Optimization via Multimodel Simulation

CIplus Band 1/2018 Optimization via Multimodel Simulation A New Approach to Optimization of Cyclone Separator Geometries Thomas Bartz-Beielstein, Martin Zaefferer, Quoc Cuong Pham This is a pre-print of an article published in Structural and Multidisciplinary Optimization . The final authenticated version is available online at: https://doi.org/10.1007/s00158-018-1934-2 Structural and Multidisciplinary Optimization manuscript No. (will be inserted by the editor) Optimization via Multimodel Simulation A New Approach to Optimization of Cyclone Separator Geometries Thomas Bartz-Beielstein ·Martin Zaefferer ·Quoc Cuong Pham Received: date / Accepted: date Abstract Increasing computational power and the availability of 3D printers provide new tools for the combination of modeling and experimentation. Several simulation tools can be run independently and in parallel, e.g., long running computational fluid dynamics simulations can be accompanied by experiments with 3D printers. Furthermore, results from analytical and data-driven models can be incorporated. However, there are fundamental differences between these modeling approaches: some models, e.g., analytical models, use domain knowledge, whereas data-driven models do not require any information about the underlying processes. At the same time, data-driven models require input and output data, but analytical models do not. Combining results from models with different input-output structures might improve and accelerate the optimization process. The optimization via multimodel simulation (OMMS) approach, which is able to combine results from these different models, is introduced in this paper. Using cyclonic dust separators as a real-world simulation problem, the feasibility of this approach is demonstrated and a proof-of-concept is presented. Cyclones are popular devices used to filter dust from the emitThomas Bartz-Beielstein (corresponding author) Technische Hochschule K¨oln Steinm¨ullerallee 1, 51643 Gummersbach, Germany Tel.: +49-2261-8196-6391 Fax: +49-2261-8196-6666 E-mail: [email protected] ORCID: 0000-0002-5938-5158 Martin Zaefferer Technische Hochschule K¨oln Steinm¨ullerallee 1, 51643 Gummersbach, Germany ORCID: 0000-0003-2372-2092 Quoc Cuong Pham Technische Hochschule K¨oln Steinm¨ullerallee 1, 51643 Gummersbach, Germany ted flue gases. They are applied as pre-filters in many industrial processes including energy production and grain processing facilities. Pros and cons of this multimodel optimization approach are discussed and experiences from experiments are presented. Keywords Combined simulation ·multimodeling · simulation-based optimization ·metamodel ·multifidelity optimization ·stacking ·response surface methodology ·3D printing ·computational fluid dynamics 1 Introduction Modeling allows the estimation of system performance under new conditions as well as the comparison of different operating conditions and parameterizations, e.g., new geometries. This article describes different model types, namely analytical, surrogate, computational fluid dynamics (CFD), and 3D printing models. Because every modeling approach has its pros and cons, a combination, which uses information from several models at the same time, might be beneficial. Starting with mathematical modeling, we will describe different modeling approaches first. Loosely speaking, mathematical modeling is “the link between mathematics and the rest of the world” (Meerschaert 2013). Mathematical modeling can be performed using analytical and numerical models: Analytical models are mathematical models that have a closed form solution, i.e., the solution to the equations used to describe changes in a system can be expressed as a mathematical analytic function. Nelson (1995) refers to analytical models as “rough-cut models”, i.e., mathematically solvable and typically less detailed models. 2 Thomas Bartz-Beielstein et al. Numerical (simulation) models are mathematical models that use some sort of numerical time-stepping methods such as Newton’s method to simulate the model’s behavior over time. In contrast to analytical models, solutions of simulation models are usually presented as tables or plots. Simulation is a widely used method for studying complex real-world systems, because many systems cannot be completely described by analytical models and experimentation with the real system is infeasible or expensive (Law 2007). Nowadays, CFD simulation is a well established technique. It is also used in many studies, which describe the topic discussed in this publication: the optimization of cyclone separator geometries (Hoffmann and Stein 2007; Elsayed and Lacor 2010). Over the last decades, surrogate models, also known as metamodels, gained importance (Jin et al. 2001; BartzBeielstein and Zaefferer 2017). They are build from and then used instead of the underlying real processes or simulation models. Popular metamodelling techniques include regression, radial basis functions, and Kriging (Santner et al. 2003; Kleijnen 2008). 3D-printing is a popular modeling technique. It is commonly used to validate the results, e.g., a certain geometry, from CFD simulations. Recently, 3D-printing was integrated into the optimization via simulation loop (Preen and Bull 2014). Although the model based approach can be considered a success story, it also causes some problems. Several critical issues in simulation studies are related to errors (Nelson 1995). These errors can be due to bias (e.g., initial-condition effects) or to problems with the pseudorandom-number generators. If feasible, an analytical analysis is in many cases preferable to simulation, because of the lack of sampling error. Simulation models can also be computationally demanding, because each simulation describes only one single setting. Therefore several repeats with varying input data are necessary, whereas an analytical model allows the calculation of the exact characteristics of the system for several settings. Furthermore, an inappropriate level of model detail, failure to collect adequate system data, and using wrong performance indicators for comparisons are common pitfalls in both analytical and numerical simulation studies (Law 2007). Many textbooks describe methods for finding the best model, but do not discuss the combination of several models. Nelson (1995) stated that textbooks “tend to give the impression that there is a unique best model of any real or conceptual system. This is not correct.” More than one type of model will be used in practice. The increasing computational power and the availability of 3D printers provide tools for new modeling approaches. Several simulations can be run in parallel, e.g., long running CFD simulations can be accompanied by experiments with 3D printers, whereas the analytical model is evaluated as a baseline. Combinations of the following approaches are possible: (i) analytical models, (ii) numerical simulation, (iii) surrogate models, (iv) lab experiments, and (v) field experiments. The central question in this context is: Are there any benefits in combining different simulation approaches and can the weakness of one approach be compensated by other approaches? To answer this question, an approach for combining these heterogenous results is necessary. This article presents a new approach for handling several simulation models in parallel, which will be referred to as optimization via multimodel simulation (OMMS). The OMMS approach can be used as the central part of the well-established optimization via simulation methodology (Fu 1994). To exemplify OMMS, a real-world application is used: cyclone dust collectors. This article presents results from an experimental study, which can be regarded as a proofof-concept for OMMS. For the experiments, we have chosen a combination of four different modeling approaches: (M-A) analytical, (M-C) CFD simulation, (M-S) surrogate (metamodels), and (M-P) 3D printing models. This paper is structured as follows: Section 2 describes related work. Cyclone dust absorbers are briefly described in Section 3. Section 4 presents the OMMS loop. Section 5 compares results from different modeling approaches. Experimental results based on these modeling approaches are presented in Section 6. How to combine results from various models via ensemble building is shown in Section 7. Finally, Section 8 gives a conclusion and an outlook. 2 Related Work The idea of using different models with different resolutions has been discussed in the literature for many years. Zeigler and Oren (1986) describe multiple levels of model aggregation (resolution, abstraction). These levels depend on the objectives, knowledge, and the available budget (resources, e.g., time). Fishwick and Zeigler (1992) present a formalism and a methodology for developing multiple, cooperative models of physical systems from qualitative physics. Barzier and Perry (1991) describe a two-level modeling approach for developing simulation models in the shipbuilding industry. Chaudhuri et al. (2015) describe a flapping wing OMMS: Optimization via Multimodel Simulation 3 optimization task. They use multiple surrogates, multiple infill criteria, and multiple points for the same experimental data set. Kazemi et al. (2016) use different machine learning approaches to create simple and reliable models for predicting granule size distributions. An iterative procedure assisted by cross validation was implemented to find out the best model among thousands. The cyclone modeling, simulation, and optimization approach presented in our study is related to the work from Preen and Bull (2014), who optimized verticalaxis wind turbines using miniaturized 3D-printed wind turbines. Yang (2003) states that selection of one model can be better when the errors in prediction are small and that the model combination works better when the errors are large. Simpson et al. (2012) present a thoughtful review of several multimodel approaches. They state that “the use of multiple surrogates (i.e., a set of surrogates and possibly a weighted average surrogate) is very appealing in design optimization due to the fact that the best surrogate may not lead to the best result; and complementary because fitting many surrogates and repeating optimizations is cheap compared to cost of simulation.” They also describe a multidisciplinary approach which is not directly comparable to OMMS, because independent models for different subsystems are combined rather than integrating several models of the same system. Furthermore, co-Kriging, which is a popular method that combines results from fine and coarse grained models, can be mentioned in this context (Forrester et al. 2007). Typically, co-Kriging tries to combine data from models which have different fidelity, e.g., a fine model that is expensive to compute and a less accurate, coarse model, which is cheaper to compute. In contrast to single-fidelity Kriging models, co-Kriging attempts to learn the correlation between the coarse and fine model, thus being able to exploit the larger amount of data derived from the coarse model to improve the representation of the expensive, fine model. This could be used for the meta-modeling step, especially when different levels of fidelity are available. In general, there are two options to deal with multiple models: (i) selection of the best model and (ii) combination of results from several models. Most approaches try to select one model, whereas OMMS combines results from several models using stacked regression (Wolpert 1992; Bartz-Beielstein 2016). Our study presents an integrated simulation and experimentation methodology on various scales (or layers). Da Da Dt Dt be be he he ht ht hh be be Da Da Dt Dt Front&view Top&view Du Du Du Du hz hz Fig. 1 Standard geometry of the cyclone considered in this study. The corresponding geometry parameters, xg, are described in Table 1. 3 Cyclone Dust Collectors Cyclones are used in oil and gas, iron and steel, chemical and food industry to filter a maximal amount of dust from flue gas (Hoffmann and Stein 2007). They can be applied in extremely harsh and demanding environments, but show a relatively low separation compared to electrostatic dust collectors. An efficient cyclone requires the optimization of its geometry parameters, which are shown in Figure 1. Even with today’s modern tools, the complexity of cyclone behavior is such that experimental studies are necessary for a solid understanding of the phenomena governing their behavior. The cyclone geometry can be specified by the parameter vector, xg, with the following entries: inlet width be, body diameter Da, diameter of the vortex finder Dt, diameter of the dust exit Du, total height h, inlet height he, vortex finder immersion ht, and cylinder height hz. In addition to these geometry parameters, xg, the specification of the operating parameters, xp, is necessary. The geometry and process parameter sets are shown in Table 1. We will concentrate in this study on the collection efficiency as specified in L¨offler (1988), which will be explained in Section 5.1. 4 Thomas Bartz-Beielstein et al. Table 1 Nomenclature from L¨offler (1988). Values (L, M, S) refers to the values of the geometry parameters xgfor the L¨offler, Muschelknautz E., and Stairmand high efficiency cyclones, respectively. The vortex finder immersion, ht, is modified for every cyclone geometry. The type “xp” denotes operating parameters. Parameter values, which depend on other values, are labeled as “*” in the Type column. Parameters to be optimized are labeled in the last column. Parameter Units Values (L, M, S) Type Description Optimized bemm 12.8; 9.92; 7.97 xginlet width yes Damm 80.64; 116.48; 39.97 xgbody diameter yes Dtmm 26.88; 29.12; 19.98 xgdiameter of the vortex finder yes Dumm 26.88; 39.04; 15.04 xgdiameter of the dust exit yes hmm 160; 160; 160 xgtotal height of the cyclone yes hemm 38.4; 29.6; 19.98 xginlet height yes htmm 0; 35; 44 xgvortex finder (outlet pipe) immersion yes hzmm 44.8; 29.64; 59.95 xgcylinder height yes ramm Da/2 * cyclone radius no rimm Dt/2 * radius of the vortex finder no himm h−ht* height of the imaginary cylinder CS no remm ra−be/2 * mean inlet pipe radius no F-Fe/Fi* ratio between inlet and outlet area no Femm2he×be* inlet area no Fimm2π×r2 i* outlet area no vems−120 xpinlet velocity no λg0.005 xpload-free friction coefficient no µPa s 1.8×10−5xpviscosity no %fkg/m31.2000 xpgas density no %pkg/m32700 xpparticle density no croh kg/m30.061 xpraw gas concentration no B-B=croh/ρf* mass load no vims−1˙ V /(πr2 i) * velocity vortex finder (outlet pipe) no vr(ri) ms−1Eq. (1) * radial gas velocity on the outlet pipe no vϕi ms−1Eq. (2) * tangential velocity at CS no ˙ Vm3/hFe×ve* volumetric flowrate through the cyclone no λ-λg(1 + 2√B) * wall friction factor; friction coefficient no 4 Optimization via Multimodel Simulation in the Loop In the optimization via simulation setting, the goal is to perform runs of the simulation model in an efficient manner and to determine those input variables, which result in an optimal (or near optimal) solution (Fu 1994). The OMMS approach extends the standard optimization via simulation setting by integrating results from several model types. In contrast to mathematical models, which usually require some input values only, datadriven models require the specification of input and output values. To clarify the data flow and model building process in the OMMS approach, the following model categories will be used: –X-models use input parameters, e.g., geometry and process parameters. –XY -models use the input parameters as well as the corresponding output values, e.g., collection efficiency. So, the analytical (M-A), CFD (M-C), and 3D printing (M-P) models are considered as X-models, whereas the surrogate (M-S) models are XY -models. The general concept of OMMS is illustrated in Figure 2. Here, we consider the optimization of the cyclone’s geometry parameters, which should be distinguished from the process parameters. It consists of the following steps: (S-1) Select an initial design. Set t= 1, where tdenotes the number of parameter sets. The first set of geometry parameters, x(t) g, is generated. (S-2) Specify the process parameters xp. They are not changed during the optimization. (S-3) Select X-models (e.g., CFD, analytical). In addition to the geometry and process parameter sets, further parameters might be necessary for each separate model. These model specific parameters will be referred to as xm. For example, the CFD simulator requires the specification of parameters for heat transfer, surface properties, damping, collision, and radiation. These parameters are not used in other simulation models. They are not changed during the optimization. The set x(t)= (x(t) g,xp,xm) will be used to build the X-models. (S-4) Build X-models. For building these models no information about the dependent (output) variables yis needed. In this step, one or several models (f1, . . .,fp) from the set of X-models, which comprehends 3D-printed objects, analytical model formulas, or CFD simulation models, are generated. The OMMS: Optimization via Multimodel Simulation 5 Legend (S-3) Select X-models (S-7) Select XY-models (S-1) Initial design (S-5) Evaluate X-models (S-11) Store optimized design (S-4) Build X-models (S-2) Process parameters External data (S-6) Collect results (S-9) Optimize on metamodel (S10) Terminate? Process Parallel Processes Database (S-8) Build metamodel Fig. 2 Optimization via multimodel simulation in the loop. Several simulation models are used in parallel. Elements of the first set of models, i.e., during steps (S-3), (S-4), and (S-5), can be one or several CFD simulators, analytical models, or experiments based on 3D-printed objects. Results from these different models are collected and optionally combined with additional results, which were stored in a database. The second set of models is build during step (S-8). Models from the second set are classical surrogate models, e.g., neural networks, linear regression models, or Kriging models. Because simulation results, i.e., y-values are available at this stage of the multimodel simulation process, a broader set of models can be used than during the first steps (S-3) to (S-5). Results from these models can combined in several ways. We describe an approach that is based on stacked generalization (Wolpert 1992). Optimization is performed on the stacked model (S-9). construction process results in several models, which use the same set of parameters x(t). (S-5) Evaluate models. The models are evaluated, i.e., each model generates an output: fj:x(t)→y(t) j. Note, some models generate a deterministic output, e.g., CFD models, whereas other, e.g., 3D-printed models, generate stochastic (noisy) outputs. Therefore, repeats should be considered for the stochastic models, to improve the quality of the measured values (Law 2007; Haftka et al. 2016). (S-6) Collect results. Besides the set of pairs {(x(k), y(k) j)}, for k= 1, . . . , t and j= 1, . . . , p, additional results {(x(m), y(m) l)}, for m= 1, . . . , s and l= 1, . . . , q, e.g., from historical data or data from the literature, can be used in the construction of the metamodels. (S-7) Select XY -models. XY -models use the parameter set, x(k)= (x(k) g,xp) as well as the corresponding output values y(k) ifor model building, with k= 1, ..., (t+s). In general the number of design points (p+s) is required to be large enough to allow building reasonable models. (S-8) Build metamodel. An ensemble engine builds a metamodel by combining information from several models, say Fi. It implements stacking methods. The metamodel will be referred to as F∗. The ensemble engine selects several models from the huge variety of surrogate models (e.g., random forest, or 6 Thomas Bartz-Beielstein et al. Kriging). These serve as basic or level-0 models. Cross validation is used to build an ensemble model from the portfolio of level-0 models. The level-1 training algorithm is typically a relatively simple linear model. Instead of stacking, a weighted combination of models Fior co-Kriging can be used. If models of similar fidelity are combined, we would suggest to employ to stacking. In a mixed case, a coKriging model could be integrated into a stacked metamodel (i.e., as a single model Fi). Other ensemble techniques may also be applicable, e.g., bagging or boosting (Murphy 2012). However, stacking is very effective even when combining only few, strong learners and it provides additional information, e.g., the contribution of each of the combined models to the ensemble. (S-9) Optimize on the metamodel. The model F∗is used as a surrogate for performing the optimization step. The optimization results in a new set of promising geometry parameters, which will be evaluated in the following step. The counter for the number of parameter sets tis incremented and the new design can be referred to as x(t) g. Instead of increasing tby one, several new design points, e.g., from models with different run times, can be added to the parameter set. (S-10) Check the termination criterion. (S-11) Store the optimized design. Optionally, it can be added to a database. 5 Modeling Approaches To exemplify the OMMS approach, four different modeling approaches are described in the following: analytical (M-A), surrogate (M-S), CFD simulation (M-C) and 3D printing (M-P) . 5.1 The Analytical Model (M-A) A broad variety of analytical models intended to predict cyclone separation performance exists in the literature (L¨offler 1988; Overcamp and Mantha 1998; Hoffmann and Stein 2007). The analytical approach developed by Barth (1956) and Muschelknautz (1972) can be considered as standard. It will be referred to as the Bart-Muschelknautz method of modeling. This method is based on the assumption that a particle carried by the vortex is influenced by two forces: a centrifugal force and a flow resistance. They are expressed at the outlet pipe radius riwhere the highest tangential velocity occurs. Some assumptions can be considered reasonable enough to obtain a good compromise between accurate prediction and simplification of the equations, e.g., the particles are spherical, the particle motion is not influenced by the presence of neighboring particles, and the radial force on the particle is given by Stokes’s law. Based on the geometry and operating parameters from Table 1, the following calculations can be performed. The equilibrium-orbit model assumes a cylindrical control-surface (CS), which is constructed by extending the vortex finder wall to the bottom of the cyclone. Let hidenote the height of the CS. The radial velocity at riequals to: vr(ri) = ˙ V 2πri(h−ht).(1) For a given mass load B=croh/ρf, the wall friction factor λcan be calculated as λ=λg(1 + 2√B). The correction factor αfor contraction is equal to: α= 1.0−0.54 −0.153 FB 1 3 e. Using the outlet pipe velocity vi=˙ V πr2 i,Barth (1956) derived the following equation vϕi vi =U=1 Fα ·ri re+λ·h ri =rireπ αFe+hireπλ.(2) These velocities are used to determine the collection efficiency. The equilibrium-orbit model is based on a force balance on a particle that is rotating at radius ri. Small particles leave the cyclone through the vortex finder, whereas large particles are moving to the cyclone wall. The cut size, x50, plays a central role in these calculations. For cyclones, particles of size x50 have a 5050 chance of being captured, smaller particles are less likely to be captured, larger particles are more likely to be captured. The forces acting on a particle rotating on the CS, which is assumed to separate the outer region of downward flow from the inner region of upward flow, are (i) the centrifugal force acting outward with a magnitude of πx3ρpv2 ϕi/(6ri) and (ii) the Stokesian drag acting inward 3πxµvr(ri).By equating these forces, Barth (1956) developed an analytical model for the cut size as follows: x50 =s18µvr(ri)ri (%p−%f)v2 ϕi . The fractional efficiency curve assigns an efficiency to the particle diameter. It is described by T(x) =   1 + 2 x x50 3.564    −1.235 , OMMS: Optimization via Multimodel Simulation 7 Table 2 Particle size distribution table. Values correspond to the dust used in the 3D printing experiments. Particle Size x[µm]∆x Mean ˜x [µm] ∆Qe(x) Cumulative 0-1 1 0.5 0.1 0.1 1-2.7 1.7 1.85 0.1 0.2 2.7-5.5 2.8 4.1 0.1 0.3 5.5-8.7 3.2 7.1 0.1 0.4 8.7-12.7 4 10.7 0.1 0.5 12.7-16.9 4.2 14.8 0.1 0.6 16.9-21.2 4.2 19 0.1 0.7 21.2-25.4 4.2 23.25 0.1 0.8 25.4-30.8 5.4 28.1 0.1 0.9 30.8-63 31.2 46.9 0.1 1.0 where xis the particle size. The overall collection efficiency Eis predicted according to: E=Zxmax xmin T(x)qe(x)dx ≈ xmax X xmin T( ˜xi)∆Qe(xi),(3) where xmin is the lower bound of the particle size, xmax is the upper bound of the particle size, ˜xiis the mean particle size in each fraction, ∆Qe(xi) is the change in distribution of particle sizes and qe(x) = ∆Qe(xi)/∆xi. The particle size distribution table, which was used in our studies, is shown in Table 2. Results from our collection efficiency Ecalculations for models from the literature and for models used in our experiments are shown in Table 3 and Table 5, respectively. The corresponding function is available in the R package SPOT as funCyclone(). 5.2 CFD Simulations (M-C) Computational Fluid Dynamics simulations have proven to be useful for studying the fluid and particle flows in cyclones (Hoekstra et al. 1999). They have clear advantages for understanding the details of the flow in cyclones, but also limitations in terms of modeling cyclone separation performance accurately (Hoffmann and Stein 2007). Numerical simulations are performed by solving the unsteady-state, three-dimensional Reynolds averaged Navier-Stokes (RANS) equations combined with a closure model for the turbulent stresses and the large eddy simulation approach. The CFD simulations were carried out with the open source software OpenFOAM, which has been developed for solving numerical problems (Konan and Huckaby 2015). The mesh for these CFD simulations consists of approximately 30,000 to 50,000 hexahedral cells. The transient MPPICFoam solver was chosen to calculate the two-phase flow (Euler-Lagrange). The cyclone simulation from the OpenFOAM cyclone tutorial was used as a basis (OpenFOAM Foundation 2016). The settings for fvSchemes,fvSolution,transportProperties, and turbulenceProperties were adapted to obtain the same setup as for the 3D printing experiments. The settings in the kinematicCloudProperties file were adjusted to the characteristics of the used particles. The density of the particles was changed to 2,700 kg/m3(as in Table 1 above). Using the generalDistribution model, the particle distribution from Table 2 can be precisely mapped. In the simulations, 20,000 parcels represent the entirety of the particles, where each parcel has the same mass. The amount of 20,000 parcels was chosen to minimize the represented mass per parcel and not to blow up the calculation time for each timestep. The minimization causes a lower error when a parcel escapes at an outlet. The heatTransfer,surfaceFilm,damping,stochasticCollision, and radiation submodels were left unchanged at the “off” state. In the experiments, a total of 6 g was spread over 10 thrusts and the waiting time between each thrust was approximately 3 seconds. The simulation takes only one thrust of 0.6 g instead of performing the 10 repetitions in order to avoid very long simulation times. The particle velocity in the simulation was set to the same value as the determined velocity of the air at the inlet. Overall, a time frame of 3 seconds is simulated. For this, a total calculation time of approximately 96 hours (wall clock time) using 16 processor cores is required. The simulation was controlled by the time step and relaxation factors and behaved relatively stable. After each experiment, a certain amount of dust remains in the cyclone. We consider dust as separated, if it leaves the cyclone through the dust exit (usually at the bottom of the cyclone). The evaluation of the simulation results is shown in column (M-C) in Table 5. If the remaining dust in the cyclone is also considered as separated, the collection efficiency is increased. 5.3 Surrogate Modeling (M-S) Computational fluid dynamics simulations are computationally expensive. Data-driven models of cyclone separators, which are substantially cheaper to evaluate, can be used instead. Well-known approaches to handle costly objective functions is to employ response surface or surrogate models (Jin 2003; Kleijnen 2008). That is, data-driven surrogate models may be constructed based on experimental results. Then, an optimization algorithm may work on the surrogate model instead of the actual objective function. To exemplify this approach, This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 692286.