Diferencia y similitudes entre el Modelo OSI y TCP/IP

This section introduces the preliminary theory of the proposed modular FDP method. Figure 5.1 shows the proposed FDP System.

The proposed FDP system includes FDD unit, PE unit, and RUL unit. In the following, various HCV failures are discussed, and brief underlying theories of the proposed techniques are presented.

5.2.1 The HCV failures

Three most common failures in the HCV system are considered as follows: piston leakage, drain blockage, and filter malfunction [11]. It must be noted that two areas in the front (zone 17 in Figure 3.5) and back (zone 18 in Figure 3.5) of the piston are sealed from each other. If there is a leakage in the sealed area around the piston, it leads to performance degradation of the system, and eventually, instability in the operation of the system. The drain blockage is a result of any congestion in the drain pipe (zone 19 in Figure 3.5). The drain pipe can get congested by impurities in the fluid, even though, the filter (zone 8 in Figure 3.5) is responsible for extracting the suspended impurities in the liquid. However, if the contamination gradually passes

through the filter over a long period, it may lead to congestion in the drain pipe. Filter malfunction can occur due to filter degradation. This happens due to the impurities in the fluid.

5.2.2 The fault detection and diagnosis (FDD) method

This section introduces the design methodology for the FDD unit. The main aim is to detect and identify the types of the failures. The proposed FDD method includes feature selection technique and SVM method. The feature selection technique is utilized to choose proper measurements for the input of SVM method. The SVM method is considered as a classifier to isolate the type of a failure in the system.

Feature selection

Pre-processing of data and proper feature selection are often necessary steps in ma- chine learning applications where a significant amount of data or measurements are available. It is often the case that data pre-processing, and judicious feature selection can lead to more accuracy and less computational complexity in the classification scheme, see, e.g., [151]. In this work, correlation analysis is used to select relevant measurements of the sensors to be used in monitoring. For this aim, the Pearson product-moment rank correlation coefficient is formulated as follows [152]:

r = Pn i=1(xi− ¯x)(yi− ¯y) pPn i=1(xi− ¯x)2 pPn i=1(yi− ¯y)2 (5.1) where xi is a variable which is desired to determine its dependency on output vari-

able, yi. Variables ¯x and ¯y are the mean values of xi and yi, respectively. Parameter n

is the number of each variable. Variable r is correlation coefficient which get a value in range of [−1, 1]. An absolute value near one signifies a high dependency between variables, and the value near zero reveals a weak dependency or independence.

minw 1 2w T_{w + c} m X i=1 ξi yi(wφ(xi) + b) ≥ 1 − ξi; ∀i = 1, · · · , m; ξi ≥ 0 (5.2)

where w is a normal vector to the hyperplane, and c ≥ 0 is a penalty parameter. Variables ξi are positive slack. Function φ(0) is a feature mapping rule. Eq. (5.2)

can be solved by Lagrange method, and a hyperplane is obtained as follows:

f (x) = sgn(

m

X

i=1

yiαiK(xi, xj) + b) (5.3)

where K(xi, xj) = φ(xi)φ(xj) is known as a kernel of SVM classifier. The hyper-

plane, f (x), is a surface which separates classes from each other. Different kernels can be used for the SVM methods such as linear, Gaussian, RBF. If more than two classes exist, binary SVM cannot directly solve the classification problem. In this case, There are two popular approaches which attempt to combine binary SVM to solve the problem. These are commonly known as “one against one” and “one against all” [153].

5.2.3 The parameter estimation (PE) method based on ANFIS networks The ANFIS was introduced by Takagi and Hayashi [154] and benefits from a combina- tion of fuzzy logic and neural network structure. ANFIS is chosen for the parameter estimation since it can provide accurate results for this task.

Figure 5.2: A Typical ANFIS Network with two inputs.

ANFIS network is an adaptive network that applies a supervised learning algorithm with an inference system similar to Takagi-Sugeno and is computationally efficient [151]. A set of rules are derived with respect to Sugeno fuzzy model as follows:

Rule 1: If x1 is A1 and x2 is B1, then f1 = p1x1+ q1x2+ r1

Rule 2: If x1 is A2 and x2 is B2, then f2 = p2x1+ q2x2+ r2

where Aiand Bi are the membership functions of input x1 and x2, respectively, and

pi, qi and ri denote adaptive parameters. Figure 5.2 shows a typical ANFIS network

with two inputs and one output. As indicated in Figure 5.2, the ANFIS network contains five layers with a feed-forward structure. The mathematical representation of each layer is given as follows [141]:

Layer 1: Each adaptive node has a linguistic label, and the output of the node is the membership function of that label:

O1,i= µAi(x1), i = 1, 2.

O1,i= µBi−2(x2), i = 3, 4.

(5.4)

Layer 2: Each node in this layer is fixed. Each node of this layer depicts a firing strength (wi) for each rule. A T-norm operator like “AND operator” is considered to

firing strengths and the adaptive parameters are considered to formulate the outputs as follows:

O4,i = ¯wifi = ¯wi(pix1+ qix2+ ri) i = 1, 2. (5.7)

Layer 5: This layer has only one node whose output is the summation of all signals obtained by the previous layer:

O5,1= 2 X i=1 ¯ wifi = P2 i wifi P2 i wi (5.8) Backpropagation algorithm or hybrid learning which combines gradient descent and the least-squares schemes can be used to train the ANFIS network. These algorithms optimize the adaptive parameters in layers 1 and 4 to achieve a minimum error in the output of the network.

5.2.4 The remaining useful life (RUL)

The RUL task is to predict the remaining lifetime of the system before complete failure occurs. In here, a similar Bayesian algorithm like the one introduced in the previous chapter is applied to compute the RUL of the system.