**5. Health monitoring of fuel system using ANFIS**

#### **5.1 Adaptive neural fuzzy inference system**

ANFIS is a supervised gradient descent algorithm. In this, fuzzy rules configured upon the NN structure provide a qualitative description for the fault analysis of aircraft fuel system. In the resultant hybrid model, the NN recognize the fault pattern and adapt to the changing atmosphere. On the contrary, the FIS integrates the data and performs inferencing and decision making. The dynamic performance of the system can be represented by modeling the neuro-fuzzy method by extracting the numerical data from the model. Based on this approach, the system modeling serves two purposes. They are: the functional behavior of the assumed system can be predicted from the derived model, and the design of a controller is done using the resultant model. The ANFIS model is built first by initializing the input variables with the rules extracted from the input–output data of the assumed system. Later, the NN is utilized to fine tune the rules of the fuzzy model. The flow chart for ANFIS training procedure is as shown in **Figure 20**. In this work, ANFIS is used to detect and identify the presence of faults in the aircraft fuel system.

#### **5.2 Implementation of ANFIS algorithm**

The ANFIS structure developed is based on the model developed by [11]. The ANFIS network is mapping of input and output variables in a multi-layer network with a single target output [12]. The operating model of the ANFIS controller is depicted in **Figure 21**. The ANFIS methodology as a fault diagnosis and prognosis process for aircraft fuel system is briefly described in the following sub-sections. ANFIS is a structural plan that links expert's knowledge and the knowledge capability of the neural networks. ANFIS builds a FIS whose membership function parameters are obtained by training appropriately. Consider FIS with two inputs '*x'* and '*y',* two connected Membership Functions (MFs) and one output '*z'*. The fuzzy if-then rules for the present work based on the model [13] are framed as follows. If '*x'* is A1 and '*y*' is A2, then the target '*z'* is *f*(*x,y*)*,* where *A1* and *A2* are the sets in the antecedents, and *z=f*(*x,y*) is a crisp function in the consequent. *f*(*x,y*) is a polynomial for *x* and *y* input variables. A zero-order Sugeno fuzzy model is formed when *f* (*x,y*) is zero or constant which is a Mamdani FIS [14]. A first-order Sugeno fuzzy system model is formed if *f*(*x,y*) is first order polynomial. **Figure 22** shows a five-layer ANFIS architecture.

ANFIS is a five-layered feed-forward neural network, *viz* the input layer, product layer, defuzzy layer, normalized layer, and an output layer. The nodes may be

**Figure 20.** *Flowchart for ANFIS training procedure.*

adaptive or fixed. The nodes in a square shape are adaptive and the nodes in the form of a circle are fixed. In this case, the inputs to the ANFIS considered are the flow of fuel at prior instant '*x*' and engine's fuel consumption '*y*'. The output signals of the fuel tank '*z*' are measured as the target output. These parameters aid the ANFIS in formulating the rules as well as realizing a better tuning performance. Every rule covers the unity weight, and the learning procedure of ANFIS is achived on the classified signals. In the ANFIS architecture, two if then rules based on first order Takagi and Sugeno [14] are considered as below:

*Rule 1:* If *xi* is *A*<sup>1</sup> and *yi* is *A*<sup>1</sup> then *f* <sup>1</sup> ¼ *P*1*x* þ *Q*1*y* þ *C*1. *Rule 2:* If *xi* is *A*<sup>2</sup> and *yi* is *A*<sup>2</sup> then *f* <sup>2</sup> ¼ *P*2*x* þ *Q*2*y* þ *C*2.

where, *P*1, *P*2, *Q*1, *Q*2,*C*<sup>1</sup> *and C*<sup>2</sup> are the linear parameters, *A*<sup>1</sup> 1, *A*<sup>1</sup> 2, *A*<sup>2</sup> <sup>1</sup> *and A*<sup>2</sup> <sup>2</sup> are the nonlinear parameters. Activation levels of the fuzzy rules are considered using the realtion of Eq. (9),

$$\mathcal{W}\_{i} = P\_{i}(\boldsymbol{\pi}) \* \mathcal{Q}\_{i}(\boldsymbol{\mathcal{y}}), \ i = \mathbf{1}, \mathbf{2}, \ldots n \tag{9}$$

*Health Monitoring of an Aircraft Fuel System Using Artificial Intelligence Techniques DOI: http://dx.doi.org/10.5772/intechopen.99665*

where the logical operator "and" is modeled as continuous term an in this case it is stated as a product. The individual o/p of all rules is obtained as a linear combination among parameters of the antecedents of every rule as signified by Eq. (10).

$$Z\_i = P\_i \* \mathcal{X} + Q\_i \* \mathcal{Y} + \mathcal{C}\_i, \ i = 1, 2, \ldots n \tag{10}$$

The output of the model *Z*<sup>0</sup> is found by multiplying the standardized activation degree of the rules by the individual output of all rule, and it is stated by subsequent Eq. (11).

$$Z\_0 = \frac{W\_1 Z\_1 + W\_2 Z\_2}{W\_1 + W\_2} \Rightarrow Z\_0 = \overline{W}\_1 \overline{Z}\_1 + \overline{W}\_2 \overline{Z}\_2 \tag{11}$$

where, *W*<sup>1</sup> and *W*<sup>2</sup> are the normalized values of W1 and W2.

**Figure 21.** *Working model of the ANFIS controller.*

**Figure 22.** *The equivalent ANFIS architecture.*

The hybrid ANN signifying this inference is an adaptable network with five layers. All layers indicating the operation of the Fuzzy Inference System of the ANFIS is examined as follows.

#### *5.2.1 Fuzzification layer*

In this method, every input layer is represented as an input variable, and it refers to the fuzzification layer. The input parameters *xi* and *yi* have the nodes *A*1 1, *A*<sup>1</sup> 2, *A*<sup>2</sup> <sup>1</sup> *and A*<sup>2</sup> <sup>2</sup> which are the linguistic labels of fuzzy system for isolating the membership performances. The output of the fuzzy layer is given by,

$$F\_{L1,i} = \mu A^1{}\_i(\infty) \; , i = 1,2;\tag{12}$$

$$F\_{L1j} = \mu A^2 \, \_j(\text{y}) \, \_j j = \mathbf{1}, \text{2};\tag{13}$$

where, *FL*1,*<sup>i</sup>* and *FL*1,*<sup>j</sup>* are the outputs of the fuzzy layer, '*x'* and '*y'* are the input to nodes *i* and *j*. *μA*<sup>1</sup> *<sup>i</sup>*ð Þ *<sup>x</sup>* and *<sup>μ</sup>A*<sup>2</sup> *<sup>j</sup>*ð Þ*y* are the membership performance of the fuzzy layer.

#### *5.2.2 Product layer*

This layer may be identified as the *π* that performs logical "AND" operation, *i.e.*, the multiplication of the input membership functions. In this process, the output is the weighted input function of the next node which is symbolized by W1 and W2. The output is described by,

$$Z\_1 = F\_{\rm L2,i} = \mu A^1(\infty) \,\mu A^2(y), \; i = \mathbf{1}, \mathbf{2} \tag{14}$$

$$Z\_2 = F\_{L2,j} = \mu A^1{}\_j(\infty).\mu A^2{}\_j(\mathcal{Y}), \quad j = 1, 2 \tag{15}$$

#### *5.2.3 Normalization layer*

In this layer each node of this layer is fixed which represents the "if" part of a fuzzy rule. It is process of normalization of the input weights that can complete the fuzzy "and" operation. In this layer, each node computes the ratio of the *i th* rule firing strength to the total firing strength of all rules. The normalized firing strength of the *i th* node is given by,

$$\overline{Z\_1} = F\_{\mathbf{L}3,i} = \frac{Z\_i}{Z\_1 + Z\_2}, \quad i = \mathbf{1}, 2 \tag{16}$$

$$\overline{Z\_2} = F\_{\mathbf{L}3j} = \frac{Z\_j}{Z\_1 + Z\_2}, \quad j = \mathbf{1}, 2 \tag{17}$$

where, *Z*<sup>1</sup> *and Z*<sup>2</sup> are the outputs of this layer.

#### *5.2.4 Defuzzification layer*

This is an adaptive layer that gives output membership function based on predetermined fuzzy rules. The node function is given by Eqs. (18) and (19).

$$\overline{Z\_1}f\_i = F\_{L4,i} = \frac{Z\_i}{Z\_1 + Z\_2} \left[ A\_1^1(\mathbf{x}) + A\_2^1(\mathbf{y}) + \mathbf{C}\_1 \right] \tag{18}$$

*Health Monitoring of an Aircraft Fuel System Using Artificial Intelligence Techniques DOI: http://dx.doi.org/10.5772/intechopen.99665*

$$\overline{Z\_2}f\_{\,\,j} = F\_{L4\,\,j} = \frac{Z\_{\,\,j}}{Z\_1 + Z\_2} \left[ A\_1^2(\mathbf{x}) + A\_2^2(\mathbf{y}) + \mathbf{C}\_2 \right] \tag{19}$$

where, *Zi* is the o/p of the third layer and *{Pi, Qi, Ci}* is the consequent parameters set.

#### *5.2.5 Output layer*

The output layer is symbolizing the THEN part of the fuzzy rule. This consists of one fixed node that computes the total output which is the summation of the input signals given by the following Eq. (20).

$$f = F\_{L5,i} = \sum \overline{Z\_l} f\_i = \frac{\sum \overline{Z\_l} f\_i}{\sum Z\_i} \tag{20}$$

Where, f is the total output and the function of ANFIS is verified by considering a higher number of signals. Training the ANFIS model for the given inputs generate the control signals which help to maintain the fuel flow rate within the aircraft fuel system.

The important benefits of ANFIS are improved learning capacity, the ability to incorporate the non-linear structure of the system and rapid adaption capability. ANFIS can achieve exceptionally nonlinear mapping, far better than other techniques. Some of the drawbacks of this technique are: there are no standard methodologies to incorporate the changing human learning or experience into the base of a FIS and also there is a need for agent techniques used for tuning the membership functions to diminish or minimize the error during execution.

#### **5.3 Simulation of fuel system using ANFIS methodology**

This section defines the simulation procedure of health management of aircraft fuel system using ANFIS as a controller. **Figure 23** shows the model of aircraft fuel system with ANFIS as controller. It includes fuel tanks, pumps, pipelines that connects the tanks and pumps with the engines. The fuel system function is to distribute clean fuel at the required pressure and fuel flow rate to the engines in different operating conditions. The diagnostic and prognostic process of small aircraft fuel system is regulated by the ANFIS intelligent control model, that provides better fuel flow rate compared to ANN methodology. That is because of ANFIS's significant features of significant reasoning ability and the low level of computational power during training process. The main purpose of the ANFIS control model is to direct the fuel flow to the engine and to access the essential engine fuel consumption rate. If a fault arises in any of the fuel tanks, the controller model detects the fault and activates the necessary actions as per the fuel requirement of fuel engine.

The ANFIS controller is concentrated on the optimization of parameters of the aircraft fuel system. Similar to the ANN controller, the ANFIS controller is assessed with the previous instance fuel flow and the engine fuel consumption value of the fuel system.

#### **5.4 Simulation results and discussions using ANFIS**

ANFIS's learning ability carried out through the five-layer structure of the Fuzzy Logic system helps to approximate the non-linear functions which depends on the

**Figure 23.** *Structure of the aircraft fuel system with ANFIS as controller.*

#### **Figure 24.**

*The structure of the proposed controller.*

antecedent and consequent parameters. ANFIS is more robust and has better performance compared to conventional computing methods. These unique properties of the ANFIS such as improved computational power and high reasoning ability, permit it to be used in the fault diagnosis and prognosis of the fuel system to manage fuel flow rate as per engine consumption. The structure of the ANFIS process implemented for the health management of the fuel system is as depicted in **Figure 24**. The control signals generated are decided based upon the input parameters such as engine fuel consumption and previous instance fuel flow to the engine.

#### *Health Monitoring of an Aircraft Fuel System Using Artificial Intelligence Techniques DOI: http://dx.doi.org/10.5772/intechopen.99665*

The rule structure of ANFIS is determined by the interpretation of the features of the variables of the fuel system model. ANFIS learn details of the input data points, calculate the membership function that best suits to track the input data and output data. The parameters related to the membership functions varies with the learning process of the fuzzy system which depends on the gradient vector. This gradient provides the measure to check the ability of the FIS for the given set of system parameters. The performance is evaluated by considering the error the difference between the actual and desired outputs. **Table 5** shows the fuzzy inference rules framed for the four-tank fuel system. Based on these seven logical rules the learning of the system parameters related to the fuel system with the fault data is carried out. The training data points of input data and output data sets applied to the ANFIS scheme is configured similarly as applied to the ANN.

During the evaluation, the ANFIS structure enables the change in the rules of the FIS. This property of ANFIS helps to optimize itself for the given number of iterations by changing the shape of the membership function, rules and also removes the unnecessary rules during training. A suitable ANFIS Simulink model is designed and developed for the health management purpose of the aircraft fuel system. ANFIS as a controller is designed for the aircraft fuel system with two input


**Table 5.** *Fuzzy inference rules.*

**Figure 25.** *Snapshot of the Simulink model of a fuel system with ANFIS as a controller.*

### *Fuzzy Systems - Theory and Applications*


*ANFIS target data.*

**Figure 26.** *Training process of ANFIS.*

**Figure 27.** *Fuel consumption by the engine using ANFIS as a controller.*

#### *Health Monitoring of an Aircraft Fuel System Using Artificial Intelligence Techniques DOI: http://dx.doi.org/10.5772/intechopen.99665*

parameters and five bell membership functions for each input unit. **Figure 25** shows Simulink model of aircraft fuel system with ANFIS controller.

**Table 6** gives the details of the target output generated by the ANFIS. Similar to the ANN, ANFIS performance is evaluated based on the MSE value. **Figure 26** depicts the curve of convergence of the training data with ANFIS target data indicated as reduction of MSE error. As the number of iterations are increased the MSE reduces indicating the fulfillment of desired target data from the training process of the ANFIS.

**Figures 27** and **28** shows the rate of fuel consumption and management test using ANFIS as a controller. The target output generated as control signal identifies the presence of a fault and provide 2700 kg/hr. of fuel flow rate which is almost

**Figure 28.** *Fuel management test with the ANFIS controller.*


*Fuel fetched from each tank using ANFIS as controller.*

**Figure 29.** *Comparisons of fuel consumption.*

near to the engine requirement 2800 kg/hr. **Figure 27** also illustrates that the learning ability of the ANFIS reproduces accurately the desired output as compared to the ANN process. Thus, the error difference between the actual output value and the obtained output value is very small which is of 100 kg/hr. of flow rate. The ANFIS controller predicts the required fuel by fetching the fuel from the other tanks as per the **Table 7**.

The effectiveness of the ANFIS health management scheme is evaluated by comparing with ANN and fuel system without a controller. The details of the ANFIS based fault diagnosis process is presented in work of [15]. Both techniques uses similar fault conditions. In terms of comparison of training process using ANFIS and ANN techniques, it is clear from the **Figure 29** that ANFIS provides better results. ANN and ANFIS methods detect the time of the fault, diagnose and predict the required flow rate by injecting the additional fuel from other tanks. However, the weight updation process of ANN is based on the historical dataset, which gives the mismatching results during the testing time. Due to this reason, the fuel flow rate obtained by the ANN method is 2600 kg/hr. and is not the desired requirement of fuel by the engine. Hence, it shows that ANFIS technique manage the health status of the aircraft fuel system by monitoring and managing the accurate fuel flow to the engine.

### **6. Conclusion**

Soft computing methodologies like ANN and ANFIS are described in this chapter. A comparison study is made in [16]. All the simulation done is considered for the laboratory conditions only. Based on the theory of NN and FIS, the concept of hybrid five-layer ANFIS structure is implemented and simulated for the health management of the fuel system. Both the techniques help to monitor and manage the rate of fuel flow as required by the aircraft's engine by generating the control signals. Further, based on an adaptive algorithm fault analysis is carried by the author in paper [17]. Diagnostic and prognostic process are carried out through managing the previous fuel flow and fuel consumption by the aircraft engine using ANFIS. ANFIS is a hybrid computational tool, which helps to tune and explain past data and predict future behavior of the system. The fuzzy inference rules that are created in ANFIS rely on both the input and the target output. Tuning can be accomplished with the learning ability of NN. To achieve flawless performance possible faults in the fuel system are detected and corrected by generating the appropriate control signals before the occurrence of massive damages in terms of economy and human life. In this scenario, health management tools have been encouraged.

#### **Acknowledgements**

First of all, I would like to thank the Supreme power, the Almighty, being with me and always guiding me to work on the right path of life. Without His grace, this would not have been possible. I would like to express my sincere thanks to my Research Guide Dr. Vanam Upendranath, Senior Principal Scientist, Aerospace Electronics and Systems Division, CSIR-National Aerospace Laboratories (NAL) Bangalore, Karnataka, India and Co-guide Dr. D. S. Jangamshetti, Prof. Dept. of EEE, Basaveshwar Engineering College, Bagalkot, Karnataka. This work would not have been possible without their support, encouragement and able guidance.

*Health Monitoring of an Aircraft Fuel System Using Artificial Intelligence Techniques DOI: http://dx.doi.org/10.5772/intechopen.99665*
