# Fault Detection and Isolation System Based on Structural Analysis of an Industrial Seawater Reverse Osmosis Desalination Plant

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Structural Analysis for Model Based Diagnosis

**Definition**

**1**(System)

**.**

**Definition**

**2**(Structural model)

**.**

**Definition**

**3**(Matching)

**.**

- Overdetermined subgraph ${G}^{+}$, with a X-complete matching that is not $\mathsf{\Sigma}$-complete,
- Just-determined subgraph ${G}^{0}$, with a complete matching,
- Underdetermined subgraph ${G}^{-}$, with a $\mathsf{\Sigma}$-complete matching that is not X-complete.

**Definition**

**4**(Structural redundancy)

**.**

#### Structural Diagnosability

**Definition**

**5**(ARR)

**.**

**Definition**

**6**(Residual generator)

**.**

**Definition**

**7**(FMSO set)

**.**

## 3. Modeling of the Seawater RO Desalination Process

#### 3.1. Brief Description of the Industrial Seawater RO Desalination Plant

^{3}/day and provides new water supplies for industrial and domestic sectors. The technology applied in this plant is RO. The daily processed seawater volume by the plant is 76,800 m

^{3}; of this volume, 42,240 m

^{3}of brine is sent back into the sea in a dispersive way. Thus, the conversion rate of the plant is 45%; this means that 45 L of guaranteed high quality freshwater are obtained from every 100 L of seawater.

^{3}/day. Each membranes rack consists of 140 pressure vessels, and each one has seven aromatic polyamide membranes. Figure 5 shows a view of the RO racks, and Figure 6 exhibits a schematic of one of the pressure vessels of these RO racks.

#### 3.2. Modeling of the Seawater RO Desalination Process

## 4. FDI System for the RO Desalination Plant under Study

#### 4.1. FMSO Sets’ Calculation

#### 4.2. Fault Detection and Isolation

#### 4.3. FMSO Sets’ Selection by the BILP Method

#### 4.4. Residual Generation

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Bipartite graph of fault-driven minimal structurally overdetermined (FMSO) set ${\phi}_{1}$ of the academic example.

FMSO Set | Equations Involved |
---|---|

${\phi}_{1}$ | $\{{e}_{7},{e}_{8},{e}_{9},{e}_{10},{e}_{18},{e}_{19},{e}_{20}\}$ |

${\phi}_{2}$ | $\{{e}_{4},{e}_{6},{e}_{13},{e}_{15},{e}_{16}\}$ |

${\phi}_{3}$ | $\{{e}_{2},{e}_{12},{e}_{13},{e}_{14},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{4}$ | $\{{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{14},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{5}$ | $\{{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{13},{e}_{14},{e}_{16},{e}_{17}\}$ |

${\phi}_{6}$ | $\{{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{13},{e}_{14},{e}_{15},{e}_{17}\}$ |

${\phi}_{7}$ | $\{{e}_{1},{e}_{12},{e}_{13},{e}_{14}\}$ |

${\phi}_{8}$ | $\{{e}_{1},{e}_{4},{e}_{6},{e}_{12},{e}_{14},{e}_{15},{e}_{16}\}$ |

${\phi}_{9}$ | $\{{e}_{1},{e}_{2},{e}_{13},{e}_{14},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{10}$ | $\{{e}_{1},{e}_{2},{e}_{12},{e}_{14},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{11}$ | $\{{e}_{1},{e}_{2},{e}_{12},{e}_{13},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{12}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{14},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{13}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{13},{e}_{14},{e}_{16},{e}_{17}\}$ |

${\phi}_{14}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{13},{e}_{14},{e}_{15},{e}_{17}\}$ |

${\phi}_{15}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{15},{e}_{16},{e}_{17}\}$ |

${\phi}_{16}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{14},{e}_{16},{e}_{17}\}$ |

${\phi}_{17}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{14},{e}_{15},{e}_{17}\}$ |

${\phi}_{18}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{13},{e}_{16},{e}_{17}\}$ |

${\phi}_{19}$ | $\{{e}_{1},{e}_{2},{e}_{4},{e}_{6},{e}_{12},{e}_{13},{e}_{15},{e}_{17}\}$ |

${\mathit{f}}_{1}$ | ${\mathit{f}}_{2}$ | ${\mathit{f}}_{3}$ | ${\mathit{f}}_{4}$ | ${\mathit{f}}_{5}$ | ${\mathit{f}}_{6}$ | ${\mathit{f}}_{7},{\mathit{f}}_{8},{\mathit{f}}_{9}$ | ${\mathit{f}}_{10}$ | |
---|---|---|---|---|---|---|---|---|

$ar{r}_{1}$ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |

$ar{r}_{6}$ | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |

$ar{r}_{7}$ | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |

$ar{r}_{9}$ | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |

$ar{r}_{16}$ | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |

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**MDPI and ACS Style**

Pérez-Zuñiga, G.; Rivas-Perez, R.; Sotomayor-Moriano, J.; Sánchez-Zurita, V.
Fault Detection and Isolation System Based on Structural Analysis of an Industrial Seawater Reverse Osmosis Desalination Plant. *Processes* **2020**, *8*, 1100.
https://doi.org/10.3390/pr8091100

**AMA Style**

Pérez-Zuñiga G, Rivas-Perez R, Sotomayor-Moriano J, Sánchez-Zurita V.
Fault Detection and Isolation System Based on Structural Analysis of an Industrial Seawater Reverse Osmosis Desalination Plant. *Processes*. 2020; 8(9):1100.
https://doi.org/10.3390/pr8091100

**Chicago/Turabian Style**

Pérez-Zuñiga, Gustavo, Raul Rivas-Perez, Javier Sotomayor-Moriano, and Victor Sánchez-Zurita.
2020. "Fault Detection and Isolation System Based on Structural Analysis of an Industrial Seawater Reverse Osmosis Desalination Plant" *Processes* 8, no. 9: 1100.
https://doi.org/10.3390/pr8091100