1 Introduction

Today, all the manufacturing processes generate large amount of harmful substances in various forms such as solid, liquid and gases, which results in serious occupational health and environmental issues (Sivapirakasam et al. 2011). Also, the process used for manufacturing is considered to be an energy-intensive activity that indirectly affects the environment apart from the generation of wastages only (Tan et al. 2002; Yeo et al. 1998). Minimization of these issues in the manufacturing industries is a challenging task. In order to improve the efficiency as well as minimization of environmental impacts during the manufacturing process, an advance manufacturing mode called green manufacturing (GM) is presented (Sheng and Srinivasan 1995).

The performance of the GM process and amount of waste generated from it depend on various process parameters which are directly or indirectly effects on the efficiency of the process. Traditionally, the preferred process parameters are determined based on the operator experience or handbook values and this does not ensure the optimal performance of machining (Weller 1984). Also, the selection of process parameters based on expert’s judgment is not an ideal approach, since human decisions are usually determined according to general attributes of limited and unstructured experience. Moreover, GM process is considered to be a complex system with many interlinking process parameters considering the multiple responses. These process parameters are again highly complex and nonlinear in nature, and it is therefore very difficult to develop an exact mathematical model to control the GM process. In spite of these reasons, the process parameters selection for any machining process is considered to be a still ill-defined optimization problem and involves degree of uncertainty, imprecise and subjective data and vagueness information, which makes the optimization process more complex and challenging (Yadav and Patel 2013). Therefore, effective modeling and optimization of process parameters are an essential requirement for GM process.

In the literature, several investigators have proposed numerous techniques for modeling and optimization of various systems such as Deng et al. (2012) proposed a novel two-stage hybrid swarm intelligent optimization algorithm which comprises of genetic algorithm (GA)–particle swarm optimization (PSO)–ant colony optimization algorithms. The various benchmark traveling salesmen problems (TSP) have been tested to show the effectiveness and working significance of the proposed algorithm. They found that GA–PSO–ACO algorithm dominances the existing algorithms and greatly improves the computing efficiency. Also, the experimental results exhibit that faster and better convergence when the scale of TSP increases. In another research, Deng et al. (2015) proposed an improved chaotic ant colony optimization (CACO) algorithm based on adaptive multi-variant strategies (AMS) for solving complex optimization problems. The parameter optimization of PID controller has been done to show the effectiveness and working significance of the CACOAMS algorithm. The simulation result shows that the CACOAMS algorithm found to be feasible in optimizing the PID controller process parameters. Similarly, Deng et al. (2017a) also presented an optimization method for solving the complex optimization problems. The work proposed collaborative optimization (MGACACO) algorithm is based on the GA, ACO, the chaotic optimization method, multi-population strategy, adaptive control parameters and collaborative strategy. An experimental study has been carried out using 28 TSP instances and batches of 30 tries. Later, performance of the MGACACO algorithm has been done by comparing the results MGACACO algorithm results of GA, ACO, PGACS, Pasti’s method, Marinakis’ method and Escario’ method. It has been observed that MGACACO algorithm provides better results compared to the results of the other algorithms.

In another theoretical model, Deng et al. (2017b) discussed on novel intelligent method for detection and diagnosis of early faults in the rotating machinery. The proposed method consists of least squares support vector machines (LS-SVM) with particle swarm optimization (PSO) algorithm. They used LS-SVM method for classifying the fault while PSO for optimization of the parameters. Later, the justification of the intelligent model has been carried out using experiments of motor bearing. The experimental results showed that LS-SVM method outperforms the other mentioned methods and provides a better result for fault diagnosis of rotating machinery. Similarly, in the same year, Deng et al. (2017c) presented the performance study of improved adaptive PSO algorithm by solving the multi-objective gate assignment problem for effective assigning the gates to different flights in different time. The typical flight schedule for one day in the airport has been taken for the study. Further, proposed algorithms have been tested comparing the results of other methods like GA, SA, TS, MA, SATS, HGA, ESWO, BB-BC and BA-ACO algorithms. It has been found that optimization performance of the proposed improved adaptive PSO algorithm found to be better than GA, SA, TS, MA, SATS, HGA, ESWO, BB-BC and BA-ACO algorithms and also provides a valuable reference for assigning the gates in hub airport, balances the utilization rate of gates, reduces the walking distance and improves the service level of the airport. Xiong et al. (2017) presented a novel reversible data hiding (RDH) scheme for encrypted digital images. They used integer wavelet transform, histogram shifting and orthogonal decomposition method for encrypted digital images. The validation of the scheme has been done based on the experimental data and results which shows that proposed scheme outperforms the other existing scheme and provides better results. Zhao et al. (2017a) proposed a feature extraction method called EDOMFE method based on integrating ensemble empirical mode decomposition (EEMD), mode selection and multi-scale fuzzy entropy. The effectiveness of the proposed method has been validated by considering the real bearing vibration signals of motor with different load and fault difficulties. It was observed from the results that proposed EDOMFE method has been capable to extract fault feature from the vibration signal. The work also suggested that proposed method can be used as a framework model for fault diagnosis technology for rotating machinery. Zhao et al. (2017b) presented a new strategy for suppression of vibration in motor using fractional-order control strategy. They used fractional proportional-integral-derivative (PID) and integer-order proportional-integral-derivative (PID) controller for adjusting the input current to control the 15 kW and 1.5 kW motor. The experimental result shows that fractional-order PID controller has the multipoint control over integer-order PID controller and can be used for better method for vibration suppression of rotating machinery. Wang et al. (2017) presented the theoretical simulation of two multiplicative mulitiwatermaking decoders, i.e., optimum and locally optimum for copyright protection. Later, experimental results have been used to confirm the validity of the theoretical and empirical analysis. It has been found that proposed schemes found to be feasible and better to design a multi-bit mulitiwatermaking for copyright protection. Tian and Chen (2017) presented the demonstration of correlation representation learning (CRL) for cross-heterogeneous database age estimation. They developed first, correlation component manifold space learning (CCMSL) to learn a common feature space from heterogeneous aging database, and then CRL model was used to perform cross-heterogeneous database age estimation in the resulting common sample space. Later, illustration of the model was done through experimental and shows that model provides found to be feasible and comparable. Xue et al. (2018) proposed a new algorithm, i.e., self-adaptive artificial bee colony (ABC) algorithm based on the global best (GB) candidate (SABCGB) to solve global optimization problems. Experiments are conducted on a set of 25 benchmark functions and maintain same initial population size on each benchmark function in order to compare the results of proposed algorithm with others. It has been observed that SABCGB algorithm outperforms GABC, ABC/best/1 and ABC/best/2 algorithms and provides feasible results compare to the other algorithms. Gu and Sheng (2017) presented robust regularization path algorithm for V-support vector classification and margin errors. Later, effectiveness and working significance of the algorithm has been tested via theoretical as well as experimental analysis. The results show that algorithm fits the entire solution path with fewer steps and less running time than other algorithms.

Beside the other applications, the modeling and optimization aspects of GM process have also been highlighted by various empirical and mathematical models such as Taguchi method (Kumar et al. 2011; Guharaja et al.2006; Yeo and New 1999), Fuzzy set theory (Tan et al. 2002), Fuzzy-Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS; Tang and Du 2014; Sivapirakasam et al. 2011; Jagadish and Ray 2015), Taguchi-VIKOR (Yadav and Patel 2013), Taguchi-gray relational analysis (GRA; Tang and Du 2014), GRA-principal component analysis (PCA; Jagadish and Ray 2014a), Taguchi-response surface methodology (RSM; Jagadish et al. 2015), Entropy-GRA (Jagadish and Ray 2014b). It was observed that these models were quite complex and require a thorough understanding of several cutting processes (Hashish 1991; Lemma et al. 2002) and they were built with several assumptions during optimization (Caydas and Hascalik 2008).

In addition, as the GM process is considered to be a complex system with multiple responses and involves degree of uncertainty, imprecise and subjective data, this makes the modeling of this process more complex and challenging by both empirical and mathematical models. In order to evaluate such data, the decision experts usually considered the risk in terms of linguistic variables such as low, medium, high, very high, very low. Fuzzy set theory (Zadeh 1965; Bortolan and Degami 1985) deals effectively with this type of uncertainty (vagueness), thus allowing linguistic variables to be used for approximate reasoning via membership function (MF). However, the correlation aspects among the responses cannot be taken care of by fuzzy system unless these are eliminated initially. Apart from empirical and mathematical models, various authors have tried to model some of the nonconventional machining (NCM) process using soft computing models such as Mamdani-based fuzzy expert systems (Chakravarthy and Babu 1999; Todkar and Patkure 2014; Vundavilli et al. 2012; Zaina et al. 2011; Mariajayaprakash et al.2015). It was observed that model was found to be quite time-consuming process due to the use of defuzzification process; model has output membership functions; less flexible in system design; difficult in formulation of IF–THEN rules and computational burdens. To resolve these issues, the Takagi–Sugeno–Kang fuzzy logic (TSK-FL) model (Takagi and Sugeno 1985; Sugeno and Kang 1986) has been presented. The major merits of TSK-FL model were compact and computationally efficient representation and work well with optimization and adaptive techniques, which makes it very attractive in control problems, particularly for dynamic nonlinear systems, more flexible, and it uses less number of rules than the Mamdani-based fuzzy expert systems (Haman and Geogranas 2008). Furthermore, development of fuzzy rules in Mamdani-based fuzzy expert systems was done based on the expert knowledge. However, this did not ensure optimal fuzzy rules for fuzzy system (Chiu 1994). It is therefore necessary to determine the optimal fuzzy rules for the fuzzy system. In this paper, subtractive clustering (SC) technique is presented, which estimates the number of clusters and the cluster centers in a set of available data based on the density of surrounding data points (Chiu 1994). The cluster center and number of cluster obtained by SC technique define the optimal number of rules and its corresponding center distance of the available data. Thereafter, cluster information obtained from SC method has been used for development of TSK fuzzy rules in the TSK-FL model.

The limitations of the above models in prediction and optimization of process parameters have made to the development an integrated fuzzy system consists of SC with TSK-FL system or fuzzy logic-based decision support (FLDS) system for GM process that can play an active role in process variables prediction within the shortest possible time (Chakravarthy and Babu 1999). This can eliminate the need of extensive experimental work, provides enough flexibility to extend other ranges of operations, handle the uncertainty (vagueness) information and subjective data and should not depend on any process related assumptions and subsequently select the most optimal parameters for the GM process.

2 Fuzzy logic-based decision support system

The complete structure of FLDS system (Fig. 1), which comprises of SC-based TSK-FL model for optimum prediction and optimization multi-response problems in GM, has been described in this section. In this model, at first, structuring and development of database include selection of appropriate orthogonal array (OA) and plan for the experimentation and generation of experimental data using the design of experiments (DoE) or Taguchi Method (Taguchi 1990; Ross 1996). Second, data normalization is performed on the experimental data to transforms original experimental data sequence to comparable sequence data into a range of 0–1 and to determine the normalized relational grades (NRG) for each response. This process is required because the multi-response parameters optimization problems usually include more than one responses with different data measurement and also contains a certain degree of uncertainty and vagueness information in the definition of response characteristics such as ‘lower-the-better’ (LB), higher-the-better’ (HB) or nominal-the-better’ (NB). The normalization process for the n no. of experiments and m no. of parameters using the following expressions (Jung and Kwon 2010):

Fig. 1
figure 1

Proposed flowchart of FLDS system for GM process

Full size image

For higher-the-better:

$$\begin{aligned} & X_{ij} = \frac{{Y_{ij} - {\text{Min}}(Y_{ij} )}}{{[{\text{Max}}(Y_{ij} ) - {\text{Min}}(Y_{ij} )]}} \\ & \quad {\text{For}}\quad (i = 1,2, \ldots n,j = 1,2, \ldots m)\end{aligned} $$
(1)

For lower-the-better:

$$\begin{aligned} & X_{ij} = \frac{{{\text{Max}}(Y_{ij} ) - Y_{ij} }}{{[{\text{Max}}(Y_{ij} ) - {\text{Min}}(Y_{ij} )]}}\\ & \quad {\text{For}}\quad (i = 1,2, \ldots n,j = 1,2, \ldots m)\end{aligned} $$
(2)

and for the nominal the better:

$$\begin{aligned} & X_{ij} = 1 - \frac{{\left| {Y_{ij} - Y_{ob} (j)} \right|}}{{[{\text{Max}}(Y_{ij} ) - {\text{Min}}(Y_{ij} )]}}\\ & \quad {\text{For}}\quad (i = 1,2, \ldots n,j = 1,2, \ldots m)\end{aligned} $$
(3)

where Yij is the original sequence (i.e., response value) of the parameter jth of experiment ith, Xij is the sequence after the preprocessing, Max(Yij) is the largest value of Yij, and Min(Yij) is the smallest value of Yij. Yob(j) is the target of Xij. A higher the Xij value means that the corresponding experimental result is closer to the optimal normalized value for the single response. Then, the normalized relational grades (NRG) values for each of the response are calculated by average value of normalized for each sequence using following expression:

$$ {\text{NRG}}_{i} = \frac{1}{m}\sum\limits_{j = 1}^{m} {X_{ij} } $$
(4)

where m is the number of response parameters. In this analysis, the single NRG can easily simplify the optimization of process parameters but the GM process simultaneously request complex multiple responses. The relationship from the NRG can be categorized into three grades of influence, and they are shown in Table 1.

Table 1 The four grades of the NRG
Full size table

Third, NRG values for each of the responses obtained from normalization are then provided as input to the FLDS system. However, for the prediction problems is concern, the input for the FLDS as machining parameters and their corresponding levels of that process. In the fourth step, fuzzification of input data, i.e., the normalized (Xij) value of each response sequence obtained by normalization process has been carried out using membership function (MF). It defines the degree of membership of an object (each input value) in a fuzzy set between 0 and 1. In this paper, triangular type of MF is used for representation of fuzzy sets (Shabgarda et al. 2013). Thereafter, SC-based TSK fuzzy interference engine will perform the fuzzy interface in order to generate the SC-based TSK fuzzy rules. In this study, the SC-based TSK fuzzy rules are formulated based on the cluster information obtained using SC techniques (Chiu 1994).

The SC technique initially developed by (Chiu 1994) and used in many applications for getting the cluster information. Mainly, this method estimates both cluster numbers and its corresponding cluster centers and subsequently extracts the TSK fuzzy rules from the input/output data. This method operates by assuming each data point as a potential cluster center and estimates a measure of the possibility that each data point would define the cluster center, based on the density of surrounding data points. A brief description of SC method is as follows: For example, for the K data points, the measure of density (Di) is defined for each data points as:

$$ D_{i} = \sum\limits_{j = 1}^{K} {e^{{\left( {{{\left( {X_{i} - \left. {X_{j} } \right|^{2} } \right)} \mathord{\left/ {\vphantom {{\left( {X_{i} - \left. {X_{j} } \right|^{2} } \right)} {(r_{a} /2)^{2} }}} \right. \kern-0pt} {(r_{a} /2)^{2} }}} \right)^{2} }} } $$
(5)

where ra is a positive constant defines the cluster radius and values fall in the range of [0, 1]. In this, it is observed that the Di for a data point is a function of its distance to all other data points. Thus, a data point that has many neighboring points will have a high potential of being a cluster center. In this approach, data which have highest density (Di) measures are chosen first. Then, density (Di) measure for each data points Xi is calculated by following expression:

$$ D_{i} = D_{i} - D_{{c_{1} }} {\text{e}}^{{ - \left( {\left( {{\raise0.7ex\hbox{${ - \left| {X_{i} - X_{{c_{1} }} } \right|}$} \!\mathord{\left/ {\vphantom {{ - \left| {X_{i} - X_{{c_{1} }} } \right|} {{{r_{b} } \mathord{\left/ {\vphantom {{r_{b} } 2}} \right. \kern-0pt} 2}}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{{r_{b} } \mathord{\left/ {\vphantom {{r_{b} } 2}} \right. \kern-0pt} 2}}$}}} \right)} \right)^{2} }} $$
(6)

where Xc1 represents the first cluster center and Dc1 represents the density of the first cluster and rb is the constant cluster radius and is usually greater than the ra to prevent processing closely spaced center. Data points close to the cluster center will have significantly decreased density measure so that they have neglected to be chosen as next cluster center. Further, another next cluster center is selected and density measure reduced again. This process continues until a sufficient number of clusters is achieved. Furthermore, the variable ra has most important role in determining the number of clusters. This represents the range of influence of a cluster of the considered the data space as a unit hypercube (Chiu 1994).

The smaller value of ra will lead to more and smaller clusters in the data, which is subsequently, lead to more rules and vice versa. In this study, the value of ra is changed from 0 and 1 with step of 0.1. Then, TSK-FL model of each parameters are tested and corresponding root mean square error (RMSE) values are calculated. The TSK-FL model with lowest RMSE has been taken for the further analysis. The cluster information generated using SC method is then utilized to construct the TSK-FL model that best fit the data using minimum rules. This model consists of set of fuzzy rules, each describing a local linear input–output relationship of the system. A generalized type-I order TSK-FL model (Takagi and Sugeno 1985; Sugeno and Kang 1986) for multi-input and single-output (MISO), its Kth rule can be expressed as:

$$ \begin{aligned} & R_{i} :{\text{IF }}\,X_{1} \,{\text{is}}\, \, S_{i1} \,{\text{AND}}\,{\text{ IF}}\, \, X_{2} \,{\text{is}}\, \, S_{i2} \,{\text{AND }}\,{\text{IF}}\, \, X_{3} \,{\text{is}}\, \, S_{i3}\\ & \quad \,{\text{AND}} \ldots {\text{AND}}\,{\text{ IF}}\, \, X_{n} \,{\text{is }}\,S_{in} \,{\text{THEN}} \\ & E_{mi} = C_{i1} A_{1} + C_{i2} A_{2} + \, C_{i3} A_{3} + \cdots + \, C_{in} A_{n} + \, b_{i} \\ & \quad {\text{For}}\quad i = 1,2, \ldots K \\ \end{aligned} $$
(7)

where R(i) is the ih rule, X1, X2, X3,… Xn are the fuzzy (normalized) parameters, Si1, Si2…Sin are the fuzzy cluster sets defined in the antecedent space, K indicates the number of rules, Ci1, Ci2, Ci3 and bi are unknown parameters to be estimated for the ith rule (Shabgarda et al. 2013). The output level, Emi, is weighted by the firing strength which is the degree of fulfillment of the rule, calculated as

$$ w_{i} (X_{ij} ) = \prod\limits_{l = 1}^{n} {\mu_{{S_{ij} }} \left( {X_{j} } \right)} \quad i = 1,2, \ldots K $$
(8)

where \( \mu_{{S_{ij} }} \) is the membership function of the fuzzy set Sin in the antecedence Ri. Thereafter, the defuzzification of the data is carried out; in which a crisp value is extracted from a fuzzy set as a representative value, i.e., fuzzy performance grades (FPG) and optimum response parameters for the GM process. The final output level of the system Em, is the weighted average of all rule outputs, calculated using following expression:

$$ E_{m} = \frac{{\sum\nolimits_{i = 1}^{K} {w_{i} (X)E_{mi} } }}{{\sum\nolimits_{i = 1}^{K} {w_{i} (X)} }} $$
(9)

However, there are several defuzzification methods which are used in the literature. In this paper, singleton method is adopted to get the FPG values and prediction values. At last, ANOVA is performed to select the optimal process parameters for GM process and followed by performance test and confirmation test to verify the results.

3 A case study

In this section, an experimental case study on machining of natural filler-reinforced polymer (NFRP) composites in abrasive water jet machining (AWJM) process has been described. Due to the environmental issues and need for more flexible materials, the use polymer composites with natural organic fillers (Chandramohan 2014; La-Mantia and Morreale 2011; Georgios et al. 2013; Chauhan et al. 2012) become more in the manufacturing industries. Natural filler used in this work is the wood dust with size of 2 μm and density 0.799 gm/cc after cleaning due to their unique properties and exceptional merits over the other natural fillers (Markarian 2002; Pritchard 2004). Again, due to the anisotropic and inhomogeneous properties, the machining of these composites by conventional manufacturing process is extremely difficult and a costly attempt (Weller 1984; Komanduri et al. 1991) and also these process results many serious occupational health and environmental issues during machining (Sivapirakasam et al. 2011; Chandramohan 2014; La-Mantia and Morreale 2011; Georgios et al. 2013; Chauhan et al. 2012). Therefore, nontraditional machining process called AWJM is used in this study. The working principle of this process has been detailed described in the literature (Momber and Kovacevic 1992). This process does not require any cooling or lubricating oils so there are no chemically contaminated chips to dispose of (Olsen 2008). In addition, this process does not generate any forms of harmful components and takes minimal preprocessing. Moreover, the minimal scrap that remains is free of chemical contamination and can be easily recycled, which results in raw material, energy, and cost savings for recyclable materials. Hence, this process inherently called an environmentally friendly process or green process.

The performance of the AWJM process strongly depends on various process parameters which are directly or indirectly effects on the efficiency of the process. These process parameters are again highly complex and nonlinear in nature. Thus, it is very difficult to develop an exact mathematical model to control the AWJM process. Also, the AWJM process contains a certain degree of uncertainty and vagueness information in the definition of response characteristics such as LB, HB and NB characteristics which makes the AWJM process more complex and challenging (Yadav and Patel 2013). Thus, effective modeling and optimization of process parameters is an essential requirement for AWJM process.

3.1 Specimen preparation

In this work, sundi: wood dust obtained from sundi tree wood (available in the northeastern part of the India) has been used for preparation of NFRP composite or wood dust-based filler-reinforced polymer (WDFRP) composite. The sundi tree belongs to ‘Michelia Montana’ tree species family and has four principle organic components as cellulose, glucomannan, xylan and lignin. During the specimen preparation, first a sundi wood dust with size of 2 μm and density 0.799 gm/cc after cleaning has been reinforced into the matrix material (low-temperature epoxy resin (Araldite LY 556) and corresponding hardener (HY 951)) in a ratio of 10:8 by weight as recommended (Chandramohan 2014; Chauhan et al. 2012) and then stirred manually in order to ensure the fillers disperse in the matrix material. After that, this mixer has been gradually poured into the vacuum glass chamber and allowed to cure for 24–48 h at room temperature (Chandramohan 2014). At last, a size of 200 mm × 120 mm × 5 mm has been prepaid for the experimental work (Fig. 2).

Fig. 2
figure 2

Work Specimen for AWJM process

Full size image

3.2 Experimental setup

The AWJM manufactured by KMT water jet systems (Fig. 3) has been employed for performing the experimental runs. In this work, Taguchi-based orthogonal array technique (Taguchi 1990; Ross 1996) has been used for development of experimental design based on the number of input parameters and their corresponding levels. There are five independent parameters (Table 2) namely, abrasive material grain size (AMGS), pressure within the pumping system (PwPS), stand-off distance (SoD), abrasive mass flow rate (AMFR) and nozzle speed (NS) have been considered as input parameters or machining parameters while material removal rate (MRR), process time (PT) and surface roughness (Ra), have been considered as output parameter or response parameters (Chen et al.2002; Jegaraj and Babu 2005; Hascalik et al. 2007; Akkurt et al.2004). According to the five input parameters with three levels each, Taguchi (L27) orthogonal array (Taguchi 1990; Ross 1996)-based design has been developed (Table 2). The complete configuration and dimensions of the workpiece are shown in Fig. 4.

Fig. 3
figure 3

The AWJM experimental setup

Full size image
Table 2 Machining parameters and levels in Taguchi design
Full size table
Fig. 4
figure 4

Configuration and dimensions of workpiece for Taguchi (L27) experimental plan

Full size image

During machining process, a square hole of 15 mm × 15 mm has been drilled for each experimental setting according to design (Table 3). To attain more accuracy in results, each experiment at a particular parametric setting has been repeated three times and the average values of the results were taken for analysis. Subsequently, MRR (in mm3/min) and PT (in s) have been calculated using following expressions:

$$ {\text{MRR}} = \left( {\frac{{W_{a} - W_{b} }}{{t_{m} }}} \right) $$
(10)
$$ {\text{PT}} = \frac{60}{\text{MRR}} $$
(11)

where Wa is Weight of the workpiece after the experiments, Wb is the weight of the workpiece before the experiments and tm is the machining time in min. At last, surface roughness (in µm) at the machined surface is measured using surface texture measuring instrument (SURFCOM 130A- Monochrome) manufactured by TOKYO SEIMITSU CO.LTD in micrometer, and average value of MRR, PT and Ra (Table 3) has been taken for the analysis.

Table 3 Taguchi (L27) planning matrix and their experimental results
Full size table

4 Result and discussions

4.1 Optimization of process parameters

In this section, optimal factors level combination for AWJM process during the machining of NFRP composite has been illustrated. The optimization is done by using help MATLAB code (MATLAB 2006). During the optimization process, at first, experimentations are performed on AWJM process based on Taguchi design (Table 2) and subsequently, corresponding response parameters are evaluated using Eqs. 10 and 11. Then, evaluated responses are normalized to get the normalized response values (Xij) and NRG using Eqs. 1–4 which are then provide as input to the FLDS system. In the FLDS simulation system, first, input data (i.e., Xij values) are fuzzified to fuzzy sets via MF (Fig. 5a–c).

Fig. 5
figure 5

a Membership Function for MRR. b Membership Function for PT. c Membership Function for Ra

Full size image

Second, the clustering of data specified by a membership grades is performed using SC technique (Chiu 1994) with value of ra is 0.5. This groups the response data in a multi-dimensional space into a specific number of different clusters and respective cluster centers (C) matrix and sigma values (S) have been established (Table 4). The C value represents the position of the clusters center in each dimension, and S value represents the range of influence of cluster center in each of the data dimensions.

Table 4 Cluster centers and Sigma values
Full size table

Thereafter, SC-based TSK fuzzy IF-TEHN rules are formulated using the SC-based TSK-FL algorithm (Takagi and Sugeno 1985; Sugeno and Kang 1986) as explained in the Sect. 2. Accordingly, there are 10 rules which have been formulated in this work (Table 5).

Table 5 Formation of TSK Fuzzy IF–THEN rules for AWJM process
Full size table

Afterward, the degree of fulfillment (wi (Xij) of the rule and weighted average of all rule outputs (Emi) are evaluated using Eqs. 8 and 9, respectively. Subsequently, the defuzzification of the data has been carried out and corresponding crisp value has been extracted from a fuzzy set as a representative value, i.e., fuzzy performance grade (FPG). Finally, the highest FPG value has been selected as optimal rank among the other runs. The result shows that (Table 6) the experiment no. 25 yield highest FPG value and found to be the optimal experimental setup for the desirable responses among the 27 experiments. The FPG value for optimal parameter setting is obtained to be 0.945. According to the highest FPG value as obtained for Exp. no. 25 as 0.945, the following parameter setting yield the best combination of process parameters for AWJM process, i.e., AMGS as 100 mesh with level 3; SoD as 3.5 mm with level 3; PwPS as 225 MPa with level 3; AMFR as 3 g/s with level 1 and NS as 125 mm/min with level 1.

Table 6 Fuzzy relational Grades
Full size table

The optimal setting obtained using FLDS system provides the most optimal response parameter such as higher MRR, lesser PT and good Ra for the AWJM process. The optimal response parameter reduces the generation of wastes and pollution due to the different chemical composition, different materials behavior and diverse properties of WDFRP composites machining. Therefore, it is recommended that the optimal settings, i.e., AMGS as 100 mesh with level 3; SoD as 3.5 mm with level 3; PwPS as 225 MPa with level 3; AMFR as 3 g/s with level 1 and NS as 125 mm/min with level 1 is used for effective machining of WDFRP composites using AWJM process and creates the less environmental issues during machining. Furthermore, the present research suggests that FLDS system is used as a systematic framework model for optimal selection of process parameter for effective machining of WDFRP composites in the AWJM process under green manufacturing environment.

4.2 Performing the response table, response graph and ANOVA

This research also analyzes the response of input parameters using the response table obtained from proposed method by calculating the average FPG value for each level of the input parameter (Table 7). Since the FPG value represents the level of correlation between the reference and comparability sequence. Therefore, comparability sequences with higher FPG value are the optimal process parameters. The following parameter shows highest FPG values are AMGS (100 mesh, level 3); SoD (3.5 mm, level 3); PwPS (150 MPa, Level 1); AMFR (3 g/s, level 1) and NS (175 mm/min, level 2).

Table 7 Response values for FPG
Full size table

The influence of parameters on the response FPG values is identified using response graph. The response graph (Fig. 6) shows that two machining parameters namely, AMGS and SoD have greater influence on the FPG values while other parameters like PwPS, AMFR and NS are found to be least influence on the FPG values.

Fig. 6
figure 6

Response graph for each process parameter level

Full size image

It is also noted from the response plot (Fig. 6) that as AMGS increase from 60 to 100 mesh, the FPG value from (0.3206 to 0.7179) is rapidly increased during the machining of WDFRP composite; this is expected because an increase in AMGS determines the speed at which the metal is removed and also large quantity of abrasive particles impinge on the workpiece at very high velocity, results in higher MRR, lesser Ra and lesser PT which subsequently increase in higher FPG value (Arola and Ramulu 1993). Similarly, for the parameter SoD shows same behavior as AMGS, i.e., increase in SoD values from 1.5 to 3.5 mm the value of FPG values from 0.4406 to 0.5442 is gradually increased. This due to the fact that increase in SoD between the nozzle and workpiece increases the impact surface area of the abrasive particles results in larger MRR, lesser Ra and lesser PT which directly increases the FPG values as shown in Fig. 6.

On the other hand, in the case of PwPS and AMFR, the rate of FPG values is found to be rapidly decreased, i.e., with the increase in PwPS from 150 to 300 MPa and AMFR from 3 to 7 g/s, the FPG values decreases 0.5487–0.4109 for PwPS and 0.6221–0.3356 for AMFR. This is due to the fact that, both increase in PwPS and AMFR, bombardment of abrasive particles on the workpiece is faster and kinetic energy of the abrasive particles increases, results in lesser MRR, higher Ra and higher PT which directly decreases the FPG values during the machining of WDFRP composites. With reference to the parameter NS is found to be moderate behavior, i.e., increases of spindle speed from 125 to 225 mm/min there is moderate increase in FPG values from 0.4790 to 0.4767 as depicted in Fig. 6. In the end, it is observed that parameters namely, AMGS and SoD have major influence while PwPS, AMFR and NS have least influence on the FPG values. Based on the response graph (Fig. 6), the recommended optimal combination of process parameters for higher FPG value are AMGS (100 mesh, level 3), SoD (3.5 mm, level 3), PwPS (150 MPa, level 1), AMFR (3 g/s, level 1) and NS (175 mm/min, level 2).

Furthermore, percentage contributions of different input parameters on FPG value are obtained by decomposition of variance, which is called analysis of variance (ANOVA; Taguchi 1990; Ross 1996). From the ANOVA results (Table 8), the percentage contributions of the process parameters calculated as AMGS is 58.53%, AMFR is 30.44% followed by PwPS is 7.04%, SoD is 3.98% and NS is 0.00%, respectively. Furthermore, most significance of the parameter is tested using an F-test. The value of (F) for the parameter, AMGS and AMFR as shown in Table 8 are obtained to be highest, i.e., 83.70 and 43.53 for FPG while for the parameter NS is 0.00. This shows that parameters AMGS and AMFR have more influence/contribution on the FPG values compare to the other parameters. Similarly, the statistical significance of the parameters is tested by p (probability)-values (Prabhu et al. 2015; Shabgarda et al. 2013). Since values of p-values for all the parameters (Table 8) are found to be less than 0.05, it indicates that model and associated terms are statically significant.

Table 8 Result of ANOVA for FPG
Full size table

Subsequently, sufficiency of the model is determined by calculating the coefficient of determination (R2) values (Prabhu et al. 2015). The value of R2 is calculated to be 0.9612 for FPG; it implies that 95% of experimental data are well-suited. Higher the R2 gives the satisfactory model to the experimental data. Thereafter, the adequacy and fitness of the model are calculated by adjusted coefficient of determination (R2) values (Prabhu et al. 2015). The high value of adjusted-R2 (0.945 for FPG) supports a high correlation between the experimental and the predicted values.

Additionally, the normality of the obtained data points is analyzed by plotting (Fig. 7) the normality of the residuals (Shabgarda et al. 2013) for a FPG values. The normality plot for FPG is based on the predicted results obtained using FLDS system. The graphical results (Fig. 7) show that data points (as indicated by black dots) for each of the predicted FPG values, are found to be close to the straight line. This indicates that, the FPG values, for each of the experimental setting obtained by FLDS system follows a normal distribution and the normality assumption is valid.

Fig. 7
figure 7

Normal probability plot for FPG values

Full size image

4.3 Modeling of MRR, PT and Ra using FLDS system

In this section, an attempt has also been made to develop the prediction models for MRR, PT and Ra separately for AWJM process using FLDS system. These prediction models create the mapping between the process (input) parameters and response (output) parameters using FLDS system which includes fuzzify the input data, creation of SC-based TSK Fuzzy rules, and defuzzification of the data and finally, establishes the optimal predictions for the AWJM process. In this analysis, the input for the FLDS system as machining parameters and their corresponding levels (Table 2) and output will be the optimal prediction of responses such as MRR, PT and Ra. First, machining parameters are fuzzified using triangular MF and they are shown in Fig. 8a–e. Second, cluster centers (C) and sigma (S) values are determined using SC technique (Chiu 1994) with ra is 0.5.

Fig. 8
figure 8

a Membership functions of AMGS. b Membership functions of SoD. c Membership functions of PwPS. d Membership functions of AMFR. e Membership functions of NS

Full size image

Thereafter, fuzzy IF-TEHN rules are then formulated using the SC-based TSK-FL algorithm or FLDS system (Takagi and Sugeno 1985; Sugeno and Kang 1986) as explained in the Sect. 2. Afterward, the degree of fulfillment (\( w_{i} (X_{ij} ) \)) of the rule and weighted average of all rule outputs (Emi) are evaluated using Eqs. 8 and 9, respectively. Subsequently, the defuzzification of the data has been carried out and corresponding crisp value has been extracted from a fuzzy set as a representative value, i.e., predicated values. The prediction results for MRR, PT and Ra using FLDS system are shown in Table 9. In addition to the prediction model; investigation of accuracy level and error rate of prediction values obtained by FLDS system are analyzed using accuracy and error tests. The error rates and accuracy levels of the FLDS system are calculated using following expressions (Ross 1996):

$$ \% \varepsilon = \left( {\frac{{\left| {R_{e} - R_{p} } \right|}}{{R_{e} }}} \right) $$
(12)

where Re is experimental value, Rp is the predicted value, \( \varepsilon \)i represents the individual % error.

Table 9 Error and accuracy of the FLDS prediction model
Full size table

The results show lower error level between the predicted values and experimental results (Table 9). The agreements between the experimental and predicted values have been demonstrated by plotting the predicted values with the experimental values and they are shown in Figs. 9, 10 and 11 and the graph shows that agreement between the predicted model and experimental values are within the permissible limit.

Fig. 9
figure 9

Comparison between predicted and experimental values of MRR

Full size image
Fig. 10
figure 10

Comparison between predicted and experimental values of PT

Full size image
Fig. 11
figure 11

Comparison between predicted and experimental values of Ra

Full size image

Additionally, the normality of the obtained data points is analyzed by plotting the normality of the residuals (Shabgarda et al. 2013) for MRR, PT and Ra. The normality plot for each of the response parameters is based on the predicted results obtained using FLDS system as tabulated in Table 9. The normality plot for each of the response parameters such as MRR, PT, and Ra is shown in Fig. 12a–c. The graphical results show that data points (as indicated by black dots) for each of the predicted response parameters, i.e., for MRR, PT and Ra are found to be close to the straight line. This indicates that parameters MRR, PT and Ra for each of the experimental setting obtained by FLDS system follows a normal distribution and the normality assumption is valid.

Fig. 12
figure 12

Normal probability plot for a MRR b PT and c PT

Full size image

5 Confirmation tests

5.1 Confirmatory test

The confirmatory test is carried out to verify the optimum results with experimental results. The predicted FPG at the optimal level of the machining parameters can be calculated using following expression:

$$ \tau_{\text{predicted}} = \tau_{m} + \sum\limits_{j = 1}^{n} {\left( {\tau_{o} - \tau_{m} } \right)} $$
(13)

where \( \tau_{m} \) is the overall mean value of FPG for all the experimental runs, \( \tau_{o} \) is the mean of FPG values at the optimum level of ith parameter, and n is the number of input parameters that significantly affect FPG values according to the ANOVA. In order to find out the quality improvement, the initial machining parameters are presumed to be AMGS is 60 mesh, SoD is 2.5 mm, PwPS is 225 MPa, AMFR is 5 g/s and NS is 125 mm/min which is the Exp. no 4 in Table 3.

The confirmation test results indicate that the response values for the optimal parameter condition (100 mesh, 3.5 mm, 225 Mpa, 3 g/s and 125 mm/min) is higher than (which is an improvement of 66.52%) that of the initial setting parameter conditions (60 mesh, 2.5 mm, 225 Mpa, 5 g/s and 125 mm/min) and also predicted response value is higher than the experimental value which are depicted in Table 10. The optimal results are verified through confirmatory experiments and the results are in good agreement with the predicted values. Thus, it can be concluded that the response parameters can be greatly improved through this study.

Table 10 Confirmatory test
Full size table

5.2 Performance test of the FLDS model

5.2.1 Performance of FLDS system using ANOVA analysis

The performance of the FLDS system has been tested by using ANOVA analysis (Jung and Kwon 2010; Shabgarda et al. 2013) between experimental MRR, PT and Ra and FLDS system MRR, PT and Ra. The result of ANOVA for both experimental and FLDS system values is depicted in Table 11.

Table 11 Comparison of ANOVA analysis
Full size table

The ANOVA result shows that the value of R2 for experimental and FLDS system MRR, PT and Ra is found to be well-suited with the 95% of confidence interval and shows high satisfaction with the experimental data (Table 10). The adequacy and fitness of the model are calculated by adjusted-R2 values. The high value of adjusted-R2 supports the high correlation between the experimental and the predicted values (Shabgarda et al. 2013). The value of R2 and adjusted-R2 values for FLDS system MRR, PT and Ra are found to be higher than the value of R2, for experimental MRR, PT and Ra, Thus, the FLDS system gives better than the experimental results. Moreover, the most important influencing parameters obtained from the ANOVA analysis of predicted MRR, PT and Ra are used further for construction of surface plot for MRR, PT and Ra as shown in Figs. 13, 14 and 15. The most influencing parameters obtained by ANOVA are AMGS and SoD for MRR, PwPS and NS for PT while AMGS, AMFR and SoD for Ra.

Fig. 13
figure 13

a The surface plot between AMGS and SoD of predicted MRR in AWJM process. b Plot between AMGS vs experimental MRR in AWJM process (SoD kept Constant)

Full size image
Fig. 14
figure 14

a The surface plot between PwPS and NS of predicted PT in AWJM process. b Plot between NS vs experimental PT in AWJM process (PwPS kept Constant). c Plot between PwPS vs experimental PT in AWJM process (NS kept Constant)

Full size image
Fig. 15
figure 15

a The surface plot between AMGS and AMFR of predicted Ra in AWJM process. b Plot between AMGS vs experimental Ra in AWJM process (AMFR kept Constant). c Surface plot between SoD and AMFR of predicted Ra in AWJM process. d Plot between SoD vs experimental Ra in AWJM process (AMFR kept Constant)

Full size image

Figure 13a shows the variation of MRR with respect to the parameters AMGS and SoD in the AWJM process. The blue region in the figure indicates that less significant region, magenta and green region indicates the intermediate region while yellow region indicates the high significant region of MRR, i.e., MRR is significantly increased when AMGS and SoD are increased from lower level to higher level in the AWJM process. Similarly, Fig. 13b shows the variation of MRR with respect to the AMGS when SoD is kept constant. The pattern of MRR obtained when considering the SoD as a fixed variable (at 2.5 mm), by increasing the AMGS (from 60 to 100 mesh) in Fig. 13b is well match with that of surface plot as depicted in Fig. 13a obtained using FLDS system under same conditions.

Figure 14a shows the variation of PT with respect to the parameters PwPS and NS in the AWJM process. The blue region in the figure indicates that less significant region, magenta and green region indicates the intermediate region while yellow region indicates the high significant region of PT. Surface plot shows that lesser PT is obtained when both the PwPS and NS are at lower level as shown with blue color region in Fig. 14a. On the other hand, higher PT is obtained when PwPS at higher level while NS at lower level as shown with yellow color region in Fig. 14a. Similarly, Fig. 14b and c shows the variation of PT with respect to the NS when PwPS is kept constant and PwPS when NS is kept constant. The pattern of PT obtained when considering the PwPS as a fixed variable (at 250 MPa), by increasing the NS (from 225 to 125 mm/min) and when considering the NS as a fixed variable (at 180 mm/min), by increasing the PwPS (from 150 to 300 MPa) in Fig. 14b, c is well match with that of surface plot as depicted in Fig. 14a obtained using FLDS system under same conditions.

Figure 15a and c shows the variation of Ra with respect to the parameters AMFR and AMGS and SoD and AMFR in the AWJM process. The blue region in the figure indicates that less significant region, magenta and green region indicates the intermediate region while yellow region indicates the high significant region of Ra. Similarly, Fig. 15b and d shows the variation of Ra with respect to the AMGS when AMFR is kept constant and SoD when AMFR is kept constant. The pattern of Ra obtained when considering the AMFR as a fixed variable (at 5 g/s), by increasing the AMGS (from 60 to 100 mesh) and when considering the AMFR as a fixed variable (at 5 g/s), by increasing the SoD (from 1.5 to 3.5 mm) in Fig. 15b and d is well match with that of surface plot as depicted in Fig. 15a and c obtained using FLDS system under same conditions. The results depicted in Figs. 13, 14 and 15 show that results obtained from FLDS system are in good agreement with the experimental results for MRR, PT and Ra. This justifies the result of ANOVA analysis of the experimental MRR, PT and Ra with FLDS system.

5.2.2 Performance of FLDS system using artificially generated data

The performance of FLDS system has also been tested for its accuracy in prediction using a batch mode of training data. The training data is generated artificially, with help of regression analysis using experimental data (Table 3). The statistical software (Minitab 14 2003) is used for regression analysis (Caydas and Hascalik 2008) and proposed regression equation which is used to generate the data required for training the FLDS system is given below (Eqs. 13–18). According to the regression analysis, 15 test data is generated which is used to measure the performance of FLDS system results. The result of this analysis is depicted in Table 12. This shows that the percentage deviation in prediction of the MRR, PT and Ra, as obtained by FLDS system found to be comparable with the results of experimental results.

Table 12 Results of prediction of response parameters FLDS model via artificial generated data
Full size table
$$ {\text{MRR}}_{{{\text{\_Pre}}}} = - \,222.3 \, + 4.821 \,{\text{AMGS}} + 16.4 \,{\text{SoD}} - 0.202 \,{\text{PwPS}} - 7.55 \,{\text{AMFR}} + 0.124 \,{\text{NS}} $$
(14)
$$ {\text{PT}}_{{{\text{\_Pre}}}} = 1.612 - 0.01689 \,{\text{AMGS}} + 0.0109 \,{\text{SoD}} + 0.001200 \,{\text{PwPS}} + 0.0329 \,{\text{AMFR}} - 0.000709\,{\text{NS}} $$
(15)
$$ {\text{Ra}}_{{\_{\text{Pre}}}} = - \,0.0276 + 0.001625\, {\text{AMGS}} - 0.03900\, {\text{SoD}} + 0.000141 \,{\text{PwPS}} + 0.04339 \,{\text{AMFR}} + 0.000258\,{\text{NS}} $$
(16)
$$ {\text{MRR}}_{{\_{\text{Exp}}.}} = - \,219.4 \, + 4.807\,{\text{AMGS}} + 16.0\, {\text{SoD}} - 0.210 \,{\text{PwPS}} - 7.64 \,{\text{AMFR}} + 0.130\, {\text{NS}} $$
(17)
$$ {\text{PT}}_{{\_{\text{Exp}}.}} = 1.617 - 0.01708 \,{\text{AMGS}} + 0.0126 \,{\text{SoD}} + 0.001208\, {\text{PwPS}} + 0.0332\, {\text{AMFR}} - 0.000687 \,{\text{NS}} $$
(18)
$$ {\text{Ra}}_{{\_{\text{Exp}}}} = - \,0.0714 + 0.00121\,{\text{AMGS}} - 0.0349\,{\text{PwPS}} + 0.000237\,{\text{SoD}} + 0.0469\,{\text{AMFR}} + 0.000378 \, \,{\text{NS }} $$
(19)

6 Conclusions

In this article, an attempt has been made to develop a fuzzy logic-based decision support system for optimum prediction and multi-response parameters optimization problems in GM. A case study of AWJM process on machining of NFRP composite has been illustrated to verify the feasibility and effectiveness of the proposed model. The optimum combinations of machining parameters and prediction of response parameters have been evaluated. The result shows that optimum parameter setting is obtained to be AMGS (100 mesh, level 3); SoD (3.5 mm, level 3); PwPS (150 MPa, Level 1); AMFR (3 g/s, level 1) and NS (175 mm/min, level 2). Subsequently, ANOVA has been performed to determine the most significant parameters, indicating that the parameters AMGS, AMFR and PwPS have found to be major influencing parameters among the other. Finally, the confirmatory and performance analysis have been tested to verify with experimentally and for its accuracy in prediction of response parameters in the selected case study using artificially generated test cases and ANOVA analysis. The results of the confirmatory and performance analysis show that predictions through FLDS approach are comparable with experimental results with accuracies more than 95% and establish the most optimal combinations of process parameters for GM process which directly or indirectly improves the efficiency as well as performance of GM process. The work suggests that the developed model can be used as systematic approach for prediction and parameter optimization of any GM processes.