mimic human control of an airport, modeled with a combined discrete ...... San Diego, CA, The Society of Computer Simulation International, vol. 20, no. 3, pp.
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 22, NO. 2, MARCWAPRIL 1992
Discrete Event Fuzzy Airport Control John R. Clymer, Philip D. Corey, and Judith A. Gardner
Abstract-Several researchers have developed analog fuzzy logic controllers based on a continuous state space model to control nonlinear, time-varying systems. In contrast, a discrete event simulation that uses a modified expert system as a controller is described. Fuzzy logic concepts from analog controllers are applied in the expert system controller to mimic human control of an airport, modeled with a combined discrete and continuous state space. The controller is adaptive so rule confidences are automatically varied to achieve near optimum system performance. An explicit formalism, called operational evaluation modeling (OpEM), is used to describe airport operations. This formalism assists a systems analyst in visualizing system operation and, in particular, greatly assists performing the knowledge engineering required to determine control rules.
I. INTRODUCTION A Pascal expert consultation system [ 181 has been extensively altered to make control decisions during simulation of complex, context sensitive systems. The data structure of facts and rules had to be modified to permit a variable number of entity or process facts to be considered in a decision. An example of a rule with a variable premise is discussed at the end of the next section. The changes most important to this paper, however, are the addition of the capability of having fuzzy facts in the premise of a rule and the ability to optimize decision making by adaptive rule strength modification. Fuzzy facts allow the degree of belief in a fact, or semantics, to influence decision making in relation to the goals of a system. For example, the degree of belief in aircraft being close or far apart as a function of distance can affect the decision made. Adaptive rule strength modification is an optimization technique that allows feedback of system effectiveness measures to cause changes in rule strength in relation to success or failure of rules in control decisions. Applying this technique resulted in near optimal performance of the airport model discussed in this paper. Combining fuzzy fact definitions and rule strength adaptation allows the system to optimize its effectiveness. It can be seen that the adaptive, fuzzy logic expert system controller has behavior similar to a fuzzy neural network, but the controller has the distinct advantage that it explains its reasoning as it makes decisions. Extraction of such information from neural network weights is not easy. Further, knowledge can be extracted from experts in the form of the rules that can assist expert system decision making. Rules are not explicit in neural networks so expert knowledge cannot be used directly. Both techniques can employ inductive techniques to learn from a set of cases. An induction program that discovers control rules, given a set of cases obtained from simulated system operation, is the subject of another paper. In this paper, a simulation of a small airport demonstrates that higher throughput of aircraft with greatly reduced chance of collision is achieved using an expert system to make control decisions based on an optimal rule set. A set of moving object routines [7] was used Manuscript received June 17, 1989; revised July 14, 1990 and July 1, 1991. J. R. Clymer is with the Applied Research Center for Systems Science, California State University, Fullerton, CA 92634. P. D. Corey is with Rockwell International, 1549 Havasu Place, Placentia, CA 92670. J. A. Gardner is with Hughes Aircraft, Fullerton, CA. IEEE Log Number 9104100.
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to simulate continuous aircraft motion using discrete events, thus as aircraft move through airport space they pass from one discrete state to another. A set of rules is postulated that depend not only on position and velocity of aircraft but also the current discrete state of each aircraft. Rule confidences are varied automatically to provide optimal performance. The authors feel the approach taken can be extended to considerably larger airports to develop an optimal rule set for them. Air traffic control requires many complex decisions. These decisions determine the sequence of actions and resource allocations occurring during airport operation. Human experts must make judicious decisions that follow complex heuristic logic. An expert system controller provides the means to combine appropriately the many control rules that may be provided by these human experts. An expert system must tolerate the fuzziness of human expert linguistic rules. For example, rules 15 through 20, listed in the appendix, use aircraft separation concepts of close and not close that have fuzzy meanings in airport control. Humans generally do not require high levels of precision to make decisions. An approximate collection, or summarization, of data usually suffices. Mental blocks, or chunks, of task-related data (fuzzy sets), which in some way are related to the system goals, are created. These chunks are hierarchically organized to provide concept association and reasoning. An example hierarchy for the decision to enter the airport approach corridor is depicted in Fig. 9 and in the appendix. An airport simulation, discussed in chapter nine of [4], makes decisions using an algorithmic controller based on crisp logic. Because of the complexity of the system (it is nonlinear and time varying with many conflicting goals to be satisfied), this algorithmic controller is complicated and not as effective as desired. An adaptive, fuzzy logic expert system controller has been developed to make use of experience of a human expert. A set of fuzzy object-value couplets (facts) and rules have been defined to mimic the human ability to handle linguistic information during airport control. Fig. 13 shows airport effectiveness achieved using the adaptive, fuzzy logic expert system controller that is close to optimal. The algorithmic controller required 20 times as much waiting time for the approach and takeoff queues as the expert system controller for 900 operations per 9-h day, though the algorithmic controller was much more effective than no control at all in an unregulated airport. Also, optimizing the expert system controller performance was much easier because of the adaptive reasoning allowed by automatic rule strength modification and a runtime user interface. An explicit formalism, called operational evaluation modeling (OpEM) [4], [5], was used to describe airport operations. This greatly assisted in the knowledge engineering performed for determining airport control rules. Airport controller performance is optimized by varying fact and rule confidences. A user interface is provided so an analyst can add or delete rules, modify rule strengths, change fuzzy logic set function parameters, and evaluate causes of bad decisions while a simulation is running. The OpEM formalism and the run time user interface help the analyst visualize context sensitive interactions that occur during airport operation and assist him in modifying decision making to optimize airport effectiveness. Zadeh [22]-[24] introduced fuzzy set theory to mimic human operation and to provide acceptable control for a system. Tong [20] provides a good review of research using this control strategy. A variety of fuzzy control applications have been studied. All were initially controlled by a human operator and designed based on an operator’s experience and all were nonlinear and time-varying in nature.
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Mamdani and Assilian [13], [14] published the first in-depth report of a practical application of fuzzy set theory to control a dynamic process. They used look-up tables to implement the fuzzy control and trial and error to optimize control. Bad or contradictory rules were eliminated or modified. Pappis and Mamdani [17] deal with traffic junction control. A crucial conclusion of this research is that fuzzy set theory offers much convenience by implementing linguistic rules. Sutton and Towill [19] simulated and controlled frigate ship maneuvers. They observed that a fuzzy logic controller has some desirable noise rejection properties a classical controller doesn’t have. The degree of fuzziness and fuzzy set overlap affect overall operation and effectiveness of a controller. This research has shown that heuristics and fuzzy set theory can be applied with results as good as or better than control using classical control algorithms in many applications, especially when the system input/output relationships are nonlinear or known information is mostly qualitative. Current fuzzy controller literature seems rooted in the classical analog control theory view based on a continuous state space. An analog fuzzy logic controller, modeled by continuous state variables, is a special case of a discrete event process controller, modeled by combined discrete and continuous state variables. The adaptive, fuzzy logic expert system controller extends classical fuzzy logic control to include discrete event processes based on an explicit formalism for discrete event operations. A definition of the term “system” is presented to provide a basis for comparing analog with discrete event system controllers. The cybernetic system concept is discussed to introduce the airport control problem. An airport scenario is described and an OpEM directed graph model is discussed to assist visualizing airport operation. A comparison of analog with discrete event system views introduces the next section of the paper describing discrete event controllers. Implementation of fuzzy logic in a discrete event system controller is presented, and some sensitivity curves showing optimization of system effectiveness are discussed.
CYBERNETICS, VOL. 22, NO.
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Fig. 1. Structure, operation, and decision making.
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Fig. 1 represents a system in terms of structure, operation, and decision making. Structure describes that part of the system that is constrained by the laws of physics, and it is described by a set of interconnected entities. Operation describes that part of the system that is constrained by the laws of synchronicity, and it is described by a set of communicating processes. The decision making part learns these constraints to make optimal decisions that maximize system effectiveness. The constraints to be learned are described by subsets of the global state space. A decision is implemented by an event chain. Decision making to select operations and allocate resources to achieve system goals is described in Fig. 2. The system process is divided into three types of subprocesses that interact (originally discussed in [l], [2]). An expert system can make highly context sensitive decisions or an algorithm can implement a very simple set of rules in less context sensitive or context free situations. The disturbance process describes operation of the environment with which a system interacts. For the airport scenario, the disturbance is the variation in interarrival time and speed of aircraft. The object process represents operation of system entities. The regulator process represents decision making of the system which selects from among all possible system behaviors the action it considers potentially most effective. The regulator process receives information from the object process on the status of the disturbance, system entities, and system processes. The regulator considers this information and evaluates possible system behaviors in anticipation of the disturbance. When a
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decision is made, the regulator process directly executes an event(s) in the object process that starts a system response. A. Airport Scenario
Fig. 3 presents a diagram of the example airport that shows aircraft takeoffs and landings. Corey [7] explains how moving object routines are used to simulate aircraft motion. Aircraft queue up southwest of the airport for entry into the approach corridor. Within the approach corridor, aircraft are lined up single file with enough spacing that aircraft will not overtake aircraft ahead of them. Aircraft make a final decision to land or turn away to avoid collision when the aircraft is 0.25 mi (in FIN) from touch down. An aircraft lands while traveling west. The aircraft touches down on the runway, slows down, and exits the runway. Aircraft ready for takeoff wait at their tiedowns (TDNs). When the controller instructs them, they queue up on the taxiway (TKQ). Aircraft are then instructed when to enter the runway at its extreme eastern end and take off. All departures and landings occur in the same direction and share the same runway.
B. Operational Evaluation Modeling The first step in developing an air traffic fuzzy control system is
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Fig. 4. Directed graph of airport operation.
to use OpEM to develop a simulation [4], [5]. This system design and analysis methodology enhances a system designer's visualization, understanding, and definition of system operation to determine system requirements. It assists system analysts and engineers to identify problems, evaluate system operation, and conduct trade-off studies and sensitivity analyses. OpEM provides a technique to form an operational view of what the system does and why it is done. To accomplish this, OpEM features a two-dimensional directed graph language to represent process flow and interactions between parallel processes in a system. A parallel process is a collection of all possible sequences of states and events a system may undergo during operation. A system state is the current discrete state of each parallel process plus the current status of all state variables. A state variable identifies the current status of some portion of the system's structure or functions. An event marks the time when system state (and possibly state variable) changes occur. Via the directed graph language, OpEM allows system operation to be understood by nonprogrammers, thereby allowing the designer, programmers, and users to envision the system design. Refer to [4], [5] for additional information on the OpEM directed graph language. The airport operational model consists of four parallel processes for approach aircraft arrival, ground aircraft arrival, aircraft approach, and aircraft takeoff. Fig. 4 presents the directed graph model of the airport simulation. Circles represent states of the system and the connecting line segments represent discrete events.
The top parallel process of the airport simulation models time between approach aircraft arrivals to the system. The approach regulator process is a subprocess of process 1 that controls time separation between approaching aircraft in the approach corridor. The second parallel process models the ground arrival of aircraft wishing to depart. The ground regulator process, a subprocess of this second parallel process, controls these ground arrivals. Parallel process 3 is the approach aircraft process describing motion and position of aircraft during approach and landing (or turning away and reentering the approach path later) at the airport. The fourth parallel process, or ground aircraft process, models motion and position of departing aircraft. Processes 3 and 4 are duplicated for each airplane in the approach or departure sequence. They also each include the collision parallel process. C . Comparison of Analog Versus Discrete Event Views
The difference between the analog and discrete event views is largely a matter of emphasis since all systems must be described in terms of structure, operations, and decision making. The analog view generally focuses on structure. Using the analog view, an airport scenario is represented as a set of entities (aircraft) that move in space in relation to the runway. Each entity is described by its position and velocity relative to the runway and its type (high or low wing). Aircraft interact when they come within specified distances
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relative to other aircraft, or the runway, where decisions must be made (slow down or turn away and reenter the approach queue). The discrete event view, used in OpEM, includes this analog view, but an additional level of meaning is added, providing an explicit description of system operation. The discrete states APQ,APP, EST, NOR, WST, FIN, and LND, shown in process 3 of Fig. 4, give meaning to aircraft position. For example, the state FIN implies that aircraft position is somewhere along the final approach glide path ending in touch down on the runway. To avoid a possible collision, an aircraft taking off should not be allowed to enter the runway if another aircraft is in final approach. A decision rule using this is IF ANYapproach-aircraft-state =fin THEN Takeoff-decision = wait-in-takeoff-queue. Use of the fact that an aircraft is in final approach in the previous rule simplifies the rule and makes it easier for customers of the airport study, such as the airport manager and pilots using the airport, to understand. A less meaningful alternative is to specify in the rule premise the range of positions defining final approach. This is the approach typically taken by analog fuzzy logic controllers.
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Fig. 5. Simple rule tree. GOAL-OBJECT
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It is beyond the scope of this paper to provide a complete discussion of AI and expert systems; however, issues relevant to conversion of a consultation system into a controller are presented. These issues are: 1) transmitting status information from the simulation system to the knowledge-based system, 2) decision making using local and global decision rules, and 3) transmitting knowledge-based system decisions to the simulation system. For a more complete description of the OpEM expert system controller see [3], [6]. There are two kinds of objects in OpEM simulations: 1) entity or process objects that represent system state and its environment and 2) symbolic objects that represent what is known about the system and its environment needed to make decisions. Symbolic objects are usually described by an object-attribute-value triplet. The object part is the name of an entity or process. An example is an aircraft ahead in the approach corridor of another aircraft in the queue, called aqaircraft-ahead. The attribute part is one of several object features. An example is position. The expert system described in this paper combines the object part and attribute part into the object name. For example, an object name could be aqaircraft-aheadgosition. The value part provides a value for an object-attribute (object is this paper), forming an object-value couplet or fact. An example fact is aircraft ahead in the approach corridor of another aircraft in the queue when position is close (aqaircraft-aheadgosition=close). An expert system [18] written in Pascal has been modified so it can be called to make decisions in OpEM simulation programs. Object oriented simulation routines Send-MSG-to-Object and Read-Object allow symbolic object-value couplets (facts) to be created and manipulated by the simulation program. The Controller routine interfaces the expert system with a simulation program. It allows the decision with the highest confidence factor to be executed. A set of events associated with the best decision is executed to implement that decision. Fig. 5 shows a simple rule tree to assign a resource. The goal object to be pursued is Allocate-Res that can be given a value of either “yes” or “no.” Two rules are shown that connect knowledge base objects Tgt-Needs-Res and Tgt-Priority to the goal. If the value of Tgt-Needs-Res is “Yes” and the value of Tgt-Priority is “High,” the rule on the left side of the figures fires and the goal object is given the value “yes.” If the value of Tgt-Needs-Res is “No” or the
value of Tgt-Priority is ‘‘Low,” the rule on the right side of the figure fires and the goal object is given the value “No.” An object can have several values at a time, each with its own confidence factor (forming several facts). Some of these multivalued objects can be fuzzy. In the rule tree shown in Fig. 5 if the objects are fuzzy, both rules will conclude values for the goal object. The goal value having highest confidence is implemented. Fuzzy object confidence factor values can be varied to optimize system effectiveness. This is done manually in OpEM using the runtime user interface. A more complex rule tree is shown in Fig. 6. This tree has intermediate rules that give values to decision objects. These intermediate rules include both general (few premise objects) and more specific rules (many premise objects) to form a default hierarchy of decision rules. A default hierarchy makes it possible for decisions to be made even when some knowledge needed to decide with complete confidence is not available. The top of a rule tree is the goal object. All rules that have the goal object in their conclusion form the top branches of the tree. At each level rules connect premises to conclusions. Premises of rules contain either knowledge base objects or decision objects. A premise is a list of object-value couplets (facts) related by OR and AND as shown in Fig. 7 with rule syntax expressed in Backus Naur form (BNF) notation. A fact is evaluated true if it can be found in the knowledge base. A nonfuzzy, inverse fact has a NOT in front of it and is evaluated true if it can not be found. If a fact is fuzzy, a NOT in front causes the confidence in this fact to be 100 minus the confidence value obtained from its set function. Several facts can be combined by the OR operation to form a composite fact. A composite fact is evaluated true if at least one comprising fact is true. Several facts or composite facts can be combined by the AND operation to form a premise. A premise is true if all facts and composite facts are true. A conclusion is a list of object-value couplets related by AND as shown. If the premise is true, only the conclusion object being pursued is given a value (fact added to knowledge base) even though other conclusions (object-value couplets) are specified. These other conclusions are given values only when pursued. Thus, a rule with multiple conclusions can be considered as a set of related rules all having the same premise. A rule must have only one instance of any particular object as a conclusion.
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->
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Fig. 7. Rule syntax The inference engine used by the OpEM expert system controller is based on the one described in [18]. It is a backward-chaining expert system that begins with a goal object. For the first step of the inference process, the engine scans the rule list for any rules with the goal as the conclusion and tests the premise within each such rule for truth. The procedure within the program that tests the premise is appropriately called “pursue.” It scans the rule list for a rule that has a conclusion that matches the premise of the previous rule or goal for the first iteration. The function that scans the rule list is called “find rule.” It searches the rule list from beginning to end for any rule that contains the required object as a conclusion. The inference engine recursively pursues rules in the tree, starting at the goal and proceeding out along branches of the rule tree until a knowledge base object is reached. Goal and decision objects may also have multiple values. The controller selects the value for the goal object that has highest confidence. All other values for the goal and decision objects are deleted. These objects are deleted to avoid interfering with subsequent consultations and to conserve dynamic memory. Using the OpEM expert system controller to make decisions is simpler than writing a custom program. An expert in system operation specifies rules and knowledge base objects for the scenario of interest. If no expert exists, the analyst becomes an expert by visualizing system operation assisted by an OpEM directed graph model and timeline analysis. The expert specifies events in the parallel process to be executed when each decision object is concluded with a particular value by controller. The programmer adds code to give each knowledge base object a value or values for fuzzy objects and other multivalued objects, inserts calls to controller where decisions must be made, and adds code to modify the knowledge base object values to indicate results of decisions. A. Fuzzy Facts
The fuzzy functions of the air traffic controller all have the Sfunction form 100/1+ [ ( l / A ) ( z - C ) ]* * B where A, B , and C
Fig. 8. Fuzzy logic set functions (S-curves). are all integer values with both A and C positive. The shape of the fuzzy membership function can be defined by specifying A, B, and C . A is the spread of the membership function, C A is the mean value of the function (i.e., where the evaluated certainty factor equals SO), and B controls the slope, C is kept zero unless a symmetrical function is desired. If B is a positive integer, a typical S-function results. An inverted S-function results when B is negative. If B is even, the function becomes a rounded peak about the mean value of (C A). In this case, C should not be zero and should be large enough to allow the membership function to be symmetric everywhere. If C is zero, a typical S-function will again result. These membership functions are depicted in Fig. 8. Domains of discourse are defined that measure various states of the system control. The 2 values in the fuzzy membership functions are elements of these domains of discourse. The command “fuzzyfact” is added to the user-generated rule file “rules.pas“to specify a fuzzy object name, its legal value, the A, B , and C values, and the domain of discourse for use in calculating the membership function certainties for each legal value. Pursue, in addition to finding rules, calculates certainty factors for fuzzy facts by using the A , B , C , and domain values to calculate 100/1 [ ( l / A ) ( x- C ) ]* * B for the S-function. All calculated certainties are rounded to integer values and restricted to fit on the range [0,100].
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B. Adaptive Rule Strength Modification The adaptive algorithm is called the “bucket brigade method [ l l ] . This algorithm is based on the concept of “support value” of an inferred fact in the knowledge base. The support value of an inferred fact is defined as the sum of bids for all rules concluding the fact. The confidence factor for an inferred fact is its support value times 8 truncated to an integer in the range 0 to 100. A rule bid is the product of the rule support, proportional to specificity, and rule strength, divided by eight hundred. The rule support is the sum of the support values of all facts or composite facts comprising the rule premise. The support value of a composite fact is the average support value of the facts comprising it. Rule strength is the confidence value associated with the conclusion being pursued (integer 0 to 100). Specificity is the number of facts plus composite facts in the premise. A specific rule has a higher bid than a more general rule in the default hierarchy. A bid is not made unless all facts and composite facts in the premise are evaluated true as
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discussed previously. When a bid is made, it is randomized using a multiplier (1 O.l5*Random) to enhance convergence to optimal system operation. Rules strengths are modified after the goal object has been pursued by the inference engine, identifying all alternative decisions, and the goal object value (decision) having highest confidence has been determined. Only rules supporting the decision are modified. For each supporting rule (except for rules supporting the decision directly), subtract the rule bid from its strength. Apportion the bid of each rule to its supporting rules by adding to their strengths. Such rewards are in proportion to each supporting rule bid relative to the bids of the other supporting rules. Rules supporting the decision directly have their strengths modified by the Reward-Punish-Rules procedure. Rule strengths are modified until a “supply and demand” balance between payout and reward is achieved for each rule. Reward or punishment of rules supporting decisions directly changes this balance. However, it has been observed that, for a given rule tree, steady state rule strength values are achieved.
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used to calculate the aircraft wait time prior to begin approach. For example, the wait time for short-wait is calculated (10 + CF). Thus, the inputs to the approach queue decision are analog slant IV. ADAPTIVE, FUZZY LoGIC EXPERTSYSTEM CONTROLLER range and closing velocity values, comparing an aircraft with the closTo incorporate fuzzy logic in the airport controller, a priori est aircraft ahead in the corridor. These analog values are transformed knowledge of the process inputs and outputs, the heuristic decisions using fuzzy logic set functions into discrete concepts that form the being made, and the physical laws under which the system functions premise facts of rules 15 through 20. The goal fact having highest are all required. Operational trends were observed and the appropriate confidence is obtained using rules 00 through 14, and the decision is concepts (fuzzy subsets) with which the controller is to operate were transformed into an analog wait time to schedule begin approach. Other decisions are made similarly. Whenever an approaching chosen. A set of linguistic control rules was formulated and the shape of each fuzzy subset membership function was decided. Experience aircraft turns west, the global controller directs the first plane in the and knowledge of the expert operators and analysis of system takeoff queue to enter the runway and take off. The approaching performance measures provided guidelines for establishing control aircraft then lands about 42 s later after the departing plane has left rules. Correct values of membership functions were determined by the runway. If aircraft separation at turn west is less than the goal and an aircraft is closing on an aircraft ahead, the aircraft can be trial and error. The controller implements global airport control, making more directed to slow down by reducing airspeed or weaving. When an efficient rise of the runway than local control of an unregulated aircraft reaches final approach the pilot is directed to turn away to airport. Rules providing global control are categorized according avoid collision or land. The global controller spaces aircraft entering the takeoff queue from the tiedown area to keep the takeoff queue to their goal objects. Rules containing “approach-queue-decision” control decisions for planes entering the approach corridor from supplied with planes and reduce wait time while engines are running. the approach queue. Rules with the goal “approach~west~decision” The adaptive, fuzzy logic airport controller performs multidimendetermine approach aircraft separations and closing velocities when sional optimization using the adaptive rule strength modification they turn west. The final approach decision, to land or turn away, algorithm discussed. The dimensions of optimization considered are uses rules with “final-approach-decision” as their goal. Rules with a separation time goal, variance threshold for separation time goal, goal of “tiedown-decision” space aircraft leaving the tiedown queue fuzzy set function parameters, and alternate rule trees. Fig. 10 shows by approximately 40 s. the effect of varying the separation time goal. The best variance The controller directs each aircraft to enter the approach corridor to threshold for the separation time goal was found to be a function of achieve an approximate 42-s s separation time goal when the aircraft the rules used. In particular, variance reduction of time separation turn west event occurs A rule tree for the approach queue decision is was greatly improved by using three levels of speed variation shown in Fig. 9, and a rule list is provided in the appendix. The goal (closing-slow, closing-fast, and closing-very-fast) instead of two. object values are no-wait, short-wait, long-wait, and very-long-wait. Each fuzzy membership function contains A, B , and C values. The premise facts for these rules represent an opinion about the System analysis determines the optimal membership function threshaircraft separation time needed at begin approach to achieve the 42-s old values. Many missions are run to vary fuzzy object membership separation time goal when the aircraft turns west. The premise object parameter values to obtain an optimal set of threshold values. The values are very-small, small, low-medium, high-medium, large, and overall goal of this sensitivity analysis, shown in Figs. 11 and 12, very-large. is to optimize user satisfaction with the airport. This requires that Confidences in these premise facts are derived from rules 15 planes land and take-off safely without unnecessary delays. through 20 in the appendix. An example shows that these rules To achieve user satisfaction, performance criteria were estabconsider aircraft spacing and speed variation to decide the best aircraft lished to balance aircraft wait times, collisions, and turnaways while time separation at begin approach. maximizing runway utilization. These performance criteria were rulel5:IF both complementary and conflicting. By reducing turnaways and aq-aircraft-aheadgosition =close AND collisions, the runway could be utilized more completely. To decrease apaircraft-ahead-speed =closing-very-fast collisions, probability of turnaways increased. By decreasing average THEN wait time in the tiedown queue, average wait time in the takeoff queue apaircraft-separation =very-large, CF=40. increased. Weighting factors had to be given to each performance The highest confidence factor obtained for rules 00 through 14 criterion before optimization could adequately be performed. Since no indicates the best decision. This confidence factor value, CF, is collisions are acceptable, this criterion was given the highest weight.
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0 TurMways 10 kft Separation
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Since a productive airport is desired, high runway utilization was also given weight. Probability of turnaways was chosen to be less than 10% and average wait times of 5 min, or less, in the approach and takeoff queues were desirable. Large takeoff queue wait times are not cost effective because fuel consumption increases so a larger wait time in the tiedown queue was more acceptable. These weights were used to select the reward and punish feedbacks needed for automatic rule strength modification. By observing system performance, certain rules were found inappropriate. In such cases, new objects were created and rule modifications made. For example, by watching approaching aircraft turn west and noting the high percentage that later turned away or collided with another plane, a fuzzy object for aircraft closing velocities was added to “approach-west-decision” rules. This was used to modify rules so an aircraft traveling too fast could be instructed to slow down. It was also observed that proper separation time with good variance reduction for aircraft in the approach corridor reduced the danger. Thus a fuzzy object for evaluating time separations between aircraft was created and added to the “approach-queue-decision” rules as discussed previously. The airport adaptive, fuzzy logic expert system controller optimized wait times as shown in Fig. 13. Average wait in the approach queue achieved is 1.5 min and wait time in the takeoff queue is 2.5 min for 900 operations (takeoffs and landings) per 9-h day. Wait time in the tiedown queue is less than 1 min. Probability of turn-away was reduced to near zero with a greatly reduced risk of collision
Fig. 13. Sensitivity of airport effectiveness
compared to an unregulated airport. Wait times for the airport with a crisp logic, algorithmic control was 20 times the wait times for comparable fuzzy logic, expert system control; though algorithmic control was superior to no control. Timeline analysis shows that fuzzy logic control achieves airport effectiveness that is close to the maximum possible when no interarrival time or speed variation occurs [4].
V. CONCLUSION
The expert system controller is called upon to pursue a goal or goals when an event of a parallel process must make a decision. The controller has been applied in simple decisions involving a single process or process duplicate and more complex global reasoning. Global reasoning may use the BST function where a list of previous simple decisions is considered and the decision with highest confidence executed. Thus, the context of a global decision must be evaluated sequentially. Sequential evaluation of context is required to simplify developing global decision rules and inferencing during global decision making. One example of a global decision is assigning a resource to one of several competing process duplicates. Another example is deciding which task, among several conflicting tasks, should be executed next.
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To make a decision, the system state of the parallel process is provided to the expert system by the event requiring a decision. The Send-MSG-to-Object routine is called to add required information to the knowledge base, and it can create an object or change the symbolic value, data values, and confidence factor of an object value. A object can have more than one value at the same time and each value has a confidence factor. Each object-value couplet is a fact in the knowledge base. A set of fuzzy facts (i.e., aqapproach-separation is close or not-close) can express variable confidence in each concept in the set; however, other multivalued objects (i.e., dog is brown and big) express fixed, often definite (CF = loo), confidence in each concept in the set. After information is placed in the knowledge base, controller is called. Controller pursues a goal object for a process duplicate (simple decision) or duplicates using the BST function (global decision) and returns the decision having highest confidence and its confidence value. If event execution is specified, controller executes all events associated with the selected goal object value. To complete a decision, the Send-MSG-to-Object routine may be required to update the knowledge base to indicate what decision was made. The goal of this paper has been to present the concept and use of fuzzy subset theory to incorporate control into a discrete event, nonlinear air traffic simulation. It was shown that optimal control can be achieved by manipulation of object and rule confidence factors given an appropriate set of rules. A human expert’s verbal fuzzy advice is translated into machine-usable certainty factor form and fuzzy logic provides a systematic manipulation of these certainty factors in much the same way as a human operator would in reaching conclusions. The airport fuzzy logic controller takes the fuzzy logic concepts used previously in analog controllers and extends them to a discrete process system using OpEM techniques. The resultant discrete airport controller is shown to optimize its own effectiveness. Much research on design and development of self-organizing analog controllers has been occurring. Mamdani and Baaklini [ 131, [14] proposed such a method. Daley and Gill [8], [9] and Yamazaki and Mamdani [21] provided direct applications of this theory. The analysis presented here confirms that the optimization potential with a fuzzy controller is great; indeed, the adaptive, self-organizing controller discussed in this paper has been shown to optimize itself using its own effectiveness as feedback.
APPENDIX FACTSAND RULESTO MAKE APPROACH QUEUE DECISIONS
legalvals(approach-queue-decision)=no-wai t,short-wai t, long-wait,verylong-wait legalvals(apaircraft_aheadgosition)=close,not-close legalvals(aq_aircraft-ahead-speed)=closing-slow, closing-fast,closing-very-fast legalvals(approach-corridor-status)=full,not-full fuzzyfact(apaircraft-aheadgosition)=close: 10000,2,0,slant~range. fuzzyfact(aq-aircraft-aheadgosition)=not-close: 10000,-2,0,slant~range. fuzzyfact(aq-aircraft-ahead-speed)=closing-slow: 20,-4,0,closing~velocity. fuzzyfact(aq-aircrafahead-speed)=closing-fast : 20,2,20,closing~velocity. fuzzyfact(aq-aircraft-ahead-speed)=closing-very-fast: 20,4,0,closing~velocity. fuzzyfact(appr0ach-corridor-status)=not-full: 5,9,0,number-in-corridor. fuzzyfact(approach-corridor-status)=full:
5,-9,0,number-in-corridor. multivalued(aqaircraft-aheadqosition) multivalued(aqaircraft-ahead-speed) multivalued(approach-corridor-status) rule00:IF approach-corridor-status=not-full AND
akaircraft-separation=ver y-small THEN approach-queue-decision=no-wait, CF=34. ruleO1:IF approach-corridor-status=not-full AND aq-aircraft-separation=small THEN approach-queue-decision=no-wait, CF=34. rule02:IF approach-corridor-status=not-full AND aq-aircraft-separation=low-medium THEN approach-queue-decision=no-wait, CF=36. ruleO3:IF approach-corridor-status=not-full AND apaircraft-separation=small THEN approach-queue-decision=short-wait, CF=23. rule04:IF approach-corridor-status=full AND aqaircraft-separation=small THEN approach-queue-decision=short-wait, CF=22. ruleO5:IF approach-corridor-status=not-full AND aq-aircraft-separation=low-medium THEN approach-queue-decision=short-wait, CF=25. rule06:IF approach-corridor-status=not-full AND aq-aircraft-separation=high-medium THEN approach-queue-decision=short-wait, CF=25. rule07:IF approach-corridor-status=not-full AND aq-aircraft-separation=low-medium THEN approach-queue-decision=long-wait, CF=29. rule08:IF approach-corridor-status=full AND apaircraft-separation=low-medium THEN approach-queue-decision=long-wait, CF=17. rule09:IF approach-corridor-status=not-full AND aq-aircraft-separation=high-medium THEN approach-queue-decision=long-wait, CF=27. rulel0:IF approach-corridor-status=not-full AND apaircraft-separation=large THEN approach-queue-decision=long-wait, CF=28. rule11:IF approach-corridor-status=not-full AND aqaircraft-separation=high-medium THEN approach-queue-decision=very-long-wait, CF=31. rulel2:IF approach-corridor-status=full AND apaircraft-separation=high-medium THEN
approach-queue-decision=very-long-wait, CF=22. rulel3:IF approach-corridor-status=not-full AND apaircraft-separation=large THEN approach-queue-decision=very-long-wait, CF=31. rulel4:IF approach-corridor-status=not-full AND aq-aircraft-separation=very-large THEN approach-queue-decision=very-long-wait, CF=32. rulel5:IF
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apaircraft-aheadqosition=close AND apaircraft-ahead-speed=closing-very-fast THEN aq-aircraft-separation=very-large, CF=40. rulel6:IF aq-aircraft-aheadqosition=not-close AND aq-aircraft-ahead-speed=closing-very-fast THEN aqaircraft-separation=large, CF=69. rulel7:IF aq-aircraft-aheadqosition=close AND aq-aircraft-ahead-speed=closing-fast THEN aq-aircraft-separation=high-medium, CF=43. rulel8:IF aq-aircraft-aheadqosition=not-close AND aq-aircraft-ahead-speed=closing-fast THEN apaircraft-separation=low-medium, CF=97. rulel9:IF aq-aircraft-aheadqosition=close AND aq-aircraft-ahead-speed=closing-slow THEN aq-aircraft-separation=small, CF=43. rule20:IF aq-aircraft-aheadqosition=not-close AND aq-aircraft-ahead-speed=closing-slow THEN ataircraft-separation=very-small, CF=78.
[17] [18] [19] [20] [21] [22] [23] [24]
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Projects Agency, Navy Personnel Research and Development Center, Mar. 1975, 1975. C. P. Pappis and E. H. Mamdani, “A fuzzy logic controller for a traffic junction,” ZEEE Trans. Syst., Man, Cybern., vol. SMC-7, pp. 707-717, Oct. 1977. B.Sawyer and D. Foster, Programming Expert Systems in Pascal. New York Wiley, 1986. R. Sutton and D. R. Towill, “An introduction to the use of fuzzy sets on the implementation of control algorithms,” J. Znstit. Electron. Radio Eng., vol. 55, no. 10, pp. 357-367, Oct. 1985. R. M. Tong, “A control engineering review of fuzzy systems,” Automatica, vol. 13, no. 6, pp. 559-569, Nov. 1977. T. Yamazaki and E. H. Mamdani, “On the performance of a rule based self-organizing controller,” in Proc. ZEEE Con$ Appl. Adaptive and Multivariable Control, London, England, July 19-21, 1982, pp. 50-55. L. A. Zadeh, ‘‘Fuzzy sets,” Inform. and Contr., vol. 8, pp. 338-353, 1965. -, “Outline of a new approach to the analysis of complex systems and decision processes,” ZEEE Trans. Syst., Man, Cybern., vol. SMC-3, pp. 2844, Jan. 1973. -, “Fuzzy logic,” Computer, vol. 21, pp. 83-93, Apr. 1988.
Epistemological Aspects of Object Schemes Santosh S. Venkatraman and Arun Sen
REFERENCES [l] W. R. Ashby, An Introduction to Cybernetics. London: Chapman & Hall, 1956. [2] -, Design for a Brain: The Origin ofAdaptive Behavior. London: Chapman & Hall, 1960. [3] J. R. Clymer, “OpEM expert system controller,” in Simulation and AI, San Diego, CA, The Society of Computer Simulation International, vol. 20, no. 3, pp. 20- 26, 1989. [4] -, Systems Analysis Using Simulation and Markov Models. Englewood Cliffs, NJ: Prentice-Hall, 1990. [5] J. R. Clymer, P. D. Corey, and N. Nili, “Operational evaluation modeling,” in Simulation, San Diego, CA, The Society of Computer Simulation International, pp. 261-270, Dec. 1990. [6] J. R. Clymer, “System design using OpEM inductive/adaptive expert system controller,” in ZASTED Znt. J. Modeling Simulation, vol. 10, no. 4, pp. 129-136, 1990. [7] P. D. Corey and J. R. Clymer, “Discrete event simulation of object movement and interactions,” in Simulation, San Diego, CA, The Society of Computer Simulation International, vol. 56, no. 3, pp. 167-174, Mar. 1991. [8] S. Daley and K. F. Gill., “A design study of a self-organizing fuzzy logic controller,” in Proc. Instit. Mech. Eng., pt. C, vol. 200, no. C1, pp. 59-69, 1986. [9] -, “Attitude control of a spacecraft using an extended self-organizing fuzzy logic controller,” in Proc. Inst. Mech. Eng., Part C 201, no. C2, 1987, pp. 97-106. [lo] J. A. Gardner, “Fuzzy logic as applied to airport control, ” unpublished Masters thesis, California State University, Fullerton, 1989. [ll] J. H. Holland, K. J. Holyoak, R. E. Nisbett, and P. R. Thagard,Induction: Process of Inference, Learning, and Discovery Cambridge, MA: The MIT Press, 1986. [12] G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty, and Information. Englewood Cliffs, NJ: Prentice Hall, 1988. [13] E. H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” Znt. J. Man-Machine Studies, vol. 7, pp. 1-13, 1975. [14] E. H. Mamdani and N. Baaklini, “Prescriptive ðod for deriving control policy in a fuzzy logic controller,” Elecrron. Lett. 11, no. 25/26, pp. 25-26, Dec. 1975. [15] C. V. Negoita, Expert Systems and F w t y Systems. Reading, M A Benjamin Cummings, 1985. [16] J. Offir, “Adaptive computer-assisted tutorials: A cybernetic optimization with finite-state machines,” San Diego, C A Advanced Research
Abstract- There is an increasing demand on database management systems to support nontraditional applications such as computer aided design (CAD) and decision support systems @SS), which deal with complex objects. Complex objects are objects that have nonatomic components (unlike the traditional relational model). Many researchers have designed object systems to support complex objects. Five levels of scheme representations are identified in the paper-they are: 1) record-structure level (lowest), 2) relational level, 3) logical level, 4) semantic level, and 5) object level (highest). Different object schemes proposed in the literature differ in their levels of representation. The paper motivates the need for a formalism for the object level of representation, and it describes a formalism for an object scheme called NEXUS.
I. INTRODUCTION The database management system (DBMS) area is evolving rapidly to accommodate nontraditional, advanced applications like computer-aided design (CAD), computer-aided manufacturing (CAM), computer-integrated manufacturing (CIM), multimedia object management, software engineering, and decision support systems (DSS). These applications often deal with objects that have other objects as components. Moreover, these components are often intricately interrelated. Such objects are referred to as complex objects, and the interrelationships among their components constitute the object semantics. The object semantics of complex objects include the abstraction mechanisms aggregation, association, IS-A relationships, and their associated constraints. The relational model 191, which is good for traditional business applications, is not appropriate for these “new” applications due to Manuscript received October 6, 1990; revised August 22, 1991. S. S. Venkatraman is with the Department of Computer and Office In-
formation Systems, College of Business Administration, Northeast Louisiana University, Monroe, LA 71209-0120. A. Sen is with the Department of Business Analysis and Research, College of Business Administration, Texas A&M University, College Station, TX 77843-4217. IEEE Log Number 9104548.
0018-9472/92$03.00 0 1992 IEEE
