TACDSS: Adaptation Using a Hybrid Neuro-Fuzzy System
Cong Tran, Ajith Abraham* and Lakhmi Jain School of Electrical and Information Engineering, University of South Australia, Adelaide, Australia. Email:
[email protected] *
Department of Computer Science, Oklahoma State University, 700 N Greenwood Avenue, Tulsa, USA Email:
[email protected]
Abstract.
Normally an intelligent decision support system is build to solve complex problems involving multi-criteria decisions. The knowledgebase is the vital part of the decision support system containing the knowledge or data that is used for decision-making. Several works have been done where engineers and scientists have applied intelligent techniques and heuristics to obtain optimal decisions f rom imprecise information. In this paper, we present a hybrid neuro -fuzzy technique for the adaptive learning of Takagi-Sugeno type fuzzy if-then rules for the Tactical Air Combat Decision Support System (TACDSS). Experiment results clearly demonstrate the efficiency of the proposed technique. Some simulation results demonstrating the difficulties to decide the optimal number and shape of the membership functions are also provided.
1. Introduction and Related Research Several decision support systems have been applied mostly in the fields of medical diagnosis [1], business management, control system, command and control of defence and air traffic control [4]. In most cases, decision support systems are designed for a particular application [5]. Several decision support techniques have been developed using artificial intelligence techniques. These techniques try to mimic the human way of reasoning and interpretation using expe rt systems, fuzzy inference systems, rough sets and neural network learning methods. We require a system that is able to learn from the data/information and automatically provide the if-then decision rules as desired by the user. The decision rules obtaine d will be further evaluated by computer simulation or by a human expert (knowledge). If the obtained decision rules are not satisfactory, the learning process is to be fine tuned to get the desired results. Figure 2 shows the database learning process in the decision support system. Our adaptive database -learning framework using evolutionary algorithms [5] could deliver fuzzy if-then rules. The two disadvantages of the evolutionary approach are the requirement of expert
knowledge to model the objective function ( decision score to set up fuzzy rules) and the computational complexity leading to huge amount of simulation time. There are several techniques for extracting fuzzy decision rules but most of them use "training data" to cr eate the fuzzy rules. Cattral developed a technique of RAGA (rule acquisition using genetic algorithm) based data mining system suitable for supervised and unsupervised knowledge extraction from large and possible noisy database [3]. Jagielska used the neural networks to extract the fuzzy rules [6]. Hung combined unsupervised learning technique (self organizing maps) and the supervised technique (learning vector quantisation) to create the two stage-training network for generating the fuzzy decision rules [8]. In this paper, we propose a neural network learning technique for the automatic adaptation of fuzzy inference system. In Section 2, we introduce the some theoretical c oncepts on neuro-fuzzy systems followed by the complexity of the problem in tactical air combat environment (decision -making process) in Section 3. Experimentation results are provided in Section 4 and some conclusions are also provided towards the end.
2. Hybrid Neuro-Fuzzy Model The advantage of neural network (NN) is the adaptive learning capability. The fuzzy sets introduced by Zadeh [11] has provided an inference methodology that enables approximate human reasoning capabilit ies, which could be applied to knowledge-based systems. The main disadvantage of Fuzzy Logic (FL) is the requirement of expert knowledge to set up the knowledge base ( if-then rules). FL cannot learn the data and then adaptive the fuzzy rules. Neural networ ks can learn from the data and automatically adjust their connection weight between the layers. An analysis reveals that the drawbacks pertaining to these approaches seem complementary and therefore it is natural to consider building an integrated system c ombining the concepts. While the learning capability is an advantage from the viewpoint of fuzzy inference system the formation of linguistic rule base will be advantage from the viewpoint of neural networks. During the last decade, several neuro -fuzzy sy stems have been developed and a summary could be obtained from [2].
3. Decision Making in Tactical Air Combat We considered a case study based on a tactical environment problem. The air operation division of Defence Science Te chnology Organization (DSTO) and our research team has a collaborative project to develop a tactical environment decision support system for a pilot or mission commander in tactical air combat. In Figure 1 a typical scenario of air combat tactical environm ent is presented. The Airborne Early Warning and Control (AEW&C) is performing surveillance in a particular area of operation. It has two hornets (F/A -18s) under its control at the ground base as shown "+" in the left corner of Figure 1. An air -to-air fuel tanker (KB707) " ? " is on station and the location and status are known to the AEW&C.
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Two of the hornets are on patrol in the area of combat air patrol (CAP). Sometime later, the AEW&C on -board sensors detects 4 hostile aircrafts (Mig -29) that is shown as "O". When the hostile aircrafts enter the surveillance region (shown as dashed circle) the mission system software is able to identify the enemy aircraft and its distance from the Hornets in the ground base or in the CAP. The mission operator has few opt ions to make a decision on the allocation of hornets to intercept the enemy aircraft. Send the Hornet directly to the spotted area and intercept. Call the Hornet in the area back to ground base and send another Hornet from the ground base. Call the Hornet in the area for refuel before intercepting the enemy aircraft. The mission operator will base his decisions on a number of decision factors, such as: Fuel used and weapon status of hornet in the area. Interrupt time of Hornet in the ground base in the Ho rnet at the CAP to stop the hostile. The speed of the enemy fighter aircraft and the type of weapons it possesses. The information of enemy aircraft (number and type of aircrafts, weapon, etc.) Surveillance Boundary
Hostiles
Fighter on CAP Tanker aircraft Fighters at ground base
Figure 1. A simple scenario of the air combat From the above simple scenario, it is evident that there are several important decision factors to be taken into account to make the overall decision. For easy demonstration of our proposed approach, we will simplify the problem by handling only a few important decision factors such as " fuel status ", " weapon possession status" and "interrupt time" (Hornet in the ground base and the H ornet in the area of CAP ) and the “ danger situation” (friend or hostile), which is commonly known as situation awareness in a battlefield.
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3.1 The Knowledge of Tactical Air Combat Data How human knowledge could be extracted to a database? Very often people express knowledge as natural language (spoken language) or using letters or symbolic terms. The human knowle dge can be analysed and converted into an information table. There are several methods to extract human knowledge. DSTO researchers use the Cognitive Work Analysis (CWA) [10] and the Cognitive Task Analysis (CTA) [9]. The CWA is a technique to analyse, design and evaluate the human computer interactive systems. The CTA is a method to identify cognitive skill, mental demands and needs to perform task proficiency. The CTA focuses on describing the repr esentation of the cognitive elements that defines goal generation and decision making. The CTA is a reliable method to extract the human knowledge because it is based on the observations or an interview. Militallo has clearly explained the interview method to analyse the different tasks of a problem and to extract the human knowledge [9]. We made use of the CTA technique to make an interview with the expertise in the AEW&C of DSTO in Australia to set up the expert knowledge ba se to formulate a key knowledge for building up the complete decision support system. For the simple TACS discussed before, we have four decision factors that could affect the final decision options of “hornet in the CAP” or “hornet at the ground base”. These are “fuel status” that is the quantity of fuel available to perform the intercept, the “weapon possession status” presenting the state of available weapons inside the hornet, the “interrupt time” which is required for the hornet to fly and interrupt th e hostile and the “danger situation” providing information whether the aircraft is a friend or hostile. Each of the above -mentioned factors has difference range of unit such as the fuel (0 to 1000 litres), interrupt time (0 to 60 minutes), weapon status (0 to 100 %) and the danger situation (0 to 10 points). The following are two important decision selection rules, which were formulated using expert knowledge: The decision selection will have small value if the fuel used being too low, the interrupt time is too long, the hornet has low weapon status and the danger situation of FOE is high value. The decision selection will have high value if the fuel used being full, the interrupt time is fast enough, the hornet has high weapon status and the danger situation of FOE is low value. In the TACS environment, decision -making is always based on all states of all the decision factors. But sometime, a mission operator/commander can make a decision based on an important factor, such as the fuel used of the hornet i s too low, enemy has more power weapon, quality and quantity of enemy aircraft etc.
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3.2 Modeling TACDSS Using Adaptive Network based Fuzzy Inference System This section will explain the modelling aspects of the TACDSS using the hybrid neuro-fuzzy learning technique ANFIS. The ANFIS is the hybrid neural -fuzzy system, which was developed by Jang [7]. This ANFIS is based on the architecture of the Takagi -Sugeno fuzzy inference system. The six -layered architecture of ANFIS is shown in Figure 2. W1
A1
X
Ai
W1 f 1
A3
f
Wi
B1
Y
Bi
Wi fi
Wn
+
Wn fn
B3 Layer 1 Input layer
Layer 2 Fuzzification
layer
Layer 3 Antecedent layer
Layer 4 Rule strength layer
Layer 5 Consequent layer
Layer 6 Output layer
Figure 2. Architecture of ANFIS Suppose there are two Input Linguistic Variables (ILV) X and Y and each ILV have three membership functions (MF) A 1, A 2 and A 3 and B 1, B 2 and B 3 respectively. Takagi-Sugeno type fuzzy if-then rule is set up as following: Fuzzy Rulei : If x is Ai and y is Bi then fi = pix + qiy + ri Where i is an index i = 1,2,3 and p, q and r are linear parameters of function f Some layers of the ANFIS have the same number of nodes and the nodes in the same layer have similar functions. If the output of nodes in layer l is denoted as Ol,,i with l as the layer number and i is neuron number of next layer. The function of each layer is described as follows. Layer 1 The output of this node is the input values of the ANFIS O1,x = x O1,y = y For TACS the four inputs are intercept and the danger situation.
fuel status , weapons inventory levels , time
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Layer 2 The output of nodes in this layer are presented as Ol,ip,i where ip is th e ILV and m is the degree of membership function of particular MF. O2,x,i=
Ai(x)
or O2,y,i =
Bi(y)
for i = 1,2 and 3
With three MFs for each input variable, "fuel status" has 3 -membership functions: full, half and low, " time intercept" has 3 membership functions: fast, normal and slow, "weapon status" has 3 membership func tions: sufficient, enough and insufficient and the “danger situation of FOE” has 3 membership functions: very danger, danger and endanger. Layer 3 The output of nodes in this layer is the product of all the incoming signals which denotes O3,n = Wn=
Ai(x)
x
Bi(y),
where i = 1,2 and 3, n is number of fuzzy rule. In general, any T -norm operator will perform the fuzzy AND operation in this layer. With 4 ILV and MFs for each input variable the TACS decision support system will have 81 fuzzy if-then rules. Layer 4 The node in this layer is an adaptive node with the node function calculates the ratio of the ith fuzzy rules firing strength (RFS) to the sum of RFS. wn O4,n = wn = 81 where n = 1,2,..,81 wn n 1
The number of neuron in this layer is the same as the number of neuron in layer 3 that is 81 neurons. The output of this layer is also called normalized firing strength. Layer 5 The node in this layer is an adaptive node being defined as O5,n = wn fn = wn (pnx + qny + rn) {pn, q n, r n) is the parameter set of the particular node and is referred to as consequent parameters. This layer also has the same number of nodes in layer 4 (81 nos). Layer 6 The single node in this layer is responsible for the defuzzification process using the center of gravity technique to computes the overall output as the summation of the incoming signal.
6
81
wnfn
81
O6,1 =
wn f n = n 1
n 1 81
wn n 1
ANFIS uses a hybrid-learning rule with a combination of gradient descent (to learn the membership function parameters) and least squares estimate algorithm to learn the rule consequent parameters [7].
4. Experimentations result Our experiments were simulated using Matlab. In additi on to the development of the decision support system, we also investigated the behaviour of TACDSS decision support system for different membership functions (shape and quantity per ILV), and learning techniques. 4.1 Comparison of TACDSS MF tuning before and after training Figure 3(a) and (b) shows the three MFs for the ILV “fuel used” before and after training. The consequent parameters of fuzzy rule before training was set to zero and the parameters were learned using the hybrid learning approach.
a
b
Figure 3. The membership functions of the ILF “fuel used” (a) before and (b) after learning 4.2 Testing of the developed TACDSS decision support system We tested the capabilities of the developed fuzzy inference system. The TACDSS has 4 inputs and each input has three MFs. The input and its MF were named as “fuel used ”: full, half and low, “ intercept time”: fast, normal and slow, “ weapon efficiency”: insufficien t, enough and sufficient, “ danger situation ”: endanger, danger and very dangerous. We have tested the decision making ability of the developed model by changing only one input variable and all other input variable were set to 0.5.
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When the “ fuel used” was set at 0.2, the solution obtained was 0.0922 and when the fuel tank was set at 0.9 then the solution was 0.965. When the “ interrupt time” was set to 0.2, the solution was 0.421 and when the setting was increased to 0.9, the solution obtained was 0.399. For “ weapon efficiency ” set at 0.1, the decision score obtained was 0.434 and the decision core increased to 0.524 when the setting was increased to 0.9. When the “ danger situation” is set at 0.2, the solution obtained was 0.471 and for danger situation set at 0.9, the score was reduced to 0.154. The simulation results clearly demonstrate that the developed TACDSS fuzzy inference system could provide the decision scores as same as a tactical air combat expert. 4.3 Comparison between the learning methods of FIS We also investigated the different learning methods for learning the fuzzy inference system. Keeping the consequent parameters constant, we fine -tuned the membership functions alone using the gradient descent technique (backpropagation). Further, we us ed the hybrid learning method wherein the consequent parameters were also adjusted according to the least squares algorithm. Even though backpropagation is faster than the hybrid technique, learning error and the decision scores were better for the latter technique. We used 3 Gaussian MFs for each ILV. Table 1 illustrates the performance of the two learning methods for different input variable settings. Fuel Used 0.2 0.5 0.9 0.5 0.5 0.5 0.5 0.5 0.5
Intercept Time 0.5 0.5 0.5 0.2 0.9 0.5 0.5 0.5 0.5
Weapon Efficiency
Danger Situation
0.5 0.5 0.5 0.5 0.5 0.2 0.9 0.5 0.5
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.9
Hybrid Learning Solution 0.0920 0.0100 0.9650 0.4210 0.3990 0.4580 0.5240 0.4710 0.1540
BP Learning Solution 0.0045 0.4990 0.0040 0.0052 0.0029 0.0042 0.0093 0.0059 0.0023
Table 1. Performance comparison for different learning techniques. 4.4 Comparison of the shape of membership functions of FIS
In this section, we will demonstrate the importance of the shape of membership functions. We used the hybri d-learning technique and each ILV has three MFs. Table 2 shows the training error value during the 15 epochs learning using
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different membership functions. We considered Generalised Bell (Gbell), Gaussian (Gaus), Gaussian 2 (Gaus2), Trapezoidal (Trap), Is osceles Triangular (Isoc) and Different Sigmoidal (Diff) membership functions. Figure 7 illustrates the training convergence curve for different MF’s.
No. of epoch
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Gbell
1.393 1.348 1.315 1.296 1.288 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291
Root Mean Square Error (e-005) Gausian Gaus2 Trap Isoc
1.183 1.157 1.137 1.127 1.108 1.097 1.085 1.074 1.062 1.052 1.043 1.038 1.039 1.039 1.039
2.198 2.137 2.039 1.970 1.912 1.813 1.673 1.495 1.412 1.479 1.479 1.479 1.479 1.479 1.479
2.183 2.073 2.275 2.275 2.275 2.275 2.275 2.275 2.275 2.275 2.275 2.275 2.275 2.275 2.275
0.783 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558 1.558
Diff
1.942 1.929 1.903 1.894 1.902 1.902 1.902 1.902 1.902 1.902 1.902 1.902 1.902 1.902 1.902
Table 2. The performance with different shape of membership functions As evident from Figure 4, the lowest training error was for Gaussian MF. We also tested the TACDSS models for different MFs. The input of TACDSS were set to “ fuel used” 0.9, “i nterrupt time” 0.1, “w eapon efficiency” 0.9 and “ danger situation” 0.1. TACDSS gave a decision score of 0.864 (Gaussian), 0.88 (Trapezoidal), 0.861 (Gaussian Bell), 0.874 (Gaussian 2), 0.849 (Isosceles triangle) and 0.870 (Different Sigmoidal). The best decision score was obtained using the Gaussian MF and the worst using the trapezoidal MF. 4.5 Effect of Increasing Number of Membership Functions of Inputs We used the hybrid learning and the Gaussian membership function for each input variable. The number of MF were increased from 3 to 4 for each ILV. The observation from the simulation results for 3 MFs and 4 MFs are as follows: With a setting of fuel used 0.9, interrupt time 0.1, weapon efficiency 0.9 and danger situation 0.1, the decision score for 3 MFs was 0.865 being greater than for 4 MFs 0.857. More MFs per ILV could improve the accuracy of the decision scores. 4.6 Testing the TACDSS
We passed a randomly extracted test data set through the developed TACDSS. For example: when the ILVs are fuel used 0.9, i nterrupt time 0.0833, w eapon
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efficiency 0.96, danger situation 0.2 the required decision score should be 0.9. TACDSS was simulated using different MFs such as Gaussian, Gaussian bell, and Gaussian 2 an d so on. We obtained a decision score 0.90 for all the different simulations (same as the required solution). We also extracted 20 percent of master data set to form the test data and remain of master data set being the training data of the TACDSS. The sha pe MFs of the ILV and OLV is the Gaussian. The comparison between the actual and the desired output is shown in figure 5, the RMSE for test data is 1.498 e-5.
Figure 4. Effect on learning error for the different membership functions
Figure 5. Comparison between the actual and desired output of TACDSS
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5. Conclusion and future research In this paper, we have proposed the automatic construction of TACDSS using a Takagi-Sugeno neuro-fuzzy system. We used ANFIS algorithm for the automatic construction of if-then fuzzy rules using neural network learning techniques. Empirical results clearly reveal the developed TACDSS model could perform as efficiently as a tactical air combat expert. Our experiments also demonstrate the importance of the shape and number o f membership functions for each input variable for obtaining the best performance. Compared to our previous work using evolutionary algorithms, neuro -fuzzy approach is more efficient in terms of less computational complexity and modelling simplicity. Our f uture research will be oriented to develop other adaptive fuzzy inference systems for the TACDSS, using decision tree analysis or unsupervised learning techniques and compare the results with current and previous works.
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