Development of Systematic Framework for an Intelligent Decision

Article pubs.acs.org/IECR

Development of Systematic Framework for an Intelligent Decision Support System in Gas Transmission Network Sayyed Ahmad Khadem and Ramin Bozorgmehry Boozarjomehry* Department of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 14155-4838, Azadi Avenue, Tehran, Iran ABSTRACT: In a gas transmission network (GTN), faults can easily propagate due to the interconnections of streams. The main objective of this paper is to develop a systematic framework for an online decision support system (DSS) in order to make the right decisions to get the GTN out of critical conditions (which cannot be handled by the plant controllers) smoothly. One of the key features of the proposed scheme is its lack of dependence on prior knowledge of the fault signals (e.g., number of faults, and their origin). In this article, the GTN is modeled by a fuzzy directed graph (FDG). The proposed approach utilizes a reasoning algorithm based on the deviations that exist in the process variables (attributes) of target nodes, in order to detect the most crucial attributes (equipment) whose manipulating variables can be changed appropriately (i.e., upward or downward) to get the GTN out of the abnormal condition gracefully. Thereafter, quantitative decisions are made from qualitative decisions, after which the forward reasoning is used to determine the impact of each quantitative decision on the attributes of target nodes. The attributes of the affected nodes are obtained based on their estimations by a fuzzy inference system (FIS) through traversing from affecting nodes to other nodes in a sequential manner. To keep the generality and flexibility of the proposed scheme, FIS uses preliminary intuitive rules between two connected nodes rather than empirical rules for the entire GTN. Eventually, all tentative feasible decisions are built. These feasible decisions get ranked and prioritized through an analytic hierarchy process method. The decision set with highest priority is then implemented whose effect on the GTN operation is assessed, and if it seems the GTN still requires some changes to get out of an abnormal situation, once again DSS is invoked based on the newly established condition and the appropriate set of decision is obtained accordingly. The performance of the proposed scheme is shown by its application for two GTNs as benchmarks. It is capable not only of offering decisions to alleviate an abnormal condition but also of leading the plant to a new desired state from a normal condition.

1. INTRODUCTION In all industrial plants, particularly in large scale systems, occurrences of faults are inevitable because of the interaction of numerous units comprising the system. After an outbreak of fault, the required actions should immediately be carried out, to cancel out adverse aftermath as quickly as possible. In crisis, it is probable that the responsible person that must certainly be an expert, however, may not overcome his/her stress and cannot make the right decision in a short time. The other problem that can arise is the event of new abnormal condition that the expert has not experienced yet. It should be further noticed that the expert person owing to various reasons may not be at control room at the occurrence time of the failures. These problems point out the need of developing an appropriate computer-based system in order to assist the responsible person in emergency conditions. In this regard, several attempts have been made to design the fault diagnosing systems, particularly to handle multiple concurrent faults.1−4 By analyzing the symptoms, fault diagnosing systems try to find the main cause of faults, unlike the decision support system (DSS) in which the goal is to keep the desired condition, despite the existence of the cause of the fault. This provides enough time to diagnose the origin of the fault and to fix the problem and get the system out of critical condition in a smooth and calm manner. The concept of DSS is a generic subject, and there might be various objectives for its application according to which its definition and specifications might vary in different research areas. In this article, by DSS the authors mean an interactive © XXXX American Chemical Society

computer-based system that facilitates the process of decision making of responsible persons such that they can make decision quickly, effectively, and calmly. DSS tasks fall into two main categories: first, proposing the feasible solutions in a faulty condition of a gas transmission network (GTN) to keep the attributes of target nodes in their corresponding desired values regardless of the prior acquaintance with the fault signalsand second, offering solutions to lead the GTN to operate at the desired normal condition. The target nodes are important places such as delivery points corresponding to exporting terminals, civil, and industrial consumers. An outbreak of failure for these consumers will result in financial losses or even injuries and casualties for the countries whose energy demands (corresponding to both civil and industrial purposes) are majorly provided by natural gas. To clarify this, consider an abnormality in the GTN delivering gas to a couple of target nodes including an export terminal and a highly populated city, along with a power generation plant. Because of the increase in the demand of major consumers (i.e., the city or power generation plant), pressures of various nodes would be decreased which lead to a decrease of the gas flow rate at the export terminal. If the level of abnormality is such that, its Received: May 5, 2015 Revised: September 6, 2015 Accepted: October 5, 2015

A

DOI: 10.1021/acs.iecr.5b01681 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Schematic diagram of the constituting elements of the intelligent DSS.

A considerable amount of literature has been published on designing DSS in various areas such as environmental issues,5 health care services,6 waste minimization in chemical processes,7 etc. The authors found, after a careful and thorough search of the literature, that there was no article that discusses the topic of designing a DSS for a dynamic plant-wide system. According to the available literature, Nokhbeh Foghahaayee et al.8 are the only researchers that have worked on designing a DSS of a GTN as an example of a distributed and large scale system. They also claimed that there has been no DSS designed for the GTN so far other than their papers. They have developed the DSS for a GTN that is based on the experience gathered from experts; this fact makes the DSS case-dependent, even a small change in the network’s topology or operating condition may cause the DSS not to work well to generate appropriate decisions. On the other hand, collecting this information requires a long history of the plant, which is not always possible. They assumed the prior knowledge of faults; however, this assumption may require the DSS to be coupled with the fault diagnosing system. On the basis of previous studies, fault diagnosis is not a trivial task, particularly for an interconnected system like a GTN.1 This paper presents a novel method to design a DSS, notably a DSS for the GTN. The proposed scheme is able to provide solutions which cancel out the adverse effects of existent failures on the performance of the system, regardless of the knowledge of faults origin and/or the number of concurrent faults. Partitioning the plant into various subsystems along with the fuzzy interference system (FIS) which uses preliminary intuitive rules for each subsystem implies that the DSS is not only capable of handling any change in the network’s topology but also capable of handling large scale networks which have not been analyzed by the DSS yet. Another advantage of the proposed approach is that it does not need the trends and histories of the plant supervisory control and data acquisition (SCADA) system (the SCADA system regularly monitors the plant and provides all required information, such as pressure, temperature, flow, etc.). The remaining sections of this article are organized as follows. section 2 discusses the methodology of the proposed scheme. In section 3, the performance of the proposed method is evaluated through its implementation for two GTNs as benchmarks. Finally, discussion and concluding remarks are presented in section 4.

cancellation requires an increase of natural gas in the supply node which is beyond the design specification of the network, all the controllers would fail and the operator in the dispatching center would have to make a trade-off analysis and compensation of various objectives in order to stabilize the network operation for a limited time interval. Such a task cannot be accomplished by any of the controllers nor is it accomplishable by changing the network topology and structure owing to the time required for these purposes. In this case the operator has to deal with a challenging problem which is obtaining the level of back-off in each of the operational objectives (e.g., finding the amount of cutback required for each of the delivery points and their corresponding time frame). What makes it worse is the fact that all these analyses need to be done quite rapidly. Despite the fact that there are various approaches in the development of a DSS, they all share couple of common characteristics which are as follows: Explanation Ability. DSS should offer the rationales behind decisions being proposed. This is to let the user select the appropriate decision based on the current condition. Generality. So as to not make DSS case dependent, such that it can easily deal with problems to which it has not been exposed, it must be capable of handling various problems in its corresponding domain. Fast in responding. Since the operator(s) should make the decisions almost instantaneously, DSS should come up with tentative decisions very rapidly. Hence, it should not rely on the solution of large and complicated mathematical models. Fulfilment of the above requirements for a DSS used to operate GTNs, enforces one to use the fuzzy inference method in order to cope with uncertainties that inherently exist in the system behavior. Furthermore, because most of the abnormalities in GTN operations might not have been previously experienced, or the topology of the GTN might have been changed since the occurrence of such an abnormality, one should not rely on the historical data representing the network conditions and the corresponding decisions made at the time of previous abnormalities. This, reinforces the use of rule-based systems as opposed to their data driven alternatives (e.g., neuromorphic ones). These incentives which justify the use of the fuzzy inference method in the development of the DSS will be more elaborated throughout the article. B


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2. THE SYSTEMATIC FRAMEWORK FOR DESIGN OF INTELLIGENT DSS In this section the methodology of designing intelligent DSS is explained through seven subsections, the schematic diagram of the constituting elements of the intelligent DSS is shown in Figure 1. Subsection 2.1 describes the approach used in qualitative modeling and simulation of network. The method of searching in a graph, in other words, through which paths decision variables can affect the target nodes, is discussed in subsection 2.2. There are two pivotal elements in the process of decision making which are the qualitative and quantitative decision making. First, the right direction of changes for each one of decision variables are qualitatively specified, after which the amount of changes in each decision variables are determined. These two constituting elements are described in subsections 2.3 and 2.4, respectively. The assessment mechanism of the effects of quantitative decisions on the system performance is elaborated in subsection 2.5, after which the prioritization of the decisions is discussed in subsection 2.6. 2.1. Designing Fuzzy Directed Graph (FDG) for Rapid Simulation. Since it is intended to develop a flexible and extendable DSS, it seems a good idea that the system is segmented into couple of subsystems. To come up with a general procedure which can be used as a guideline for such segmentation, one has to keep in mind that the subsystems should possess two characteristics. First, their qualitative behavior should be comprehensible, so that due to manipulating their inputs the response of their outputs can be qualitatively predicted. Second, a characteristic of the subsystems is their modularity, which means that they have been used in various parts of the GTN or even similar GTN. Each subsystem is also divided into a number of important comprising elements that are named as nodes. Each node contains some attributes indicating process variables. These nodes are connected to each other by a directed edge whose direction represents the causality between them, this kind of representation is called directed graph (DG). Researchers proposed various methods to generate DG or signed directed graph (SDG).9−11 In this work, DG was used to show what nodes will be affected based on a change in an attribute of a given node (called triggering or manipulative node). A DG is defined by the ordered pair DG = (V,E) where V is a finite nonempty set of nodes and E denotes a set of edges between the nodes E = {(u,v)|u,v, ∈ V}. There are two types of representing formats for a DG; adjacency matrix and adjacency list.12 • Adjacency matrix: if there are n = |V| nodes v1,...,vn, this is an n × n matrix whose (i,j)th element is determined by eq 1. ⎧ ⎪1 ⇔ (vi , vj) ∈ E a ij = ⎨ ⎪ ⎩ 0 ⇔ (vi, vj) ∉ E

In this scheme, there are three types of nodes; manipulative, intermediate, and target nodes. Manipulative nodes are those from which reasoning starts. In fact, manipulative nodes are those having at least one attribute which can be manipulated, in other words, their attributes are decision variables. The target nodes on the other hand are those nodes having at least one attribute which must meet a specific requirement. The main objective of the DSS is to keep the attributes of target nodes as close as possible to their corresponding desired values. The remaining nodes in the DG which are neither manipulative nor target nodes are called intermediate nodes. To find out the cause and effect relationships among nodes, it is enough to stimulate manipulative nodes and then track the sequence of nodes that are affected either explicitly (those which are directly connected to the manipulative nodes) or indirectly (those which are connected to the manipulative nodes via some other nodes). To complete the qualitative modeling of the plant, each subsystem should individually be modeled qualitatively. Since it is assumed, for generality, there is no numerical information about the subsystems and there is only an intuition that comes from our knowledge, FIS is used to qualitatively model the behavior of each subsystem. To put it another way, according to eq 2, FIS gives a mapping from the attributes of the affecting node (which affects the next node) onto the attributes of the affected node (which is affected by affecting node), Figure 2.

FIS: X̲ → Y̲

(2)

Figure 2. Representation of the causality between affecting and affected node.

where X and Y represents the vector of attributes of affecting and affected nodes, respectively. Since this approach is based on the linguistic rules, the Mamdani fuzzy model is used.13 This is the approach which is most frequently used in qualitative modeling of systems based on Fuzzy Logic and Fuzzy Set theory; the interested readers are referred to the various articles that exist in this area for further information.14,15 The advantage of this approach is that it is fairly easy to get the qualitative and intuitive model of each subsystem into isolation. These models can be then used to come up with the integrated qualitative model of the whole plant. Another advantage of this approach is its speed of response. The simulation of a plant-wide system is usually time-consuming due to complexity of governing equations representing the quantitative and rigorous behavior of the system; however, this approach can give an acceptable estimation very quickly. This desired characteristic makes the DSS capable of providing its solutions very rapidly. More importantly, FDG makes DSS able not to work like a black-box model. Instead, it is capable of explaining why the proposed solutions seem right. This is due to the fact that for each suggestion, DG produces the sequences of connections between a manipulative node to target nodes, and FIS provides the amount of effect which the affecting nodes put into the affected nodes. Consequently, FDG provides the feature of node-to-node reasoning for DSS. To summarize, this approach provides a facility that a broad spectrum of the GTN can be modeled, and the result of the approximate simulation is rapidly determined.

(1)

2

This form takes up O(n ) space; hence, it is better to be used for a dense graph (i.e., a graph in which the number of edges, |E|, is near the maximum possible number of edges, | V|2). • Adjacency list: Using an array of n = |V| lists of nodes. List u contains node v if there is an edge from node u to node v so it is concluded that this representation format takes up O(n+m) where m = |E|. The adjacency list is preferred when the graph is sparse (i.e., |E| is much less than |V|2). C


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Industrial & Engineering Chemistry Research Illustrative Example: The Modeling of a Typical Valve. For example a valve with its inlet and outlet can be considered as a subsystem which consists of three nodes: opening percentage of valve, attribute of inlet, and attribute of outlet, see Figure 3.

before proceeding to describe the strategy of qualitative decision making, some sets are defined for the sake of specifying the indices for target nodes and their attributes. Γ: The set of indices of all target nodes Bi: The set of indices of all attributes which are within i’th target node B′i : Those members of Bi which must be altered (i.e., increase or decrease), (Bi′ ⊆ Bi) Whenever DSS is invoked, it monitors the attributes of the target nodes from the network then compares them with their corresponding desired amounts. On the basis of this comparison, the set of required qualitative changes within all target nodes are determined according to eq 3.

Figure 3. DG for the subsystem which corresponds to a typical valve.

χi = {x j ∈ U|

The attributes of inlet, outlet, and valve node are xi = {Pi,Ti,Fi}, x0 = {P0,T0,F0} and xv = {OP}. Where P, T, F, and OP indicate pressure, temperature, flow rate, and opening percentage of the valve, respectively. Depending on the subsystem the appropriate rule tables must therefore be prepared based on the process knowledge. The complete rule table for the former example is shown in Table 1. As can be seen, the qualitative behavior of this subsystem is comprehensible; moreover, it is capable of being used in many places of the network.

x j indicates the desired change for the j th attribute of the i th target node} U = {I, D, NI} (3)

Where I, D, and NI stand for increase, decrease and not important, respectively. It is noticeable that the user should directly assign NI for those attributes whose decrease or increase is not important. Despite the fact that it seems to be necessary for U to have a member like NC (representing “No Change”), since this can be regarded as an infinitesimal change in either direction, it is not considered as a member of U in order to reduce the dimensions of the search space for tentative decisions. Hence, the user can keep the current value of an arbitrary attribute via setting the desired amount near the current value. As shown in eq 4, the target set is defined to consist of entire goals. Furthermore, TS(i,j) is the desired change for the jth attribute of the ith target node.

Table 1. Rule Table for Subsystem of a Typical Valvea antecedent

consequent, inlet

consequent, outlet

Δopening

ΔPi

ΔTi

ΔFi

ΔP0

ΔT0

ΔF0

NL NM NS Z PS PM PL

PL PM PS Z NS NM NL

NS Z Z Z Z Z NS

NL NM NS Z PS PM PL

NL NM NS Z PS PM PL

NS Z Z Z Z Z NS

NL NM NS Z PS PM PL

∀ i ∈ Γ, ∀ j ∈ Bi

TS = {χi |

a

The desired changes for the i th target node} (4)

∀i∈Γ

NL, NM, NS, Z, PS, PM, PL are abbreviations of negative large, negative medium, negative small, zero, positive small, positive medium, positive large.

On the other hand, DSS identifies which decision variables (i.e., available manipulating variables of various nodes or pieces of equipment exist in the network) should be increased or decreased in order for each one of the attributes of target nodes to reach their corresponding desired conditions. In this regard, the set TEff(i,j) is defined as eq 5. i,j

2.2. Navigating from Manipulative to Target Nodes. The meaning of all paths is the edges through which the target nodes are affected when a given manipulative node is stimulated. Mathematically speaking, it is required to find all paths between two nodes in the DG. In this work, the depth first search (DFS) algorithm has been used since it is capable of finding all paths in a graph.12 Paths that were found throughout the graph along with FIS make DSS able to elucidate the reasons why its proposed decisions are correct. It is done by giving all logical chains of node-to-node reasoning. Therefore, one of the advantages of the proposed scheme is that not only does it describe the behavior of the system but also it can help the user to know about the rational by which the DSS reaches the right decisions as well. 2.3. Qualitative Decision Making. The important benefit of making qualitative decisions is that it provides insights into all possible opportunities to reach the targeted desired condition. Even though qualitative decisions usually rely on the experiences gathered from expertise, the rational methodology of qualitative decision making is described in this subsection. In the graph theory each node has a unique index; moreover, each attribute within a node has a unique index as well. Thus,

i , j) TiEff( = {x ∈ M| ,j

j th attribute of the i th target node to be Eff(i , j)} ∀ i ∈ Γ, ∀ j ∈ B′i

(5)

The superscript Eff(i,j) represents the desired direction of change which can be either I or D for the jth attribute of ith target node. On the basis of the target set which has been built, DSS specifies the right value of Eff(i,j). This issue will subsequently be further elaborated. M consists of the signed indicesplus and minus stand for increase and decrease, respectivelyof the decision variables. Therefore, the elements of Ti,jEff(i,j) are the signed indices of manipulative attributes which are capable of forcing the jth attribute of the ith target node to be Eff(i,j). A major bottleneck in the procedure of qualitative decision making is the preparation of Ti,jEff(i,j). To do so, the paths between target nodes and decision variables are determined through a depth-first search (DFS) algorithm, after which there are two D


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Industrial & Engineering Chemistry Research methods to find the right direction of change for the attributes of manipulative nodes. When DSS is invoked, it prepares the target set by a simple comparison between current and desired values of attributes which belong to target nodes. Thereafter the required superscripts of TEff(i,j) should be determined. According to the i,j definition of Ti,jEff(i,j) and the target set, as shown in eqs 4 and 5, it can be concluded that Eff(i,j) should be equal to TS(i,j) (see eq 6). Eff(i , j) = TS(i , j)

∀ i ∈ Γ, ∀ j ∈ B′i

It should be noted that eq 8 takes into account all the tentative decisions even those which are inconsistent. As an example of an inconsistent decision, one can mention a decision leading to simultaneous increase and decrease of an attribute. Hence, the number of tentative decisions should be obtained in such a way that inconsistent decisions are excluded from the list of tentative decisions. Another remark on eq 8 is that the duplicate members should be omitted as well. Furthermore, in order to avoid producing redundant quantitative decisions, those qualitative decisions which can be considered as specific instances of other decisions must be excluded from the set of tentative qualitative decisions. Illustrative Example: The Qualitative Decision Making. For instance, assume that the result of plant monitoring is that the flow rate of the first and second target nodes are decreased and increased, respectively; hence it should be intended to increase the flow rate of first target, while that of the second target is decreased. For this case the set of indices of target nodes can be considered as Γ = {5, 20}. The attributes of target nodes are pressure, temperature, and molar flow rate whose indices for both target nodes are 1, 2, and 3, respectively. In this example, it is desired that the molar flow rates will be maintained so B1 = B2 = {1,2,3}, B1′ = B2′ = {3}. As shown in Figure 1, the blocks corresponding to Input and Definitions have been completed. DSS then uses the DFS algorithm and the DG of network to determine all paths through which the manipulative and target nodes are connected. From Figure 1 we can see that producing possible qualitative solutions to increase or decrease predefined attributes (i.e., molar flow rates in this example) of target nodes, Ti,jEff(i,j), requires “Paths”, “Fuzzy Information” blocks, and the results of “Make target set” module. SCADA sends current values of targets, afterward, DSS gets the desired values from the responsible person, and compares them to the construct target set. Going through this procedure leads to the following TS = {{NI NI I},{NI NI D}. It is now assumed that the results of detecting the right direction of changes for decision variables are shown in eqs 9 and 10.

(6)

After it was clarified which sets of TEff(i,j) should be determined, in i,j order to find the right direction of changes for attributes of manipulative nodes, DSS individually triggers every one of the available decision variables in two directions (i.e., increasing and decreasing). The manipulative nodes (affecting nodes) stimulate a number of adjacent nodes (affected nodes), after which affected nodes play the same role of affecting nodes for their own adjacent nodes, and this continues through a chain of cause and effect until the target nodes are affected. This process is called forward chaining or reasoning. It is an inference method that starts with facts (i.e., those conditions have been applied) and works forward from the antecedent to the consequent until the goals are achieved.16,17 Here, facts and goals are the attributes of manipulative nodes and target nodes, respectively. Due to triggering decision variables and then forward chaining through traversing from manipulative node to target node, whose path have been determined based on the method described in subsection 2.2, the effect of increasing and decreasing of each decision variable upon the attributes of target nodes is separately determined. These results give us the information on how each one of decision variable can affect the attributes of target nodes so the sets Ti,jEff(i,j) can easily be constructed. The sets TEff(i,j) can also be obtained by using backward i,j chaining or backward reasoning. It is an inference method that starts from goal and works backward from the consequent to the antecedent until it can determine what initial conditions must occur in order to achieve the goal.16,17 Since backward reasoning is more computationally demanding and might result in an inverse problem which might not get to a specific solution due to the interaction of various antecedents on each consequence, in this study the forward reasoning has been used. It is a conclusive evidence that any nonempty subsets of TEff(i,j) i,j can be another solution such that the jth attribute of the ith target to be Eff(i,j). On the basis of this evidence, all possible qualitative solutions such that the jth attribute of the ith target to be Eff(i,j) are formulated as eq 7. i , j) Eff(i , j) APQSiEff( = 7(Ti,j )\{⌀} ,j

I T5,3 = {+1, − 16, + 14} D T20,3 = {−16}

I APQS5,3 = {{+ 1} {− 16} {+ 14} {+ 1, − 16}

{+1, +14} {− 16, + 14} {+ 1, − 16, + 14}} D APQS20,3 = {{− 16}}

(7)

(11) (12)

It can be seen from Figure 1 that all requirements of qualitative decisions making have been provided, hence according to eq 8 the tentative qualitative decisions can be represented by eq 13.

I D × APQS20,3 QualDL = APQS5,3

Qualitative Decisions List (QualDL)

⎧{−16} ⎫ ⎪ ⎪ ⎪{+1, −16} ⎪ ⎬ =⎨ ⎪{+14, −16} ⎪ ⎪ ⎪ ⎩{+1, +14, −16} ⎭ (13)

i , j) ∏ APQSiEff( ,j i ∈Γ j ∈ B′i

(10)

As shown in eqs 11 and 12, the sets APQS are determined by substituting the eqs 9 and 10 into eq 7.

7 and \ are symbols of power set and subtraction in set theory.18,19 Therefore, APQSi,jEff(i,j) is the power set of TEff(i,j) i,j where its empty set has been omitted. Hence, the cardinality of APQSEff(i,j) is 2n − 1, if the cardinality of Ti,jEff(i,j) is n. i,j To sum up, each set of APQSi,jEff(i,j) consists of a number of solutions to satisfy TS(i,j) so it is expected that the Cartesian product of APQSi,jEff(i,j) gives all qualitative alternatives so that target set is entirely satisfied (see eq 8).

(QualDL) =

(9)

According to the screening mechanism of qualitative decisions, the last member of set QualDL (i.e., increasing the first and 14th

(8) E


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Industrial & Engineering Chemistry Research manipulative variables and decreasing the 16th manipulative variable) would remain in the set of qualitative decisions which can be used in the quantification step; since it includes all other members of QualDL. This issue will be elaborated more in the following subsection. It should be further noticed that in the rest of this article the members of qualitative decision will often be called commands (e.g., the last member of set QualDL consists of three commands). 2.4. Quantitative Decision Making. The outcome of the previous subsection was a number of commands which just indicate increasing or decreasing of decision variables; however, there are really interactions among them. Here, interaction means that applying a command defiantly improves an attribute of a target node even though it may worsen other target attributes. The target attributes have different sensitivities to the commands; hence, there should be a quantitative trade-off between decision variables in order to get the system to a point in which all target attributes reach the acceptable tolerances of their own desired values. In this subsection a number of quantitative decisions will be made, with the aim of evaluating them in subsection 2.5. In this work, the normalized value of attributes was used, with the aim of making more sense. Equation 14 represents normalization of a value into the interval of [−1 1]. ⎧ v − v̅ ⎪v − v ⎪ max ̅ vn = ⎨ ⎪ v − v̅ ⎪v − v ⎩ ̅ min

(18)

TV3 = {0 −0.5}

(19)

(14)

The distributions of attributes are formulated as follows: Molar flow rate: The distribution of molar flow rate is shown as eqs 21 and 22. It is simply derived by applying the law of conservation of mass and assumption of no change in density of streams due to split.

m i=1

(20)

Figure 4. Typical spilt of streams.

Quantitative Decisions List (QuanDL)

∏ TVi

0 ⎤ ⎥ −0.5⎥ 0 ⎥ ⎥ −0.5⎥ 0 ⎥ ⎥ −0.5⎥ 0 ⎥ ⎥ −0.5⎦

(15)

where m represents the number of commands in the qualitative decision, Sji indicates the value of jth desired step for ith command. Furthermore, sign(QualDec{i}) shows the sign of ith command of the qualitative decision. The steps (Sji) should not have large values due to a restriction imposed by the superposition assumption which will be further described in the next subsection. Ultimately, according to eq 15, a couple of tentative quantities for each command are selected therefore the quantitative decisions are made by Cartesian product of the sets TV, as shown in eq 16.

(QuanDL) =

0 0 0.5 0.5 0 0 0.5 0.5

As it is mentioned in an earlier subsection, quantifying the largest member of set QualDL is capable of covering all other qualitative decisions that have been made. For example, note that the second row in QuanDL is equivalent to the first member of QualDL, the fourth row in QuanDL is equivalent to the third member of QualDL and the sixth row in QuanDL is equivalent to the second member of QualDL. 2.5. The Effect of Each Quantitative Decision on the Attributes of Target Nodes. This part elaborates the procedure by which the effect of each quantitative decision on the attributes of target nodes is obtained. Take, for instance, {v1 v2 v3... vn} as a path between manipulating attribute, v1, and target node, vn. By triggering v1, FIS gives the attributes of v2. Forward chaining is going on and it will be terminated when the attributes of vn is obtained. A crucial issue in this node-to-node traverse is how the attributes are changed in the junctions. Assume that the node-to-node traversing is reached to a junction of pipes as shown in Figure 4, at which the stream m is split into streams 1 through n.

j j TVi = {CV} i ∪ {CVi + Si | sign(Si ) = sign(QualDec{i})}

j = 1, ..., n

TV2 = {0 +0.5}

⎡0 ⎢ ⎢0 ⎢0 ⎢ 0 (QuanDL) = ⎢ ⎢ 0.5 ⎢ ⎢ 0.5 ⎢ 0.5 ⎢⎣ 0.5

Using this approach, each one of the commands in a qualitative decision is going to have a set of tentative quantitative values which should be specified. This set, which is denoted by TV, includes the current value (CV) that comes from SCADA and a number of tentative values in the desired direction of change. TV is defined as eq 15.

i = 1, ..., m

(17)

The tentative quantitative decisions are therefore produced by eq 16 as shown in eq 20.

v > v̅ v < v̅

TV1 = {0 +0.5}

Fi = (16)

Illustrative Example: Preparing the Quantitative Decisions from Qualitative Decisions. In the previous subsection the qualitative decision was {+1,+14,−16} so m = 3. For i = 1,2,3 assume current values are CVi = 0 and desired steps are S11 = S12 = −S13 = +0.5 so n = 1 and using eq 15 leads to the tentative values for each command as shown in eqs 17 through 19.

aj =

aiFm n ∑ j = 1 aj

(21)

Fj

F (22) * where aj indicates the ratio of the molar flow rate of stream j to an arbitrary stream. This ratio can be calculated for incompressible fluid by Hagen−Poiseuille equation, 20 eq 23, and for F


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Industrial & Engineering Chemistry Research compressible fluid by Weymouth,21 eq 24. Furthermore, in Figure 4 if the direction of stream k from outlet streams is changed, the sign of corresponding term in denominator (i.e., j = k) will be changed. aj =

aj =

P1j − P2j P1 * − P2 * P12j − P22j P12* − P22*

⎛ Dj ⎞4 L ×⎜ ⎟ × * Lj ⎝ D* ⎠

(23)

⎛ Dj ⎞16/3 L T ×⎜ ⎟ × * × * Lj Tj ⎝ D* ⎠

(24)

powerful tool for comparing alternatives to achieve a goal; it is categorized as a method in multicriteria decision making. This method breaks down the problem into a hierarchy of subproblems which can better be understood. The methodology of AHP is briefly discussed through the following steps; the interested readers are referred to various articles that exist in this area for detailed information on this method.22,23 1. The problem should be decomposed into goal, criteria, subcriteria, and alternatives as shown in Figure 5. This figure is called hierarchic structure of the problem.

where P, T, D, and L represent pressure, temperature, diameter, and length, respectively. The subscripts 1 and 2 show the inlet and outlet of the pipe. In eqs 23 and 24, it is assumed that pipes are horizontal. In addition, in eq 24, f = D−1/3 where f is the friction factor.21 For applying eq 24, it is noticed that temperatures are calculated at the available previous time. As can be seen in eq 22, aj can also be determined if the flow rates of all nodes in the path are available at a previous time. Temperature: The distribution of temperature is shown as eqs 25 and 26. It is also simply derived by applying the law of conservation of energy and assumption of no change in heat capacity of streams due to split. Fi × Ti =

bj = aj

biFm × Tm n ∑ j = 1 bj

(25)

Tj

T (26) * It is noticed that bj values are calculated at the available previous time. Pressure: in the junction equalize pressure is applied, eq 27. Pi = Pm

Figure 5. Hierarchic structure of the problem.

2. A matrix, called a comparison matrix, is built for criteria, subcriteria, and alternatives according to the procedure described in Table 2. This matrix shows the relative importance of ith member comparing to jth member.

(27)

Composition: it is evident that there is no change in compositions due to split. Up to here, the steps corresponding to triggering one command was explained. There are two other issues that have to be addressed: the procedure to implement a decision which consists of more than one command; how to handle the cases in which target nodes are affected through various paths. The proposed solution to tackle these issues is the assumption of superposition at target nodes. Using this assumption means that if the attribute ‘v’ of a specific target node is affected through P paths when N commands are been applied, the total change in ‘v’ can be estimated by eq 28. P

Δvtotal =

Table 2. Scale of Preference between Two Elements description

1 3 5 7 9

i and j are equally important i is slightly more important than j i is more important than j i is strongly more important than j i is absolutely more important than j

3. Since human judgments are not always consistent, AHP allows a small inconsistency in judgments among pairwise comparisons. In this step, the consistency of the comparison matrix should be checked through eqs 29 and 30.

N

∑ ∑ Δvi ,j i=1 j=1

aij

(28)

According to eq 28, each quantitative decision can be triggered and the chaining is propagated node to node from manipulative to target, and all the attributes of target nodes are finally estimated fairly quickly. In order not to violate the superposition assumption reflected in eq 28, the steps (Sji) are better not to get large values. 2.6. Prioritization. After obtaining various decisions that exist to reduce the adverse effects of an abnormal situation in the system, one has to prioritize them, before choosing one of them. The prioritization of various decisions is made based on the “Analytic Hierarchy Process” (AHP) method. This method is a

CI =

λmax − n n−1

(29)

CI < 0.1 (30) RI where λmax is the maximum eigenvalue of the comparison matrix. The Random Index, RI, can be determined based on Table 3 4. The weight vector for each comparison matrix is calculated through the following steps: CR =

G


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Industrial & Engineering Chemistry Research Table 3. Random Index n RI

1 0

2 0

3 0.58

4 0.9

5 1.12

6 1.24

7 1.32

8 1.41

9 1.45

10 1.49

11 1.51

12 1.48

13 1.56

14 1.57

15 1.59

Figure 6. Schematic illustration of the GTNcase study 1.

provides the appropriate decisions, which have been validated in a commercial dynamic simulator. The only requirement that a simulator (either in-house or commercial ones) should support is the remote procedure call (RPC) in general whose instances in the Windows Operating System are COM or ActiveX protocols. In this scenario the simulator is acting as a virtual GTN on which the decisions are implemented in order to mitigate the operational abnormalities. However, in practice as shown in Figure 1, DSS receives the operational variables representing the GTN status from the SCADA system. Therefore, there is literally no restriction to use the developed DSS either on commercial simulators or real life GTNs which are able to communicate (through the mentioned protocols) with DSS. 3.1. Case Study 1. In Figure 6 the circles show the considered nodes and the inside number of circles indicate its index. This GTN includes one supplier and two consumers. Each one of the arrows indicates a pipe; moreover, the directions show the direction of flow in nominal conditions. The specifications of pipes are shown in Table 4. It is assumed that there are three decision variables; the powers of two compressors and opening percentage of the valve, node 14. These manipulative variables are the attributes of nodes 1, 16, and 14, respectively. Heat loss in all compressors and coolers are assumed to be negligible, furthermore outlet pressure of each compressor is kept at its desired value using a PI controller whose manipulating variable is compressor power. Parameters of the PI controller for each compressor along with minimum/maximum power are

4.1. First, normalize the comparison matrix, eq 31. a ij a ijnormalized = n ∑i = 1 a ij (31) aij and anormalized denote the value and normalized ij value of element of ith row and jth column of the comparison matrix. 4.2. Second, calculate the weight vector, eq 32. n

wi =

∑ j = 1 a ijnormalized

(32) n wi represents the weight of ith element. 5. Calculating the weight of each alternative versus subcriteria, eq 33. m

Wi =

∑ wijwj j=1

(33)

i, j indicate the alternative and subcriteria, respectively. 6. Weighted average of subcriteria weights dictate the importance of various criteria.

3. VALIDATION To demonstrate the reliability and effectiveness of the proposed scheme, it has been applied to two typical GTNs. In addition, the algorithm has been implemented as a standalone application that H


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Industrial & Engineering Chemistry Research Table 4. Specification of Various Pipes Existing in the NetworkCase Study 1 indices

internal diameter (in)

external diameter (in)

length (km)

roughness

35−11 10−9 12−13 2−3 5−6 33−34 7−8 27−28 31−32 22−23 24−25 17−18 20−21

43 33 35 33 25 23 29 15 27 25 27 27 33

43.5 33.5 35.5 33.5 25.5 23.5 29.5 15.5 27.5 25.5 27.5 27.5 33.5

12 100 5 25 1 1 3 0.5 1 4 25 15 5

0.259 9.1 0.259 0.259 0.259 0.259 0.259 0.259 0.259 0.259 0.259 0.259 0.259

presented in Table 5. The ambient temperature and heat transfer coefficient are 20 °C and 5.1104 (kj/(h m2 C)), respectively. The Directed Graph (DG) of the GTN is shown as Figure 7. In contrast to the direction of the schematic illustration of the GTN, the directions in Figure 7 show the causality between the nodes when the decision variables are stimulated. It should be further noticed that the edges 9 to 37, 24 to 39, and 15 to 13 are conditional edges; it means that they are connected if there is a connection between nodes 10 to 9, and 25 to 24, and 36 to 15, respectively. There are significant nonlinearities in the governing equations for GTNs; therefore, its precise modeling includes many technical difficulties.24−26 However, the rough simulation is easily attainable by using the method mentioned in subsection 2.1. To obtain the FDG representing each subsystem in the plant, in addition to the rule table representing its qualitative behavior, one has to select the membership functions of its variables. Furthermore, t-norm and s-norm used in the fuzzy inference must also be selected. In this study the symmetric triangle membership function (with the width of 0.6) is used for each fuzzy set that exits in the universe of discourse of each input variable, Furthermore, the universe of discourses corresponding to output variables of the subsystems are represented by fuzzy sets with singleton membership functions. The t-norm and snorm used in this study are minimum and maximum, respectively. The center-of-area defuzzification method is used to obtain the numeric values of the output variables of each subsystem. The Table 6 represents the characteristics of fuzzy sets discretizing each universe of discourse. Therefore, the GTN is divided into four subsystems corresponding to valves, pipes, coolers, and compressors that exist in GTN. The rule table representing qualitative behavior of the valve has been shown in Table 1, while those corresponding to compressors and pipes are shown in Tables 7 and 8.

Figure 7. DG model of the GTN benchmarkcase study 1.

Table 6. Center of Fuzzy Sets Representing Each Universe of Discourse of Variables That Exist for Each Subsystem linguistic value

PL

PM

PS

Z

NS

NM

NL

crisp value

1

0.6

0.3

0

−0.3

−0.6

−1

Table 7. Rule Table of a Typical Compressor antecedent

inlet consequent, NSuction

Δopening

ΔPi

ΔTi

ΔFi

outlent consequent, NDischarge ΔP0

ΔT0

ΔF0

NL NM NS Z PS PM PL

PL PM PS Z NS NM NL

Z Z Z Z Z Z Z

NL NM NS Z PS PM PL

NL NM NS Z PS PM PL

NL NM NS Z PS PM PL

NL NM NS Z PS PM PL

As in the problem statement that was mentioned above, in this case study, the coolers are not decision variables so it is merely required that the streams which are passed through coolers (e.g., nodes 37 → 2 and 39 → 17) should be modeled. Therefore, it is assumed the temperature controllers are perfect so the temperature of the outlets always return to nominal temperature. According to the material balance it is evident that the differences in the molar flow rate for outlets are the same as those for inlets. Also, it is an acceptable assumption to take the differences in pressure in affected nodes (i.e., 2 and 17) as the same as that in

Table 5. Minimum and Maximum Power and Tunings of PI Controllers along with the Set-Points of Compressors and Coolers Case Study 1 index

min/max power (kj/h)

set point

Kc

τI

1 16 38 40

(0.25 × max = 32500000)/130000000 (0.1 × max = 5704600)/57046000 0/200000000 0/100000000

8617.49 kPa 7612.95 kPa 30.00 °C 30.00 °C

2.615 2.099 0.15 0.36

1.195 × 10−02 1.866 × 10−02 9.576 × 10−02 0.1820

I


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Industrial & Engineering Chemistry Research Table 8. Rule Table of a Typical Pipe antecedent

Table 10. Antecedent Table of Updating Weights in AHP consequent

ΔPi

ΔTi

ΔFi

ΔP0

ΔT0

ΔF0

NL NL ... NL NL ... NM NM ... NS NS ...

NL NL ... NM NM ... NL NL ... NL NL ...

NL NM ... NL NL ... NL NM ... NL NM ...

NL NL ... NL NL ... NM NM ... Z Z ...



affecting nodes (i.e., 37 and 39). Table 9 represents the rule table of a typical cooler. Table 9. Rule Table of a Typical Cooler antecedent

index

fragility

type of consumer

amount of flow

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

normal normal normal normal normal normal high high high high high high low low low low low low

export export export civil civil civil export export export civil civil civil export export export civil civil civil

high medium low high medium low high medium low high medium low high medium low high medium low

Table 11. Consequence Table of Updating Weights in AHP

consequent

ΔPi

ΔTi

ΔFi

ΔP0

ΔT0

ΔF0





Z Z ... Z Z ... Z Z ... Z Z ...


criteria

Since the controller of each compressor is assumed to act perfectly, the outlet pressure does not deviate from its own setpoint. For conational edges of compressors, the differences of temperature and flow rate of the affected nodes (i.e., 37 and 39) are similar to those of affecting nodes (i.e., 9 and 24). Furthermore, for the conditional edge of valve the differences in the attributes of the affected node (i.e., node 13) are the same as affecting node (i.e., node 15). Before proceeding to evaluate the performance of the proposed method, it is necessary to elaborate the determination of comparison matrices in the step of prioritization. There are two target nodes (i.e., nodes 5 and 20) each of which includes three attributes; pressure, temperature, and flow. According to Figure 5, each target node and their attributes are used as “criteria” and “subcriteria” in the hierarchic structure of AHP, respectively. Depending on the condition of target nodes the weights (importance) of criteria and subcriteria can change. Hence, whenever DSS is invoked the weights of criteria and subcriteria are updated by a FIS whose antecedent and consequent tables are shown in Tables 10 and 11, respectively. As shown in Table 10, fragility, type of consumer, and the amount of flow are chosen as significant parameters which can affect the weights. In this work, type of consumer is divided into two categories; export and domestic. Attributes of export target nodes are of higher importance comparing to those of domestic nodes. The amount

subcriteria

index

node

pressure

temperature

flow

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

very high very high very high high high high very high very high very high very high very high very high medium medium medium low low low

very high high medium medium medium medium very high very high very high very high very high very high medium medium medium medium medium medium

high high medium medium medium medium very high very high very high high high high medium medium medium medium medium medium

very high very high very high high high medium very high very high very high very high very high very high high high medium medium medium medium

of flow also can change the weights. The large value of flow causes the stronger effect. Since, there might be some other parameters which are not taken into account, while their effects should be considered later on, a parameter called “fragility” has been used whose value can depend on these parameter and is calculated based on another fuzzy relation which will be defined later (if necessary). The higher the fragility value is, the higher the weights values would get. The elements of comparison matrix for the alternatives are defined in eq 34.

a ij =

1 1 + eik 1 1 + ekj

(34)

eik

where shows the absolute difference between desired and estimated value of subcriterion k if the ith alternative (quantitative decision) is triggered. J


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Figure 8. Response of flow rate of consumer I (node 5)case study 1, senario 1.

Figure 9. Response of pressure of consumer I (node 5)case study 1, senario 1.

Figure 10. Response of temperature of consumer I (node 5)case study 1, senario 1.

The final remark on filling the comparison matrices is that their elements must be obtained in such a way that they all lie in the same interval. Thus, in order to determine the comparison matrix in accordance with the Saaty rating scale,22 the elements should be mapped in the interval of 1 through 9. Scenarios Description 1. Suppose that two abnormalities simultaneously occur at nominal condition of the network, these abnormalities are increase by 5% in the pressure of supplier (i.e., 9400 kPa) and the decrease by 40% in percentage of opening of the highlighted valve in Figure 6. The proposed algorithm is used to come up with various decisions that can be used to alleviate the adverse effect of these abnormalities. Figures 8 through 13 illustrate the result of this assessment. The algorithm shows that the occurrence time of failures was at tf = 20 s and the DSS was invoked 10 min later without prior knowledge of the origin of abnormalities. The remainder of the details of damping this failure has been reported in Table 12. It is

noticeable that the values of commands in the fourth column (suggested quantitative decisions) are percentage of normalized values. In Figures 8 and 13, the black solid line shows the performance of DSS on the corresponding parameter, the green dash line indicates the dynamic of corresponding parameter with closed loop controllers and without intervening DSS’s suggestions, vertical dash lines are the moments of applying decision which was given by DSS, and finally, horizontal dash line demonstrates the desired value. Even though the status of all controllers are automatic as shown in Figures 8 and 11, the difference between desired and steady state value after the outbreak of failure for molar flow of consumer I (node 5) and consumer II becomes 1.74 × 104 (kg mol/h) and 2.64 × 103 (kg mol/h), respectively. However, using DSS causes these differences to descend to 660 (kg mol/h) and 1.25 × 103 (kg mol/h), respectively. Since the controllers of K


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Figure 11. Response of flow rate of consumer II (node 20)case study 1, senario 1.

Figure 12. Response of pressure of consumer II (node 20)case study 1, senario 1.

Figure 13. Response of temperature of consumer II (node 20)case study 1, senario 1.

temperature are assumed to be perfect controllers, the temperature of the target nodes varies in a narrow and acceptable range in the first scenario. It is conclusive evidence that the pressure of the target nodes cannot highly change because at nodes 6 and 21 the pressures are fixed as boundary conditions. However, Figures 9 and 12 show that the DSS tried to tend pressures to the corresponding desired values. As shown in

Figures 8 through 13, the adverse effect of failures has been successfully canceled out. As can be seen in Table 5, the minimum value of decision variable 1 is 25%; moreover, the minimum value of decision variable 14 was assumed to be 15%. According to Table 12, in the second decision making, all decision variables are saturated so there will not be conclusively any improvements anymore. L


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Industrial & Engineering Chemistry Research Table 12. Results of Scenario 1 of First Case Study invoking number

the moment of invoking the DSS (minute)

DSS response time (minute)

qualitative decision

suggested quantitative decisions:

1

30

0.64

[−1 +16 −14]

2

74

0.67

[−1 +16 −14]

3

223

0.71

[−1 +16 −14]

[34 86 32] [34 86 50] [54 86 32] [34 64 32] [54 86 50] [34 64 50] [54 64 32] [54 64 50] [24 100 15] [34 100 15] [24 100 32] [25 86 15] [34 100 32] [34 86 15] [25 86 32] [34 86 32] [25 100 15]

well-chosen decision [34 86 32] detailed information: current values = [54 64 50]

[25 100 15] detailed information: current values = [34 86 32]


Table 13. Results of Scenario 2 of First Case Study invoking number

moment of invoking the DSS (minute)




1

3.5

0.47

[+1 −16 + 14]

2

53

0.36

[+1−16 + 14]

3

262

0.38

[+1−16 + 14]

[82, 33, 75] [82, 33, 62] [82, 33, 50] [82, 45, 50] [73, 33, 50] [82, 45, 62] [73, 33, 62] [82, 45, 75] [82, 21, 100] [82, 33, 100] [82, 33, 87] [91, 33, 100] [91, 33, 87] [82, 21, 87] [91, 33, 75] [100, 33, 100] [82, 15, 100] [91, 21, 100] [82, 10, 100] [91, 15, 100] [100, 21, 100] [91, 10, 100] [100, 15, 100] [100, 105, 100]

The changing set-point is common due to some considerations such as the change in the demand of consumers; hence, it is expected that DSS should be capable of proposing solutions for supervisory control. Scenarios Description 2. Suppose that the network’s manager wants to increase the flow rate in the first consumer node by 25% and decrease the second consumer’s flow rate by 6%. Table 13 and Figures 14 through 19 show the performance of the DSS in this scenario. As shown in Figures 14 and 17, after three times invoking DSS and applying the first suggestion, the flow rate of target nodes

well-chosen decision [82 33 75] detailed information: current values = [54 64 50]



reach the desired values with acceptable tolerance. Also,Figures 15, 16, 18, and 19 show the temperature and pressure of the target nodes did not extremely change. The third columns of Tables 12 and 13 show the response time of the DSS which is the time required by the DSS to come up with tentative solutions. These elapsed times are reported based on a computer with the following configuration; CPU: core i5− 2.5 GHz, RAM: 4GB. These elapsed times truly enlighten that the proposed methodology can well be used for GTN described in section 3.1 as a real-time operating system. Because the total required time for the computer-based system, DSS, to suggest its M


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Figure 14. Response of flow rate of consumer I (node 5)case study 1, senario 2.

Figure 15. Response of pressure of consumer I (node 5)case study 1, senario 2.

Figure 16. Response of temperature of consumer I (node 5)case study 1, senario 2.

Figure 17. Response of flow rate of consumer II (node 20)case study 1, senario 2.

N


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Figure 18. Response of pressure of consumer II (node 20)case study 1, senario 2.

Figure 19. Response of temperature of consumer II (node 20)case study 1, senario 2.

Figure 20. Schematic illustration of the GTNcase study 2.

variables in this assessment. The specifications of GTN are summarized through Table 14 and Table 15. It should also noticed that the roughness and internal and external diameters of all gas pipe are respectively 0.259 mm and 55 and 55.5 in. Furthermore, in Figure 21, for simplicity the majority of isolated nodes are not shown. Scenario: Consider in the GTN shown in Figure 20, the inlet energy of the compressor indicated by node 58 is suddenly decreased by 56% and then stuck on this value at tf = 35 min. The tentative decisions that can be made to cancel out this fault are reported in Figures 22 through 24 and Table 16. Table 16 summarizes the top five suggestions with higher priorities. The flow rate of demands 1 and 2 start decreasing right after the failure, of course the decrease in demand 1 is considerably higher than demand 2. Fifteen minutes after the occurrence of

solutions is quite short compared to the time required for the GTN to get to the desired operating point (i.e., canceling out the faults or approaching to the a new set-points). 3.2. Case Study 2. In comparison to the previous case study, the second case study is more complicated with respect to diversification of gas suppliers, demands, manipulative variables, length of pipelines, etc. This case study aims to assess the algorithm’s performance with the complexity of a practical GTN, decision variables, and targets. The schematic illustration of the GTN and its DG are respectively shown in Figures 20 and 21. As shown in Figure 20, it consists of two suppliers, four demands, and six compressor stations. Five out of six compressors (i.e., K-101, K-102, K-103, K-104, and K-105, which are respectively shown as nodes 1, 17, 27, 38, and 13) and the valve named node 8, are available decision O


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Figure 21. DG model of the GTN benchmarkcase study 2.

the fault (i.e., t = 50 min) DSS is invoked, as shown in Figure 22. In this time the flow rate of demands 3 and 4 are not apparently affected. Therefore, in the first decision set shown in Table 16, DSS just proposes those commands which can get demands 1 and 2 out of faulty conditionincreasing the power of compressor K-101(node 1), K-102(node 17), and K-103(node 27). The demands of 1 and 2 tend to the corresponding desired values due to the first decision, while demand 4 deviates from its normal value not because of the decision made but for the inherent delay in its response to the original fault. The deviation in demand 4 along with the deviations of the demands of 1 and 2 from their corresponding desired values implies invocation of DSS for the second time at t = 90 min The second decision set reflects that the power of K-101, K-102, and K-103 should be increased and that of power of K-104 should be lowered to decrease the flow rate of demand 4. As shown in Figure 22, the consequence of making the second decision set is the flow rate of demand 1 gets closer to its normal value, the desired value for demand 2 is successfully attained, and the flow rate of demand 4 at first gets closer to its normal value, but it has tendency to get away from its normal value. This leads to the course of actions corresponding to the third decision which is the reduction of K104 power which can only affect the flow rate of demand 4. Ultimately, this fault is well canceled out in 14 h by invoking the DSS three times. It is obvious that during this assessment, demand 3 is not affected by fault and DSS did not truly suggest the decisions which affect its flow rate. Because of reasons like those in the previous case study, the temperature and pressure of demands change in an acceptable range. They are respectively shown in Figures 23 and 24. The third column of Table 16, like the previous case study, shows the response time of the DSS. In this assessment, DSS also takes less than a minute to come up with the tentative decision. Consequently, it is evident that such a system can have an appropriate performance in real-time applications for large GTNs existing in practical and industrial systems.

Table 14. Lengths of Various Pipes Existing in the Network Case Study 2 indices

length (km)

56−57 55−54 53−52 49−50 48−47 45−46 40−44 43−39 31−32 21−22 33−34 25−26 36−37 11−12 15−16 5−6 51−41

1 1 100 100 90 1 56 30 24 60 100 18 40 14 40 24 20

Table 15. Minimum and Maximum Power and Tunings of PI Controllers along with the Set-Points of Compressors and Coolerscase Study 2 index

min/max power (horse power) ×10−3

1

0/20

17 27 38 13 58 59 60 61 64 63 62

0/5 0/75 0/20 0/50 0/65 0/47 0/0.8 0/66 0/100 0/20 0/30

set point

Kc

τI

1049.3 psia 1036 psia 1064 psia 1400 psia 900 psia 1025 psia 22 °C 22 °C 5 °C 25 °C 25 °C 27 °C

1.5

6.7 × 10−2

12.3 3.5 11.3 3.35 4.88 0.45 28 0.432 0.578 0.289 1.07

2.48 × 10−2 2.21 × 10−2 2.43 × 10−2 3.17 × 10−2 2.55 × 10−2 0.182 0.213 0.177 0.181 0.228 0.362

4. CONCLUSIONS The aim of this article was to come up with an algorithmic framework to develop a decision support system for a gas transmission network, to assist responsible persons in order to make rapid decision with more confidence. To do so, the P


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Figure 22. Flow rate of demands during mitigating the faultcase study 2.

Table 16. Results of Second Case Study invoking number

moment of invoking the DSS (minute)


1

50

0.73



⎡ + 1 + 17 + 27 ⎤ ⎢ ⎥ ⎣ ⎦ − 38

⎡ 76 81 80 ⎤ ⎢ ⎥ ⎣ ⎦ 50

⎡ 76 81 80 ⎤ ⎢ ⎥ ⎣ ⎦ 50

⎡ 76 71 80 ⎤ ⎢ ⎥ ⎣ ⎦ 50

⎡ 51 61 60 ⎤ detailed information: current values = ⎢ ⎥ ⎦ ⎣ 50

well-chosen decision

⎡ 76 81 70 ⎤ ⎢ ⎥ ⎣ ⎦ 50

⎡ 76 71 70 ⎤ ⎢ ⎥ ⎣ ⎦ 50 ⎡ 76 81 60 ⎤ ⎢ ⎥ ⎣ ⎦ 50 2

90

0.68

⎡ + 1 + 17 + 27 ⎤ ⎢ ⎥ ⎣ ⎦ − 38

⎡ 100 100 100 ⎤ ⎢ ⎥ ⎣ ⎦ 24

⎡ 100 100 100 ⎤ ⎢ ⎥ ⎣ ⎦ 24

⎡ 100 100 90 ⎤ ⎢ ⎥ ⎣ ⎦ 24

⎡ 76 81 80 ⎤ detailed information: current values = ⎢ ⎥ ⎣ ⎦ 50

⎡ 100 90 100 ⎤ ⎢ ⎥ ⎣ ⎦ 24 ⎡ 100 90 90 ⎤ ⎢ ⎥ ⎣ ⎦ 24

⎡ 100 100 80 ⎤ ⎢ ⎥ ⎣ ⎦ 24 3

250

0.7

⎡ + 17 + 27 + 8 ⎤ ⎢ ⎥ ⎣ ⎦ − 38

⎡ 100 100 50 ⎤ ⎢ ⎥ ⎣ ⎦ 12

⎡ 100 100 50 ⎤ ⎢ ⎥ ⎣ ⎦ 12

⎡ 100 100 60 ⎤ ⎢ ⎥ ⎣ ⎦ 12

⎡ 100 100 50 ⎤ detailed information: current values = ⎢ ⎥ ⎣ ⎦ 24

⎡ 100 100 70 ⎤ ⎢ ⎥ ⎣ ⎦ 12

⎡ 100 100 50 ⎤ ⎢ ⎥ ⎣ ⎦ 0 ⎡ 100 100 60 ⎤ ⎢ ⎥ ⎣ ⎦ 24

Q


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Figure 23. Temperature of demands during mitigating the faultcase study 2.

Figure 24. Pressure of demands during mitigating the faultcase study 2.

behavior of the GTN and its response to various stimuli imposed by decision variables are modeled by FDG. Using an efficient search method, one can enumerate all qualitative and then quantitative decisions. Finally, to evaluate their degree of desirability, every one of quantitative decisions is triggered and its effects on the targets are assessed. The performance of the proposed method has been shown by using it in the operation of a typical industrial gas transmission network. The main characteristics of the proposed method can be listed as follows: Owing to the appropriate assessment method for tentative decisions, DSS can offer its tentative decisions in an online manner, in other words, it is a real-time system; moreover, the framework is flexible such that it can handle changes in the network’s topology or even be used for a new GTN. To get the plant to the desired condition, DSS tries to generate all possible alternatives while the suggested solutions are independent of the prior knowledge of faults existing in the transmission network. Several tentative decisions are generated by reasoning rather than using associative memories or through which empirical rules are obtained based on the historical data of the GTN operation. Tentative decisions obtained in each case are prioritized based on the AHP method according to their corresponding desirability index obtained through the assessment of the decisions consequences based on the FDG model of the system. In the method of AHP, the comparison matrixes are updated according to the most recent condition of the GTN at the time of invoking DSS. According to the above characteristics, the proposed method seems to be a flexible yet efficient method whose development requires neither the exact mathematical model nor the history and trends of network operational data.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +98-21-66166445. Fax: +98-21-66022853. Notes

The authors declare no competing financial interest.

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REFERENCES

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Development of Systematic Framework for an Intelligent Decision

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