## Microsoft word - neuro-fuzzy_measurement_2014_v5_revision.doc

**Viharos, Zs. J.; Kis K. B.**: Survey on Neuro-Fuzzy Systems and their Applications in Technical

Diagnostics and Measurement,

*Measurement*, Vol. 67., 2015., pp. 126-136., (doi: http:// dx.doi.org/10.1016/j.measurement.2015.02.001),

*SCI, Impact Factor: 1.526.*

Survey on Neuro-Fuzzy Systems and their Applications in Technical Diagnostics and

Measurement

Survey on Neuro-Fuzzy Systems and their Applications in Technical Diagnostics and

Measurement

Dr. Zs. J. Viharos*, K. B. Kis

*The Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, H-1111 Hungary*

Tel.: +36 1 279 6 195, E-mail address: {viharos.zsolt*, kis.krisztian}@sztaki.mta.hu

Tel.: +36 1 279 6 195, E-mail address: {viharos.zsolt*, kis.krisztian}@sztaki.mta.hu

**A b s t r a c t**

Both fuzzy logic, as the basis of many inference systems, and Neural Networks, as a powerful computational

model for classification and estimation, have been used in many application fields since their birth. These two

techniques are somewhat supplementary to each other in a way that what one is lacking of the other can provide.

This led to the creation of Neuro-Fuzzy systems which utilize fuzzy logic to construct a complex model by

extending the capabilities of Artificial Neural Networks. Generally speaking all type of systems that integrate

these two techniques can be called Neuro-Fuzzy systems. Key feature of these systems is that they use input-

output patterns to adjust the fuzzy sets and rules inside the model. The paper reviews the principles of a Neuro-

Fuzzy system and the key methods presented in this field, furthermore provides survey on their applications for

technical diagnostics and measurement.

*Keywords*: Technical diagnostics, Neuro-Fuzzy systems, Measurement

**1. Introduction**

**2. Application of Neuro-Fuzzy Systems to**

**Technical Diagnostics and Measurement**

As two important techniques of artificial intelligence, Fuzzy Systems (FS) and Artificial This section gives a survey on Neuro-Fuzzy system Neural Networks (ANNs) have many applications applications in the field of technical diagnostics and in various fields such as production, control measurement. Different Neuro-Fuzzy architectures systems, diagnostic, supervision, etc. They evolved are named here, their history and a more detailed and improved throughout the years to adapt arising description are presented in the next sections. At needs and technological advancements. As ANNs the end of this section a table is also presented and Fuzzy Systems had been often applied together which gives a comprehensive overview of these the concept of a fusion between them started to take applications and their fields categorically. shape. Neuro-Fuzzy systems were born which utilize the advantages of both techniques: they have learning and generalization capabilities and at the same time they reveal the functionality stored in the In the early 90s Neuro-Fuzzy was still a new model. To reach this behaviour they are able to concept to be shaped by different implementations learn and tune their parameters based on input- and applications. In these years a relatively small output patterns (learning phase) and then they work amount of Neuro-Fuzzy application was published like a fuzzy logic system (execution phase), too. and naturally these were unique approaches rather These combined features make this type of systems than utilisation of existing solutions. For example useful when solving complex problems also for among the pioneers, Ayoubi presented a structure technical diagnostic and measurement assignments. that models the fuzzy inference mechanism based The paper contains seven sections. After the on neural units [1]. He tested the system on two introduction the second section presents Neuro- real-world problems: monitoring the state of a Fuzzy applications of the last two decades in turbocharger and supervision of air pressure in technical diagnostics and measurement. The third vehicle wheels. The implemented model proved to section describes the two main components of a be efficient when the problem space is low- Neuro-Fuzzy system followed by the forth one dimensional; however, when it had significantly reviewing the progression of the Neuro-Fuzzy more dimensions, Multi-Layer Perceptron (MLP) systems and the modern solutions used today. The performed far better than the fuzzy inference last three sections are conclusions, acknowledgments and references. Zhang and Morris also used a Neuro-Fuzzy solution for fault diagnosis of continuous stirred tank reactor process [2]. The chosen test problem is well known about its highly nonlinear dynamics which is a One of the first and probably most widespread result of the phenomenon that process gain changes Neuro-Fuzzy architecture is the Adaptive-Network- drastically with any operating condition based Fuzzy Inference System (ANFIS) which has modification. The network applied for this problem similar accuracy as the Multi-Layer Perceptron consists of 4 layers: an input layer, a fuzzification (MLP) which makes it ideal for function layer, a hidden layer and an output layer. The input approximation. This architecture was used for layer has 14 neurons, because the system has 14 mechanical fault diagnostics of induction motors measured signal values, the fuzzification layer has 3 with variable speed drives by Sadeghian and Wu neurons for each input neuron, because each input [7]. The authors managed to significantly reduce information is ordered to 3 individual fuzzy the system complexity and learning duration of the membership function, the hidden layer has 10 network by using multiple ANFIS units in their neurons representing 10 fuzzy rules and the output layer has 11 neurons, each corresponding to a particular fault. They achieved much better performance than with a conventional feed forward neural network while the system also provided a more interpretable structure.

*2.2. 2000s*Neuro-Fuzzy systems became more widespread in the 2000s especially in technical diagnostics and measurement. For example Sakuntala Mahapatra et

**Fig. 1.**Multiple ANFIS units for multiple fault

al. built such systems for adaptive filtering of oscillatory signals [3]. The used model proved to be more efficient than other alternative fuzzy adaptive Fig. 1. shows the multiple ANFIS units where each systems; moreover, it can be used for on-line one is responsible for detecting a specific fault type monitoring of signals, independently whether they as these fault types have different feature are described by linguistic variables or crisp coefficients. This modular structure provides an easy way to make extensions for detecting other Frey et al. used a Neuro-Fuzzy model to control a fault types and also has the advantage that the units rotary hammer drill [4]. For solving this problem can be easily trained due to their simplicity. In the authors had to find the optimal settings of another application Lei et al. used multiple ANFIS rotational speed and strike rate to achieve optimal combination with genetic algorithm for fault drill penetration. A self-learning Neuro-Fuzzy diagnostics of rotating machinery [8]. They model was developed to intelligently control these implemented a classifier system where the features two variables during the drilling process to achieve describing the problem were divided into six optimal performance. predetermined and separated groups and individual Detecting the onset of damage in gear systems was Neuro-Fuzzy classifiers were constructed for each the goal of Wang et al., for which they developed a group. The final classification result of the system Neuro-Fuzzy based diagnostic system [5]. The is the weighted average of the individual groups. diagnosis of the gear system is conducted gear-by- During training, genetic algorithm was applied for gear, which means that for every gear there is a optimising these weights. This method can yield separated Neuro-Fuzzy model. Each model has better classification result than the member three inputs and one output: the inputs are reference classifiers individually. functions that reduce the feature dimensions, i.e. Amaral et al. applied a diagnostic technique based they aggregate multiple features of the real system on the identification of a specified current pattern to one variable; the output is the condition of the for detection of motor stator fault and used a Neuro- gear, which can be normal or damaged. To train the Fuzzy model for an image feature extraction based implemented model they proposed a constrained- identification [9]. They used the Neuro-Fuzzy gradient-reliability algorithm which can effectively strategy to get a better linguistic knowledge about update the membership function parameters and set the underlying fault detection and diagnosis the rule weights. Evsukoff and Gentil created a recurrent Neuro- Machinery malfunctions often reduce productivity Fuzzy system for fault detection and isolation in and increase maintenance costs in various industrial nuclear reactors [6]. In their model a fuzzification fields. Zio and Gole proposed a Neuro-Fuzzy module is linked to a neural network based approach to solve fault diagnosis of rotating inference module which was adapted to recognize machinery by pattern classification while obtaining related faults based on the process variables. a model which remained easily interpretable [10].

Particle Swarm Optimization (PSO) to improve the model's learning capability. Via this solution, they showed that PSO can be effectively employed for developing industrial model-based control schemes. *2.3. Nowadays * Nowadays the emphasis of the research of Neuro-Fuzzy systems is concentrating mainly on their applications on wide practical fields. For instance Guzinski et al. presented a diagnostic system for shaft misalignment detection based on the ANFIS model [13]. They used this system in an adjustable
speed sensorless induction motor drive where the
**Fig. 2.** A sketch of a bearing assembly [10]

model is based on the analysis of the stator current,
motor speed and load torque processing. The results
Fig. 2. shows components of a bearing assembly
showed that it can effectively indicate the shaft
which can be damaged leading to malfunction. For
misalignment. Karimi and Salahshoor also used the
the diagnosis of these components the authors
ANFIS model and combined it with Principal
created a Neuro-Fuzzy algorithm which consists of
Component Analysis (PCA) for fault detection and
multiple modules. First, an initial set of fuzzy rules
diagnosis of distillation column [14]. They used
are determined, where the initial large number of
PCA to extract the most informative features and at
rules is reduced with a heuristic solution based on
the same time reduce dimensionality of the
the firing strength of each rule. Then the forward
measured data then fed the reduced data to ANFIS
algorithm calculates the relative strengths of the
to discriminate the occurred fault. They
rules and the next module uses these values for
demonstrated the effectiveness of the proposed
creating new rules if necessary. The optimisation
method via extensive conducted tests in a
module tunes the parameters of the member
distillation column benchmark.
functions and finally, a pruning is applied to reduce
Wali et al. compared intelligent controllers such as
the size of the rule set. After the initial set of rules
Fuzzy and Neuro-Fuzzy in the task of monitoring
has been established, the algorithm repeats itself
and control of novel advanced microwave biodiesel
iteratively until the desired accuracy is reached.
Chen, Roberts and Weston used Neuro-Fuzzy
Systems for fault detection and diagnostics of railway track circuits [11].
**Fig. 3.** Scheme of neuro-fuzzy for fault detection

and diagnosis [11]
**Fig. 4.** The basic block diagram for fuzzy controller

Fig. 3. Shows the scheme of the implemented
model where the measurement data associated with
different operating conditions is mapped to each
Fig. 4. shows the block diagram of the fuzzy
failure mode. In their solution, they use a
controller which was applied for temperature
generalized version of the ANFIS to support
control inside the reactor. The authors found that
multiple outputs. Each one of the eleven outputs
the ANFIS controller is more robust to parameter
corresponds to a condition (1 healthy and 10 faulty
variations while a pure fuzzy solution is able to
condition) while eight current and voltage
regulate in minimal overshoot. ANFIS model was
measurements are used as the input variables.
used by Eristi for fault diagnosis of series
Another research was aiming at Neuro-Fuzzy based
compensated transmission lines, too [16].
state modelling of a flexible robotic arm using real sensor data [12]. The authors also utilized improved

**Fig. 5.** Main structure of the proposed algorithm for fault diagnosis, classification and location isolation [16]

Fig. 5. shows the structure of the algorithm where
the clustering based fuzzy inference system and the
Vabc denotes the Voltage signal and Iabc denotes the
ANN method and concluded that it is due to the fact
Current signal. Eristi utilized Wavelet
that ANFIS inherits the advantages of both of the
Transformation (WT) and Norm entropy to achieve
effective feature extraction of the fault signals. To
One of the major factors in catalytic performance is
test the proposed method an extensive data set of
the size of the catalyst. In the next application the
23 436 fault cases were used and the results showed
authors used response surface methodology and the
that the algorithm is effective and robust to
ANFIS model to quantify the effects of physical
parameter variations.
characteristics of magnetite on Fenton-like
Concentration estimation of volatile organic
oxidation efficiency of methylene blue [18]. For
compounds was the goal of Jha et al. [17]. They
petroleum products monitoring Roshani et al.
built multiple models to measure and compare their
applied the ANFIS model to predict fluid density
performance on the problem. They found that the
for a gamma ray densitometer [19].
Neuro-Fuzzy system (ANFIS) outperformed both
**Fig. 6.** The proposed ANFIS structure to predict fluid density for a gamma ray densitometer [19]

Fig. 6. shows the proposed model where A1-A9
the output values of the corresponding nodes. The
denotes the membership functions of the *pipe *
authors simulated the operation of the densitometer
*diameter* variable and B1-B9 denotes the
device to obtain the testing dataset and after
membership functions of the *number of counts (per *
application of the model they concluded that it can
*photon)* variable. W1-W9, W1-W9 and f1-f9 denotes
estimate the fluid density with high accuracy.

In many cases very different application fields are
Fig. 8. shows a typical artificial accelerogram from
targeted by Neuro-Fuzzy solutions as in the case of
which the 20 parameters were extracted. The
another ANFIS model which was used to detect
proposed models were able to produce 98%
alterations in sleep EEG activity during hypopnoea
recognition rate and thus their application can be
episodes by Übeyli et al. [20]. The authors used the
tested in real circumstances.
ANFIS for classification and they performed
Benyamin Khoshnevisan et al. adopted an ANFIS
feature extraction by computing of wavelet
and an ANN based system to predict potato yield
coefficients. In their case four models was used:
from energy inputs [23]. The purpose of the study
three were fed directly by measured data on the
was to create model which helps farmers to
electrodes and the fourth had the purpose of
estimate the level of production in advance and
improving diagnostic accuracy by gaining its inputs
make an appropriate plan for the future. The authors
from the outputs of the other three systems. Lee and
evaluated various topologies to find the optimal
Lim also used hybrid fuzzy neural methods to
one; moreover they compared the ANN and ANFIS
compare Deep Brain Stimulation (DBS) and
models and found that the latter one is more capable
levodopa as two treatments of Parkinsonian resting
of overcoming the problem of inconsistent data
because of its rule based architecture.
Another application aimed at prediction of vertical stress transmission in real soil profile using ANFIS [24]. The authors built multiple models with different membership function types and for this specific dataset the gauss membership function proved to be the most efficient. Moharana et al. also used the ANFIS model to estimate the roughness coefficients of a meandering channel [25]. This is a
complex problem because the coefficients depend
**Fig. 7.** Velocity laser recording of resting tremor

on many hydraulic, geometric and roughness
parameters. They compared the result with earlier
studies and concluded that the Neuro-Fuzzy model
Fig. 7. shows a method for recording resting
is more effective than others in terms of estimation
tremors which was applied to 16 subjects to build a
dataset. The study not only showed that DBS is
There is a wide variety of other applications where
more effective than levodopa but it did it in a way
this kind of systems was successfully implemented
that is less time-consuming and less expensive than
from the fields of biology and environment to fault
MRI and other medical expert dependant solutions.
detection and diagnostics as by Kar et al. [26].
In another case ANN and Neuro-Fuzzy based
models were applied to classify earthquake
Neuro-Fuzzy applications are widely used for
damages in buildings which can be utilized to help
technical diagnosis and measurement purposes;
engineers decide whether some structures are
however, neural and fuzzy methods are often used
remained safe or not [22]. The presented
individually, too. For instance Bilski used an
classification models used 20 seismic parameters of
artificial intelligence-based model for diagnostics of
accelerograms to estimate 4 damage categories.
analog systems [27]. He preprocessed the training
and testing data sets using statistical methods to minimize the amount of information to be measured in order to optimize the performance of the Artificial Neural Network (ANN) diagnostic modules. In another application Catelani and Ciani analysed the problem of disturbance induced by high energy particles on electronic devices and developed a model to determine whether a system respond to specific requirements [28]. *2.4. Overview of Neuro-Fuzzy System applications to Technical Diagnostics and Measurement *Table 1 gives a comprehensive structure to all
overviewed applications appointing the main
**Fig. 8.** Artificial seismic accelerogram processed to

functionalities and application fields and the related
classify earthquake damages in buildings [22]
** Table 1 **Applications functionalities, with their fields and related publications

**Application field**

**Authors and Reference**

Turbocharger state, air pressure of vehicle wheels

**Monitoring and**

Fenton-like oxidation efficiency Pouran et al. [18]

**supervision**

fluid density for a gamma ray densitometer Roshani et al. [19] Analogue systems Continuous stirred tank reactor process Zhang and Morris [2] Nuclear reactors Evsukoff and Gentil [6] Induction motors Guzinski et al. [13]

**Fault diagnosis**

Rotating machinery Zio and Gole [10] Railway track circuits Chen et al. [11] Distillation column Karimi and Salahshoor [14] Series compensated transmission lines Disturbance induced by high energy particles Catelani and Ciani [28]

**Adaptive filtering**

Oscillatory signal Sakuntala Mahapatra et al. [3] Rotary hammer drill Microwave biodiesel reactors Wali et al. [15]

**Pattern identification**

Amaral et al. [9]

**System state modelling**

Flexible robotic arm Amitava et al. [12] Volatile organic compounds Khoshnevisan et al. [23]

**Variable estimation**

Hamid Taghavifar et al. [24] Meandering channel Moharana et al. [25]

**Variable change**

Sleep EEG activity during hypopnoea episodes Übeyli et al. [20]

**detection**

Parkinsonian resting tremors Lee and Lim [21]

**Damage classification**

Earthquake damages in buildings Alvanitopoulos et al. [22] inspired by the behaviour of biological neural

**3. Prelude of Neuro-Fuzzy Systems**

networks inside the human brain. An ANN implements the functionality of the biological This section discusses the techniques that provided neural networks by building up a network of the theoretical basis and allowed the concept of autonomous computational units (neurons) and Neuro-Fuzzy system to be formed. These connecting them via weighted links defined by the techniques are the Neural Networks and the Fuzzy first pioneers W. S. McCulloch and W. Pitts [29]. Systems which will be presented in the following Such a computational unit e.g. an artificial neuron is shown on Fig. 9. It consists of input links (special neurons sometimes don't have any input links), a

*3.1. Artificial Neural Networks (ANNs)*transfer function, an activation function and an optional memory component while the weighted links between them are represented by real numbers. In Fig. 9. x1-xn denotes the input values of the neuron, oj denotes the output value and w1j-wnj denotes the weights of the input links. The transfer function aggregate the outputs of the other neurons connected via the input links weighted with the strength of the links. The activation function produces the output value based on the output of the transfer function and the memory serves as a container to store previous states of the neuron (in

**Fig. 9.**An artificial neuron

many cases it is not used or only a part of the state is stored). When a neuron fires the signal The concept of the ANN was established seven propagates through the output links to the decades ago and, as the name suggests, it was connected neurons and the weight of a link (represented by a real number) determines the strength of the connection and weakens the signal Yet another class of ANNs is the Radial Basis Function Network (RBFN) which uses radial basis In 1957 Frank Rosenblatt created the perceptron functions as the activation function of the neurons algorithm for supervised classification of an input [33]. Their training algorithms are extended to into one of two possible outputs [30]. This is a type adjust not only the network's weights but the of linear classifier and at the time, only the single- activation function parameters, too. They have layer perceptron could be trained. many uses such as function approximation, time 18 years later Werbos created the backpropagation series prediction, classification, etc. algorithm for training the MLP [31]. Over the decades ANNs proved to be powerful computational models for solving complex estimation and classification problems as they are robust and are capable of high level generalization, moreover they can already handle incomplete data, too [34]. However no information can be extracted from a trained ANN about the connections between the parameters, e.g. a generic ANN model can only approximate the output parameters but cannot tell what kind of connections exist between the input and output parameters. This is a key disadvantage of the Neural Network model which led to the

**Fig. 10.**The MuliLayer Perceptron model

creation of Neuro-Fuzzy Systems. Fig. 10. shows an MLP model where the neurons

*3.2. Fuzzy Systems*are organized into layers and each layer is fully connected with the next one. Supervised training of Real life problems often have the tendency to be not an MLP means repeated adjustment of the weight discrete but continuous in nature. A somewhat of each link to receive more and more favourable special case of this phenomenon is to categorize output on specific neurons (output neurons) while objects or theoretical entities because in many stimulating other neurons (input neurons). The cases, categories don't have precisely defined backpropagation algorithm achieves this by criteria of membership. To solve this problem Lofti calculating the derivatives of the network's error Zadeh [35] introduced fuzzy set theory, where the with respect to all of its weights and adjusting the membership of an element is no longer a binary weights to a position where, based on the state but a continuous value e.g. instead of saying derivatives, the error is smaller e.g. moving the that

*a*is an element of

*A*set and not element of

*B*, weights in the direction of the descent of the we can say that a is an element of

*A*fuzzy set by derivatives where the error is a measure of the 0.67 degree and element of

*B*by 0.23 degree. difference between the network's output and the Fuzzy logic is a type of logic that uses fuzzy sets to target values for the same input. represent truth values and consequently it provides After 1975 the MLP became more popular and an effective way to represent human knowledge in a widespread and during the years many other, but mathematical language. Fuzzy logic uses fuzzy not so highly popular ANN model types were inference rules which are able to process the defined, moreover, currently the basic research in continuous truth values and produce an also the field of neural networks is emphasising on the continuous output. Each rule has the form of study of biological neural systems and define new learning algorithms and architectures that are maps

*if <premise> then <consequent>,*of the biological brain systems. One of these new types is the Self-Organizing Map (SOM) which can that uses linguistics variables with symbolic terms. be trained by unsupervised learning to produce a Each term represents a fuzzy set. The terms of the low dimensional representation of the input space input space (typically 5-7 for each linguistic [32]. They are mainly used for visualizing high variable) compose the fuzzy partition. The fuzzy dimensional data in low dimensional views. inference mechanism consists of three stages: in the Another type is the Recurrent Neural Network first stage, the values of the numerical inputs are (RNN), they are different from the common mapped by a function according to a degree of feedforward networks as they allow circles in their compatibility of the respective fuzzy sets; this structure e.g. some links propagate the signal back operation can be called fuzzification. In the second to such neurons that sent the original signal. This stage, the fuzzy system processes the rules in feature allows them to establish an internal memory accordance with the firing strengths of the inputs. which can be used to process arbitrary sequences of In the third stage, the resultant fuzzy values are

transformed again into numerical values; this
architecture is called ANFIS and it uses the Takagi-
operation can be called defuzzification. Essentially,
Sugeno-Kang inference system.
this procedure makes possible the use fuzzy
categories in representation of words and abstracts ideas of the human beings in the description of the decision taking procedure [36]. Fuzzy inference systems have two main type based on the mathematical calculation of the inference. These are the Mamdani type inference [37] and the Takagi-Sugeno-Kang (TSK) type inference [38]. A Mamdani type fuzzy rule can be described as
*if A is X1 and B is X2 then C is X3,*

where A, B, C are variables and X

**Fig. 11.**The ANFIS architecture [39] where x and y

fuzzy sets. In contrast to the Mamdani type, a TSK denote the input variables and z denotes the output rule has the form of

*if*

**A**is**X**Fig. 11. shows the ANFIS architecture consisting of

**1**and**B**is**X2**then**C**=**aA**+**bB**+**c**,six layers. The first layer contains two nodes for where a, b and c are constants. As a result of the input x and y, the second layer is responsible for form of the rules the Mamdani type inference mapping input values to the membership functions. systems are more interpretable because both the The nodes of the third layer correspond to the fuzzy premises and consequents of the rules are fuzzy sets rules in the form of production functions; their while the Takagi-Sugeno-Kang types are more output values are the firing strengths of each rule accurate and computationally efficient, e.g. they while the nodes in the fourth layer calculate the build up more accurate models, however, here, only ratio to the sum of all rules' firing strengths. the premises of the rules are fuzzy sets. Defuzzification happens in the fifth layer and the All in all, Fuzzy Systems have the advantage that sixth layer's output nodes sum their input values. the fuzzy rules, which store the information, are Iterative learning of ANFIS is composed of two easily interpretable. Furthermore they provide a stages. In the first stage the parameters of the simple interface for extending the system with new consequent functions (in the fifth layer) are tuned information (by adding new rules) or manipulating via a least mean square method. During the second the existing rules. The problem with Fuzzy Systems stage the parameters of the premise functions (in lies in the fact that they completely depend on the the second layer) are adjusted by a backpropagation experts who design them. It only uses the algorithm. These two stages are repeated iteratively information which were encoded in the system and for training of the system. It is also worth to cannot learn on its own and it is incapable of mention that this model has the best estimation generalization. The described nature of Fuzzy accuracy based on various benchmarking and Systems indicates that a fusion with ANNs may application results. possibly lead to a new powerful computational

*4.2. FALCON Architecture*

**4. Neuro-Fuzzy System Architectures**

Approximately in the same time as ANFIS, the Fuzzy Adaptive Learning Control Network The previous section briefly described the concept (FALCON) architecture was introduced, which is a of the two main components building up a Neuro- system with five layers and uses Mamdani type Fuzzy system individually, so in this section the different architectures can be discussed to show Fig. 12. shows the FALCON architecture. Input how different approaches managed to combine nodes are located in the first layer; second layer has ANNs with Fuzzy Systems. At the end of this term nodes which represent the membership section a table is also presented summarizing the functions for the input values. Each node of the advantages and drawbacks of each presented third layer acts as a fuzzy rule. The fourth layer also consists of term nodes; these represent the membership functions for the outputs. Finally the

*4.1. ANFIS Architecture*fifth layer is the output layer; here for every output there are two nodes: one is for training data which One of the first Neuro-Fuzzy Systems was is the desired output and the other is for decision introduced by Jang in year 1993 [39][40]. This signal which is the actual output.

Fig. 13. shows the ASN component. The ASN is a five layer network which is responsible for selecting an action based on the current state of the system using fuzzy inference. Input nodes are in the first layer and the second one holds the membership functions. Each node in the third layer represents a fuzzy rule and nodes of the forth layer correspond to consequent labels, e.g. if a consequent label is in a rule then there is a link between the label's node and the rule's node. The fifth layer's nodes calculate the real output values based on the rules' firing strength and the forth layer's outputs. The AEN component of this architecture is a simple feedforward network which predicts reinforcements based on the state variables of the system. And the SAM component stochastically generates an action from based on the recommendation of the AEN GARIC uses gradient descending and reinforcement learning to adjust its internal parameters. *4.4. NEFCON Architecture *
In parallel with the models mentioned earlier, the
**Fig. 12.** The FALCON architecture

Neural Fuzzy Controller (NEFCON) architecture
had been created, which has three layers and
Training is done by a two-phase-algorithm. The
implements a Mamdani type inference system [43].
first phase is responsible for finding the initial membership functions by a self-organized learning scheme. In the second phase the parameters of the membership functions are adjusted using supervised learning. During the training nodes and links can be deleted or merged reforming the structure of the network. *4.3. GARIC Architecture *Another early Neuro-Fuzzy model is the Generalized Approximate Reasoning based Intelligence Control (GARIC) system, which is composed of three components: the Action Selection Network (ASN), the Action Evaluation
**Fig. 14.** The NEFCON architecture where x

Network (AEN) and the Stochastic Action Modifier
denote the input variables and c denotes the output
Fig. 14. Shows the NEFCON architecture where the circles indicate the nodes which are forming the layers and the rectangles indicate the shared weights of the network. The first layer consists of the input nodes, in the second layer the nodes represent the fuzzy rules and the third layer holds the output nodes. In this architecture the links connecting the nodes are weighted with fuzzy sets. The learning procedure uses reinforcement learning
with backpropagation algorithm to either learn the
**Fig. 13.** The ASN component of the GARIC

rule base from the beginning or to optimise an
architecture [42]
initially defined rule base. Two other systems were
developed based on NEFCON which are

specialized versions of the original architecture.
These systems are the NEFCLASS [44] which is
specialized in classification problems and the NEFPROX [45] which was created for function approximation. *4.5. SONFIN Architecture *Self-Constructing Neural Fuzzy Inference Network (SONFIN) is a Takagi-Sugeno-Kang-type fuzzy rule-based model which consists of six layers [46].
**Fig. 16.** The dmEfuNN architecture

Fig. 16. shows the dmEfuNN architecture. The first layer contains the input nodes and membership functions are in the second layer. Fuzzy rules are represented by the nodes in the third layer. Fourth layer selects a number of rules from the third layer which are the closest to the fuzzy inputs and the fifth layer does the defuzzification and produces
**Fig. 15.** The SONFIN architecture [46] where x1

The dmEfuNN can optimize global generalization
and x2 denote the input variables, y1 denotes the
error and local generalization error in contrast to
output variable, R1-R3 denotes the rule nodes and x
MLP and ANFIS which can only optimize global
represents the input vector
error. As the name suggests the number of nodes
and links in the structure can dynamically increase
Fig. 15. shows the SONFIN architecture which, in
or decrease during the on-line learning while off-
fact, is similar to the ANFIS. Layer 1-4 and 6 are
line training uses a given structure and optimizes
functioning as they are in the ANFIS architecture.
internal parameters.
The fifth, consequent layer can hold two types of
nodes. The first type represents the fuzzy sets by membership functions while the second type is optional and gains its inputs from the first and fourth layer. Constructing of SONFIN happens concurrently by a structure and a parameter learning method. The structure learning identifies both the precondition and consequent parts of the rules by minimizing the number of rules and membership functions for the input and by optimally generating new membership functions for the output variables. Parameter learning uses LMS or RLS algorithms to adjust consequent parameters and backpropagation for precondition parameters. *4.6. dmEfuNN Architecture *The Dynamic Evolving Fuzzy Neural Network (dmEfuNN) is a system with five layers which uses the Takagi-Sugeno fuzzy inference mechanism [47]. The predecessors of this model are FuNN [48] and EFuNN [49] which both uses the Mamdani
*4.6. Comparison of the Neuro-Fuzzy architectures *
overviewed Neuro-Fuzzy system types appointing
the main advantages and drawbacks of each
Table 2 gives a comprehensive comparison to all
** Table 2 **Advantages and drawbacks of the presented architectures.

**Architecture**

**Advantages Drawbacks**

As it implements a Takagi-Sugeno- Cannot handle multiple output systems Kang inference mechanism, it is a Only fully defined structures can be trained very accurate model (most accurate There is no dynamic rule creation or reduction among the presented architectures and more accurate than Multi-Layer Perceptron and pure Fuzzy systems) It has a learning phase for building up Its Mamdani type inference makes it less its initial structure (number of rules accurate especially for parameter estimation and membership functions can be determined via training) Its Mamdani type inference makes it more interpretable It is one of the earliest presented Isn't a single model but consists of multiple Neuro-Fuzzy system It is able to reduce the number of Its Mamdani type inference makes it less rules during its training accurate especially for parameter estimation Its Mamdani type inference makes it more interpretable There are no initial rules but rules are Not as accurate as the ANFIS (which has the created and adapted as on-line most similar structure to this) learning proceeds via simultaneous structure and parameter identification The number of generated rules and membership functions is small even for modelling of a sophisticated system During its on-line training it can Not as accurate as the ANFIS increase or decrease the number of rules in the system

**5. Conclusions**

work differently in different parts of the parameter space providing a more detailed and somehow Different applications of Neuro-Fuzzy Systems distributed model instead of a general solution. were discussed to show their high potential in The paper briefly reviewed the concept of Artificial technical diagnostics and measurement. This survey Neural Networks and Fuzzy Systems as summarizes in a comprehensive overview the computational models and how they inspired the Neuro-Fuzzy applications in technical diagnostics creation of Neuro-Fuzzy Systems. As it was and measurement with appointing the generalized, discussed this fusion can unite the generalization main, typical functionalities and with highlighting capabilities of Neural Networks with the easy their great variety of application areas. interpretability and high expressive power of fuzzy These systems are successful because of their rules in an effective way. nature that they reveal the nature of the important Six different architectures were presented and it can interdependence between the parameters of the be concluded that these are the most important ones modelled system while they are, in fact, powerful although there are other structure variations, too. approximators. Their ability to discover Usually each architecture organizes its nodes a connections between parameter intervals can be slightly different way and consequently they use extremely useful when applying the model for specific learning algorithms which are adapted to diagnostic and control tasks because entirely the different structures. The different Neuro-Fuzzy different rules can be used to specific subsets of the models were also compared and a table is also problem, e.g. these systems have the capability to presented summarizing the advantages and drawbacks of each presented architecture. ANFIS combination with GAs",

*Mechanical*All in all it can be said that ANFIS architecture is

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Source: http://eprints.sztaki.hu/8231/1/Viharos_126_2885145_ny.pdf

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