Ration power plants, to generate power, have become common worldwide. One such one is the steam power plant. In such plants, various moving parts of heavy machines generate a lot of noise. Operators are subjected to high levels of noise. High noise level exposure leads to psychological as well physiological problems; different kinds of ill effects. It results in deteriorated work efficiency, although the exact nature of work performance is still unknown. To predict work efficiency deterioration, neuro-fuzzy tools are being used in research. It has been established that a neuro-fuzzy computing system helps in identification and analysis of fuzzy models. The last decade has seen substantial growth in development of various neuro-fuzzy systems. Among them, adaptive neuro-fuzzy inference system provides a systematic and directed approach for model building and gives the best possible design parameters in minimum possible time. This study aims to develop a neuro-fuzzy model to predict the effects of noise pollution on human work efficiency as a function of noise level, exposure time, and age of the operators doing complex type of task. **Keywords:** Age, complex task, neural network, neuro- fuzzy model, noise pollution
**How to cite this article:** Ahmed HK, Zulquernain M. Expert system to predict effects of noise pollution on operators of power plant using neuro-fuzzy approach. Noise Health 2009;11:206-16 |
Introduction | | |
Neuro-fuzzy computing provides solutions for problems of varied nature which require predictions in output characteristics. The traditional equation based technique provides solutions for modeling systems with linear interrelationships. Last two decades has seen an exponentional growth in the use of model free techniques such as fuzzy logic and neural networks. This model free technique has been used to provide an alternative to accommodate the nonlinearity imprecise information found in the real world to model the complex problems. Truly speaking, the fuzzy logic has two distinct senses. In the wider prospective, fuzzy logic (FLw) is very close to fuzzy set theory while in the narrow sense, fuzzy logic (FLn) is a logical system, i.e., manifestation of multivalued logic intended to serve as logic of approximate reasoning. Currently, the use of fuzzy logic falls in the wider sense domain.^{ [1]} Fuzzy set theory is the answer to imperfection and uncertainty found in complex systems.^{ [2]} A pioneering work in fuzzy algorithm design, in the area of human thinking or decision making, was proposed.^{ [3]}
Fuzzy system is a powerful tool for modeling the human knowledge in the form of easily understandable linguistic labels. Therefore an expert in the area of fuzzy system approach can develop fuzzy IF-THEN rules for problems of varied nature. However, applicability of the approach under reference does not work when there is a need to turn linguistic knowledge of the expert with the available data. Fuzzy system does not provide system parameters in an optimized way, a must for better results. Literature surveyed on the topic revealed that different optimization techniques based on mathematical programming and optimization theory have been suggested but all of them converge to give inconclusive results.
A neural network has the characteristics of good learning capabilities. They develop suitable learning algorithm based on given input/output data pairs and adjustment of design parameters through minimization of error function. However, the neural network technique lacks in interpretation capabilities. Worded differently, it is unable to explain human-decision explicitly. Learning and interpretability embedded together in a single system is on high demand; hybridization of the two systems, i.e., neural network and fuzzy system approach seems to be possible solution. Our present investigation is to predict the effects of noise pollution on human work efficiency as a function of noise level, exposure time and age of the operators.
Noise and Performance | | |
Noise is unwanted sound that may distract attention from cues that are important for task performance. Significant background noise may negatively affect performance in a number of ways. In some cases the noise may directly affect one's ability to perform a task but there are also many ways in which noise can disturb task performance indirectly.
Noise is also recognized as a serious health problem in our modern societies.^{ [4],[5]} The effects of noise on human physical and mental performance can be divided into effects on nonauditory task performance and effects on auditory task performance (e.g. interference with speech communication, etc). Among nonauditory deleterious effects of noise, sleep disturbances are clearly studied and documented.^{ [6],[7] } On the other hand, in humans, direct effects of noise on various cognitive abilities such as long-term memory, mental arithmetic activity, visual tasks, etc have been demonstrated.^{ [8],[9]} It was reported.^{ [10]} The level of noise necessary to produce adverse effects greatly depends upon the type of task. Simple tasks remain unaffected at noise level as high as 115 dB or above, while more complex tasks get disrupted even at much lower levels. Frequency and temporal characteristics also play an important role. High frequency sound is more disruptive than low frequency sound; an intermittent noise can affect performance more adversely than continuous noise of equivalent energy. Long term exposure to noise causes noise-induced hearing loss. Obvious reason for the same is damage to sensors in the inner ear. The effect is in terms of reduced sensitivity to certain frequencies of noise. Initially reduced sensitivity usually occurs in the region of 4 kHz. As the condition becomes more severe, sensitivity is further reduced. Much research has been carried out to determine cutoff noise levels below which operators can be exposed to an eight-hour day without increased risk of hearing loss. The concept of a maximum daily noise dose can be used for the purpose of correct assessment of noise induced effects for both auditory and non-auditory type of effect. A practical approach to assessing the noise health hazard is to use the index dB (A) Leq.^{ [11]} OSHA has specified 90 dB (A) as the maximum permissible exposure to continuous noise for an eight-hour shift. Indirect effects on workers' health could include physiological responses (changes in heart rate, blood pressure, adrenalin production, etc). However, it is difficult to relate these changes directly to harmful effects on the body. Psychological responses to noise can also produce effects on mental health and emotional state especially if the noise adds to an already stressful environment. In, addition, noise also effects work efficiency. The effects on work efficiency may have serious implications for industrial workers and other occupants. Indirect effects of noise are often difficult to demonstrate and also to quantify in practice. Guidelines on their effects are therefore difficult to formulate. However, attempts can be made to assess through subjective or objective methods.
Age Related Noise Effects | | |
As age effects, sensitivity to the high frequencies is lost first and the loss is irreversible. In audiometry, such loss is described as a permanent threshold shift. Audiometric testing consists of determination of the minimum intensity (the threshold) at which a person can detect sound at a particular frequency. As sensitivity to particular frequencies is lost as a result of age or damage, the intensity at which a stimulus can be detected increases. It is in this sense that hearing loss can be described as a threshold shift. Studies have shown age decrements in performance of sustained attention tasks.^{ [12]} In yet another study it was found that although the allocation of attention across trials was similar for young and older subjects, there was an age-related increase in the time required to allocate attention within the individual.^{ [13]} It was also found that in a dual task situation reaction time (RT) for the older subjects was greater than that observed in case of the younger ones.^{ [14]} Studies reported that there was no significant age difference in situations where divided attention kind of task was involved.^{ [15]} Presence of vibrations in a working environment acts as a stressor leading to poor performance of humans with a prespecified threshold of tolerance to vibration-induced stress. The areas in which performance of operators is generally affected are visual tasks, motor tasks and cognitive tasks. In the case of grass trimmers, noise of magnitude ranging from 105 to 115 dB (A) was measured. The likely outcome of this level of noise exposure for five to six hours daily is decrement in cognitive as well as work efficiency of the workers involved in this profession. This study has been planned keeping in view this fact. A survey of literature on the theme under reference reveals that much room is still left for work in this area. However, no linkage between the type of task and associated reductions in work efficiency in the presence of noising levels of noise has been established. Perhaps predicting models can provide a solution.
Description of Study Area | | |
A 330 MW Pragati power station is located in New Delhi, latitude (28°37^{´}-28°38^{´}) at longitude (77°14^{´}-77°15^{´}) in (Income Tax Office) ITO beside the highway 0.3 Km from World Health Organization (WHO) building as shown in [Figure 1].
The noise level was measured with the help of Cirrus sound level meter, model CR: 710B, UK. The instrument is sensitive to sound pressure between 20 and 20000 HZ was used to measure the noise level calibrated by microphone adapter. The range and sensitivity of the instrument is 30 dB(A) to 100 dB(A) for low sound pressure and 60 dB(A) to 130 dB(A) for high sound pressure with accuracy plus/minus three per cent.^{ [16]} The noise level was recorded at distances of 1.5-3 meters on the base where the cumulative noise was expected from different sources or at workers, monitoring was done at a height of 1.5 meter and one meter away from the chest covering 20 locations for 30 minutes at an interval of 15 seconds.
Prior to the actual experiment, the need to find out noise induced effects qualitatively among the workers was felt. Prior consent was taken from workers and a questionnaire form Appendix was arranged for this purpose. Three hundred workers were questioned about the age, exposure time, type of task, and workers performance for three interval time, two, five, and eight hours respectively. The task on which the present study is based is categorized on the basic of difficulty.
Cognitive performance of workers largely depends upon the type of task they perform e.g. simple task or complex task. In this study, study workers were operating in the occupational environment under the impact of noise and heat both. According to,^{ [17]} heat generally produces performance decrement at temperatures above (about) 26.7° to 29.4°C. Heat stress interacts with an individual's existing state of arousal and may lead to performance increment or decrement; depending on an individual's existing state making the task complex. During summer, for different levels of parameters, i.e., noise levels, ages and exposure time, the effect of high temperature makes the task complex and further reduces the cognitive performance of the worker. The average ages for young, medium, and old groups were 22.5, 43, and 56.6 years respectively. Three hundred workers were questioned by the questionnaire forms. Only 130 workers matched complex task criteria of the present study. The remaining represented other kinds of task and hence their tasks were cancelled.
Neuro-Fuzzy Computing | | |
Neuro-fuzzy computing is a judicious integration of the merits of neural and fuzzy approaches. This incorporates the generic advantages of artificial neural networks like massive parallelism, robustness, and learning in data-rich environments into the system. The modeling of imprecise and qualitative knowledge as well as the transmission of uncertainty is possible though the use of fuzzy logic. Besides these generic advantages, the neuro-fuzzy approach also provides the corresponding application specific merits.^{ [18],[19],[20]} Some of the neuro-fuzzy systems are popular by their shorts names. For example ANFIS,^{ [21]} DENFIS,^{ [22]} SANFIS^{ [23]} and FLEXNFIS,^{ [24]} etc.
Our present model is based on adaptive neuro-fuzzy inference system (ANFIS). An ANFIS is a fuzzy inference system implement in framework of adaptive neural networks. ANFIS either uses input/output data sets to construct a fuzzy inference system whose membership functions are tuned using a learning algorithm or an expert may specify a fuzzy inference system and then the system is trained with the data pairs by an adaptive network. The conceptual diagram of ANFIS based on latter approach shown in [Figure 2] consists of two major components - fuzzy inference system and adaptive neural network. A fuzzy inference system has five functional blocks. A fuzzifier converts real numbers of input into fuzzy sets. This functional unit essentially transforms the crisp inputs into a degree of match with linguistic values. The database (or dictionary) contains the membership functions of fuzzy sets. The membership function provides flexibility to fuzzy sets in modeling commonly used linguistic expressions such as "the noise level is low" or "person is young."A rule base consist of a set of linguistic statements of the form, if *x* is *A* then *y* is *B*, where *A* and *B* are labels of fuzzy sets on universes of discourse characterized by appropriate membership function of database. An inference engine performs the inference operations on the rules to infer the output by a fuzzy reasoning method. Defuzzifier converts the fuzzy outputs obtained by inference engine into a non-fuzzy output real number domain.
In order to incorporate the capability of learning from input/output data sets in fuzzy inference systems, a corresponding adaptive neural network is generated. An adaptive network is a multilayer feed-forward network consisting of nodes and directional links through which nodes are connected. As shown in [Figure 2], layer 1 is the input layer, layer 2 describes the membership functions of each fuzzy input, layer 3 is inference layer and normalizing is performed in layer 4. Layer 5 gives the output and layer 6 is the defuzzification layer. The layers consist of fixed and adaptive nodes, each adaptive node has asset of parameters and performs a particular function (node function) on incoming signals.
The learning model may consist of either back propagation or hybrid learning algorithm, the learning rules specifies how the parameter of adaptive node should be change to minimize a prescribed error measure.^{ [25]} The change in values of the parameters results in change in shape of membership functions associated with fuzzy inference system.
System Modeling | | |
The modeling process based on ANFIS can broadly be classified in three steps:
** Step 1: System identification**
The first step in system modeling is identification of input and output variables called system's Takagi-Sugeno-Kang (TSK) model;^{ [21,22]} by which antecedents are defined be a set of non-linear parameters and consequents are either linear combination of input variables and constant terms or may be constants, generally called, singletons.
** Step 2: Determining network structure **
Once the input and output variables are identified, the neuro-fuzzy system is realized using a six-layered network as shown in [Figure 3] the input, output and node functions of each layer are explained in the subsequent paragraphs.
*Layer 1 (input layer) *
Each node in layer 1 represents the input variables of the model identified in step 1 this layer simply transmits these input variables to the fuzzification layer.
*Layer 2 (fuzzification layer)*
The fuzzification layer describes the membership function of each input fuzzy set, membership functions are used to characterize fuzziness in fuzzy sets, the output of each node *i* in this layer is given by μ_{Ai} (x_{i})where the symbol μ_{A}(x) is the membership function. Its value on the unit interval (0, 1) measure the degree to which elements *x* belongs to the fuzzy set *A*, *x*_{ i} is the input to the node *i* and *A*_{ i} is the linguistic label for each input variable associated with this node.
Each node in this layer is an adaptive node, i.e. the output of each node depends on parameters pertaining to these nodes. Thus the membership function for *A* can be any appropriate parameterized membership function. The most commonly used membership functions are triangular, trapezoidal, Gaussian, and bell shaped. Any of these choices may be used, for specifying fuzzy sets as they are non-linear and smooth and their derivatives are continuous gradient methods can be used easily for optimizing their design parameters. Thus in this model, we have used bell shapes memberships functions. The bell or generalized bell (or gbell) shaped membership function is specified by a set of three fitting parameters {*a,b,c*} as:
The desired shape of gbell membership function can be obtained by proper selection of the parameters. More specifically, we can adjust *c* and *a* to vary the center and width of membership function, and *b* to control the slope at the crossover points. The parameter *b* gives gbell shaped membership function one more degree of freedom than the Gaussian membership function and allows adjusting the steepness at crossover points. The parameters in this layer are referred to as premise parameters.
*Layer 3 (inference layer)*
The third layer is inference layer. Each node in this layer is fixed node and represents the IF part of a fuzzy rule. This layer aggregates the membership grades using any fuzzy intersection operator which can perform fuzzy AND operation.^{ [23]} The intersection operator is commonly referred to as T-norm operators are min or product operators. For instance
IF *x*_{ 1} is *A*_{ 1} AND *x*_{ 2} is *A*_{ 2} AND *x*_{ 3} is *A*_{ 3 }THEN *y* is *f*(*x*_{ 1},* x*_{ 2,} x_{ 3})
Where *f*(*x*_{ 1},* x*_{ 2,} x_{ 3}) is a linear functions of input variables or may be constant, the output of *i*th node is given as:
*Layer 4 (normalization layer) *
The *i*th node of this layer is also a fixed node and calculates the ratio of the *i*th rules' firing strength in interference layer to the sum of all the rules firing strengths:
Where *i* =1, 2, ,* R* and *R* is total number of rules. The outputs of this layer are called normalized firing strengths.
*Layer 5 (output layer)*
This layer represents the THEN part (i.e., the consequent) of the fuzzy rule. The operation performed by the nodes in this layer is to generate the qualified consequent (either fuzzy or crisp) of each rule depending on firing strength. Every node *i* in this layer is an adaptive node. The output of the node is computed as
Where is normalized firing strength from layer 3 and f_{i} is a linear function of input variables of the form (*p*_{ i} x_{ 1} +q_{ i} x_{ 2} +r_{ i})where {*p*_{ i} , q_{ i} , r_{ i}} is the parameter set of the node *i*, referred to as consequent parameters or *f* may be a constant if *f*_{i} is linear function of input variables then it is called first order Sugeno fuzzy model and if *f*_{i} is a constant (as in our present model) then it is called zero order Sugeno fuzzy model. This consequent can be linear function as long as it appropriately describes the output of the model within the fuzzy region specified by the antecedent of the rule. But in the present case, the relationship between input variables (noise level, exposure time, and age) and output (reduction in work efficiency) is highly non-linear. In the Sugeno model, consequent can be taken as singleton, i.e. real numbers without losing the performance of the system.
*Layer 6 (defuzzification layer)*
This layer aggregate the qualified consequent to produce a crisp output. The single node in this layer is a fixed node. It computes the weighted average of output signals of the output layer as:
** Step 3: Learning algorithm and parameter tuning**
The ANFIS model fine-tunes the parameters of membership functions using either the back propagation learning algorithm^{ [24] } or hybrid learning rule (fuzzy logic toolbox for use with MATLAB).^{ [26] } Back propagation algorithm is an error-based supervised learning algorithm. It employs an external reference signal, which acts like a teacher and generate an error signal by comparing the reference with the obtained response. Based on error signal, the network modifies the design parameters to improve the system performance. It uses gradient descent method to update the parameters. The input/output data pairs are often called as training data or learning patterns. They are clamped onto the network and functions are propagated to the output unit. The network output is compared with the desired output values. The error measure *E*^{ P}, for *P* pattern at the output node in layer 6 may be given as:
Where T^{p} is the target or desired output and O^{p}_{6} the single node output of defuzzification layer in the network. Further the sum of squared errors for the entire training data set is:
The error measure with respect to node output in layer 6 is given by delta (δ):
This delta value gives the rate at which the output must be changed in order to minimize the error function, since the output of adaptive nodes of the given adaptive network depend on the design parameters so the design parameters must be updated accordingly. Now this delta value of the output unit must be propagated backward to the inner layers in order to distribute the error of output unit to all the layers connected to it and adjust the corresponding parameters the delta value for the layer 5 is given as:
Similarly for any *k*^{}th layer, the delta value may be calculated using the chain rule as:
Now if α is a set of design parameters of the given adaptive network then:
Where *P* is the set of adaptive nodes whose output depends on α thus update for the parameter α is given by:
Where η is the learning rate and may be calculated as:
Where 'k' is the step size. The value of k must be properly chosen as the change in value of k influences the rate of convergence
Thus the design parameters are tuned according to the real input/output data pairs for the system .The change in value of parameter results in change in shape of membership functions initially defined by an expert .The new membership functions thus obtained after training gives a more realistic model of the system the back propagation algorithm though widely used for training neural networks may suffer from some problems. The back propagation algorithm is never assured of finding the global minimum. The error surface may have many local minima so it may get stuck during the learning process on flat or near flat regions of the error surface. This makes progress slow and uncertain.
Another efficient learning algorithm which can be used for training the network is hybrid learning rule. Hybrid learning rule is a combination of least square estimator (LSE) and gradient descent method (used in back propagation algorithm). It converges faster and gives more interpretable results. The training is done in two passes. In forward pass, when training data is supplied at the input layer, the functional signals go forward to calculate each node output. The non-linear or premise parameters in layer 2 remain fixed in this pass. Thus the overall output can be expressed as the linear combination of consequents parameters. These consequents parameters can be identified using least square estimator (LSE) method. The output of layer 6 is compared with the actual output and the error measure can be calculated as in equations 6-7. in backward pass , error rate prorogates backward from output end toward the input end and non-linear parameters in layer 2 are update using the gradient descent method [equations (8-13)] as discussed in back propagation algorithm . Since the conquest parameters are optimally identified using LSE under the condition that the premise parameters are fixed, the hybrid algorithm converges much faster as it reduces the search space dimensions of the original pure back propagation algorithm.
Implementation | | |
We have implemented our model using ANFIS.^{ [26]} The system is first designed using Sugeno fuzzy interference system. It is three inputs-one output systems. The input variables are the noise level, exposure time, and age and the reduction in work efficiency is taken as the output variable. The input parameters are represented by fuzzy sets (or linguistics variables). We have chosen gbell shaped membership functions to characterize these fuzzy sets. The membership functions for input variables are shown in [Figure 4].
The membership functions are then aggregated using T-norm product to construct fuzzy IF-THEN rules that have a fuzzy antecedent part and constant consequent. The total number for rules is 27. Some of the rules are given below:
R6: IF noise level is low AND exposure time is medium AND age is old THEN reduction in work efficiency is approximately 4%.
R18: IF noise level is high AND exposure time is long AND age is old THEN reduction in work efficiency is approximately 25%.
R25: IF noise level is very high AND exposure time is long AND age is young THEN reduction in work efficiency is approximately 50%.
After construction of fuzzy inference system, the model parameters are optimized using ANFIS. The network structure consists of 78 nodes. The total number of fitting parameters is 54, of which 27 are premise and 27 are consequent parameters. A hybrid learning rule is used to train the model according to input/output data pairs. The data pairs were obtained from steam power plant workers using questionnaire it was established for this purpose, out of the total 130 input/output data sets 109(80%) data pairs were used for training the model. the model was trained for 50 epochs with error step size of 0.01 (automatically selected by the ANFIS) and error tolerance 0%. to validate the model 26(20%) data sets were used testing purpose.
Result and Discussion | | |
The model was trained for 50 epochs and it was observed that the most of the learning was completed in the first 38 epochs as the root mean square error (RMSE) settles down to almost 0.09% at 38^{ th} epoch. [Figure 5]a shows the training RMSE curve for the model after training the fuzzy inference system. It is found that the shape of membership function is slightly modified. And data tested as shown in [Figure 5]b for model validity.
This is because of the close agreement between the knowledge provided by the expert and input/output data pairs. Hence, the impact of the noise level on human work efficiency is represented in the form of graphs in [Figure 6] with the ages as parameters for different exposure time. The reduction in work efficiency up to the noise level of 85 dB(A)is almost negligible for all ages irrespective of exposure times assuming effects of 25% reduction in work efficiency as negligible [Figure 6](a) show the reduction in work efficiency versus noise level with "short"(0-2h)exposure time for 'young', 'medium', and 'old' ages . The work efficiency reduced to almost 27 and 33% at 105 dB (A) and above noise level s for 'medium' and 'old' ages but the 'young' age remain 'unaffected'.
From [Figure 6](b) it is to be observed that the work efficiency is not affected (only 17%) at 100 dB (A) for 'young' age whereas for 'medium' and 'old' ages the reduction in work efficiency is 30 and 50% respectively at the same noise levels for 'medium' exposure times. However, the reduction in work efficiency is almost 23, 42, and 63% for 'young', 'medium' and 'old' ages, respectively at 105 dB(A) and above noise levels.
[Figure 6]c depicts the reduction in work efficiency with noise level at 'long' exposure time for 'young', 'medium', and 'old' ages. it is evident from this figure that the reduction in work efficiency is negligible up to the noise level of 90 dB(A) for 'young' and 'medium' age group of operators while it is about 30% for 'old' ages the work efficiency start reducing after 90 dB(A) even for 'young' and 'medium' ages. At 100 dB(A), work efficiency reduces to 29% , 47% and 62% for 'young', 'medium' and 'old' ages, respectively . There is significant reduction in work efficiency after 100 dB(A) for all ages. When noise level is in the interval of 110-115 dB(A), it is 45% for 'young', 68% for 'medium' , and 90% for 'old' ages , respectively.
An alternative representatioan to [Figure 6]a-c discussed above is shown in [Figure 7]a-c, in which the reduction in work efficiency with noise level for 'short', 'medium' and 'long' exposure times at deferent ages is presented the following inference are readily down:
- If age is 'young' as shown in [Figure 7]a the work efficiency reduces to 18% for 'medium' and 28% for 'long' exposure times while it reduces to eight per cent for 'short' exposure time at 100 dB(A) above noise levels.
- In case of 'medium' age, the work efficiency is reduced to 30%, 48%, and 67% at 110 dB(A) for 'short', 'medium' and 'long' exposure times respectively, as is evident from [Figure 7]b.
- For 'old' ages, the reduction in work efficiency occurs even at much lower noise levels as can be observed from [Figure 7]c it is 35%, 70%, and 88% at 110 dB(A) for 'short', 'medium' and 'long' exposure times, respectively.
To validate the model, we have compared some of our model results with deduction based on the criterion of safe exposure limit recommended for industrial workers. The Recommended Exposure Limit (REL) for workers engaged in occupation such as engineering controls, administrative controls, and/or work practices is 85 dB(A) for 8 h duration (National Institute for Occupational Safety and Health. DHEW ((NIOSH) (1996)).^{ [27] } DHEW ((NIOSH) (1972)).^{ [28]} Also recommended a ceiling limit of 115 dB(A). Exposure to noise levels greater than 115 dB (A) would not be permitted regardless of the duration of the exposure time. There is almost no (zero per cent) reduction in work efficiency when a person is exposed to the maximum permissible limit of 85 dB (A) for eight hours and maximum (100%) reduction in work efficiency for a noise exposure of 105-115 dB(A) for eight hours.
Conclusion | | |
The main thrust for the present work has been to develop a neuro-fuzzy model for the prediction of work efficiency as a function of noise level, exposure time and age. It is evident from the graph that work efficiency, for the same exposure time, depends to a large extent upon the noise level and age. It has also been verified that young age group of people are not affected even at very high noise level while old ages get significantly affected at much lower noise level. It is to be appreciated that the training done using ANFIS is computationally very efficient as the desired RMSE value is obtained in very less number of epochs. Moreover, minor changes are observed in the shape of the membership functions after training the model. This is because of close agreement between the knowledge provided by expert and input/output data pairs.
Acknowledgement | | |
The authors thank Mr. Arshad Noor Siddiquee, Associate Professor, Mechanical Engineering Department, Jamia Millia Islamia, New Delhi, India for his constructive ideas and support.
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**Correspondence Address**: Hameed Kaleel Ahmed Department of Mechanical Engineering, Jamia Millia Islamia, New Delhi-110 025 India
**Source of Support:** None, **Conflict of Interest:** None
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**DOI:** 10.4103/1463-1741.56214
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7] |