**6. Adaptive neural- Fuzzy inference system**

ANFIS, proposed by Jang [14, 15], is an architecture which functionally integrates the interpretability of a fuzzy inference system with adaptability of a neural network. Loosely speaking ANFIS is a method for tuning an existing rule base of fuzzy system with a learning algorithm based on a collection of training data found in artificial neural network. Due to the less tunable use of parameters of fuzzy system compared with conventional artificial neural network, ANFIS is trained faster and more accurately than the conventional artificial neural network. An ANFIS which corresponds to a Sugeno type fuzzy model of two inputs and single output is shown in Fig. 1. A rule set of first order Sugeno fuzzy system is the following form:

Rule i: If x is Ai and y is Bi then fi = pix+qiy+ri.

ANFIS structure as shown in Figure 1 is a weightless multi-layer array of five different elements [15]:

	- O*l,i* is the output of the *i*th node of the layer l.
	- Every node *i* in this layer is an adaptive node with a node function

$$\mathbf{O}\_{1,i} = \mu \mathbf{A}\_i(\mathbf{x}) \text{ for } i = 1, 2, \text{ or } 1$$

A Multi Adaptive Neuro Fuzzy Inference System for

overall output = O5,1 = <sup>∑</sup> ��� f�= ∑� ����

algorithm used to train the ANFIS for this purpose.

Some examples:

networks and neural-fuzzy networks.

(multi ANFIS).

There are many ways of using this function.

 ��*i* is the normalized firing strenght from layer 3. {p*i*, q*i*, r*i*} is the parameter set of this node. These are referred to as consequent parameters.

Short Term Load Forecasting by Using Previous Day Features 347

O4,1 = ��*i*f*i* = ��*i*(p*x* + q*i*y + r*i*)

The single node in this layer is a fixed node labeled *sum*, which computes the

The main objective of the ANFIS design is to optimize the ANFIS parameters. There are two steps in the ANFIS design. First is design of the premise parameters and the other is consequent parameter training. There are several methods proposed for designing the premise parameter such as grid partition, fuzzy C-means clustering and subtractive clustering. Once the premise parameters are fixed, the consequent parameters are obtained based on the input-output training data. A hybrid learning algorithm is a popular learning

 ANFIS uses a hybrid learning algorithm to identify the membership function parameters of single-output, Sugeno type fuzzy inference systems (FIS).

[FIS,ERROR] = ANFIS(TRNDATA)

[FIS,ERROR] = ANFIS(TRNDATA,INITFIS)

Since fuzzy methods and systems were presented for using in different applications, researchers noticed that making a fuzzy powerful system is not a simple work. The reason is that finding suitable fuzzy rules and membership functions is not a systematic work and mainly requires many trails and errors to reach to the best possible efficiency. Therefore the idea of using learning algorithms was proposed for fuzzy systems. Meanwhile learning of fuzzy network proposed them as the first goals for being unified in fuzzy methods in order to make the development and usage process of fuzzy systems automatic for different applications. Function estimation by using the learning methods is proposed in neural

In the suggested methods we forecast load consume and its improvement by the help of the offered method. One of the famous neural-fuzzy systems for function estimation is ANFIS model. We used this system for power consumed load forecasting in this paper too, but with this difference that we used one separate adaptive neural-fuzzy system for each season of the year. Although at the time of training these systems data overlapping is considered, because data of each season of the year is not completely independent and there is some similarities between the first days of a season with its previous season regarding the amount of load consumption. Figure 2 shows the diagram of multi adaptive neural-fuzzy system

**7. The proposed method for power consumed load forecasting** 

Layer 5: The NFN output is produced by an algebraic sum over all rules outputs.

∑� ��

overall output as the summation of all incoming signals:

O*1,i* = µB*i−2*(x) for *i* = 3, 4


$$\mu A(\chi) = \frac{1}{1 + |\frac{x - ct}{al}| 2bl}.$$


Fig. 1. ANFIS architecture

	- Every node in this layer is a fixed node labeled Prod.
	- The output is the product of all the incoming signals.
	- O*2,i* = w*i* = µA*i*(x) µB*i*(y), *i* = 1, 2
	- Each node represents the fire strength of the rule
	- Any other T-norm operator that perform the AND operator can be used
	- Every node in this layer is a fixed node labeled Norm.
	- The *i*th node calculates the ratio of the *i*th rulet's firing strenght to the sum of all rulet's firing strengths.
	- O3,i = ݓഥi = ௪ ௪భା௪మ , i = 1, 2
	- Outputs are called normalized firing strengths.
	- Every node *i* in this layer is an adaptive node with a node function:

$$\mathbf{O}\_{4,1} = \overline{\mathbf{w}}\_i \mathbf{f}\_i = \overline{\mathbf{w}}\_i (\mathbf{p}\_x + \mathbf{q}\_i \mathbf{y} + \mathbf{r}\_i)$$

	- The single node in this layer is a fixed node labeled *sum*, which computes the overall output as the summation of all incoming signals:
	- overall output = O5,1 = <sup>∑</sup> ��� f�= ∑� ���� ∑� ��

The main objective of the ANFIS design is to optimize the ANFIS parameters. There are two steps in the ANFIS design. First is design of the premise parameters and the other is consequent parameter training. There are several methods proposed for designing the premise parameter such as grid partition, fuzzy C-means clustering and subtractive clustering. Once the premise parameters are fixed, the consequent parameters are obtained based on the input-output training data. A hybrid learning algorithm is a popular learning algorithm used to train the ANFIS for this purpose.


346 Fuzzy Inference System – Theory and Applications

O*1,i* = µB*i−2*(x) for *i* = 3, 4 *x* (or *y*) is the input node *i* and A*i* (or B*i−2*) is a linguistic label associated with this

Therefore O*1,i* is the membership grade of a fuzzy set (A1,A2,B1,B2).

µA(x) = <sup>ଵ</sup> ଵାȁೣష ೌ ȁଶ

Layer 2: The activation of fuzzy rules is calculated via differentiable T-norms (usually,

The *i*th node calculates the ratio of the *i*th rulet's firing strenght to the sum of all

Layer 4: The consequent part is obtained via linear regression or multiplication between

the normalized activation level and the output of the respective rule; Every node *i* in this layer is an adaptive node with a node function:

 Any other T-norm operator that perform the AND operator can be used Layer 3: A normalization (arithmetic division) operation is realized over the rules

node

Fig. 1. ANFIS architecture

matching values;

O3,i = ݓഥi = ௪

the soft-min or product);

O*2,i* = w*i* = µA*i*(x) µB*i*(y), *i* = 1, 2

rulet's firing strengths.

௪భା௪మ

, i = 1, 2 Outputs are called normalized firing strengths.

Typical membership function:

*ai, bi, ci* is the parameter set.

Parameters are referred to as premise parameters.

 Every node in this layer is a fixed node labeled Prod. The output is the product of all the incoming signals.

Every node in this layer is a fixed node labeled Norm.

Each node represents the fire strength of the rule

```
[FIS,ERROR] = ANFIS(TRNDATA)
```
#### [FIS,ERROR] = ANFIS(TRNDATA,INITFIS)
