# Super-Alarms with Diagnosis Proficiency Used as an Additional Layer of Protection Applied to an Oil Transport System

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Research Method

#### 2.1. Layers of Protection and the Super-Alarm Layer

#### 2.2. Chronicle Based Alarm Management Methodology

**Definition**

**1.**

_{1}= (a, 3) and e

_{2}= (a, 6) are two events that carry the same type of event (a).

**Definition**

**2.**

_{l}, in which l is the size of the temporal sequence S, and N

_{l}is a finite set of linearly ordered instants of cardinality l. Furthermore, l = |S| is the size of the temporal sequence, i.e., the number of event type occurrences in S. An example of a sequence representing an activity stream may be given by the sequence${S}_{1}=\left\{{e}_{1},{e}_{2},{e}_{3},{e}_{4},{e}_{5},{e}_{6}\right\}=\left\{\left(a,2\right),\left(b,4\right),\left(c,5\right),\left(a,8\right),\left(b,9\right),\left(a,10\right)\right\}$with l

_{1}= 6.

**Definition**

**3.**

- Ψ is a set of indexed event types, i.e., a finite indexed family defined by ψ: H → E, in which H ⊏ N.
- A is a set of edges between the indexed event types; there is an edge (${\sigma}_{1\left(h1\right)}$, ${\sigma}_{2\left(h2\right)}$) ∈ A if and only if there is a time constraint between ${\sigma}_{1\left(h1\right)}$, and ${\sigma}_{2\left(h2\right)}$.

**Definition**

**4.**

_{inst}= 〈 ξ´, Τ

_{v}〉 in which Τ

_{v}is a valuation of Τ. If the sequence S has finished, and at least one event that occurs violates some temporal constraint, this chronicle is not recognized. Figure 4 illustrates the above definition: the chronicle on the left is recognized in the first and second sequence. Nevertheless, it is not recognized in the third sequence, because the only set of constraints relating a,b,c, and d in this sequence (Sequence

_{3}) is: Τ

_{v}= {a[5,5]b; a[3,3]c; c[2,2]b; b[2,2]d}, and Τ

_{v}is not a valuation of T = {a[3,4]b; a[1,2]c; c[1,2]b; b[1,2]d}.

**Definition**

**5.**

_{1}, Ar

_{2}, Ar

_{3}, ……. Ar

_{n}} in which each area has φ operational modes (e.g start-up, shutdown, slow march, etc.) noted O

_{i}, i = 1,2,3...φ. The process behavior in each operating mode can be either normal or faulty. The set of failure labels is defined as Δ

_{f}= {f

_{1}, f

_{2}, f

_{3}, …. f

_{r}}, and the complete set of possible labels is $\Delta =N\bigcup {\Delta}_{f}$, in which N means normal. In order to monitor the process and to recognize the different situations (normal or faulty) of the operational modes, it is proposed to build a chronicle base for each area. For a given area, a learned chronicle ${C}_{ij}^{m}$ is associated with each couple (${O}_{i},{L}_{j}$) in which ${L}_{j}\in \Delta $. Equation (1) determines the set of chronicles C for any process area ($A{r}_{m}$).

- V = {υ
_{i}} is a set of continuous process variables which are functions of time. - D is a set of discrete variables. D = Q⋃K⋃V
_{Q}, where:- ○
- Q is a set of states qi of the transition system, which represents the system’s operation modes.
- ○
- The set of auxiliary discrete variables K = {K
_{i}}, I = 1,2,3,….n_{c}represents the system configuration in each mode q_{i}, in which K_{i}indicates the discrete state of the active components. - ○
- V
_{Q}is a set of qualitative variables whose values are obtained from the behavior of each continuous variable υ_{i}.

- E = Σ ⋃ Σ
^{c}is a finite set of observables (Σ_{o}) and unobservable (Σ_{uo}) event types, in which Σ is the set of event type associated to the procedural actions, for example, in the start-up or shutdown stages, and Σ^{c}is the set of event types associated to the behavior of the continuous process variables. - Tr:Q × Σ → Q is the transition function. The transition from mode q
_{i}to mode q_{j}with associated event σ is noted (q_{i},σ,q_{j}). - CSD ⊇ ⋃
_{i}CSD_{i}is the Causal System Description or the causal model used to represent the constraints underlying the continuous dynamics of the hybrid system.

_{i}associated to a mode q

_{i}, is given by a graph Gc = V∪K, I, in which I is the set of influences in which there is an edge $\u03f5\left({\upsilon}_{i},{\upsilon}_{j}\right)\in I$ from υ

_{i}∈ V to υ

_{j}∈ V if the variable υ

_{i}influences variable υ

_{j}. A dynamic control model $DC{M}_{{I}_{k}}$ is associated to every influence ${I}_{k}\in I$. Figure 5 presents the Dynamic Control Model where one procedural action σ

_{i}is related as an observable event that connects the industrial controller (PID) with the model of the active component (Comp. model) which corresponds to a transfer function of first order with delay. The event that closes the control loop σ

_{j}is assumed to be an unobservable event.

## 3. Results

_{1}) and the outflow sensor (FT

_{2}). The passive component is the tank (TK); in addition, the active components are two normally closed valves (V1 and V2), and one pump (Pu). Since there are three active components, the Oil Transport System obviously involves hybrid behavior. Modeling the behavior of this hybrid system involves a set of continuous variables and a set of discrete variables. The continuous variables are the level L, pressure Po, and outflow Qo(V2), V = {L,Po,Qo(V2)}. The discrete variables are related to the operational actions of the process and the changes in the continuous variables, then the event types for this process are identified in the next sub-section.

#### 3.1. Applying CBAM

#### 3.1.1. STEP 1: Event Type Identification

_{uo}. The underlying DES (Discrete event system) of the Oil Transport System represents the sequence of observable procedure actions for a start-up stage (indicated by the red or green arrows in Figure 7, corresponding to the evolution of the operation modes (i.e., q

_{0}, q

_{1}, q

_{4}, q

_{5}, q

_{7}); for instance, in the mode of operation, q

_{1}can be determined when the valve V1 is opened; therefore, the continuous variable QiTK influences the variable L, and the supervision system will wait for the event which indicates that after of a specific period of time, the level of water into the tank TK has passed its low limit. Each operation mode q

_{i}is associated with a causal system description to identify the influences between the variables L, Po and Qo(V2). These influences allow the determination of the occurrence of the events Σ

^{c}.

#### 3.1.2. STEP 2: Event Sequence Generation

_{1}, S

_{2}and S

_{3}) that show the extreme behaviors of all of the possible sequence orders of the event types.

- S
_{1}= 〈(V1,1); (L(L),21); (H(L),48); (PuO,50); (V2,51); (L(Po),60); (H(Po),75)〉 - S
_{2}= 〈(V1,1); (L(L),25); (H(L),55); (V2,56); (PuO,57); (L((Po),63); (H(Po),78)〉 - S
_{3}= 〈(V1,1); (L(L),28); (H(L),60); (PuO,61); (V2,62); (L(Po),71); (H(Po),85)〉

- For the variable of the level (L), the value of 0 corresponds to 0 m; each increase of 2 (vertical axis) corresponds to 2 m.
- For the variable of the pressure (Po), the value of 0 corresponds to 0 PSI; each increase of 2 (vertical axis) corresponds to 20 psi.

#### 3.1.3. STEP 3: Chronicle Database Construction

^{1}

_{11}from the set of chronicles of the Oil Transport System is presented, i.e., of the area Ar

_{1}of the whole system. Therefore, the chronicle C

^{1}

_{11}is associated with a failure behavior of type f

_{1}during a start-up stage. In the figures of the chronicles, the events are specified as follows: L(L) as LL; l(L) as lL; H(L) as HL; h(L) as hL; L(Po) as LP; L(Po) as lP; H(Po) as HP; h(Po) as hP; L(Qo(V 2)) as LQ; l(Qo(V 2)) as lQ; H(Qo(V 2)) as HQ; h(Qo(V 2)) as hQ. For the scenario of an abnormal start-up, the following temporal restrictions are used in the extended version of the HCDAM (Heuristic Chronicle Discovery Algorithm) [23]. The notation TR

_{PuO,V2}= PuO[−2,2]V2 corresponds to a temporal restriction which indicates that the valve V2 can be opened (V2) two time units before that the pump Pu is turned on (PuO) or, on the contrary, that PuO occurs two time units before that of V2. On the other hand, the temporal restriction noted as TR

_{HL,PuO}= HL[1,4]PuO, expresses that the pump Pu is turned on (PuO) between one and four time units after that the high limit level into the tank happens (HL). The chronicle C

^{1}

_{11}that resulted using the algorithm HCDAM is presented in Figure 9. The learning event sequences used are the S

_{1}, S

_{2}and S

_{3}which were generated before (STEP 2).

#### 3.2. Validation

^{1}

_{11,}which represents the temporal pattern for an abnormal start-up in the Oil Transport System. One sequence of evaluation that belongs to this abnormal scenario is presented below: S

_{eval}= ⟨(V1,1);(LL,26);(HL,58);(PuO,60);(V2,62);(LP,70);(HP,85)⟩, which is different to the learning event sequences, and it expresses an abnormal condition of start-up. Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16 present the recognition process of the chronicle and the generation of one Super-Alarm. In Figure 10, the first occurrence is (V1, 1); the next occurrence must be of the event LL between 20 and 28 time-units. Now, in Figure 11, the activation of LL at 26 is presented, indicating also that the next occurrence must be HL. The following events occur (PuO, V2, LP and HP) until the chronicle is recognized and the super alarm is generated. Therefore, this new element (the Super-Alarm) corresponds to one superior alarm that gives the relevant information to the operators after a diagnosis process, increasing the reliability of this protective layer.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Start-up stage of the Oil Transport System: the underlying DES and Causal System Description.

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**MDPI and ACS Style**

Vásquez, J.W.; Pérez-Zuñiga, G.; Sotomayor-Moriano, J.; Ospino, A.
Super-Alarms with Diagnosis Proficiency Used as an Additional Layer of Protection Applied to an Oil Transport System. *Entropy* **2021**, *23*, 139.
https://doi.org/10.3390/e23020139

**AMA Style**

Vásquez JW, Pérez-Zuñiga G, Sotomayor-Moriano J, Ospino A.
Super-Alarms with Diagnosis Proficiency Used as an Additional Layer of Protection Applied to an Oil Transport System. *Entropy*. 2021; 23(2):139.
https://doi.org/10.3390/e23020139

**Chicago/Turabian Style**

Vásquez, John W., Gustavo Pérez-Zuñiga, Javier Sotomayor-Moriano, and Adalberto Ospino.
2021. "Super-Alarms with Diagnosis Proficiency Used as an Additional Layer of Protection Applied to an Oil Transport System" *Entropy* 23, no. 2: 139.
https://doi.org/10.3390/e23020139