Neuro-Fuzzy Risk Calculation Model for Physiological Processes

Neuro-Fuzzy Risk Calculation Model for Physiological Processes

E. Tóth-Laufer^*, M. Takács^** and I.J. Rudas^**

* Óbuda University/Doctoral School of Applied Informatics, Budapest, Hungary

** Óbuda University/John von Neumann Faculty of Informatics, Budapest, Hungary laufer.edit@bgk.uni-obuda.hu, takacs.mart@nik.uni-obuda.hu, rudas@uni-obuda.hu

Abstract—In this paper a neuro-fuzzy risk calculation model based on the authors’ former validated hierarchical multilevel risk calculation model will be introduced. In the basic fuzzy model a fuzzy logic controller was replaced with a neural network subsystem. In this way the membership function later will be tuned depending on the patients’

characteristics. The two models were tested using several typical groups of the patients to validate the novel neuro- fuzzy model.

I. INTRODUCTION

Today it is becoming increasingly important to establish an adequate quality of life. Sport and physical exercises can make one healthier, while the lack of sport can deteriorate the health status. It is also important to note that inadequate form, intensity or duration of movement can be dangerous. The authors’ models focus on the risk occurring during sport activity, by examining physiological processes. Both models to calculate the risk level of the sport activities, explained in the paper, have a hierarchical multilevel decision structure to simplify the evaluation and it makes the model structure easily expandable. The basic model uses fuzzy logic-based decision making and into that was integrated a neural network model combining the benefits of the two approaches.

The fuzzy logic-based decision making is very beneficial when there is uncertainty, imprecision and subjectivity in data and in evaluation process. These techniques are particularly useful when there is insufficient reliable data for statistical model description, the cause and effect relationship is imprecise or the observations and conditions can be described in linguistic form [4]. Consequently the fuzzy approach provides more realistic result in a user-friendly way [15].

The neural network is a computational structure for large-scale systems involving a large number of special type coupled processors called neurons. These neurons can be connected together according to the problem with well-defined typical topologies represented by directed graph [5]. An important feature of the neural network is the learning algorithm which is generally based on patterns. To apply the learned information, it has a recall algorithm. The processing elements of the network are organized into layers according to their tasks. Neurons located in the same layer have the same or similar local processing [6].

The neural networks are not able to explain the steps leading to the decision making and rules cannot be incorporated into the system. This deficiency can be handled with fuzzy approach by appropriate settings of the problem in the fuzzy rule layer. In this way the evaluation will be more efficient [7]. Using the neural network, the fuzzy membership functions and rules can be tuned and in this way later the membership functions and rules can be adjusted to the patient characteristics.

II. BASIC MODEL STRUCTURE

The evaluation model has a hierarchical structure based on an AHP-FCE model structure [1] as it is shown in Fig.

1. The model structure from left to right follows the logic of the evaluation process. The lowest level of the hierarchy there are sub-factors, which are grouped according to the type of the factors. Each group has a Fuzzy Logic Controller (FLC) to evaluate their risk and the results are transmitted to the next highest level, where the total risk level is calculated, with an FLC again, depending on the patient. The rules of the FLC-s were set up with a contribution of a trainer. The first group of risk factors is Medical condition with sub-factors Disease condition (dis_con), Current physical status (phy_sta) and Basic physical information (bas_inf). Disease condition is maybe the most important among the sub-factors, because it fundamentally determined the load-ability of the patient.

This sub-factor includes such persistent diseases as hypertension, diabetes and cardiac diseases among others.

Current physical status is used to assess the actual parameters of physical condition as pulse or blood pressure. Basic physical information is about age, sex and the living conditions, such as occupational stress and activity.

The next group refers to the characteristics of the sport activity. These parameters describe how intensively (Intensity), how long per occasion (Duration) and how many times per week (Frequency) the patient does this activity.

The third main group is Environmental condition, this is mainly important regarding outdoor sports, but humidity and temperature together can influence the risk level indoor too. Here at the sub-factors temperature is combined with two other parameters, these are humidity and wind. The reason for this combination is that they can influence the thermal sensation together [2].

The model uses Mamdani-type inference system and based on the authors’ former study sum method is used as aggregation, and bisector method for defuzzification [8].

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Figure 1. The basic model structure

III. NEURO-FUZZY MODEL STRUCTURE

The novel neuro-fuzzy model was created based on the basic model and the authors’ goal was to implement a novel system which is equivalent to the former. The most patient-specific group is Medical condition, because this group has the most interaction between the input parameters. For these reasons this group is most needed to tune the membership functions in the future, therefore the Fuzzy Logic Controller of this group should be substituted with a neural network subsystem. Due to the easily expandable structure of the basic model only the corresponding fuzzy logic controller must be replaced with the neural network subsystem, the rest of the model structure does not change as it is shown in Fig. 2. The structure of the subsystem in the novel model is based on the ANFIS structure for Mamdani-type inference system with fixed membership function parameters.

If the fuzzy inference system is considered with two inputs x and y and one output z, the Mamdani fuzzy model with two rules can be represented as follow:

IF x is A1 and y is B1 then Z=C1 (1)

IF x is A2 and y is B2 then Z=C2 (2) The nodes in the same layer have similar functions and the output of the j^th node in the i^th layer denoted as Oi,j. The structure of this system is shown in Fig. 3. and the output of each layer is described in the following [13].

The first layer is the input layer with the risk factors of group medical condition. These inputs determined which group the patient belongs to. For the next layer these inputs must be fuzzified with (3),(4).

( ) ^x

O

_1i,

= μ

_Ai ^{, i=1,2 (3)}

( ) ^y

O

1i,

= μ

Bi₋2 ^{, i=3,4 (4)}

O1,i(x) is the membership degree of the fuzzy set A=(A1, A2, B1, B2) and it specifies the degree the input parameters matching. The membership functions are trapezoid shape as it is given in (5).

⎪ ⎪

⎪ ⎪

⎩

⎪⎪ ⎪

⎪

⎨

⎧

≤

≤

− ≤

− ≤ ≤

≤

− ≤

− ≤

= μ

x d 0

d x c c

d x d

c x b 1

b x a a

b a x

a x 0

i i i

i i i

i i

i i

i i

i

i

A (5)

where ai, bi, ci, di are the parameter set. These parameters for the time are fixed, but later by changing that the membership functions can be tuned.

The second layer is the inference layer or the rule layer whose output is the fire strength of the rule and calculated with min method by (6).

( ) ( )

( ^{x , y} )

min w

O

_2i,

=

_i

= μ

_Ai

μ

_Bi , i=1,2 (6) The third layer is the consequent layer and obtains the consequent part of the rules. O3,i(wi) is the membership degree of the fuzzy set C=(C1, C2) and it specifies the degree the input parameters matching to the consequent membership input function.

( )

i C i,

3

w

O = μ

_i ⁽⁷⁾

The membership functions are given with Matlab built- in methods, S-shaped, “product of two sigmoids” and Z- shaped membership function (psigmf). The S-shaped function belongs to the very dangerous risk level. Going from left to right this function increases from 0 to 1 and the parameters a and b locate the left and right extremes of the sloped portion of the curve. Dangerous, medium and safe risk levels are represented with psigmf function calculated by (8). The Z-shaped membership function belongs to the very safe risk level. Going from left to right this function decreases from 1 to 0 and the parameters a and b locate the left and right extremes of the sloped portion of the curve.

( )

ak₍x ck₎

k

1 e

x 1

f

_{− −}

= +

^{, k=1,2 (8)}

where the parameters a1 and a2 control the slopes of the left and right curves. The parameters c1 and c2 control the points of inflection for the left and right curves [14].

The fourth layer has the same inputs as the first layer and the links of the nodes are weighted by firing strength of the consequent output. The output of this node is generated with the product method by (9).

( )

i C i,

4

x y w

O = D D μ

i (9)

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The neural network subsystem in the authors’ model is based on Fig. 2, but there are higher number of rules applied to the input parameters and its number increase exponentially the number of the nodes. The Medical condition group has three input parameters and belongs to each of them five trapezoid shape membership functions relating to the input layer and five membership functions relating to the consequent layer as above described. The number of applied rules in this group is one hundred and twenty-five.

The fifth layer is the fuzzy aggregation layer, it uses the sum operator calculated by (10).

∑ ^μ ( )

=

C i

5

x y w

O D D

i (10)

The sixth layer is the output layer, calculated the risk level for input parameters by normalized aggregation with the outputs of the consequent layer result.

Figure 2. Structure of the neuro-fuzzy model

Figure 3. Structure of the subsystem for two inputs and two rules

IV. COMPARISON OF THE M^ETHODS A. Test environment

Both models were implemented in Matlab – Simulink, Fuzzy Logic Toolbox environment and the test was executed for several typical groups of the patients. The patients’ medical condition parameters were selected based on the American Heart Association Guidelines [8], [9], [10], [11], [12]. The test groups are “Average healthy adult,” “Middle-aged with light cardiac disease,” “Healthy senior,” and “50-65 years old in poor condition”. Group-

specific parameters for each group are shown in Table I.

The authors have tested both models with each test groups for four hundred and eighty different cases. The goal was to validate the novel neuro-fuzzy model.

B. Result of the comparison

Several metrics have been calculated to characterize the deviation of the neuro-fuzzy model results from the fuzzy model results. These metrics are minimum, maximum, mean, standard deviation (Deviation) and average absolute deviation of the average (Av. D. Av.) and correlation coefficient (Correlation) of the two models was also calculated. These metrics for each test group is shown in Table II. It has been found from these metrics that the calculated risk level for two groups, Average healthy adult and Healthy senior, is almost the same with both methods.

The average difference for these groups is less than 1%, the standard deviation is about 0.01 and the correlation coefficient is close to 1. Based on these values the difference between the two models for the above two groups is negligible. The calculated metrics for the Middle-aged person with light cardiac disease the metrics are slightly worse, but also favorable. For this group the average difference is about 6% but the range for each risk level is 20%. The correlation coefficient is 0.85 and the maximum deviation from the authors’ former model result is about 0.1, but the minimum deviation is zero.

For 50-65 years old in poor condition group the values of average and minimum difference, the standard deviation and the average absolute deviation of the average are also acceptable. For this group the maximum difference and correlation coefficient are worse than expected. Summarizing the above it can be concluded, that the novel neuro-fuzzy model is acceptable, but there is a need to examine the reason of the last group’s worse results.

TABLE II.

RESULT OF THE COMPARISON

Metrics Healthy adult

Middle- aged

Healthy senior

50-65 y.

old Minimum 0.000000 0.000000 0.00000 0.000000 Maximum 0.027779 0.107630 0.04743 0.161262 Mean 0.009032 0.064999 0.00964 0.036542 Deviation 0.010820 0.030189 0.01499 0.040234 Av. D. Av. 0.009762 0.025136 0.01203 0.035444 Correlation 0.995017 0.853068 0.99433 0.780578

∑

TABLE I.

MEDICAL CONDITION PARAMETERS

Group Dis_con Phy_sta Bas_inf

Average healthy adult 0.5 0.5 0.5 Middle-aged with light

cardiac disease 0.4 0.4 0.7

Healthy senior 0.64 0.5 0.3

50-65 years old in poor

condition 0.25 0.3 0.5

A1

A2

B1

B2

C1

C2

x y

min min

W1

W2 ∑ N

x y

∏

∏

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Depending on the result of this examination the model should be improved and in this way the results could be better.

C. Future development

The large rule base causes the system to be over-fitting and loses the capability of generalization, therefore the number of rules should be decreased. Consequently one of the tasks is to identify the appropriate methods.

Membership function parameters are actually fixed, but they should be tuned depending on the patient characteristics in the future. In this way the results of the fourth group may also become better. For this task this novel model provides a good framework.

Further investigation may be made regarding whether it is necessary for the other fuzzy logic controller to be replaced with a neural network subsystem.

V. CONCLUSION

A fuzzy logic-based decision making the model combined with the neural network subsystem has the advantages of both approaches. The neural network itself regarded the process as a black box, it is not able to explain the steps leading to the decision making and rules cannot be incorporated into the system. This problem can be handled by fuzzy approach due to the incorporation of a fuzzy rule layer. In this way the evaluation will be more efficient [7]. It is important in these kinds of applications that the membership functions and rules are patient- specific. This can be solved by using the neural network, because it can tune the fuzzy membership functions and rules.

The authors compared a fuzzy logic-based model with a fuzzy model that contains a neural network subsystem in Matlab Simulink – Fuzzy Logic Toolbox environment.

Both models have a hierarchical multilevel decision structure and they are used for body physical exercise risk level calculation. The test was executed for four typical groups of the patient for four hundred and eighty different input parameter combinations. The goal was to validate the novel neuro-fuzzy model. Based on the calculated results the novel introduced neuro-fuzzy model is acceptable for each group that was tested. Both method have almost the same result for two groups (Average healthy adult and Healthy senior), here the correlation coefficient is close to one and the other metrics are also very favorable. The third group (Middle-aged person with light cardiac disease) has slightly worse results, but they are also completely acceptable. The correlation coefficient of the fourth group (50-65 years old in poor condition) is worse than it is expected, but with tuning the membership functions the outcome can be improved.

ACKNOWLEDGMENT

The authors gratefully acknowledge the grant provided by the project TÁMOP-4.2.2/B-10/1-2010-0020, Support of the scientific training, workshops, and establish talent management system at Óbuda University, Vojvodina Academy of Science and Art (title of the project:

Mathematical Models for Decision Making under Uncertain Conditions and Their Applications ) and the Hungarian Scientific Research Fund (OTKA K 105846).

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