Int J Adv Manuf Technol (2012) 58:585–596 DOI 10.1007/s00170-011-3415-2
ORIGINAL ARTICLE
Predictive control of drying process using an adaptive neuro-fuzzy and partial least squares approach Ali Azadeh & Najme Neshat & Afsaneh Kazemi & Mortezza Saberi
Received: 12 February 2010 / Accepted: 30 May 2011 / Published online: 14 June 2011 # Springer-Verlag London Limited 2011
Abstract In this paper, adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), and partial least squares (PLS) approaches are applied to predictive control of a drying process. In the proposed approaches, the PLS analysis is used to pre-process actual data and to provide the necessary background to apply ANN and ANFIS approaches. A reasonable section of this study is assigned to the modeling with the aim at predicting the granule particle size and executing by ANFIS and ANN. ANN holds the promise of being capable of producing non-linear models, being able to work under noise conditions, and being fault tolerant to the loss of neurons or connections. Also, the ANFIS approach combines the advantages of fuzzy system and artificial neural network to design architecture and is capable of dealing A. Azadeh (*) Department of Industrial Engineering, Centre of Excellence for Intelligent-Based Experimental Mechanic, College of Engineering, University of Tehran, Tehran, Iran e-mail:
[email protected] N. Neshat Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Intersection of Jalale Ale Ahmad and Shahid Chamran Highways, P.O. Box 14155-143, Tehran, Iran M. Saberi Department of Industrial Engineering, University of Tafresh, Tafresh, Iran M. Saberi Institute for Digital Ecosystems and Business Intelligence, Curtin University of Technology, Perth, Australia A. Kazemi Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Iran
with both limitation and complexity in the data set. The efficiencies of ANFIS and ANN approaches in prediction are compared and the superior approach is selected. Finally, by deploying the preferred approach, several scenarios are presented to be used in predictive control of spray drying as an accurate, fast running, and inexpensive tool. This is the first study that presents a flexible intelligent approach for predictive control of drying process by ANN, ANFIS, and PLS. The approach of this study may be easily applied to other production process.
Keywords Neuro-fuzzy inference system . Spray-drying process . Artificial neural networks . Predictive control . Partial least squares
Nomenclature ANFIS Adaptive neuro-fuzzy inference system ANN Artificial neural network MAPE Mean absolute percentage error MFs Membership function NN Neural network PLS Partial least squares Pp Fed slip pressure Ps Air suction pressure PS Particle size R2 Absolute fraction of variance RMSE Root mean square error Tin Inlet air temperature TOUT Exhausted air temperature WRG Weight of residual granule Greek Symbol υ Viscosity ρ Density
586
1 Introduction Spray drying as a unique drying process for powder production has experienced extended applications in the foodstuff, manufacturing, and pharmaceutical industries for over a century. Spray drying is a needful phase in these industries regarding to several issues such as the year-round availability for seasonal products, lower transportation and storage costs, and customers' process requirements. In ceramic industries, spray drying has simplified the overall production process by replacing filter-pressing, drying, grinding, re-moisturing, and classification and has also reduced labor and maintenance requirements. The slip obtained from grinding raw material in an aqueous suspension is dried by way of a continuous, automatic process that provides a product of controlled moisture content, shape, and particle size that is ideal for pressing. Particle size (PS) as a quality characteristic during the granule production is controlled by measuring. The weight of the residual granule (WRG) is the weight of the output granule with a diameter greater than 300 μm in a sample which is 0.1 kg in weight. Hence, it is supposed to be closely monitored to control the granule PS. According to the spray-drying diagram shown in Fig. 1, the process response, i.e., PS is considered as a quality characteristic with respect to its proposed related variables, either properties or operating conditions which are the slip viscosity (v) and density (ρ) as well as a few in-process variables, i.e., the hot-air temperature(Tin), the air suction pressure (Ps), and the fed slip pressure (Pp). The exhausted air temperature (Tout) as an in-process variable is generated through internal treatments of spray drying [1]. Often, a full theoretical understanding of complex process treatment such as spray drying [2] may be lacking. However, this understanding is strongly penalized by the complexity of the interdependent and correlated process variables. Constructing model of process is a conventional alternative for discovering the relationships among input and output variables with the aim of controlling the process. In the late 1990s, Kieviet and Kerkhof [3] predicted the temperature and moisture of the particles being spray-dried as a function of time. In this graphic model, the airflow, temperature, and humidity pattern were modeled using a computational fluid dynamic (CFD) package. After that, Huang et al. [4, 5], Blei and Sommerfeld [6], as well as Huang and Mujumdar [7] proposed employing this computational tool for spray drier modeling. Fig. 1 Process diagram of spray drying
Int J Adv Manuf Technol (2012) 58:585–596
Oakley [8] described four approaches for modeling of spray dryers at various levels. These parametric approaches of modeling included heat and mass balances, equilibriumbased models, rate-based models, and CFD. To judge by the recent publications, conventional parametric methods are not suitable to model complex manufacturing processes [9–11], due to the non-linear nature of their relations as well as imprecision and limitation in collected data. Artificial neural networks (ANNs) and fuzzy logic approaches have been known to be a good candidate approaches for this purpose [12–17], whereas the most popular application of ANNs in sprays drying is the prediction of process parameters; there are several studies such as Chegini et al. [18] in which they predicted seven performance indices in an orange juice spray drier using ANNs. Also, the one presented by Youssefi et al. [2] compared ANN approach with response surface methodology (RSM) approach for predicting the quality parameters of spray-dried pomegranate juice. The results showed that ANN model outperforms RSM for complex spray drying. In the other side, adaptive neuro-fuzzy inference system (ANFIS) as an adaptive ANN which represents a particular type of fuzzy inference system (FIS) has been also developed largely for high non-linearity and complex practical industrial processes [19, 20]. In this study, the employed raw data to modeling, the spray-drying process is collected from production database in an uncertain and complex manufacturing environment. Moreover, the data is strongly penalized by the personal and measurement errors. Hence, we are dealing with a potentially non-crisp and complex environment. Thus, a flexible neuro-fuzzy inference system, neural network, and partial least squares approach, namely, PLS–ANN–ANFIS approach is proposed for improved modeling and predictive control of the spray drying of this study. In the light of above discussed, the superiority of the flexible approach over several approaches discussed in the some of the previous studies can be addressed to its outstanding features. The PLS–ANN–ANFIS is applicable to complex, non-linear, and ambiguous environments due to ANN and ANFIS mechanisms. It is robust against inconsistency and noise in data as well as high dimensionality and co-linearity. Besides, it pre-processes and post-processes the presented data to provide higher generalization capability and precision via eliminating possible noise in the data set. Dealing with uncertain, limited, and non-crisp data is caused this approach to have preference over conventional approach. In addition, this is the first study that has been undertaken to model the spray drying through ANN and ANFIS approaches. Consequently, PLS–ANN–ANFIS approach as a preferred approach can be a good alternative for improved predictive control in most cases (Table 1).
√ √ √
√
√ √
√
√
587
According to the proposed approach, initially, PLS analysis is used to process actual data and to provide the necessary background to apply ANN and ANFIS for granule PS prediction. As a comparative study, the performance of the ANN and ANFIS approach through different parameters is investigated. Finally, deploying the superior approach, several scenarios are presented in order to predictive control of granule PS as an accurate, fast running, and inexpensive tool. The remainder of this section is organized as follows. Section 2 briefly introduces artificial neural networks, partial least squared analysis, and adaptive neuro-fuzzy inference system. The proposed PLS–ANN–ANFIS approach is described in Section 3. Section 4 presents the experiment and the actual case study of this study. Section 5 discusses the results and scenarios. The concluding remarks of this study are addressed in Section 6.
2 Applied techniques
√ √ √ √ √ √ √
√
√ √
√
√ √
√
√
√
√
2.1 Artificial neural networks
Approach The flexible PLS– ANN–ANFIS approach Youssefi et al. [2] Chegini et al. [18] Oakley [8] Kieviet and Kerkhof [3]
Dealing Uncertain, Limited, and Non-Crisp Data Multiple Dealing Outputs Environment Capability Complexity and Non-Linearity Feature
Table 1 The features of PLS–ANN–ANFIS approach versus other approaches
Intelligent High Multiple Dealing Optimum Data Scaling, modeling Forecasting Inputs Ambiguity Prediction Pre-Processing, Capability and and PostReliability Processing
Robustness Against Noisy and Inconsistent Data
Dimension Reduction Capability
Int J Adv Manuf Technol (2012) 58:585–596
ANNs mimic the ability of the biological neural systems in a computerized way by resorting to the learning mechanism as the basis of human behavior. [21] Utilizing samples from process outputs, ANNs proposed an approximate model architecture to fit data. Therefore, ANNs can be applied to problems with non-linear nature or with too complex algorithmic solution to be found. Their ability to perform complex decision-making tasks without prior programming makes ANNs more attractive and powerful than parametric approaches especially for complex problems. Whereas accurate prediction of a quality characteristic is a key factor in the success of a manufacturing operation, ANNs have been considerably deployed to model and predict response of the complex manufacturing process. While modeling of the process, the network is trained considering input-process variables (e.g., process settings) and characteristics of the input material as its input variables, and process response/outputs (e.g., quality characteristics) as the output variables. The ANN then “learns” the governing relationships in the input and output data sets by modifying the weights between its nodes. In essence, a trained ANN model can be considered as a function that maps input vectors to output vectors. Briefly, the intention is that the network should behave exactly like the process considering its response to variables and conditions; hence, providing a model of the process, which can be used for prediction of output properties. The architecture of neural network models usually consists of three parts: an input layer, hidden layers, and an output layer. The information contained in the input
588
Int J Adv Manuf Technol (2012) 58:585–596
layer is mapped to the output layer through the hidden layers. Each neuron can receive its input only from the lower layer and send its output to the neurons only on the higher layer. Figure 2 illustrates the network architecture of ANN models consisting of one hidden layer with S neurons along with input and output layers with R and one neuron, respectively. Here, the input vector p with R input elements is represented by the solid dark vertical bar at the left. Thus, these inputs post multiply S-row, R-column matrix W. One as a constant value enters the neuron as an input and is multiplied by a vector bias b with S row and single column. The net input to the transfer function f is n, the sum of the bias b and the product Wp. This summation is passed to the transfer function f to get the neuron's output, which in this case is an S length vector [22]. There are about 31 different ANN topologies which are being employed in research at present. The most common network is multilayer perceptrons (MLP) also called multilayer feedforward networks. The MLP trained with backpropagation (BP) algorithm is suitable as blackbox model of systems whose underlying relations are vaguely known or extremely complex. The most popular algorithm in engineering applications is the standard backpropagation (BP) algorithm [23]. Based on BP algorithm, during the training process, the deviation between the network output and the desired output at each presentation is computed as an error. This error, in quadratic form, was then fed back (back propagated) to the network and used for modifying the weights by a gradient descent method. The performance of ANN model depends on the fitness of the network features (e.g., number of hidden layers, type of transfer functions, and number of neurons in each hidden layer). For instance, too few of neurons may result in underfitting, but too many neurons may yield over-fitting, which means that all the training data fit well, but ANN model performance for test data is mediocre. The optimal configuration of the network is selected according to the value of training error function. Therefore, various archi-
W
R 1
R S
+ 1
b
n S 1
f
a S 1
S
S 1
Fig. 2 The network architecture of an ANN model with one hidden layer with S neurons along with input and output layers with R and one neurons
tectures of ANN network are proposed by different features and the best one is selected by trial and error way considering the value of the user-specified training error function. During the training process, representative examples of inputs and their corresponding outputs of process are presented to the networks. Ultimately, the most fitting network based on the user-specified training error function is chosen. The validation data set is used to ensure that there is no over-fitting in the final result. In order to validate the model, a data set is randomly selected from the training data. When a significant over-fitting occurs, the error of validation data starts to increase and the training process comes to an end. By termination of process training and validation, the network is ready for prediction. Therefore, the input vectors from the separate test data are introduced to the trained network and the responses of the network, i.e., the predicted outputs, are compared with the actual ones using the performance indicators. 2.2 Partial least squares analysis The critical step in process modeling is determining the most crucial input variables and predicting process response from gathered data. However, the high dimensionality and co-linearity of such data makes it difficult to construct a reliable model of process. The need to describe the quality of process from such data led to the development of multivariate analysis for complex process. For this aim, several strategies have already been used such as principal component analysis (PCA) but the most applicable one for complex process especially when the gathered data is small compared to the number of variables is PLS analysis [24]. The orthogonality of the principal component eliminates the multi co-linearity problem regarding to the covariance between input variables. But, PLS as a dimensionality reduction method is applied to be chosen an optimum subset of input variables, which are called latent variables, considering the covariance between input variables and output variables [25]. Therefore, PCA is called an unsupervised dimension reduction methodology, and PLS a supervised dimension reduction methodology. PLS finds a set of latent variables with the constraint that these components explain as much as possible of the covariance between input set and output set of process. In the classical PLS analysis, the SIMPLS [26] algorithm is applied to the PLS regression in order to sequentially extract the latent vectors g, f and the weight vectors w, c from the X and Y matrices in decreasing order of their corresponding singular values. As a result, PLS decom-
Int J Adv Manuf Technol (2012) 58:585–596
poses X form
(n×N)
and Y
(n×M)
589
matrices with mean zero into the
X ¼ GPT þ E
ð1Þ
Y ¼ FQT þ S
ð2Þ
Where G and F are n×k matrices of the extracted k score vectors, P(N×k) and Q(M×k) are matrices of loadings, and E(n×N) and S(n×M) represent matrices of residuals. Unlike the classical PLS algorithm, the modified PLS algorithm normalizes the latent vectors g, f rather than the weight vectors w, c [27]. The PLS regression model can be expressed with regression coefficient B and residual matrix R as follows: Y ¼ XB þ R
ð3Þ
B ¼ W ðPT W Þ1 C T
ð4Þ
Where P(N×k) is the matrix consisting of loading vectors pi ¼ X T ti =ðgiT gi Þi =1, . . ., k. Due to the fact that pTi wj ¼ 0 for i>j and in general pTi wj 6¼ 0for ii derived the following equalities [28]: T
W ¼X F
ð5Þ
P ¼ X T GðGT GÞ1
ð6Þ
C ¼ Y T GðGT GÞ1
ð7Þ
Substituting Eqs. (5) to (7) into Eq. (7) using the orthogonality of the matrix G columns, matrix B is equal to: 1
B ¼ X FðG XX FÞ G Y T
T
T
T
ð8Þ
Although PLS is a linear regression method, it can be forced to cope with non-linearity by either a non-linear preprocessing function or using additional PLS factors [29]. 2.3 Adaptive neuro-fuzzy inference system Neuro-fuzzy modeling [30] refers to the way of applying various learning techniques developed in the neural network literature to fuzzy modeling or a fuzzy inference system [31]. Neuro-fuzzy system, which combines neural networks and fuzzy logic have recently gained a lot of interest in research and application.
The neuro-fuzzy approach added the advantage of reduced training time not only due to its smaller dimensions but also because the network can be initialized with parameters relating to the problem domain. Such results emphasize the benefits of the fusion of fuzzy and neural network technologies as it facilitates an accurate initialization of the network in terms of the parameters of the fuzzy reasoning system. Various types of FIS are reported in the literature [32, 33] and each is characterized by their consequent parameters only. A specific approach in neuro-fuzzy development is the adaptive neuro-fuzzy inference system (ANFIS), which has shown significant results in modeling non-linear functions [34]. ANFIS use a feedforward network to search for fuzzy decision rules that perform well on a given task. Using a given input–output data set, ANFIS creates a FIS whose membership function parameters are adjusted using a BP algorithm alone or a combination of a BP algorithm with a least squares method. This allows the fuzzy systems to learn from the data being modeled. Consider a first order Takagi–Sugeno fuzzy model with a two input, one output system having two membership functions for each input. Then, the functioning of ANFIS is a five-layered feedforward neural structure, and the functionality of the nodes in these layers can be summarized as: o1;i ¼ mAi ðxÞ o1;i ¼ mBi2 ðyÞ
ð9Þ
Where x or y is the input to the node, Ai or Bi-2 is a fuzzy set associated with this node. At the first layer, for each input, the membership grades in the corresponding fuzzy sets are estimated. At the second layer, all potential rules between the inputs are formulated by applying fuzzy intersection (AND). The product operation is used to estimate the firing strength of each rule. o2;i ¼ wi ¼ mAi ðxÞ mBi ðyÞ; i ¼ 1; 2
ð10Þ
The third layer is used for estimation of the ratio of the ith rule's firing strength to the sum of all rule's firing strengths. o4;i ¼ wi fi ¼ wi ðpi x þ qi y þ ri Þ
ð11Þ
Where wi is the output of layer 3 and {pi, qi, ri} is the parameter set. Parameters in this layer will be referred to as consequent parameters. The final layer computes the overall output as the summation of all incoming signals from layer 4.
Overall output ¼ o5;i ¼
X i
P
wi fi i wi fi ¼ P wi i
ð12Þ
590
Int J Adv Manuf Technol (2012) 58:585–596
Optimizing the values of the adaptive parameters is of vital importance for the performance of the adaptive system. Jang et al. developed a hybrid learning algorithm for ANFIS which is faster than the classical backpropagation method to approximate the precise value of the model parameters. [35] The hybrid learning algorithm of ANFIS consists of two alternating phases: (1) gradient descend which computes error signals recursively from the output layer backward to the input nodes, and (2) least squares method, which finds a feasible set of consequent parameters.
3 The PLS–ANN–ANFIS approach Modeling the complex and non-linear manufacturing processes which deals with noisy, limited, and nonintegrated data requires methods that can alleviate these problems. Thus, we proposed an integrated algorithm namely, PLS–ANN–ANFIS (according to Fig. 3) to alleviate these problems. This approach is applied to predict the granule PS in an attempt to demonstrate the superior approach. According to the proposed integrated approach, both ANN and ANFIS approaches are applied for granule PS prediction, as they result in PLS–ANN and PLS–ANFIS models, respectively. The slip viscosity, density, and the exhausted air temperature are selected by means of a PLS analysis of the data in order to eliminate less correlated variables. They are considered as explanatory variables in Fig. 3 The proposed flexible approach for optimum granule PS prediction
PLS–ANN and PLS–ANFIS models. Besides, ANN approach is applied for PS prediction in terms of the slip viscosity and density, the hot-air temperature, the air suction pressure, and the fed slip pressure regarding to the previous studies. Actual data set which consists of 300 data vectors was collected at steady-state conditions from a real system. While 80% of the data set was randomly assigned as the training set, 10% as the validation set, and the remaining 10% was employed for testing the network. All the input and output values were normalized by pre-processing and checked for integrity by histogram plot. Running and estimating all of the plausible ANN and PLS–ANN models are carried out regarding to various network features. However, type of membership function and number of linguistic variables are two ANFIS parameters considered for constructing all of the plausible PLS–ANFIS models. Mean absolute percentage error (MAPE), root mean square error (RMSE), and absolute fraction of variance (R2) [23], as performance indicators, are used for evaluation of generalization capability of proposed models. The MAPE, which shows the mean ratio between the error and the actual values, is calculated as: ^ m 1 X ðyi yi Þ ð13Þ MAPEð%Þ ¼ 100 m i¼1 yi Where byi is the predicted value by the ANN model yi is the actual value of the response process and m is the number of
Determination of input variables regarding to previous studies
Determination of input variables regarding to PLS analysis
Selection of training, validation, and test data Preprocessing training and validation data
Development all of the plausible ANN models considering various network features (ANN models)
Development all of the plausible ANFIS models regarding to PLS results for input variables (PLSANFIS models)
Development all of the plausible ANN models regarding to PLS results for input variables (PLSANN models)
Selection of preferred model for each type of models based on user- specified error function Preprocessing test data Predicting for test data by ANN, PLS-ANN, and PLS-ANFIS models Post-processing the predicted data Selection of best model for prediction regarding to the RMSE, MRE, and R2 results
Int J Adv Manuf Technol (2012) 58:585–596
591
points in the data set. The RMSE is calculated by: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m 1 X ^ 2 RMSE ¼ ðyi yi Þ m i¼1
4.1 The ANN model development ð14Þ
Finally, the R2, a statistical criteria which can be applied to multiple regression analysis, is calculated by: m P
R2 ¼ 1 ð i¼1 m P i¼1
^ 2
ðyi yi Þ
ðyi yÞ2
Þ
ð15Þ
The absolute fraction of variance ranges between zero and one. Ideally, R2 should be close to one, whereas a poor fit results in a value near zero.
4 Case study and experiment This section aims at applying the PLS–ANN–ANFIS approach to a real spray drying in a large ceramic tile manufactory in Yazd province of Iran. The collected raw data was provided randomly from production database for the period of 23 March 2005 to 22 September 2006 (please see Appendix). A few features of the proposed input, in-process, and output variables of spray drying are summarized in Table 2. It should be noted that the employed data in this study were provided in an uncertain and complex manufacturing environment. Moreover, there are biases in collection process due to human and measurement errors. Besides, the collected data was strongly penalized by the personal and measurement errors. Hence, it can be potentially noncrisp environment and require special treatment. In this section, the results of executing the ANN and PLS–ANN models by artificial neural networks as well as the PLS–ANFIS model by adaptive neuro-fuzzy inference system are presented.
Applying a global approach, the ANN model adopted for the spray-drying treatments was MLP trained with BP algorithm based on Levenberg-Marquardt algorithm. The network includes five inputs corresponding to ρ, ν, Pp, Ps, and Tin, while one output corresponding to the WRG. To meet the best performance of ANN model, training data is normalized by pre-process so that it falls in the interval [−1, 1]. For choosing the optimal configuration of network for granule PS prediction, a number of different network configurations, consisting of one to three hidden layers and different number of neurons in hidden layers with various transfer functions were considered. The training process was run in a matrix laboratory (MATLAB) environment so a minimum of the userspecification error function, i.e., RMSE was reached while the number of epochs was less than 200. The optimal configuration of each trained network was selected based on value of training RMSE. As shown in Fig. 4a, the sensitivity analysis of training RMSE function in terms of number of neurons in first and second hidden layers is conducted. In order to determine the minimum value of training RMSE function, this function is mapped to a flat surface (Fig. 4b) as the lower height, the darker point. As shown, the darkest point addresses seven and ten neurons in first and second hidden layers, respectively. However in this case, selecting number of layers more than three causes the training performance of network to decrease. The optimum network architecture of the ANN model for predicting granule PS is given in Fig. 5. This figure shows the network which includes two hidden layers with seven and ten neurons along with input and output layers with five and one neurons, is the most fitting network. Activation functions in the hidden layers were chosen as the purline, tangent sigmoid, and purline transfer functions, respectively, by trial and error.
Table 2 Characteristics of proposed variables of spray drying Units
Type
Interval Maximum
Minimum
Mean value
Standard deviation
Slip density Slip viscosity Inlet air temperature Fed Slip pressure Air suction pressure
kg m3 S °C N/m2 N/m2
Input Input In-process In-process In-process
1.66×103 57.00 540.00 13.50×10−5 18.50×10−2
1.70×103 67.00 555.00 21.50×10−5 21.00×10−2
1.68×103 59.02 549.12 15.30×10−5 18.54×10−2
0.01×103 3.04 2.94 0.70×10−5 1.30×10−2
Exhausted air temperature Weight of residual granule
°C kg
In-process Output
91.00 68.10×10−3
104.00 77.00×10−3
98.27 74.22×10−3
2.64 3.68×10−3
Training RMSE
10 -5
592
Int J Adv Manuf Technol (2012) 58:585–596
250 200 16 150
200-250 150-200 100-150 50-100 0-50
13 10
100 7 50
4
0
Number of neurons in first hidden layer
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of neurons in second hidden layer
Fig. 4 a, b The sensitivity analysis of performance learning (training RMSE) in terms of the number of neurons in first and second hidden layers
The ANN model for granule PS prediction was validated by training stop after 87 epochs when the validation RMSE started to increase. The training results of ANN model for granule PS prediction are given in Table 4. The ANN model predictions for granule PS resulted in an MAPE of 9.920%, an RMSE of 1.443×10−3 kg, and an R2 of 81.12% for the test data. 4.2 The PLS–ANN model development As mentioned, Tout as an in-process variable is generated through internal treatments of spray drying. Likewise, in order to establish the heat (energy and material) balance in the spray drier, Tout is rationally related to Tin, Ps, and PP. PLS analysis was applied to the variables of spray drying
for proper reducing the dimension of input set and consequently increasing the reliability of the ANN model. Table 3 shows the results of PLS analysis for the variables of spray drying using the MATLAB Software. It presents the amount of variance captured by each latent variable and the total amount of variance captured by the PLS algorithm for the six latent variables. The optimal number of latent variables to include in the model was determined using the eigenvalue decomposition algorithm. As illustrated, it is possible to assess which variables are the most influent in the prediction of PS. The three first latent variables are: (1) a linearity combination of Tin, Ps, Tout, and PP (Eq. 16), (2) ρ (because of its independency of other variables), and (3) ν is modeling close to 69.15% of variation in the output set.
Latent variableð1Þ ¼ 0:65 ðTout 1:19Þ=0:62 þ 0:68 ðPP 1:16Þ=0:46 0:14 ðPs 48:53Þ=17:71 þ 0:20 ðTin 2:36Þ=0:87:
The three remaining latent variables i.e., Tin, Ps, and PP only account for a total of 14.82% of variation thus it is reasonable to assume that the Tout depends on Tin, Ps, and PP and also as a hint can be a substitute for Tin, Ps, and PP. The PLS–ANN as an abstraction model form from the ANN model was developed for granule PS prediction via the slip viscosity, density, and the exhausted air temperature Fig. 5 The network architecture of the ANN model for granule PS prediction
ð16Þ
regarding to the findings of this section. The reader should note the values of the exhausted air temperature are estimated by ANNs in terms of its correlated variables. The training results of ANN model for granule PS prediction are given in the Table 4. The results showed that the network which includes two hidden layers with six and eight neurons along with input and output layers with
p1 IW 1,1
5 *1
7 1 *5 1
b1 7 1 *1
+
n1
a1
7 1 *1
7 1 *1 7
LW 2,1 10 2 * 7 1
1
1
b2 10 2 *1
+
a2 10 2 * 1
n2 10 2 * 1
LW 3,1 10 2 * 1 3
10 2 1
b3
+
n3 1 3 *1 13
Int J Adv Manuf Technol (2012) 58:585–596
593
Table 3 The results of PLS analysis for input variables of spray drying Latent variables Percentage of explained variance for input set
Cumulative percentage of explained variance for input set
Percentage of explained variance for output set
Cumulative percentage of explained variance for output set
1 2 3 4 5 6
25.3526 45.2895 59.2228 66.6242 71.6921 74.3841
27.7022 21.5759 19.8754 2.7622 5.8937 6.173
27.7022 49.2781 69.1535 71.9157 77.8094 83.9824
25.3526 19.9369 13.9333 7.4014 5.0679 2.6920
three and one neurons is the most fitted network to model the spray drying. The activation functions in the hidden layers were chosen as the purline transfer, log sigmoid, and purline transfer function. In order to show how well the trained PLS–ANN model performs, all prepared test data is normalized and presented to the trained PLS–ANN model. The PLS–ANN predictions for granule PS resulted in an MAPE of 6.834%, an RMSE of 1.794×10−3 kg and an R2 of 87.184% for the test data set. 4.3 The PLS–ANFIS model development We observe that given the fixed values of elements of premise parameters, the overall output can be expressed as a linear combination of the consequent parameters. The ANFIS architecture is not unique. Some layers can be combined and still produce the same output. In this ANFIS architecture, there are two adaptive layers (1, 4). Layer 1 has three modifiable parameters (ai, bi, and ci) pertaining to the input MFs. These parameters are called premise parameters. Layer 4 has also three modifiable parameters (pi, qi, and ri) pertaining to the first order polynomial. These parameters are called consequent parameters. Figure 6 presents the structure of the proposed ANFIS for granule PS prediction. Two parameters have been considered in constructing and examination of plausible ANFIS models. Type of membership function and number of linguistic variables are two mentioned parameters. Six different membership functions are considered in building ANFIS as follows: built-in membership function composed of difference between two sigmoidal membership functions
(dsig), Gaussian combination membership function (gauss2), Gaussian curve built-in membership function (gauss), Generalized bell-shaped built-in membership function (gbell), Πshaped built-in membership function (pi), and built-in membership function composed of product of two sigmoidally shaped membership functions (psig). Also, numbers for linguistic variables have been considered between 2 and 6. The architectures which are shown below have minimum MAPE among all of the other architectures. The architectures with minimum of MAPE are shown in Table 5. The PLS–ANFIS predictions for granule PS resulted in an MAPE of 3.682%, an RMSE of 0.834×10−3 kg and an R2 of 91.06% for the test data set. It should be noted that all plausible membership function have been used in the ANFIS modeling. The best structure has been selected based on the MAPE. The optimum range of membership function have determined based on the training module of the ANFIS.
5 Discussion and results The indicators applied for the evaluation of the model performance are MAPE, RMSE, and R2. The comparison of numerical results for performance evaluation shows that the
Table 4 The detailed information for optimum configuration of the PLS–ANN and ANN model for predicting the granule PS Model
Optimum configuration Relative error Training error Validation error
PLS–ANN ANN
3–6–8–1 6–7–10–1
1.12281 e-004 2.37658e-004
6.3349 e-004 8.1003 e-004
Fig. 6 The structure of ANFIS model for granule PS prediction
594
Int J Adv Manuf Technol (2012) 58:585–596
Table 5 The results of MAPE for the best ANFIS model
1 2 3 4 5 6
MF type
Number of MFs
MAPE (%)
gauss gauss2 dsig pi psig gbell
6 6 6 6 6 6
3.31 3.32 3.50 3.54 3.41 3.33
PLS–ANN model has an improvement in R2 of 4.064%, a decrease in MAPE of 3.086% and a decrease in RMSE of 0.263×10−3 kg when it is compared with the ANN model. This obtained results validate the properly dimension reducing of input set (regarding to the PLS analysis findings) tends to improve the performance of the PLS–ANN model. In addition, according to the results of Table 6, the PLS– ANFIS model has an improvement in R2 of 3.876%, a decrease in MAPE of 3.152% and a decrease in RMSE of 0.345×10−3 kg. These results demonstrate that the PLS– ANFIS model has a performance enhancement when it is compared with the PLS–ANN model. The significance of the proposed ANFIS for granule PS prediction is threefold. First, it uses pre-processing and postprocessing approaches to eliminate possible noise. Second, it identifies the best ANFIS model based on minimum MAPE. Third, it provides more accurate solution than previous approach (such as ANNs) because it uses ANFIS which use adaptive neural modeling and fuzzy logic. This would efficiently handle uncertainty, noise, and non-linearity in the given data set and provide optimum solution. An important feature in modeling of spray drying is that the superior model i.e., the PLS–ANFIS model can also be used for accurate investigating the effects of the input variables on the outputs. In order to visualize these capabilities, the PLS–ANFIS model predictions of granule PS as a function of ν and another input variable are shown in Figs. 7 and 8 as examples. These figures illustrate several scenarios used for the predictive process control when two input variables vary while the other input variables are kept constant. In fact, the values of Tout are estimated in terms of Tin, Ps, and PP by ANNs and then, they are used for prediction of WRG values
Fig. 7 Illustration several scenarios using the PLS–ANFIS model predictions for the process response as a function of the slip viscosity and the fed slip pressure when the other variables are kept constant (ρ= 1.68, Ps =18.54, Tin =549.12)
by the PLS–ANFIS model. Note that Figs. 7 and 8 report the predictions not only in the range of the considered inputs in the study but also those beyond the normal range. Figure 7 depicts the changes in the predicted values of WRG with respect to the values of ν and PP when the other three input variables are kept constant (ρ=1.68, Ps =18.54, Tin =549.12). It is seen that, in spite of what one expects to observe, WRG decreases with a significant increase in PP (PP =21.5). This abnormal behavior can be interpreted as follows: When PP decreases significantly, a cloud of slip particles forms due to excessive pressure of spraying the slip which in turn causes the slip particles to stick together. However, there is little exclusion considering the interactive effects among variables. Figure 8 reports the changes in the predicted values of WRG with respect to the values of ν and Ps when the other three input variables are kept constant (ρ=1.68, PP =15.30, Tin =549.12). As can be seen, WRG increases while Ps decreases and ν increases because of a greater chance of
Table 6 The results of performance evaluation of the PLS–ANN and ANN model for predicting the granule PS Model
PLS–ANFIS PLS–ANN ANN
Performance evaluation R2 (%)
MAPE (%)
RMSE (kg)
91.06 87.18 68.09
3.68 6.83 15.67
0.834×10−3 1.1794×10−3 4.056×10−3
Fig. 8 Illustration several scenarios using the PLS–ANFIS model predictions for the process response as a function of the slip viscosity and the air suction pressure when the other variables are kept constant (ρ=1.68, PP =15.30, Tin =549.12)
Int J Adv Manuf Technol (2012) 58:585–596
595
particles sticking together. However, several exclusions regarding to the interactive effects among variables can be observed.
6 Conclusions This study has undertaken to develop an integrated adaptive neuro-fuzzy inference system, artificial neural network, and partial least squares for optimum granule PS prediction. It presented three distinct models for granule PS prediction based on ANN, integrated PLS– ANN, and integrated PLS–ANFIS approaches. Granule PS is viewed as the resultant of the five explanatory variables which are the slip viscosity and density, the hot-air temperature, the air suction pressure, and the fed slip pressure in ANN model. However, the PLS–ANN and PLS–ANFIS models were developed in term of the slip viscosity, density, and the exhausted air temperature regarding to the findings of PLS analysis. The proposed models were trained and tested by considering 300 actual data covering a wide range of operating conditions and were collected randomly on an actual system at steady state conditions. The comparison study based on generalization capability of these three models revealed that first, the properly dimension reducing of input set using PLS analysis caused to improve the performance of
neural network models and second, the PLS–ANFIS model can be a better alternative for prediction of granule PS because of being capable of handling complexity and limitation in the collected data. In order to develop a predictive-control strategy, employing the PLS–ANFIS, several scenarios as an accurate and fast running method were developed to identify the optimal process settings regarding to the desired process response. Therefore, this approach requires only a limited number of tests instead of an exhaustive actual study or dealing with a complicated mathematical model. Manufacturers employing the PLS–ANFIS model as a reliable model for predictive control of spray drying, can save both engineering effort and funds. Furthermore, the approach of this study may be used for other cases to predict the quality characteristics of products in complex and imprecise systems. It should be noted that this is the first study that presents a flexible intelligent approach for predictive control of drying process by ANN, ANFIS, and PLS. The approach of this study may be easily applied to other drying process for optimum. Acknowledgment The authors are grateful for the valuable comments and suggestion from the respected reviewers. Their valuable comments and suggestions have enhanced the strength and significance of our paper. The authors would like to acknowledge the financial support of University of Tehran for this research under grant number 8106013/1/04.
Appendix Table 7 A sample of raw data of spray drying in a large ceramic tile manufactory in Yazd province of Iran Data number ρ (×103)
1
2 1.66
3 1.68
4 1.69
5 1.69
6 1.66
……. 292
7 1.67
1.67 ……
υ
60
65
59
58
70
65
58
Tin
555
543
549
547
551
552
550
……
1.67
293 1.68
294 1.68
295 1.67
296 1.66
297 1.68
298 1.68
299 1.67
300 1.69
60
61
58
59
66
58
64
64
66
…… 547
550
549
551
549
547
540
552
548
Pp (×10−5)
18.7
21.2
20.1
17.9
19.6
21.3
20.3
……
18.8
20.3
21.3
18.7
17.9
20.9
20.8
19.7
19.6
Ps (×10−2)
19
18.5
19
19.5
20
19
19.5
……
20.5
20.05
19.5
21
21
20.5
20
19
19
Tout
98
96
98
91
92
95
……
97
97
98
96
93
93
98
97
WRG (×10−3)
72
69.2
69.5
69.9
72.1
63.1
……
67.9
68.6
69.5
72.8
74.6
76.6
64.3
74.5
101 63.4
References 1. Anonymous (1989) From technology through machinery to kilns for SACMI tile. SACMI Press, Italy 2. Youssefi Sh, Emam-Djomeh Z, Mousavi SM (2009) Comparison of artificial neural network (ANN) and response surface methodology (RSM) in the prediction of quality parameters of spraydried pomegranate juice. Dry Technol 27(7):910–917 3. Kieviet FG, Kerkhof PJAM (1997) Aie flow, temperature and humidity patterns in a co-current spray dryer: modelling and measurements. Dry Technol 15(6–8):1763–1773
102 69.4
4. Hugan L, Mujumdar AS, Kumar K (2003) Use of computational fluid dynamics to evaluate alternative spray dryer chamber configurations. Dry Technol 21(3):132–147 5. Huang L, Passos ML, Kumar K, Mujumdar AS (2005) A threedimensional simulation of a spray dryer fitted with a rotary atomizer. Dry Technol 23(9–11):1859–1873 6. Blei S, Sommerfeld M (2007) Modern drying technology: computational tools at different scales. In: Tsotsas E, Mujumdar AS (eds). WILEY-VCH Verlag, Weinheim. 7. Huang L, Mujumdar AS (2007) Simulation of an industrial spray dryer and prediction of off-design performance. Dry Technol 25 (4):703–714
596 8. Oakley DE (2004) Spray dryer modeling in theory and practice. Dry Technol 22(6):1371–1402 9. Barletta M, Gisario A, Guarino S (2007) Modeling of electrostatic fluidized bed (EFB) coating process using artificial neural networks. Journal of. Eng Appl Artif Intell 20:721–733 10. Mandal S, Sivaprasad PV, Venugopal S, Murthy KPN, Raj B (2008) Artificial neural network modeling of composition– process–property correlations in austenitic stainless steels. J Mater Sci Eng 485:571–580 11. Jiang Z, Gyurova L, Zhang Z, Friedrich K, Schlarb AK (2008) Neural network based prediction on mechanical and wear properties of short fibers reinforced polyamide composites. J Mater Des 29:628–637 12. Yimnirun R, Laosiritaworn YW, Khamman O, Ananta S (2008) Artificial neural network modeling of ceramics powder preparation: Application to NiNb2O6. Ceram Int 34:809–812 13. Sukthomya W, Tannock J (2005) The training of neural networks to model manufacturing process. J Intell Manuf 16:39–51 14. Afzulpurkar NV, Saeed IA, Vyawahare VS (2006) Ceramic tile process modeling for quality improvement using ANN. IEEE International Conference on Industrial Technology, Mumbai, India, December 15–17, 2006; 2896–2900. doi:10.1109/ ICIT.2006.372691 15. Sterjovski Z, Pitrun M, Nolan D, Dunne D, Norrish J (2007) Artificial neural networks for predicting diffusible hydrogen content and cracking susceptibility in rutile flux-cored arc welds. J Mater Process Technol 184:420–427 16. Basheera AC, Dabadea UA, Joshia SS, Bhanuprasadc VV, Gadre VM (2008) Modeling of surface roughness in precision machining of metal matrix composites using ANN. J Mater Process Technol 197:439–444 17. Thyagarajan T, Shanmugam J, Panda RC, Ponnavaikko M, Rao PG (1998) Artificial neural networks: principle and application to model based control of drying systems-A review. Dry Technol 16 (6):931–966 18. Chegini GR, Khazaei J, Ghobadian B, Goudarzi AM (2008) Prediction of process and product parameters in an orange juice spray dryer using artificial neural networks. J Food Eng 84:534– 543 19. Kim J, Kasabov N (1999) HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Network 12:301–1319
Int J Adv Manuf Technol (2012) 58:585–596 20. Lin WS, Tsai CH, Liu JS (2001) Robust neuro-fuzzy control of multivariable systems by tuning consequent membership functions. Fuzzy Set Syst 124:181–195 21. Cui B, Han R (2008) Modeling of dimensional errors in slender bar turning using artificial neural networks. In: Proceedings 7th International Congress on Intelligent Control and Automation, Chongqing, China, pp. 6053–6056 22. Demuth H, Beale M (2000) Neural network toolbox user's guide, 4th edn. The Mathworks Inc, MA, USA 23. Hosoz M, Ertunc HM, Bulgurcu H (2007) Performance prediction of a cooling tower using artificial neural network. Energ Convers Manag 48:1349–1359 24. Balabin RM, Safieva RZ, Lomakina EI (2007) Comparison of linear and nonlinear calibration models based on near infrared (NIR) spectroscopy data for gasoline properties prediction. Chemom Intell Lab Syst 88:183–188 25. Rosipal R, Krämer N (2006) Overview and recent advances in partial least squares. In: Saunders C, Grobelnik M, Gunn S, Shawe-Taylor J (eds) Subspace latent structure and feature selection techniques. Springer, Berlin, Germany, pp 182–235 26. Geladi P, Kowalski BR (1986) Partial least squaress regression: a tutorial. Analytica Chimical Activity 185:1–17 27. Malthouse EC, Tamhane AC, Mah RSH (1997) Nonlinear partial least squares. Comput Chem Eng 21:875–890 28. Rannar S, Lindgren F, Geladi P, Wold S (1994) A PLS kernel algorithm for data sets with many variables and fewer objects. Part 1: theory and algorithm. J Chemom 8:111–125 29. Zhao SJ, Zhang J, Xu YM, Xiong ZH (2006) Non-linear projections to latent structures method and its applications. Ind Eng Chem Res 45:3843–3852 30. Jang JSR (1993) ANFIS: adaptive network based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–683 31. Brown M, Harris C (1994) Neuro-fuzzy adaptive modeling and control. Prentice Hall, New Jersey 32. Jang JSR, Chuen-Tsai S (1995) Neuro-fuzzy modeling and control. Proc IEEE 83(3):378–406 33. Chiu S (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2(3):267–278 34. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132 35. Jang R, Sun C, Mizutani E (1997) Neuro-fuzzy and soft computation. Prentice Hall, New Jersey
