Ind. Eng. Chem. Res. 1994,33, 2443-2452
2443
Implementation of Model-Based Optimal Temperature Profiles for Autoclave Curing of Composites Using a Knowledge-Based System? Vikram K. Pillai, Antony N. Beris,’ and Prasad S. Dhurjati Department of Chemical Engineering and Center for Composite Materials, University of Delaware, Newark, Delaware 19716
The manufacture of composite parts using the autoclave curing process requires the specification of the autoclave temperature as a function of time. It is desired to obtain a part meeting given specifications in the minimum amount of time. A recently developed methodology was used t o optimize the process using a mathematical simulation of the cure process. The optimal profile so obtained was implemented on a full-sized autoclave which is interfaced to a proprietary control system running on a Hewlett-Packard computer, using a knowledge-based system (KBS) as a supervisor. In order to account for discrepancies between the simulation and the actual process, we have followed a strategy that uses process trend analysis of the simulation output as the basis for control. The whole process is split up into episodes based on an analysis of the variable profiles. This information is used in conjunction with other knowledge about the system embedded in the KBS to adjust the set point of the autoclave temperature so that the process follows the same “trends” as dictated by the model-based optimization. Using this system, it was possible to guide the cure robustly along an “optimal” path, consistently yielding superior quality parts despite the variability of the raw materials. This procedure allows us to optimize a process independently using even an inexact simulation and apply the optimal profiles obtained therefrom.
1. Introduction Optimization of batch processes involves specifying profiles for the control variables in time. In many cases, it is preferable or even necessary to work with process simulations while doing the optimization because of cost and time considerations. The success of such an approach is extremely dependent on the quality of the model available. Unless the model exactly represents the process to be optimized, faithfully following the model-based optimized profile might lead to unpredictable results. This problem is especially acute in composites manufacturing batch processing, where there exists substantial material variability from run to run. The presence of a feedback mechanism in the control strategy to implement modelbased optimization is indispensable. The control strategy must take into consideration the divergence of the actual process with respect to the simulation. We have developed one such strategy based on process trend analysis in order to apply (near-) optimal profiles in the autoclave curing of thick laminate composites. However, the methodology is sufficiently general to be applied to other batch processes for which a reasonable model or simulation is available. An overview of the process along with a brief description of the simulation used is presented in section 2. Optimization details are furnished in section 3. The difficulties in dealing with the actual process in the context of modelbased optimization and the strategy to overcome them are outlined in section 4. Section 5 describes the results from the implementation of this methodology, within a knowledge-based system environment. The salient conclusions are highlighted in section 6. 2. Autoclave Cure of Thick Laminates 2.1. Autoclave Curing Process. The autoclave curing process is used to manufacture composites with a ther-
* Author to whom all correspondence should be addressed.
+ Dedicated to Arthur
and mentor.
B.Metzner, a superb colleague, friend,
mosetting polymer matrix. Prior to cure, the polymer is a viscous fluid. Due to the application of heat, the resin solidifies through an irreversible exothermic chemical reaction or cure. During the cure, cross-linkingtakesplace. The increase in molecular weight is accompanied by an increase in the viscosity. At the gel point, a loose threedimensional structure pervades the system, and the polymer exhibits the behavior of a gel; flow ceases. Reaction, however, continues to yield a glassy solid. In vacuum-bag autoclave molding, resin impregnated sheets (prepregs) of unidirectional fibers or woven fabrics are stacked in prescribed orientations on a metal tool plate of the same shape as the desired part. Teflon parting sheets are used to enable easy separation of the part from the tool. “Bleeder cloths” are used to absorb excess polymer resin, which may flow out. The assembly is sealed in a vacuum bag and placed in an autoclave. It is then subjected to a prescribed temperature and pressure cycle, known as a cure cycle. 2.2. Problems with the Curing of Thick Laminates. As compared to thin composites, the manufacture of components of appreciable thickness is fraught with problems. The most detrimental effect is an internal temperature exotherm resulting from the heat generation associated with the cure reaction within the thermosetting resin. This occurs because, in thick parts, the heat is not conducted away fast enough. Hence, large thermal gradients can develop, which result in nonuniform curing. In addition, reaction products and other volatile materials may be evolved, which tend to cause voids in the final part. Voids can also result from the air inevitably trapped in the prepreg during layup. These air pockets serve as nucleation sites for the growth of voids from diffusion of moisture dissolved in the resin. There is also a large specific volume change associated with the gelling of the resin. The direction of cure must be carefully controlled, else large internal stresses are created. If the part cures from the outside inward,the large thermal stresses trapped in the part will render it unusable. The traditional resolution of all these problems has been to resort to a substantially slow processing rate, with cure
OSS8-5885/94/2633-2443$04.50/00 1994 American Chemical Society
2444 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 Vacuum bag
Breather
-thyup
114" Aluminum
I i-1 I
w.0)
(0.01
0= Cnmrmitr Stark (TGCUREd ~ m ~ i i=i )D =Tooling = S
I/&' aluminum caul plate (trnl surface).
Layup
Teflon film TX IC40 Teflon Release film
&-Peg
Release film Teflon film
Figure I. Schematic of the layup sequence for the laminate cycles ranging from a few hours to, possibly, days, depending on the size of the part. The task in optimizing the process lies therefore in decreasing the process time, while simultaneously improving the reliability and quality of the final product. In order to achieve this goal, models for the curing process have been developed, taking into account heat transfer, reaction, flow, and residual stress generation. For this work, we are interested in manufacturing a model part of dimensions 15 cm X 15 em X 2.54 cm. The material used was CYCOM-4102, a commercial glasspolyester preimpregnated system available from American Cyanamid. The reinforcement is in the form of a plain weave woven roving with approximately 2 yarns/cm. The laminates were constructed by stacking together 42 plies of prepreg. Thermocouples were embedded within the laminate at various locations through the thickness. The laminate layup sequence is illustrated in Figure 1. The assembly is placed on a 0.635 cm thick aluminum plate, topped withasinglelayer ofbleeder clothand surrounded by an aluminum dam to prevent transverse resin flow. The entire assembly is placed under a vacuum bag, sealed to the caul plate with tacky tape, and subjected to a temperature profile in the autoclave. 2.3. Process Model. Pioneering work in modeling the curing of thermosetting composites was done by Loos and Springer (1983). Since then, a number of workers have elucidated various aspects of the curing process. See Berglund and Kenny (1991) for a detailed review. The original version of the model used in this work was formulated by Travis Bogetti (Bogetti, 1991,1989). This model was implemented as a numerical simulation called TGCURE and was available to us in source code form. The governing equations are the general anisotropic heat conduction equation coupled with the kinetics relating the rate of reaction to the temperature and degree of cure. The version used here solves the 1-D problem, since the critical dimension is across the thickness; for the part geometry used, analysis of the 2-D problem has demonstrated that the temperature gradients in the lateral direction were negligible (Figure 2 shows a schematic of the part geometry). The major change from TGCURE
Figure 2. Domain in which governing equations are solved. involvesthe treatment ofthe thermal boundaryconditions. TGCURE uses a convective boundary condition a t the edge; the temperature gradient at the surface is related to the temperature difference between the surface and the autoclave in a linear fashion. However, at the edge of the composite, we have opted to lump the heat transfer resistance in the autoclave, the bag, the fabric, and the mold into a single layer, henceforth referred to as the "tooling". Inaddition toaresistanceto heattransfer,such a treatment also explicitly considers the thermal capacity of the added layers; this was found to improve the simulation significantly. A parameter equal to the ratio of the thermal diffusivity (at)of the tooling to that of the composite (a,)along with its thickness (arbitrarily set to 10mm) serves to completely characterize the tooling. The new simulation is henceforth called TGVCURE. The governing equations are for T(z)in b,3: (1) Q=M& dt whereb represents tbecompmitedomainand S represents the tooling. p is the density, c, is the specific heat, k is the effective thermal conductivity in the z direction, Q is the internal heatgeneration term. Tand t are the absolute temperature and the time, respectively. a is the degree of cure, similar to an extent of reaction and ranges from O t o l . InD,p,c,,andktakeonthevalueofthecomposite physicalproperties,p., c,,and k,, respectively. Alternating direction explicit finite differences were used to solve eq 1 for the temperature field. When the temperature distribution is known, eq 2 can be used to update the degree of cure profile. Equation 1 can be used to model heat transfer in the tooling region (3) also, except that the physical parameters in this region (kt, pt, and c,J are different and the heat of reaction Q is taken to be zero. The physical parameters can be lumped together into a single parameter-the thermal diffusivity, at-which uniquely characterizes the heat transfer characteristics of the tooling. The inputs required for the simulation TGVCURE (Bogetti, 1989; Pillai, 1994)are the composite and tooling physical properties, the geometry of the domain, the kinetic model for the cross-linking reaction, and the temperature history in the autoclave. For the polyester resin we are interested in, the reaction has been modeled as an Arrhenius-type rate equation:
(3) Typical numerical values of all the parameters for CY-
Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 2445 Table 1. Parameters of Autoclave Cure Simulation
svmbol
property density specific heat thermal conductivity
P
? A
pre-exponential activation energy order parameter order parameter heat of reaction
m
range
value Physical Parameters 1.89 X 109 1.26 2.163 X lo-" Kinetic Parameters 3.7 x 1022 1.674 X 105 0.524 1.476 77.5 Tooling Parameters 3.37 x lo-'
a
m n
A",
thermal diffusivity
(3.7-5.7) x 1022 (1.650-1.680) X 106
min-1 J/mol
55-77.5
kJ/kg
(3.3-5.0) X 10-7
m2/s
I
140 120
G
140
-
120
-
100
100
-
80
80
-
60
60
40
40
*"
0
so
100
150
200
250
20
300
units
COM-4102,a glass-polyestercomposite,are listed in Table 1. The simulation predicts the temperature and degree of cure profile within the part as a function of time. The predictions have been found to be in fairly good agreement with experiment, as discussed in the next section. This cure history, in terms of the time profiles for temperature and degree of cure, can then be used as the input to a stress analysis program PIRSA (Bogetti, 1992), which determines the residual stresses set up as a result of the processing. This program couples the one-dimensional cure simulation analysisto an incremental laminated platetheory model to determine the process-induced stress and deformation from the temperature and degree of cure history within the laminate. Thermal expansion and cure shrinkage contribute to changes in material specificvolume and represent important sources of internal loading included in the analysis. Hence the thermal and cure gradients within the parts represent fundamental mechanisms that contribute to the stress development. Even though PIRSA is central to the evaluation of the cure optimization criteria, it is not further discussed here, since it was used -as is". Details regarding the theory and implementation can be found in Bogetti, 1989, 1992. Finally, although a flow model is necessary for complete description of the problem, in order to keep the problem tractable, we have simply utilized empirically derived rules for application of pressure. These rules are designed to minimize void formation. Given the relatively minor role of pressure in this process (justified by the large area of the part as compared to the thickness) and its decoupling from the thermal problem, this procedure is not seen as a major drawback. 2.4. Model Accuracy. The temperature predictions from the simulation were compared with data obtained from experimental cure runs. Figures 3 and 4 show the comparisons for the surface and center temperatures, respectively, for a typical cure cycle. In this case, the best
I
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0
50
100
Time (min)
Figure 3. Comparison of simulation and experiment: surface temperatures for run EXP1.
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Autoclave Experimental ....... TGVCURE ---TGCURE
250
300
Time (min)
Figure 4. Comparison of simulation and experiment: center temperatures for run EXP1. I
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40
60
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140 120
40 A"
80 100 120 140 160 180 200 Time (min)
Figure 5. Comparison of simulation and experiment: surface temperatures for run EXP2.
fit was obtained using the parameters listed in Table 1. However, this is not always the case; Figures 5 and 6 depict the case where the best fit was obtained using AHr = 74.1 kJ/kg, AE, = 166 300 J/mol, and at = 3.877 X lo-' m2/s. The set of parameters shown in Table 1 represents the average value of the parameters. The table also includes the ranges in variations in some of the parameters for different runs. The exact value can depend on extraneous factors. For example, the manner in which the bagging procedure is performed for a particular run determines the heat transfer resistance between the autoclave and the composite surface, thus a value for at cannot be ascertained a priori. The temperature history to which the laminate stack is exposed prior to cure (during manufacture, transport, storage, and layup) may modify the kinetics of the reaction (Day and Shephard, 1991). A point that needs to be highlighted a t this juncture is the overall quality of the simulation. It can be seen from Figures 2-5, for a specifically selected set of parameters
2446 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 Discrete choices 140 ¶
120
lh =
Slinimum h
a z f i ( x )Heuristic evaluation function
h
u-100
3
80
‘ E
60
1 0
20
40
60
80 100 120 140 160 180 200
Time (min)
Figure 6. Comparison of simulation and experiment: center temperatures for run EXPL.
determined by fitting, the prediction of the simulation is very close to the experimental data. The deviation along most of the curve lies, for the most part, within the measurement uncertainty (fl “C). There are some small regions where there are larger deviations. These may be attributable to uncertainties regarding the kinetics, drifts in some of the parameters which are assumed constant, and violation of some of the model assumptions, such as the presence of some resin flow during curing, which was not accounted for. In principle, this last effect can be included in a more complicated model. However, given the much bigger variations in the material and kinetic parameters, the simulation, as it is, was considered to be quite adequate for our purposes. 3. Optimization of the Cure 3.1. Objective Function. In optimizing the cure, it is desired to use the heat transfer with reaction simulation outlined above to design an optimal cure cycle, Le., to obtain an optimal autoclave temperature profile. It is desired to minimize the time required for the cure and the residual stresses under the following constraints: (1)A minimum acceptable degree of cure has been achieved throughout the part, typically set to 99%. (2) The temperature is kept below some critical value at all times. The degradation temperature for the polymer can be determined by TGA (thermal gravimetric analysis). (3) The magnitude of the residual stresses is to be kept small. Thisvalue is governedby twomajor factors, the uniformity of the cure and the direction of cure. An inside out cure is likely to result in lower stresses and vice versa. Ideally, the curing process is uniform and is completed in the minimum time possible. The objective function to be minimized involves a superposition of penalty functions, each one representing mathematically the three characteristics discussed above, weighted in a user-specific way. 3.2. Optimization Strategy. The objective of the present work being the implementation of a previously obtained model-based optimum, the exact procedure for optimization is a secondary issue. Thus the exact strategy followed in this work is only briefly described below, see Pillai, 1993, and Pillai et al., 1993, for more details. Given the complexity of the process, the intent of the approach used was merely to obtain a near-optimal profile. The optimization is carried out using an optimization algorithm called “local criterion optimization” (Pillai et al., 1993). This involves a dynamic programming approach wherein at each point in time, the choice of the controlled variable is made (from a discrete set) by projecting each of the choices ahead in time to determine how the process
time -
t
Figure 7. Schematic of optimization procedure. 160
140 120
1 1
0
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Autoclave AutoclaveGDTs 0 Surface Surface GDTs +
so
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Time (min)
Figure 8. Optimal cure cycle and resulting temperature profiles within the part.
would evolve if that path were followed. Figure 7 shows the discretization for a single control variable ( u )with five choices at each point in time. The quality of the projections is evaluated using a heuristic evaluation function (h),which has built-in optimization parameters. A simple form for h is shown in Figure 7, where the ai are the optimization parameters, f i are heuristic penalty functions, and x is the vector of state variables. The bold line represents the accepted choice at each time point with the minimum value of h. After a complete profile is generated based on an initial choice of the parameters, ai, the entire profile is evaluated based on our overallprocess objectivefunction, outlined in section 3.1. Thus the optimization task is reduced from afunctional optimization to avery low order traditional discrete optimization problem. 3.3. OptimalProfiles. For the default set of parameters shown in Table 1, the (near-) optimal profile for the autoclave temperature generated using the procedure outlined in section 3.2 is shown in Figure 8. The resulting surface and center temperatures are also plotted. These two values are representative of the gradients within the composite since the difference between these two values willusually be the maximum possible. The exotherm when the reaction kicks off is apparent as is the heat transfer lag in the part. A comparison to Figures 3 and 4 shows that the exotherm is more controlled and that the spatial gradients across the part (exemplified by the difference in the surface and center temperatures) during the cure is minimal. The uniformity of the cure is further evidenced by the residual stresses in the part, as shown in Figure 9.
Ind. Eng. Chem. Res., Vol. 33, No. 10,1994 2447
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Typical Cure ----
lo
.;4
-
.,
0
0.2
0.4
0.6
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0.8
1
Normalized thickness
Figure 9. Transverse residual stress profiles for parta from various cure cycles.
140
1
Autoclave Autoclave GDTs 0 Surface SurfaceGDTs + Center - Center GDTs 0
Time (min)
Figure 10. Temperature profiles during optimal cure cycle for at = at 10%.
+
The curve labeled as being a typical cure is the one recommended by the manufacturer for thin laminates. It is of interest to examine the effect of model mismatch on the optimal profiles. To this end, optimization was also carried out using alternate sets of input parameters with different values within a reasonable range, which is determined by the best fit for a number of experimental runs. The profiles obtained are largely similar to the tworamp cycle shown in Figure 8. However, with different values of one or more parameters, the second ramp is slightly modified. In most cases, this change can be explained from a physical understanding of the problem. For example, Figure 10 shows the optimal profile for a value of the tooling thermal diffusivity 10% higher than the design value. It is expected that this will lead to a faster rate of propagation of heat into the part and the process in general will show faster dynamics. In comparing Figures 10and 8, it can be seen that the ramp in the optimal autoclave temperature profile is advanced by about 10 min. It is of interest to note that, in fact, the ramp occurs almost a t the same state in the progress of the process, except that in the simulation with the higher value of at, this state occurs earlier than in the simulation with the default parameters. Thus the alteration in the optimal autoclave temperature profile is predictable, if we know the change in behavior of the process. 4. Process-Model Mismatch 4.1. MismatchProblem. In complex applications, such as composites manufacturing, we must accept the fact that the numerical simulation is not and cannot be an exact
representation of the process. The discrepancies may be of different levels of severity and are typically due to a variety of reasons, some of which are enumerated here for the autoclave curing problem: 1. Incorrect modeling of the occurring physical phenomena. For example, the heat transfer between the autoclave and the composite had been modeled as a convective resistance at the boundary of the composite. 2. Failure to account for important physics. The noflow assumption is an example of this. 3. Incorrect parameter values. This problem may occur because of incorrect material characterization or simply because each resin batch has a slightly different mix and resin volume content. The kinetic characteristics may also be altered by different aging histories depending on the environment the prepreg and the laminate stack are exposed to. Some parameters like the heat transfer resistance due to tooling are sensitive to the manner in which layup is performed and may vary with each run. The degree of deviation between the model predictions and the process depends on the extent of the model imperfections. In cases where it is large, it would be impossible, or at the least very difficult, to reconcile the differences without going back and modifying the model itself. The excursions that we expect to handle here are small, so that the qualitative or even the semiquantitative behavior of the process still remains the same. The differences may be that the same features are observed, but they are shifted slightly, either in scale (for example, in the cure process, the exotherm may be a few degrees higher) or position along the time axis (the exotherm occurs a few minutes later). Following a conservative operation strategy, such small discrepancies would not be considered a problem, but since the optimal profile is very "aggressive", even a small misstep can lead to very poor performance. The requirements of a control system to handle the above difficulties are (1)It should be fast enough to run on-line. (2) It should be robust and reliable; it should work for all, except possibly a small fraction, of the cases. Even in these cases, failure should not be catastrophic. (3)Generic applicability: the strategy should not be dependent on the specific characteristics of a process. One of the possible solutions considered was to determine the correct values of the parameters on-line by matching the process readings with a database obtained from simulations corresponding to various seta of possible parameters and then change the decision variables accordingly. One difficulty with this method is that the differences in the values of some important parameters become apparent only after some crucial decisions have (or should have) been taken and the process is beyond a "point of no return". Other potential drawbacks with this approach are that it requires the availability of a comprehensive set of optimal solutions for all possible sets of parameters and that this classification be unique. The former requirement necessitates a large amount of computational power, and the latter is by no means certain to be met. Variations in different parameters can give responses that are impossible to distinguish with confidence in an on-line application. In this particular application, it was felt that it was not necessary to even isolate the actual parameter changes that give rise to the variations in the process response; all that is required is that the optimal control decisions be modified correctly to account for these variations. The methodology proposed in the next section seeks to relate the control decisions directly to the observed response.
2448 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
4.2. Process Trend Analysis. One of the most popular ways to control the autoclave process with a view to decreasing the cycle time is to use an expert system. The system contains rules capable of determining the state of the process based on feedback from the process and taking action accordingly (LeClair and Abrams, 1988; Kalra et al., 1992;Ciriscioliand Springer, 1991;Manzini and Roehl, 1990). However, this approach is heavily dependent on the extraction of heuristics from experimental or simulation data. It is extremely process and/or system specific, and the knowledge base derived from such an effort is difficult to maintain and modify. For example, rules for autoclave curing might look like: If
temp of center > temp of surface
and
rate of rise of temp of center > 0.5
and
rate of rise of temp of surface < 0.2
then
start second ramp.
The origin of “magic” numbers like 0.2 and 0.5 in the rule above is by no means obvious. It is probably buried deep in the database of experential knowledge from which the rule is derived. This leads to obvious difficulties even if a relatively insignificant change is made in the process like changing to a different resin with different kinetic characteristics. Also, care must be taken to see that the rule base as a whole is consistent if any rules are modified or new ones are added. Our approach has centered around the idea of looking upon the optimal profile as a collection of desired trends the process should experience and perform control in such a way as to make sure the actual trajectory of the process resembles the optimal one as closely as possible. This does not take the form of minimizing a sum of squares of the differences between the optimal profile and process profiles at discrete time steps but rather making sure that the shape or trend of the process variables is the same as that given by the optimization module. Because of the kind of discrepancies we expect to handle, we opted to use an approach of converting the temperature profiles to a more condensed semiquantitative form, which is easier to understand and manipulate. The specific tool we decided to use was process trend analysis (PTA for short). PTA arose from earlier work in qualitative modeling and simulation of chemical systems (Janowski, 1987; Janusz and Venkatasubramanian, 1991). PTA results in the reduction of immense amounts of temporal data to precise and minimal semiquantitative descriptions which capture the underlying trends and events in the process. If done correctly, no essential information is lost. In fact, use of PTA has even been proposed as a means for data compression (Cheung and Stephanopoulos, 1990). PTA has been used rather widely in the chemical process industry in the areas of fault diagnosis and state identification (Whiteley and Davis, 1992; Vinson and Ungar, 1992; Janusz and Venkatasubramanian, 1991). Some implementations have used this formalism for control applications. Konstantinov and Yoshida (1992) use trend analysis to detect transitions in a complex amino acid production process. Johnson and Roberts (1989) have tried to use “event-based control” to define windows for operation of a composite process. Stephanopoulos and Bakshi (1992) use trend analysis to determine recipes for best operation of a fed-batch fermentation process. In all these cases, the trend analysis of measured data was used to aid in the extraction of control heuristics.
Figure 11. Possible shapes of the profile within an episode.
All the applications of trend analysis can be classified under the heading of generation of qualitative representations of time-varying profiles. A similar method was used to generate a qualitative description of reactant concentrations in complex kinetic schemes (Eisenberg, 1990). However, in this work, the variable profiles were split by consideringthe structure of the underlying equations. Even though the behavior of the curves within the divisions was exactly the same as in an episode, two similar “episodes” could occur one after the another because of the structure of the equations and their solutions. Section 4.3 provides details regarding the trend analysis procedure; the control strategy based on the information extracted from PTA is presented in section 4.4. 4.3. Details of the Trend Analysis. By using PTA, instead of dealing with time-stamped data directly, we are able to extract, and subsequently refer only to, the underlying trends in the process. Cheung and Stephanopoulos (1990) have developed a formal representation for generic process trends of variables which allows any level of description from fully quantitative to purely qualitative. They provide definitions for reasonable continuous and discontinuous functions and also for trends and episodes. For a “reasonably continuous function,” taking into consideration the values of the function and the first derivative, an episode represents an interval of uniform behavior of the function. An episode end point occurs when the function crosses a landmark value (zero or any other “interesting” value specific to a particular application) or the first or second derivative changes sign (an extremum or an inflection point). These points are called geometric distinguished time points (GDTs). If the function becomes constant or linear over a subinterval, only the end points of the subinterval are considered to be distinguished time points. For the generic case, the character of a profile within an episode can be classified into one of the seven categories shown in Figure 11. The notation in each box represents the signs of the derivatives. The linear episodes are defined as an extended section of the curve in which the second derivative is approximately zero (-e < D2 < E). Since this behavior is not anticipated for the cure process, the corresponding shapes are dropped from consideration. Any profile can be represented then as a series of the four remaining shapes in Figure 11.Use of a domain threshold introduces another basis for classification. The PTA procedure is illustrated with a simple example in Figure 12. The domain-specific landmark values in this case are 1 and 8. The line is the continuous function, and the dots represent distinguished time points for this function according to the above definitions. Table 2 shows a partial semiquantitative description of the function resulting from the process trend analysis (PTA). In the table, DO is a number representing the location of the episode vis-a-visthe domain landmarks (DO = 1,2, or 3 depending on whether y < 1, 1 < y < 8, or y > 8), and D1 and D2 are the sign of the first and second derivatives, respectively.
Ind. Eng. Chem. Res., Vol. 33, No. 10,1994 2449 I
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Figure 12. Example of process trend analysis. I
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Figure 13. Representation of autoclave profile within KBS. Table 2. Partial List of Episodes for Function in Figure 12 time 0.00 0.09 0.12 0.57 1.21
functionvalue
DO
D1
D2
episodeno.
1 2 2 2
+ + +
+ + -
1 2 3 4
O.OO0
1.012 1.299 3.156 0.981
-
-
Selection of the interval for discretizing time (also the sampling time) must be consistent with the following requirements: (1) It must be much less than the time scale of the process characteristics so that important features are not lost and (2) large enough so that data acquisition is not a problem and so that the backward differences used to calculate derivatives are stable. For the autoclave cure process, an interval of 30 s was chosen. 4.4. Control Strategy. The trend analysis is expected to return data of the type shown in Table 2, wherein the episode end points are flagged along with a description of the type of episode. The results from PTA of the temperature profiles from the optimization module are shown in Figure 8 as episode separator markers. The autoclave temperature is represented as a collection of piecewise linear sections, the “joints” of which are trivially the GDTs (Figure 13). For the surface and center temperatures, the GDTs are the points of change of character (in terms of D1 and D2)of the profile. Very simplistically, the crucial decision in the autoclave molding process is the decision of when to start the second ramp in Figure 8 and how steep it should be. Starting the ramp too late would mean that the center would cure much faster than the outside and there would be large gradients within the part. On the other hand, starting the ramp too early would have the even worse consequence that the cure front would travel from the outside to the center. The residual stresses
set up in such a case due to resin shrinkage would be highly undesirable. Assuming that the ramp specified by the optimum profile is the right one and is achievable in the autoclave, the question remains as to when to initiate it. Thermocouples placed in the autoclave and embedded in the part at the surface and the center measure pertinent temperatures. The temperature measurements are fed back to the control system. However, the information that we can base our reasoning on is the semiquantitative description of the process profiles that comes out of the analysis outlined in section 4.2. It is necessary to correlate the GDTs of the autoclave, surface, and center temperature profiles. (Therepresentation of the autoclave temperature and the determination of its GDTs is outlined in section 5.3.) A sequence of simulation runs with various sets of parameters were performed, with subsequent evaluation of near-optimal profiles. An observation of the episodes of the center and surface temperature profiles for the optimal cure cycles yields a first-order rule that the ramp must start 7 min after an inflection point in the center temperature or 3 min after an inflection point in the surface temperature, whichever is first. These figures are the weighted average of the same quantities in the series of simulation optimizations, the weights being the probability of the variation in the corresponding parameter. A second tier of rules can be used to modify the application of the ramp based on correlations with the position of and slope at the inflection point. As seen in section 5, application of the primary rule is quite successful in obtaining the desired uniformity of cure. However, if we have a large number of optimization runs with nonobvious correlations, there are many alternative rules that can be obtained from the PTA of the optimal profiles. If the pool of optimized profiles were large, one of the ways to get the right associations would be to use a simple neural network as a classifier. 5. Experimental Implementation of the Strategy
5.1. Autoclave System. The “autoclave” referred to in this paper is a cylindrical vessel of dimensions 2 feet (0.6 m) in diameter and 4 feet (1.2 m) in length, manufactured by Thermal Equipment Corporation of Torrance, CA. It has a maximum pressure rating of 515 psi (3550 kPa) and a maximum temperature rating of 1000 O F (538 “C). The autoclave is electrically heated using a two-stage 45 kW heater. Cooling is accomplished using a closed loop water system which delivers water to a cooling coil in the rear of the autoclave. The atmosphere in the autoclave is nitrogen, and circulation is achieved with a centrifugal fan. The vacuum system consists of two subsystems, a vacuum source subsystem connecting the part “bag” to a vacuum source and a vacuum transducer subsystem for static measurement of the part bag vacuum. The system is under the control of a proprietary control software running on a Hewlett Packard computer called autoclave cure control system (ACCS). ACCS not only adjusts set points for the temperature, pressure, and vacuum controllers but also handles a large number of alarm situations that can arise in the system. To implement the temperature control, it is necessary to take into account the nature of the response of the autoclave to a change in the temperature set point. A simple model for the autoclave was built using the measured responses to step changes in set points. The normalized response curves are shown in Figure 14. A 50 OF step was used in all cases. The responses differ slightly depending on the temperature just prior to the step (which
2450 Ind. Eng. Chem. Res., Vol. 33, No. 10,1994 1.2
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Table 3. Beat Fit Parameters for 6 2 Controlled Run property symbol G2EXP2 G2EXP5 heat of reaction AHr 58.9 65.36 activation energy AE, 167600 166450 A 5.5 X loz2 5.0 X lo2* pre-exponential factor 3.71 X lO-’ 5.05 X lO-” tooling thermal diffusivity at
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are the labels in the figure). The response is quicker at higher temperatures, but in all cases the response is complete in about 10 min. The prediction of the model for a typical two-ramp cycle is compared to the actual response in Figure 15. This information is used to design a feed-forward module to achieve control in a time window in the future. For a simple ramp, it is sufficient to notice that the same ramp is reproduced with a 2 min delay, whereas for more complicated temperature changes, the model can be inverted to determine the set points necessary to achieve the desired profiles. 5.2. Expert Control of the Autoclave. The scheme described in section 4 runs within a system developed using a real-time expert system tool called G2 (available from Gensym Corporation, Cambridge, MA) running on a Sun4/ 330 computer. The Sun communicates with the ACCS on the H P using the RS232 protocol via serial ports. Communication takes the form of either polling for data or sending set points. All the external modules performing tasks such as the process trend analysis,filtering, etc. reside on the Sun itself or on other Unix machines and run transparently over a network. It is not desired for G2 to take over entire control of the autoclave. G2 is used as a supervisory system to feed temperature, pressure, and vacuum set points to the H P running the control system. In our case the vacuum is held at the maximum possible level during the entire run and need not be updated regularly. Pressure control is implemented in a similar manner to the temperature control. Values of the degree of cure and viscosity within the part are maintained within the KBS using the measured temperature and the available kinetic and chemorheological models. Pressure is initiated when the viscositythroughout the part is less than a critical threshold
units kJ/kg J/mol min-1 mz/s
value (an event which can be represented as a change in an appropriate trend of the viscosity profile), a heuristic rule obtained from previous knowledge of the problem (Dementyev et al., 1992; Loos and Springer, 1983; Kardos et al., 1986). 5.3. Algorithm for Control. An approximate piecewise linear representation of the optimal profile is set up within the knowledge base within the expert system. The end points “float” and can be moved using embedded rules (see Figure 13) along both the time and temperature axis. They represent the GDTs of the controlled variable profile. The sequence of set points required to obtain this profile is then determined by inverting the autoclave response model described in section 5.1. Beginning at time zero, fresh set points are sent to the autoclave every 30 s on the half-minute. Calls to obtain the thermocouple measurements are done half-way between the set-point modifications. Since the temperature measurements are obtained at discrete intervals, they show discontinuities. In order to calculate reasonable derivatives for the functions presented by these profiles, the raw data is first passed through a filter which uses Fourier transforms. The high-frequency contributions of the signal are screened out, and we get a smooth curve. The smoothed curve is then passed to the PTA module, which analyzesthe data in a small window starting at the current time and extending back for a predefined interval. The output of this module goes to the expert system. The endpoint R3 in Figure 13 is then either advanced or postponed depending on the appearance of the GDTs of the type described in section 4.4. 5.4. Results. Results from two knowledge-basecontrolled cures are included here. Figure 16 shows the evolution of run G2EXP2. It can be seen that the process follows a desired trajectory even though the second ramp is initiated much earlier than dictated by optimization based on the standard set of parameters (at about 120min instead of 130). A simulation of the process with the best fit parameters based for this run (values are in Table 3) was performed. The simulated temperature profiles are shown in Figure 17. Figure 18 shows the temperature profile for run G2EXP5; in this case, the first part of the profile was modified to have an “overshoot” to decrease
Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 2461 140
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time to achieve a uniform cure. The quality of the cure is also reflected in the residual stress profiles calculated for these cures; however, the simulation diverges from the process data by an amount sufficient to render an exact comparison invalid. 5.5. Discussion. It was seen that the strategy employing PTA was successful in tackling the problem of processmodel mismatch in this particular autoclave curing application. From the data presented in section 5.4, it was seen that considerable run to run variations were accounted for. The technique was successful in ensuring that the process follows a desired trajectory. The parts produced were of aconsistently high quality. The practical application of model-based optimal profiles allows effective utilization of previous process modeling efforts. The economic impact of this particular system is realized in terms of decreased cost due to a shorter and more reliable cure cycle. 6. Conclusion
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the initial prereaction heatup time. In order to allow for consolidation of the laminate, the pressure was ramped to about 345 kPa at about 70 min. The simulation results for G2EXP5 are shown in Figure 19. The large deviation between 60 and 100 min (of the order of 5 “C)can be attributed to the application of pressure and the concomitant compaction of the stack. From the corresponding cure profiles (the two plots in Figure 20), it is seen that the degree of cure crosses over a t about CY = 0.6 and CY = 0.35, respectively. The gel point for the system is about 0.9. Hence the cure does indeed proceed inside out. In spite of the drastic change in the cure cycle and the intrinsic differences in the material (as reflected in the best fit parameters shown in Table 3),the strategy based on trend analysis is seen to initiate the second ramp a t the correct
An expert system based control scheme for a batch process was successfully demonstrated in an actual autoclave curing of a thick composite laminate. The trend analysis based scheme proposed here to translate optimal profiles developed on simulations to actual processes offers many advantages. It is robust (in as much as the simulation is reliable), generic in scope, and easily implemented. Trend analysis offers a natural basis for classification of the process into “states”; this eliminates the need for imposing external artificial definitions of state for diagnosis and control purposes. The strategy is easy to implement and is applicable for any process, since it is expected that all process variables are collections of trends and this information can be used to account successfully for reasonably small process-model mismatch while applying profiles from model-based optimization. The KBS developed for the implementation (basically a correlation of the control decisions to the occurrence of the episodes of the measured variable profiles) is transparent and is easy to modify, since there is a consistent basis for adding information. The consistency arises from the fact that all process runs (barring extreme excursions) will exhibit the same collection of trends, albeit shifted in scale or time. The methodology proposed here allows us the freedom to perform optimization using solely the simulation with the reassurance that any profile so obtained can be subsequently applied to the actual process in a straightforward manner.
2452 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
Acknowledgment Partial financial support for this work was provided by the Army Research Office URI through the Center for Composite Materials, University of Delaware. The authors are also grateful to Dr. Travis Bogetti for use of the TGCURE and PIRSA code. The assistance of LieutenantColonel Timothy Lindsay of the UAV office and David Wangza of Thermal Equipment Corporation toward establishing the communication link between the KBS and the autoclave is gratefully acknowledged. Nomenclature G2 = commercial expert system tool available from Gensym, Cambridge, MA GDT = geometric distinguished time points, the end points of a section of a profile constituting an episode HP = Hewlett-Packard, the primary computer controlling the autoclave PIRSA = process-induced residual stress analysis, software used to determine residual stress in the part, given the thermal processing history PTA = process trend analysis Literature Cited Bakshi, B. R.; Stephanopoulos,G. Temporal representation of process trends for diagnosis and control. In Proceedings of the ZFAC symposium on on-line fault detection and supervision in the chemical process industries; Newark, DE, 1992;Pergamon Press: Oxford, England, 1992;pp 109-115. Berglund, L. A.; Kenny, J. M. Processing sciencefor high performance thermoset composites. SAMPE J. 1991,27(2),27-37. Bogetti, T. A. Process-induced stress and deformation in thicksection thermosetting composites. Ph.D. thesis, University of Delaware, Newark, DE, December 1989. Bogetti, T. A.; Gillespie, J. W., Jr. Process-induced stress and deformation in thick-section thermoset composite laminates. J. Compos. Mater. 1992,26 (5),626-660. Bogetti, T. A,; Gillespie, J. W., Jr. Two-dimensional cure simulation of thick thermosetting composites. J. Compos. Mater. 1991,25, 239-273. Cheung, J. T.-Y.; Stephanopoulos, G. On the detection and representation of trends. In Proceedings of the ZSA '90international conference and exhibition v45; New Orleans, LA, 1990; ISA Services Inc.: Research Triangle Park, NC, 1990; pp 755-774. Ciriscioli,P. R.; Springer, G. S. An expert system for autoclave curing of composites. J. Compos. Mater. 1991,25,1542-1587. Day, D.R.; Shephard, D. D. Effect of advancement on epoxy prepreg processing - A dielectric analysis. Polym. Compos. 1991,12 (2), 87-90. Dementyev, V.; Kotritskiy, S.; Petuhov, M.; Torkunov, A. On the optimization of the fiber reinforced composites manufacturing process with two pressure steps. On the optimization of the fiber reinforced composites manufacturing process with two pressure steps. In CADCOMP '92 - 3rd international conference on computer aided design in composite material technology; Computational Mechanics Publ: Southampton, England, 1992;pp 3747.
Eisenberg, M. Descriptive simulation: Combining symbolic and numerical methods in the analysis of chemical reaction mechanisms. Artif. Zntell. Eng. 1990,5 (3),161-171. Janowski, R. Introduction to QSIM and qualitative simulation. Znt. J. Artif. Zntell. Eng. 1987,2 (2),65-71. Janusz, M. E.; Venkatasubramanian, V. Automatic generation of qualitative description of process trends for fault detection and diagnosis. Eng. Appl. Artif. Zntell. 1991,4 (5),329-339. Johnson, S.A,; Roberta, N. K. Production implementation of fully automated, closed loop cure control for advanced composite structures. In Proceedings of the 34th international SAMPE symposium; Reno, NV, 1989;SAMPE Covina, CA, 1989;pp 373384. Kalra, L.; Perry, M. J.; Lee, L. J. Automation of autoclave cure of graphite-epoxycomposites. J.Compos.Mater. 1992,s(17),25672584. Kardos, J. L.; Dudukovib, M. P.; Dave, R. Void growth and resin transport during processing of thermosetting-matrix composites. In Advances in polymer science - vol 80, Epoxy resins and composites ZV; Springer Verlag: Berlin, FRG, 1986;pp 101-124. Konstantinov, K.; Yoshida, T. A method for on-line reasoning about the time-profiles of process variables. In Proceedings oftheZFAC symposium on on-line fault detection and supervision in the chemical process industries; Newark, DE, 1992;Pergamon Press: Oxford, England, 1992;pp 133-138. LeClair, S. R.; Abrams, F. L. Qualitative process automation. Znt. J. Znteg. Manuf. 1988,2(4),205-211. Loos, A. C.; Springer, G. S. Curing of epoxy matrix composites. J. Compos. Mater. 1983,17 (3),135-169. Manzini, R. A.; Roehl, E. A. Flexible control of an organic matrix composite cure process using object-oriented control concepts. In Proceedings of the American Control Conference (ZEEE cat num 9OCH2896-9);American Control Council: Green Valley, AZ, 1990;pp 1980-1985. Pillai, V. K.Use of Simulations, in optimization of, and design of knowledge based control system for, a composite manufacturing process. PhD thesis, University of Delaware,Newark, DE, Winter 1993. Pillai, V. K.Modifications to cure simulation TGCURE. Technical report, Center for Composite Materials; University of Delaware: Newark, DE, 1994. Pillai, V. K.; Beris, A. N.; Dhurjati, P. S. Heuristics guided optimization of a batch composite manufacturing process. Submitted for publication in Comput. Chem. Eng., 1993. Stephanopoulos, G. Artificial intelligence in process engineeringCurrent state and future trends. Comput. Chem. Eng. 1990,14 (ll), 1259-1270. Vinson, J. M.; Ungar, L. H. Fault detection and diagnosis using qualitative modeling and interpretation. In Proceedings of the ZFAC symposium on on-line fault detection and supervision in the chemical process industries; Newark, DE, 1992;Pergamon Press: Oxford, England, 1992;pp 121-126. Whiteley, J. R.; Davis, J. F. Knowledge-based interpretation of sensor patterns. Comput. Chem. Eng. 1992,16 (4),329-346. Received for review March 7, 1994 Revised manuscript received June 29, 1994 Accepted July 8,1994' e
Abstract published in Advance ACS Abstracts, September
1, 1994.
