentioning

confidence: 99%

“…The reaction in the system is the oxidation of sodium thiosulfate by hydrogen peroxide, which is an irreversible exothermic oxido‐reduction reaction. This reaction is expressed by the following equation :

\begin{matrix} 2 {Na}_{2} {normalS}_{2} {normalO}_{3} + {4H}_{2} {normalO}_{2} - \to {Na}_{2} {normalS}_{3} {normalO}_{6} + {Na}_{2} {SO}_{4} + {4H}_{2} O \\ 2 A + 4 B - \to C + D + 4F \\ r_{normalA} = 4 k (T_{normalr}) C_{normalA} C_{normalB} = - (k_{0} + Δ k_{0}) exp (\frac{- E + Δ E}{R_{normalg} T_{normalr}}) C_{normalA} C_{normalB} \end{matrix}

where k 0 is the pre‐exponential factor, and C A and C B are the concentrations of components A and B, respectively. E is activation energy; R g is the gas constant; Δ k 0 and Δ E represent uncertainty and T r is the reactor temperature.…”

Section: Cstrmentioning

confidence: 99%

“…The system equations describe the reactant concentration, C A , reactor temperature, T r , and jacket temperature, T j :

\frac{d C_{normalA}}{d t} = \frac{F}{V} true(C_{Ain} - C_{normalA} true) - 4 k C_{normalA}^{2}

\frac{d T_{normalr}}{d t} = \frac{F_{normalr}}{V_{normalr}} true(T_{rin} - T_{normalr} true) + 4 \frac{true(- Δ H_{normalr} true) + Δ true(- Δ H_{normalr} true)}{ρ C_{normalp}} k C_{normalA}^{2} - \frac{UA + Δ UA}{ρ C_{normalp} V} (T_{normalr} - T_{normalj})

\frac{d T_{normalj}}{d t} = \frac{F_{normalw}}{V_{normalw}} true(T_{jin} - T_{normalj} true) + \frac{UA + Δ UA}{ρ_{normalw} C_{normalp}_{_{normalw}} V_{normalw}} (T_{normalr} - T_{normalj})

…”

Section: Cstrmentioning

confidence: 99%

“…To implement the Kalman filter, the nonlinear CSTR model is linearized around its nominal operating conditions. The discrete state space model coefficients are given as :

A_{k} = true[\begin{matrix} - 0.08 & - 5.89 e - 4 & - 1.26 e - 5 \\ 156.23 & 1.04 & 0.02 \\ 33.55 & 0.26 & 0.72 \end{matrix} true] B_{k} = true[\begin{matrix} - 1.69 e - 7 \\ 4.23 e - 4 \\ 0.02 \end{matrix} true] C_{k} = true[\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix} true]

…”

Section: Cstrmentioning

confidence: 99%

See 3 more Smart Citations

Dynamic risk assessment and fault detection using a multivariate technique

Zadakbar

Imtiaz

Khan

2013

Process Safety Progress

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In the context of process safety, significant improvements are needed in fault detection methods, especially, in the areas of early detection and warning. In this article, a multivariate risk‐based fault detection and diagnosis technique is proposed. The key elements of this technique are to eliminate faults that are not serious and to provide a dynamic process risk indication at each sampling instant. A multivariable residual generation process based on the Kalman filter has been combined with a risk assessment procedure. The use of the Kalman filter makes the method more robust to false alarms, which is an important aspect of any fault detection algorithm that targets the safety of a process. In addition, we consider significant differences in the severity of the faults associated with different process variables. We also take into account the varying intensity of damage caused by the increasing and decreasing rates of fault and the need to treat those cases differently. © 2013 American Institute of Chemical Engineers Process Saf Prog 32: 365–375, 2013

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“…The residual of a particular measurement at any instant is given by

r_{k} = {\overset{y}{true}}_{k} = y_{k} - {\overset{y}{true}}_{k | k - 1}

where

y_{k}

is the measured vector at a particular instant, and

\overset{y}{true}

Section: Fault Detection and Diagnosismentioning

confidence: 99%

\begin{matrix} 2 {Na}_{2} {normalS}_{2} {normalO}_{3} + {4H}_{2} {normalO}_{2} - \to {Na}_{2} {normalS}_{3} {normalO}_{6} + {Na}_{2} {SO}_{4} + {4H}_{2} O \\ 2 A + 4 B - \to C + D + 4F \\ r_{normalA} = 4 k (T_{normalr}) C_{normalA} C_{normalB} = - (k_{0} + Δ k_{0}) exp (\frac{- E + Δ E}{R_{normalg} T_{normalr}}) C_{normalA} C_{normalB} \end{matrix}

Section: Cstrmentioning

confidence: 99%

“…The system equations describe the reactant concentration, C A , reactor temperature, T r , and jacket temperature, T j :

\frac{d C_{normalA}}{d t} = \frac{F}{V} true(C_{Ain} - C_{normalA} true) - 4 k C_{normalA}^{2}

\frac{d T_{normalr}}{d t} = \frac{F_{normalr}}{V_{normalr}} true(T_{rin} - T_{normalr} true) + 4 \frac{true(- Δ H_{normalr} true) + Δ true(- Δ H_{normalr} true)}{ρ C_{normalp}} k C_{normalA}^{2} - \frac{UA + Δ UA}{ρ C_{normalp} V} (T_{normalr} - T_{normalj})

\frac{d T_{normalj}}{d t} = \frac{F_{normalw}}{V_{normalw}} true(T_{jin} - T_{normalj} true) + \frac{UA + Δ UA}{ρ_{normalw} C_{normalp}_{_{normalw}} V_{normalw}} (T_{normalr} - T_{normalj})

…”

Section: Cstrmentioning

confidence: 99%

“…To implement the Kalman filter, the nonlinear CSTR model is linearized around its nominal operating conditions. The discrete state space model coefficients are given as :

A_{k} = true[\begin{matrix} - 0.08 & - 5.89 e - 4 & - 1.26 e - 5 \\ 156.23 & 1.04 & 0.02 \\ 33.55 & 0.26 & 0.72 \end{matrix} true] B_{k} = true[\begin{matrix} - 1.69 e - 7 \\ 4.23 e - 4 \\ 0.02 \end{matrix} true] C_{k} = true[\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix} true]

…”

Section: Cstrmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic risk assessment and fault detection using a multivariate technique

Zadakbar

Imtiaz

Khan

2013

Process Safety Progress

View full text Add to dashboard Cite

show abstract

“…However, the adoption of linearized models has been proven to work properly for the Continuous Stirred Tank Reactors (CSTRs), mainly operating at steady state, due to their intrinsic unsteady behavior (Rajaraman S. & al., 2006), (Favache A. & al., 2009), (Hsoumi A. & al., 2009), (Han Z.…”

Section: Introductionmentioning

confidence: 99%

Monitoring of Chemical Processes Using Model-Based Approach

Elhsoumi¹,

Harabi²,

Naoui³

et al. 2011

Numerical Simulations of Physical and Engineering Processes

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Dynamic Risk Assessment of a Nonlinear Non‐Gaussian System Using a Particle Filter and Detailed Consequence Analysis

2015

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This paper presents a dynamic risk assessment using a comprehensive economic consequence methodology in combination with a multivariate model‐based fault detection method. The proposed approach aims to calculate process risk dynamically at each sampling instant, and also to identify and screen the faults that are not hazardous. The approach relies on a particle filter combined with a comprehensive economic consequence methodology. The fault detection module uses a state space model of the process plant and a particle filter algorithm that calculates the probability of the fault. The output of this module is then combined with the consequence module, which uses loss functions to relate process deviations to economic losses. The consequence module identifies, quantifies, and integrates losses for a given scenario. Combining the two modules for risk assessment makes this approach more reliable in the analysis of realistic nonlinear process systems, and improves decision‐making for process design and risk management.

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Diagnosis of a Continous Stirred Tank Reactor Using Kalman Filter

Cited by 10 publications

References 9 publications

Dynamic risk assessment and fault detection using a multivariate technique

Dynamic risk assessment and fault detection using a multivariate technique

Monitoring of Chemical Processes Using Model-Based Approach

Dynamic Risk Assessment of a Nonlinear Non‐Gaussian System Using a Particle Filter and Detailed Consequence Analysis

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