Ind. Eng. Chem. Res. 2006, 45, 197-205
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Optimization of the Fiber Cement Composite Process Carlos Negro,* A Ä lvaro Alonso, A Ä ngeles Blanco, and Julio Tijero Department of Chemical Engineering, Complutense UniVersity of Madrid, AVda. Complutense s/n, 28040 Madrid, Spain
This study reflects the success of combining focused beam reflectance measurement (FBRM) techniques and artificial neural networks (ANN) to make predictions of fiber cement properties, to optimize the industrial process. Three neural networks have been developed. The inputs of these networks are the FBRM sensor measurements and the densities taken from formed sheets. The outputs are final product properties, related to product resistance. With this work, a good prediction of final properties has been achieved. The conclusions reached with the analysis of the results of neural networks can be used in establishing optimal process conditions. The obtained results demonstrate that the FBRM probe can be considered to be a good soft sensor for predicting the on-line fiber cement resistance. 1. Introduction Asbestos cement has been a valuable composite for construction materials, such as roofing, cladding, and high-pressure pipes, because of its excellent cost-effectiveness and durability. In many countries, there are still some industrial sites that are using asbestos; however, all uses of asbestos are expected to be banned in the future because of adverse health effects in people exposed to the fibers. For instance, the United States banned the use of asbestos as a raw material in industry some years ago and, in Europe, the exception for existing installations expired in January 2005. The substitution of asbestos fibers by other types of fibers depends on their cost and reinforcement properties. Of the many possibilities that have been studied, the most widely used on an industrial scale are cellulose fibers from unbleached softwood Kraft pulp, alone or in combination with synthetic fibers.1-3 Asbestos is a naturally occurring fibrous silicate, and the fiber’s size, together with its chemical structure, makes asbestos very compatible with cement. However, the different chemical composition and the hygroscopic character of the cellulose fiber pulp make the compatibility of the cellulose fibers with the cement much more complex. Therefore, it is necessary to consider new aspects of manufacturing to improve the fiber/ matrix bonding; for example, in the Hatschek process, it is necessary to use a suitable flocculant. During fiber cement production, the flocculation process is crucial and requires a specific optimization because of its effect on the retention, dewatering, and formation (e.g., elephant skin appearance and delamination) of mineral fines and, as a consequence, on the overall efficiency of the machine. This is a new key issue for the industry that directly influences competitiveness, which is why there are no published papers available on this topic yet. Nowadays, the main problem is to correlate the final product quality with the performance of the flocculation process to avoid products being made out of specification. Previous studies by the authors have shown the feasibility of using a focused beam reflectance measurement (FBRM): first, as a laboratory tool to select the best flocculant and dosage and, second, as a soft sensor to monitor flocculation in-line on a Hatschek machine during the manufacturing of fiber cement.4,5 Focused beam reflectance measurement (FBRM) probes that allow the in-situ measurement of chord length distribution, over * To whom correspondence should be addressed. Phone: + 34 91 394 42 42. Fax: + 34 91 394 42 43. E-mail:
[email protected].
a wide range of solid concentrations, have been available since 1990. Since then, a number of studies have been performed in order to monitor particle systems in different fields as diverse as oceanography, pharmaceuticals, mineral processing, and effluent treatment.6-7 The relationship between process parameters and final product properties and FBRM measurements in real time can be established with the development of mathematical tools derived from experimental data. Once these correlations are established, they could be used as a predictive tool. However, this is not an easy task as there are many parameters in the fiber cement manufacturing process that affect the final properties of the product. The analysis of the relationships between those properties which can be measured immediately during production and the final product properties, that can only be obtained after a certain period of days, will be of additional help. Simple properties are normally easier to obtain, and therefore, their successful prediction could be beneficial to reduce the future number of losses. For example, in fiber cement manufacturing, the main product properties, such as flexure strength, are analyzed, according to standards, after 48 h, 7 days, or even longer periods of time. However, some variables can be measured immediately in the production line, e.g., the specific gravity of the web sheet, and it could be possible to correlate these values with the final product properties. This would help minimize the production that is out of specification. Artificial neural networks (ANNs) could be of help to simulate the relationships between manufacturing parameters and material performance, providing the basis for a computerbased process optimization system. Many papers have been published in recent years showing the feasibility of using ANNs to study different chemical engineering aspects in industry, such as multiphase flow,8-9 fluid properties,10 mass and heat transfer,11-12 control of reactors,13 catalyst design,14 control of variables such as pH,15 and modeling of blast furnaces, or at industrial plants, in very diverse fields, such as desalination, water treatment, and polymer or paper production.16-18 To a much lesser extent, there are papers related to the manufacturing of polymer composites. Zhang and Friedrich19 have published a recent review on ANNs applied to polymer composites in which the basis and potential applications of ANNs are described in detail. As a summary and as is stated in the reference, inspired by the biological nervous system, an artificial neural network (ANN) approach is a mathematical tool
10.1021/ie048907j CCC: $33.50 © 2006 American Chemical Society Published on Web 11/18/2005
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which can be used to simulate a wide variety of complex scientific and engineering problems. A powerful ANN function is largely determined by the interconnections between the artificial neurons, similar to those occurring in their natural counterparts of biological systems. A certain quantity of experimental results is still required to train a well-designed neural network. After the network has learned to solve the material problems, new data from a similar domain can be predicted without performing too many complex or long experiments. Like the biological counterparts, ANNs can learn from examples and, therefore, they can be trained to find solutions of complex, nonlinear, multidimensional functional relationships without any prior assumptions about their nature. Furthermore, the network is built directly from experimental data by its self-organizing capabilities. In this respect, the mathematical tool is especially suitable for systems in which there is not much information about the process itself and there are no assumptions that can be used. This is the case of the flocculation process during fiber cement manufacturing. The aim of this study is to establish good correlations between FBRM sensor data obtained in real time and final product properties. These correlations can be analyzed by obtaining conclusions that can be used to optimize the production process. The advantage of having good predictions is that they are instantaneous while current quality measurements are taken 48 h, 7 days, and 28 days after the production process. Thus, a good prediction can give quality values instantly, making quality control and trouble detection far easier. 2. Methodology Description and Results Trials were performed on an industrial Hatschek machine with four vats working at 60-65 m/min, producing fiber cement sheets from a mixture of highly refined Pinus radiata unbleached Kraft pulp (3%), poly(vinyl alcohol) (PVA) fibers (2%), and silica fume (6%) on a matrix of ASTM Type II A cement (89%). Fiber cement production consists of the following main steps: raw material mixing, sheet formation, pressing, moulding/ sizing, curing, and finishing. Flocculation is critical at the sheet formation step, which occurs in sieve cylinders. The best location for a sensor to monitor the flocculation process is the inlet of the vat, where the primary thin fiber cement layer is formed on the Hatschek machine. This is the place where the flocculant has just been added, and therefore, the effects will be seen quickly. Moreover, since this primary sheet formation is the critical step for the retention of solids, the selected probe location could allow us to find the correlation between the floc size and the final product properties. For measurements in this study, a commercially available nonimaging scanning laser microscope (or FBRM system), the LASENTEC FBRM M500P, has been used. The FBRM software allows particle size distributions and their evolution with time to be analyzed. From the size distribution, different statistical values can be obtained. These may be the mean size, the median size, the size intervals of particles, etc. All the measurements can be averaged over time, to avoid isolated peaks. Measurements are saved with the date and time, and this fact allows us to have FBRM data correlated with breaking load or bending strength values of the final product. The fiber cement properties analyzed in this work are the following: breaking load after 48 h (Fs(48 h), N/m), breaking load after 7 days (Fs(7 days), N/m), bending strength after 7 days (M(7 days), N‚m/m), thickness after 48 h (e(48 h), mm), thickness after 7 days (e(7 days), mm), density after 7 days (d(7
days), kg/L), and wet sheet density after forming roller (d, kg/ L). These properties represent the mechanical resistance, thickness, and density of the product, and they were measured according to EN 494. In this study, three different ANN have been developed and analyzed: (A) First, an ANN was created in order to select the best sensor statistical data to be used in further optimization. In this case, seven different sensor statistical parameters were used as input variables and seven different product properties were used as output variables. (B) Once the main sensor data were selected, it was possible to establish a second ANN with these main variables. (C) Finally, a third ANN with the same variables as used in ANN-B was established in order to validate the results for different product molds during the fiber cement manufacturing. Figure 1 shows an overview of the work carried out. The way a neural network works depends on its architecture. The feed forward neural network is the most used type of architecture in the pulp and paper industry, which is the reference industry for this work because of its similarity to that of fiber cement production.20-23 2.1. ANN-A. The first step was to build a neural network using seven input variables (different sensor statistical data) and seven output variables (product properties) (see Table 1). This network has been used for establishing the weighting of each input variable on the results in order to select the best sensor statistics for further optimization. The main characteristics of this ANN are shown in Table 2. This first study has been performed with only a few neural networks by doing some trial and error optimizations. A total prediction error of 9.3% has been achieved with this network. This error is the average made by considering the error in each output variable (see Table 3) to be a percentage of the difference between its minimum and maximum training real values. The best results are obtained in the predictions of the breaking load at 48 h and 7 days (see Figure 2) and the density after forming roller. As can be observed, the poorest results are obtained for the thickness at 48 h. The thickness predictions are not robust because they are highly dependent on manipulated variables. Operators changing the number of cycles in the sheet former cylinder fix them. Thickness has been included to evaluate the ability of the created ANNs to distinguish between predictable variables and nonpredictable ones. This distinction will be more important for ANN-B and ANN-C, as they aim to optimize the predictions. The importance of each FBRM statistic depends on how flocculation is affecting the process. After flocculant addition, as the process evolves toward an equilibrium, the particle size distribution changes. Changes in flocculant addition, process conditions, or even raw material properties modify the particle size distributions. With FBRM statistics, we can observe these differences. Changes can be more significant when data are summed or averaged or when the median is taken. Thus, a proper selection of these statistics is very important for the following steps. Chitra has described a method for analyzing the weights of a feedforward neural network, to calculate the weighting of each input.24 Following this method, the difference between the influences of the inputs is quite small (see Table 4). Taking these values into account, further analysis must be done in order to guarantee that the best statistic is chosen at this step. A detailed study has been carried out considering the ANN to be a laboratory and making a 27 factorial experimental design, varying the inputs and evaluating the effect over the outputs
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Figure 1. Scheme for the carried out work. The main ANN of the scheme could be either ANN-B (one profile) or ANN-C (different profiles). Table 1. Inputs and Outputs of ANN-A inputs (counts/s of particles with a chord size between...)a 1 and 5 µm 5 and 10 µm 10 and 32 µm 32 and 50 µm 50 and 86 µm 86 and 100 µm 100 and 1000 µm a
Table 2. Parameters (Values and Selection Criteria) Used for ANN-A outputs
parameter
value
Fs for 48 h (N/m) e for 48 h (mm) Fs for 7 days (N/m) e for 7 days (mm) M for 7 days (N‚m/m) d for 7 days (kg/L) wet sheet density after forming roller (kg/L)
training algorithm
back-propagation (gradient descent algorithm with variable learning rate) logistic (all layers) variable (because of training algorithm); initial value ) 0.05 0.95 2 20 in each layer
The units of the inputs are counts/s.
by analyzing Pareto charts. (The Pareto chart is a specialized version of a histogram that ranks the categories in the chart from most frequent to least frequent. It is used during experimental design to graphically summarize and display the relative importance of single or combined effects of each factor over the responses.) The measurement values used are shown in Table 5. The effects of each input over the breaking load at 48 h and 7 days and the bending strength at 7 days are the most important ones because these three properties are to be optimized. Thus, no other effects are considered for the main statistic selection. The main result given by this experimental design is that the variables with the most influence on the final properties are the number of counts per second measured for particles between 10 and 32 µm and that measured for particles between 5 and 10 µm. The results obtained using this analysis are presented in Table 6. In the experimental design, the effect of the number of counts per second measured for particles between 10 and 32
transfer function learning rate momentum hidden layers neurons in hidden layers iterations total data validation data a
selection criteria
30 000
fixed trial-errora linked with training algorithm trial-errora trial-errora trial-errora prediction error optimization available data selected by random
139 18
Prediction error.
Table 3. Average Percent Error for Each Output (ANN-A) after forming roller average % error
48 h
7 days
d
Fs
e
Fs
e
M
d
7.7
6.4
14.3
7.9
8.0
12.0
8.8
µm is slightly bigger than the effect of that measured for particles between 5 and 10 µm. So, for the next ANN, the number of counts per second of particles between 10 and 32 µm has been selected as the most significant sensor statistic. 2.2. ANN-B. A second neural network has been created. In this case, the inputs are the most influential measurement according to the ANN-A analysis (counts per second between
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Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 Table 7. Inputs and Outputs of ANN-B and ANN-C inputs counts/s of particles with chord size between 10 and 32 µm (counts/s) total counts/s with chord size between 1 and 1000 µm (counts/s) wet sheet density after forming roller (kg/L)
Figure 2. Comparison between real values and network results in validating samples for Fs after 7 days. Table 4. Percent Effect by Weight Analysis (ANN-A) specified intervala (µm)
% effect by weight analysis
1-5 5-10 10-32 32-50 50-86 86-100 100-1000
0.12 0.17 0.15 0.15 0.13 0.14 0.15
a Interval of particle sizes in which FBRM measurements (counts/s) were taken.
Table 5. Values Used in 27 Factorial Experimental Design specified intervala (µm)
+1 value
-1 value
1-5 5-10 10-32 32-50 50-86 86-100 100-1000
637 1245 6072 4154 3515 839 3036
63 159 875 748 1051 324 1396
a Interval of particle sizes in which FBRM measurements (counts/s) were taken.
Table 6. Summed Standardized Significant Effect of Each FBRM Statistic over Fs after 48 h, Fs after 7 days, and M after 7 days in the 27 Factorial Design specified intervala (µm)
value
1-5 5-10 10-32 32-50 50-86 86-100 100-1000
2.11 6.20 6.26 2.64 2.49 1.07 0
outputs Fs for 48 h (N/m) e for 48 h (mm) Fs for 7 days (N/m) e for 7 days (mm) M for 7 days (N‚m/m) d for 7 days (kg/L)
are two main objectives: keeping a low prediction error and obtaining recommendations for process optimization in the mill. In this situation, representative and easy to tune inputs, as well as a good result from the network, are needed. A scheme for neural networks development has been developed. This scheme (see Figure 3) consists of optimizing the following neural network parameters: number of nodes in the hidden layer, momentum, learning rate (Depending on the training algorithm used, it can oscillate periodically between two fixed values. In those cases, it is not considered to be a parameter.), and transfer functions used in the hidden and output nodes. Optimization takes place by fixing some of the parameters (for instance, the transfer functions) and combining different values of the others. The combination could be made with data tables (which is the case here) or with values taken from an experimental design. The establishment of fixed values takes place if there are previous approaches with similar neural networks in which the value given for the parameter to fix is the same or almost the same. If this is not the case, a selection of an acceptable range of values is made. Then, there would be several parameters with the range of their values. The depth and exactness of the study depends on the number of values taken in the selected range. For each possible combination, several neural networks are created (five in this work) with the purpose of avoiding the effect of random initial situations in the training process and validation errors. For each network, a study of the validation error versus the different values of the training iterations is done. The maximum number of iterations to consider is fixed by taking some of the created networks and plotting the validation
a Interval of particle sizes in which FBRM measurements (counts/s) were taken.
10 and 32 µm), the total counts per second (between 1 and 1000 µm), and the wet sheet density after forming roller. The total counts per second is the sum of all of the ANN-A inputs. It was taken as an input because of the possibility to change its value by changing flocculation conditions when optimizing the process. The density was taken as an input for making predictions because in the mill this is used as a primary quality control variable, with high values being preferred. All the inputs and outputs are shown in Table 7. This network will be used for process optimization by obtaining recommendations about optimum input values from it. Thus, in the development of this new neural network, there
Figure 3. Scheme for the optimization of the parameters of ANN-B and ANN-C.
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Figure 4. Real data vs predicted data for the density after 7 days with 26 validation samples: A ) predicted data; T ) real data; R ) correlation coefficient. Table 8. Parameters (Values and Selection Criteria) Used for ANN-B parameter
value
training algorithm back-propagation (gradient descent algorithm with variable learning rate) transfer function logistic (all layers) learning rate variable (because of training algorithm); initial value ) 0.05 momentum 0.7 hidden layers 1 neurons in hidden 28 layers iterations 7000 total data 139 validation data 26 a
Table 9. Correlation Coefficients (R) for Each Output (ANN-B) 48 h
selection criteria fixed fixed linked with training algorithm parameter optimizationa parameter optimizationa parameter optimizationa parameter optimizationa available data selected by random
Minimum validation error.
error versus the training iterations with a high enough value of iterations to show the point with the minimum validation error or the zone with acceptable stabilized values of that error. An optimal iteration value from these studies (the average from the observed networks) is established. To ensure acceptable results in most cases, the number of iterations to apply in the following validation error study is double the optimum. With all the created and properly saved networks, a simple statistical analysis of the minimum validation error must be made to establish optimal values for all the network parameters (including the elected factors such as the calculating time, the stability of the error for new neural networks, the validation error, etc.). In this case, several neural networks (105 networks with one hidden layer) have been created combining the different parameters. Optimum values are shown in Table 8. A total prediction error of 10% has been reached with this network. The best results are reached again in predictions of the breaking load at 48 h and 7 days and the density at 7 days (see Figure 4). In Table 9, correlation coefficients (R coefficients) for each output are shown. This correlation coefficient is a qualitative indicator of the capability of a model to follow general trends
R coefficient
7 days
Fs
e
Fs
e
M
d
0.81
0.36
0.80
0.40
0.74
0.81
also depending on the fluctuation of each studied quality parameter (a low correlation index indicates poor trend prediction or the predominance of noise in an output signal of the model). Predictions with correlation coefficients over 0.65 were considered acceptable according to the personnel of the mill. It can be clearly seen that the thickness is not predicted well enough by this network. Thus, ANN-B distinguishes clearly between predictable and nonpredictable outputs. With the results of ANN-B, a new analysis was carried out. It consisted of making response surfaces, fixing the density after forming roller, and varying the other two inputs between their minimum and maximum values. A mesh of values is made, and the responses of the network for each node of the mesh are plotted in a surface graph. This analysis is not focused on giving weightings for each input but on finding optimum input values for maximizing the breaking load and the bending strength. With this analysis, one initial result is that, making response surfaces for several specific gravity values, a clear positive influence of this input over product resistance can be seen. Figures 5-7 represent examples of response surfaces for Fs after 48 h, Fs after 7 days, and M after 7 days with the maximum fixed value of density after forming roller (1.98 kg/L). In these graphs, apart from the surface, there is a contour plotted at the base. In the contour plots, optimum zones are delimited with thick lines. The continuous lines delimit more stable zones if the wet sheet density, after forming roller, changes. Note that this density varies from 1.80 to 1.98 kg/L. Graphics similar to Figures 5-7 but with different values for the density have been analyzed in order to obtain final recommendations and, therefore, conclusions. Neural network prediction errors must be taken into account in all the analyses because the surfaces are made from the network predictions. The recommendations from these response surfaces are the following: (i) The higher the density after
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Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 Table 10. Fs Correction Factors for Each Production Type with PVA-A as the Reference Production Type production
PVA-A
PVA-B
PVA-C
PVA-D
Fs correction factor
1
0.82
1
1.24
Table 11. Parameters (Values and Selection Criteria) Used for ANN-C parameter
value
selection criteria
training algorithm back-propagation (gradient descent algorithm with variablelearning rate) transfer function logistic (all layers) learning rate variable (because of training algorithm); initial value ) 0.05 momentum 0.7 hidden layers 1 Figure 5. Response surface of ANN-B for Fs after 48 h. The optimum values are in the zones delimited with thick lines. The sheet density after forming roller ) 1.98 kg/L.
neurons in hidden layers iterations total data validation data a
fixed fixed linked with training algorithm
28
parameter optimizationa fixed (from previous experience) parameter optimizationa
11 000 216 45
parameter optimizationa available data selected by random
Minimum validation error.
Table 12. Correlation Coefficients (R) for Each Output (ANN-C) 48 h R coefficient
Figure 6. Response surface of ANN-B for Fs after 7 days. The optimum values are in the zones delimited with thick lines. The sheet density after forming roller ) 1.98 kg/L.
Figure 7. Response surface of ANN-B for M after 7 days. The optimum values are in the zones delimited with thick lines. The sheet density after forming roller ) 1.98 kg/L.
forming roller is, the higher the resistances are. (ii) The total counts per second (between 1 and 1000 µm) are studied in the range between 4875 and 18 295 counts per second. The optimum values are the minimum ones, but they can increase by varying
7 days
Fs
e
Fs
e
M
d
0.82
0.48
0.88
0.14
0.68
0.75
the number of counts per second of particles between 10 and 32 µm while being inside the optimum zones (see Figures 5-7). (iii) The number of counts per second of particles between 10 and 32 µm are studied in the range between 586 and 6327 counts/s. The optimum values are around 2000-3000 counts/ s. Higher values tend to be more stable than lower ones. Varying the total counts per second, the optimum values increase slightly following the optimum zones. The analysis takes into account that the best results are those that have good values in all measured resistances. 2.3. ANN-C. Finally, a third ANN has been built with data taken from different final products with different molds in order to validate the ANN methodology in a wider range of applications at an industrial site. The technique of the development of the neural network and the parameter classification has taken place with the same procedure as in the case of ANN-B. The objective of this network is to test the ability of the network to predict final properties for different productions of fiber cement with PVA (poly(vinyl alcohol)) fibers. Inputs and outputs are the same as those in ANN-B (see Table 7). Apart from prediction errors, recommendations from response surfaces will be made again in order to compare results from ANN-B, taking only PVA-A production data, with results obtained from taking data for four different productions, known as PVA-A, B, C, and D, with different profiles using ANN-C. Different correction factors must be applied to ensure that all the data is comparable because there are inherent tendencies in some outputs. These outputs are Fs at 48 h and Fs and 7 days. The factors applied for each production type are shown in Table 10. These factors have been applied using historical resistance rate variations between different sheets made with PVA fibers and theoretical calculations for each profile. All the results will be analyzed as if they were obtained after using only the PVA-A production. For instance, if we have one fiber cement sheet of PVA-B with an Fs at 48 h value of 3000 N/m, the input for the neural network should be 3000/0.82 ) 3659 N/m. Correlation coefficients can be applied in this way.
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Figure 8. Real data vs predicted data for Fs after 7 days with 45 validation samples: A ) predicted data; T ) real data; R ) the correlation coefficient.
Figure 9. Comparison between real values and network results in validating samples for Fs after 7 days.
The point is that by scaling the data with correction factors the results can be easily translated from PVA-A production to all of the other ones. While optimizing the parameters for ANN-C, knowledge acquired in the ANN-B development shows that networks with more than one hidden layer are not advantageous, so this sort of network is not studied in the new optimization. Table 11 presents all the optimized parameters as well as the selection criteria. This optimal neural network has some of its parameters equal to ANN-B ones. This fact is possible because the process has the same nature and the parameters of a neural network depend on the process, apart from other variables. The average error in this network is 11% with the same meaning as in ANN-A and ANN-B. In general, the prediction capabilities have decreased in a very small way. But when these predictions are analyzed by outputs (whose R coefficients are given, one by one, in Table 12), an important decrease in the thickness predictions can be seen. The predictions for M at 7 days and the density at 7 days are slightly worse, but a great increase in correlation coefficients takes place for Fs at 48 h and Fs at 7 days (Figures 8 and 9). By considering the fact that data averaging and the application of correction factors could have made the ANN-C less accurate,
Figure 10. Response surface of ANN-C for Fs after 48 h. The optimum values are in the zones delimited with thick lines. The sheet density after forming roller ) 1.80 kg/L.
these are quite good predictions. In this case, 45 validation samples guarantee the reliability of this neural network and this can be considered to be a great and fast prediction tool for product resistances in the mill. With these results, the analysis of response surfaces was done in the same way as in ANN-B. With maximum values of the density after forming roller, Figures 10-12 are used for making all the recommendations. Optimum zones are delimited again with thick lines. The recommendations from these response surfaces are the following: (i) The higher the density after forming roller is, the higher the resistances are (just as with ANN-B). (ii) The total number of counts per second (between 1 and 1000 µm) is studied in the range between 2322 and 18 295 counts/s. The optimum values are the minimum ones in general, but they can be increased by varying the number of counts per second of particles between 10 and 32 µm while being inside the optimum zones (see Figures 10-12). (iii) The counts per second of particles between 10 and 32 µm are studied in the range between
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could be affected by the operators such as the thickness (correlation coefficients are 0.48 and 0.14), demonstrating the robustness of the developed neural network. ANN-C has shown good prediction capabilities even for the manufacturing of different mold sheets. According to the results obtained, the FBRM probe can be considered to be a good soft sensor for predicting on-line fiber cement resistance, without modifying the process. Acknowledgment
Figure 11. Response surface of ANN-C for Fs after 7 days. The optimum values are in the zones delimited with thick lines. The sheet density after forming roller ) 1.80 kg/L.
The authors want to express their gratitude to Uralita S.A. for sponsoring this project. We are grateful for the technical support and the discussions with Jose M. Tejera during the industrial trials. We also thank the Education Council of the Madrid Community for funding the scholarship of A.A. in order to accomplish his Ph.D. thesis. Finally, the funding from the European Union and from the Spanish Department of Science and Technology to the FEDER project “Optimisation of flocculation, retention and drainage processes” is also acknowledged. Literature Cited
Figure 12. Response surface of ANN-C for M after 7 days. The optimum values are in the zones delimited with thick lines. The sheet density after forming roller ) 1.80 kg/L.
123 and 6327 counts/s. The optimum values are around 20003000 counts/s, as in ANN-B, and again, higher values tend to be more stable than lower ones. Note that in this study, with high a density after forming roller and a number of counts per second of particles between 10 and 32 µm over 2000 counts/s, the total counts per second can have any value because all the responses are quite good. These results are quite similar to the ANN-B results, and this fact demonstrates the robustness of neural network predictions made with different data for the same process. In ANN-C, a new advantage is achieved: the capability of predicting with only one neural network several types of fiber cement production. 3. Conclusions The total number of counts and the counts in the range between 10 and 32 µm are the most important statistics from the FBRM sensor to predict final product properties. The developed neural networks are able to distinguish clearly between predictable and nonpredictable outputs. Good correlations are obtained for predictable outputs such as breaking loads (correlation coefficients are 0.82 and 0.88) and bending strength (R ) 0.68). Poor correlations are obtained for variables that
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ReceiVed for reView November 12, 2004 ReVised manuscript receiVed October 3, 2005 Accepted October 14, 2005 IE048907J
