Screening fuels for autoignition with small volume experiments and

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Biofuels and Biomass

Screening fuels for autoignition with small volume experiments and Gaussian process classification Spencer Lunderman, Gina M. Fioroni, Robert L. McCormick, Mark R Nimlos, Mohammad Rahimi, and Ray Grout Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02112 • Publication Date (Web): 27 Aug 2018 Downloaded from http://pubs.acs.org on September 3, 2018

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Screening fuels for autoignition with small volume experiments and Gaussian process classification S. Lunderman,† G.M. Fioroni,‡ R. L. McCormick,‡ M. Nimlos,¶ M. J. Rahimi,§ and R. W. Grout∗,§ †Department of Mathematics, The University of Arizona ‡Transportation and Hydrogen Systems Center, National Renewable Energy Laboratory ¶Bioenergy Center, National Renewable Energy Laboratory §High performance algorithms and complex fluids group, Computational Science Center, National Renewable Energy Laboratory E-mail: [email protected]

Abstract Partially reacting candidate fuels under highly dilute conditions across a range of temperatures provides a means to classify the candidates based on traditional ignition characteristics using much lower quantities (sub-mL) than the full octante tests. Using a classifier based on a Gaussian Process model, synthetic species profiles obtained by plug flow reactor simulations at seven temperatures are used to demonstrate that the configuration can be used to classify 95% of the samples correctly for autoignition sensitivity exceeding a threshold (S ≥ 8) and 100%of the samples correctly for research octane number exceeding a threshold (RON ≥ 90). Molecular beam mass spectrometry (MBMS) experimental data at four temperatures is then used as the model input in a real-world test. Despite the non-trivial relationship between the MBMS measurements and speciation as well as experimental noise it is still possible to classify 95% of the samples correctly for RON and 85% of the sampels correctly for S in a ‘leave-one-out’ cross validation exercise. The test dataset consists of 45 fuels and includes a variety of primary reference fuels, ethanol blends and other oxygenates.

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Introduction The production of sustainable liquid fuels from lignocellulosic and algal biomass, or from waste materials, is today being pursued using a very broad array of in vivo and in vitro approaches, with a consequent broad range of product molecular structures and complex mixture compositions. 1–8 The development of a new process for production of a new fuel at the very large scale required by fuel markets is an expensive endeavor. 9 To focus better on this costly research, in recent years researchers have begun to target molecular structures with desirable properties for spark-ignition (SI; gasoline), compression-ignition (diesel), or aviation turbine (jet) engines. 2,10–13 For SI engine fuels, a fuel property screening approach using measured fuel properties has been developed and applied to several hundred potential bio-derived blendstocks. 12 A model-based approach using correlations to molecular structure has also been described. 10 Both approaches highlight the importance of being able to measure or predict the autoignition tendency of proposed fuels early in the development process. In an SI engine, the fuel is required to have a high resistance to autoignition to prevent engine knock. Knock occurs after the fuel combustion event has been initiated by the spark, when pressure and temperature in the cylinder are rapidly increasing. Under some conditions, the fuel-air mixture that has not yet been consumed in normal combustion autoignites. In extreme cases, knock can be powerful enough to cause physical damage to the engine, but more importantly, can limit engine efficiency and the potential to design more efficient SI engines. 14,15 For SI engine fuels, research octane numbers (RON) 16 and motor octane numbers (MON) 17 are commonly used engineering metrics for autoignition propensity. RON and MON are measured in standardized engine tests that require approximately 0.5 L of fuel. When these tests were introduced nearly 90 years ago, engines were thought to operate in a range between the conditions that define the test for RON (i.e., lower temperature at a given pressure, higher speed) and MON (i.e., higher temperature at a given pressure, lower speed). 18 SI engine efficiency can be improved using the following strategies: increasing compression ratio (CR), operation at lower speeds, combined engine downsizing and turbocharging, cylinder deactivation, direct injection (DI), and exhaust gas recirculation (EGR). 19,20 Thermodynamic efficiency is improved by higher CR; 21 however, a higher compression ratio also increases the temperature and pressure of the unburned fuel-air mixture, increasing the potential for knock. SI engines have lower efficiency when operated at light loads because of parasitic losses. Downsizing, turbocharging, operation at lower speed, cylinder deactivation, and DI are used to achieve higher load over a larger portion of the required operational range. 22,23 Operation at higher loads can also result in higher temperature and pressure of the unburned mixture and a commensurate increase the potential for knock. Spark-timing retard is used to mitigate knock but it is at the expense of reduced efficiency. 24 All the strategies for improving SI engine efficiency previously described could be pursued more aggressively with more knock-resistant fuels. Modern downsized, boosted DI engines operate under conditions where increased RON and lower MON lead to increased knock resistance, so-called “beyond RON conditions.” 25,26 The actual autoignition resistance of a fuel, or octane index (OI), has been described as in Equation 1: 27 OI = RON − K · S, 2


(1)

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where S is the octane sensitivity (S ≡ RON − M ON ). For modern engines, K is negative at knock-limited conditions, so increasing S or reducing MON at constant RON increases OI. 28 In early stage research into biomass or waste-derived fuel production, the roughly 1 L of fuel required to measure RON and MON is not available or is only produced at an exorbitant cost. Thus, several approaches to predicting RON and MON (or RON and S) have been developed. These fall into three broad categories: 1. Prediction from molecular structure in a pure simulation approach such as group contribution methods, quantitative structure activity relationships, or more advanced approaches. 29–31 Similar approaches consider structure as revealed by spectroscopy for example infrared 32 or nuclear magnetic resonance. 33 2. Estimation by kinetic simulations of autoignition delay, which is correlated with octane number or combined with simulation of the engine in the RON and MON tests to predict octane number. 34–38 3. Correlation of measured ignition characteristics with octane such as autoignition product species versus temperature in a flow reactor 39 or a measured ignition delay from a constant volume experiment such as the Ignition Quality Tester (IQT). 40,41 This includes correlation of measured derived cetane numbers (DCN) from the IQT with octane number. 12,41,42 Predictions from molecular structure, spectra, or kinetics, and engine simulation have the advantage of requiring little or no actual sample of the biofuel. However, for mixtures that might be produced by fermentation (acetone-butanol-ethanol, for example) or by chemical processes such as hydrothermal liquefaction or pyrolysis, a purely simulation approach may not be workable. Additionally, simulations and spectroscopy may not predict non-linear synergistic or antagonistic blending into real gasolines. Further, the resources required to develop a new detailed kinetic mechanism for simulation have been reduced in recent years the effort is still significant. Predictions from measured autoignition characteristics appear to have great promise. Currently, constant volume systems such as the IQT would require on the order of 50 mL of sample for an ignition delay measurement, a substantial reduction compared to volumes required to measure RON and MON. However, in our experience, even 50 mL can be out of reach for many early-stage processes. In the present study, we have developed a flow-reactor measurement and data-analysis approach that requires well below 0.5 mL, and may ultimately be suitable as a rapid screening tool to identify proposed materials with RON above a specified level. Screening candidates based on such small samples necessarily involves inference based on limited data. Making such inferences implies a degree of uncertainty in the decision. It is desirable to account for such uncertainty rigorously so that decisions to pursue obtaining a larger sample for more traditional analysis can be made with appreciation for the predictive power of the available data. A Gaussian process (GP) is a conditional probability on a multivariate Gaussian distribution. Given a data set of predictors and responses D = {X, y}, split into training data Xtrain , ytrain and testing data Xtest , ytest , we can build a Gaussian process by first defining the Gaussian distribution:

3


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ytrain µ(Xtrain ) κ(Xtrain , Xtrain ) κ(Xtrain , Xtest ) ∼N , ytest µ(Xtest ) κ(Xtest , Xtrain ) κ(Xtest , Xtest )

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(2)

where µ(·) is the mean function and κ(·, ·) is the Gaussian process kernel. The mean and kernel functions define and constrain the type of structures a Gaussian process can describe.

Methodology To test if it is possible to screen fuels using this device, our approach is to gather experimental data for a test set consisting of N fuels with known ignition quality (RON and MON) and then to ascertain if we could classify the mth fuel as “favorable” or “unfavorable” using the remaining N − 1 samples as training data in a cross-validation exercise. In this exercise, the training data are used in the kernel searching algorithm which yields the kernel κm . The Gaussian process is built using this kernel and the hyperparameters are tuned via the log marginal likelihood. Finally, we predict the response variable for the training data that we earlier removed. In this work, we choose to estimate RON and S independently. We attempt to answer two questions: (1) given a fuel, can we predict its RON and S value based on the experimental data and (2) can we predict whether a fuel meets a screening threshold for RON and S. Here, RON > 90 and S > 8 are used as example thresholds although the methodology should be equally applicable for other threshold. We build the Gaussian process by defining the conditional probability of y ∗ given the known observations y1 , ..., yN . This conditional probability is the one dimensional Gaussian distribution (3) P y ∗ | y1:N ∼ N η, σ 2 with and

η = µ(X ∗ ) + Σ(X ∗ , X1:N )Σ(X1:N , X1:N )-1 y1:N − µ(X1:N )

(4)

σ 2 = Σ(X ∗ , X ∗ ) − Σ(X ∗ , X1:N )Σ(X1:N , X1:N )-1 Σ(X1:N , X ∗ ).

(5)

As we can see, defining η and σ 2 only requires our knowledge of y1 , ..., yN as well as our choice of mean function µ and kernel Σ.

Gaussian process analysis with kernel search Defining a Gaussian process requires that one defines the mean function µ(·) and kernel function κ(·, ·). Here, we set the Gaussian process’s mean function be the average response values for the data D = {(Xi , yi )} i.e., µ(·) =

N 1 X yi . N k=1

(6)

We could certainly define another mean function (e.g., the predicted response after performing linear regression) but we assume that any structure given by the mean function can be 4


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represented through the kernel function. Every GP kernel has hyperparameters that can be tuned to yield stronger response estimation, see Table 1. This tuning is done by maximizing the log marginal likelihood function, defined as probability of the data given the kernel hyperparameters. In practice, capturing the structure in the mean function through the kernel makes computations easier but requires that the kernel function captures the data complexity. We find that there is insufficient flexibility in the hyperparameters of any single fundamental kernel to reflect the dataset considered here and we must be able to custom build a Gaussian process kernel, which is a nontrivial task. The kernel searching algorithm presented by Duvenaud et al. allows us to search for kernels that are constructed from addition and multiplication of standard kernels. 43 The kernels we will use to start our search are shown in Table 1. Once optimal hyperparameters are selected for each kernel in the set, we will compute the Bayesian information criterion (BIC) for each kernel and select the kernel with the largest BIC. This chosen kernel will now be used in the next step of the algorithm. Let us denote the selected kernel as κ1 . Using our algebraic properties, we build a new collection of kernels based off of κ1 . This new collection will be { κ1 , κ1 +DP, κ1 +ESS, κ1 +RQ, κ1 +M, κ1 +RBF, κ1 +C ,κ1 +WN, κ1 DP, κ1 ESS, κ1 RQ, κ1 M, κ1 RBF, κ1 C ,κ1 WN }. Note that κ1 was added into the new collection without any modification. We add the previously selected kernel into the new collection because there is no reason more kernel complexity will yield a better Gaussian process. Again, for each kernel in this new collection, we tune the hyperparameters via the log marginal likelihood and select the kernel with largest BIC. This selected kernel is now denoted κ2 , and we repeat this process until the next iteration yields no improvement or an upper bound on the iterations. This process is illustrated in Figure 1. The Bayesian information criterion is used to compare two kernels meaningfully by capturing both how well each model fits the data and its complexity. This mitigates the danger of “over-fitting” that results from using a quantity such as the log marginal likelihood which only tells us how likely the data is given a particular kernel. Complex models tend to perform well in estimating the data used to tune the model and fail terribly at predicting new information. The Bayesian information criterion is defined as: 1 (7) BIC = log p(D|G) − |G| log N , 2 where p(D|G) is the marginal likelihood of the data evaluated at the optimized kernel parameters, |G| is the number of kernel hyperparameters, and N is the number of data points in D. BIC factors in how well the model fits the data by using the log marginal likelihood and it penalizes a model for its complexity. 44 The log marginal likelihood that goes into the BIC is readily computable. Recall that when we define a Gaussian process, we make the assumption that our response y is distributed normally according to the mean and kernel function; i.e., y ∼ N µ(X), κ(X, X) . Let G denote the Gaussian process from data D with mean function µ and tuned kernel κ. 5


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We calculate the marginal likelihood as the probability of data D given G: 1 −1/2 T -1 p(D|G) = (det(2πκ(X, X))) exp − (y − µ(X)) κ(X, X) (y − µ(X)) . 2

(8)

Taking the logarithm of the above equation yields the log marginal likelihood 1 1 log(p(D|G)) = − (y − µ(X))T κ(X, X)-1 (y − µ(X)) − log (det(2πκ(X, X))) . 2 2

(9)

Table 1: Kernels used in kernel search algorithm. 45 In the Matern kernel, Kν is a modified Bessel function. Name

Hyperparameters

Exponential Sine Squared (ESS)

Function 2 |x−x0 | 0 κ(x, x ) = exp −0.5 l √ √ ν 1−ν 2ν|x−x| 2ν|x−x0 | κ(x, x0 ) = 2Γ(ν) K ν α l l |x−x0 |2 0 κ(x, x ) = 1 + 2αl2 2 sin(π/ρ|x−x0 |) 0 k(x, x ) = exp l

Dot Product (DP) Constant (C) White Noise (WN)

κ(x, x0 ) = α2 + x · x0 κ(x, x0 ) = c κ(x, x0 ) = c ∗ δ(x, x0 )

α c c

Radial Basis Function (RBF) Matern (M) Rational Quadratic (RQ)

l l, ν l, α l, ρ

Figure 1: In this figure, the first level is only the basic kernels. After calculating the Bayesian Information Criterion for each kernel, suppose the Exponential Sine Squared kernel has the highest. It is then used to generate a new collection of more complex kernels. In the second level, if the Exponential Sine Squared x Matern kernel has the highest BIC, it is then used to populate the third level, and so on. For the numerical methods outline below, the treatment of RON and S is identical. The algorithm is outlined in Table 2. The required inputs for these algorithms are the same for the kernel search: our data D, a collection of base kernels K and a predetermined maximum number of iterations.

6


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Table 2: Summary of Algorithm 1. Input: Data D = (X, y), base kernels K = {k1 , k2 , ..., kn }, max number of iteration Niter 2. for m = 1, ..., NFuels : 3. Split (X, y) into training and testing data by removing fuelm. 4. κm = Kernel Searching Algorithm: Input: 5. Build Gaussian process G with kernel κm . 6. Predict: y pred (m) = G X test 7. Output: y pred

X train , y train , K, Niter

Experimental setup

Figure 2: Flow reactor setup Laboratory experimental studies are performed using a straight quartz tube reactor that consists of an inner tube to deliver a helium/fuel mixture, which later mixes with flow from an outer tube containing helium and oxygen. Figure 2 shows a diagram of the reactor. The reactor is 79.25 cm long; the inner tube diameter is 13 mm and the outer tube diameter is 25 mm. The fuel is introduced using a syringe pump equipped with a 1 mL gas tight syringe at a rate of 10 µL/min to maintain dilute conditions. The helium flow for the inner tube where fuel is delivered is maintained at 2 slm, while the helium flow is maintained at 4 slm in the outer tube to provide adequate flow to the analytical system. Argon, as a tracer, and oxygen were also introduced in the outer tube at flow rates of 40 sccm and 34 sccm, respectively. The reactor is heated in a ceramic furnace, and data on 41 fuels is collected at 700K, 800K, 900K, and 1000K. The analysis system consisted of a molecular-beam mass spectrometer (MBMS). The MBMS settings were maintained as follows: The electron ionization energy is set to -22.5 volts, the multiplier is set to 1550 volts, and a scan time of 1 second is used. The system is set to scan from 10 to 200 atomic mass units (AMUs). An advantage of the MBMS is rapid and real-time measurement of species evolved from the reactor. In a typical experiment, a background is collected without argon tracer flow. This background is then subtracted from each of the sample runs. After background collection, a separate spectrum is gathered with argon only. This baseline allows argon to be used as an internal standard to adjust for 7


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changes in signal intensity throughout a run. The sample is then introduced by charging the syringe with the sample of interest, and purging the syringe prior to setting the flow to 10 uL/min. Once a steady state flow is achieved, the sample spectrum is collected for three minutes, the flow is stopped, and the syringe removed to be charged with the next sample of interest. The flow reactor-MBMS is used to collect mass spectral patterns of primary reference fuels (PRF), toluene primary reference fuels (TPRF), and several oxygenated species that represent various functional groups as outlined below.

Results and discussion Experimental measurements Forty-five samples with published RON and MON were prepared. Table 3 contains blending volume concentrations as well as RON, MON, and S data for fuels prepared using heptane, isooctane, toluene, and ethanol. Additionally, several oxygenate samples were tested and their RON, MON, and S data are displayed in Table 3. The nature of the signal collected for selected AMUs is shown in Figure 3, where the lines are colored by RON for the sample. These selected AMUs are indicative of AMUs where there is a discernable variation in the shape of the curve that appears to be related to the quantity of interest.

43 amu

71 amu 0.5

0.4

0.3

0.4

0.3

0.2

0.3

0.2

0.1 0.0 700

100 amu

0.2

0.1 800 900 Temperature

1000

0.0 700

0.1 800 900 Temperature

1000

0.0 700

800 900 Temperature

1000

Figure 3: MBMS signal versus temperature for all samples and selected AMUs

Regression: Prediction of RON and S When performing regression, the measured octane numbers are the response variables. Figure 4 includes cross-validation plots that show the results for predicting a fuel’s RON and S using a Gaussian process regression model with the kernel searching algorithm. The crossvalidation figure plots the actual y response variable against the predicted response. With perfect prediction, all points will lay on the “RON (predicted) = RON (measured)” line, shown as a dashed gray line for reference. For comparison, we also present the results of a ordinary least squares (OLS) linear regression model for both RON and S. 8


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Table 3: PRF, TPRF, and PRF40-ethanol blend volume %, RON, MON, and S used for flow reactor study (reference is source for RON and MON data) Sample Name vol Heptane vol Isooctane Heptanea † 100 Isooctanea † 100 Toluene† Co-Optima Surrogatea 15 55 H 9.9† 9.9 72.2 H 10† 10.0 65.0 H 16.2† 16.2 74.1 H 16.6† 16.6 69.2 H 30† 30.0 0.0 H 33† 33.3 33.3 H 34† 34.0 0.0 H 42† 42.0 0.0 H 50† 50.0 0.0 H 66† 66.7 16.7 S 2.5† 0.0 90.0 S 4.1† 48.0 32.0 S 5.4† 60.0 0.0 S 5.6† 0.0 80.0 S 7.3† 0.0 70.0 S 9.0† 40.0 0.0 S 10.7† 0.0 60.0 TPRF 60-20† 46.5 33.8 TPRF 60-40† 54.2 5.6 PRF40† (used for EtOH blends) 60.0 40.0 E10 E20 E30 E40 E50 E60 E70 E80 E90 1-butanol butyl acetate cyclopentanone dimethyl furan diisobutylene ethanol methanol methyl acetate methyl butyrate methyl ethyl ketone methyl furan 2-pentanone triptane Vertifuel a RON and MON by definition; b Co-Optima surrogate composition: 55 vol% isooctane, 25 vol% toluene, 15 vol% heptane, 5 vol% 1-hexene; † used in synthetic dataset.

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vol Toluene 100 25 17.9 25.0 9.7 14.2 70.0 33.3 66.0 58.0 50.0 16.7 10.0 20.0 40.0 20.0 30.0 60.0 40.0 19.8 40.2 0.0


RON 0 100 120 90.3 93.7 95.2 85.7 86.6 89.3 76.2 85.2 75.6 65.9 39.0 102.0 58.0 51.4 104.1 105.6 77.0 107.7 59.5 57.5 40.0 55.6 69.0 80.7 90.5 97.9 102.5 104.8 105.3 108.5 98.0 100.8 101.0 101.0 106.0 109.0 109.0 >120 107.2 111.0 103.0 105.7 112.0 104.2

MON 0 100 104 84.7 90.3 90.5 84.6 84.2 78.2 70.9 74.8 66.9 57.7 37.0 99.5 53.9 46.0 98.5 98.3 68.0 97.0 55.5 50.7 40.0 53.0 64.0 76.0 83.6 87.5 89.0 89.8 90.2 91.0 85.0 100. 89.4 88.0 86.5 90.0 89.0 >120 105.0 105.5 86.0 103.0 101.0 89.6

S 0 0 16 5.6 3.4 4.7 1.1 2.4 11.1 5.3 10.4 8.7 8.2 2.0 2.5 4.1 5.4 5.6 7.3 9.0 10.7 4.0 6.8 0.0 2.6 5.0 4.7 6.9 10.4 13.5 15.0 15.1 17.5 13.0 0.8 11.6 13.0 9.5 9.0 0.0 0.0 2.2 5.5 17.0 2.7 11.0 14.6

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Two heuristics are useful to assess the algorithm’s efficacy: the root mean square error (RMSE) and the correlation coefficient R2 . Given the true response variable y and the predicted response variable ypred , RMSE and R2 are defined as: v u Fuels u 1 NX 2 RMSE(y, ypred ) ≡ t y(m) − ypred (m) , (10) NFuels m=1 and

NX Fuels

R2 ≡ 1 −

2 ypred (m) − y¯

m=1 NX Fuels

(11)

. 2 ym − y¯

m=1

These two heuristics offer different insight into how well the prediction process works. The RMSE describes the error of the algorithm in the same units as the response variable. The correlation coefficient R2 is a unit-less description of how well the models fit the data. Table 4 shows the RMSE and R2 results for the two regression models, for RON and for S. Table 4: Linear regression measures of performance for Gaussian Process model for RON and S, compared to linear regression model.

Gaussian Process OLS Linear Regression

RON RMSE R2 7 0.9 14 -0.5

S RMSE 4 9

R2 0.5 -1.6

The RMSE is in the same units as the response variable. For the RON prediction, the Gaussian process RMSE is half that of the OLS regression. The average RON for the 41 fuels is roughly 87. Thus, an RMSE of 7 suggests a well-working predictive model. This claim is supported by considering the R2 correlation coefficient of 0.9. In a perfect prediction scenario, R2 = 1.0, thus our Gaussian process with R2 = 0.9 suggests a strong predictive model. For the prediction of S, the Gaussian process RMSE is 4 while the OLS RMSE is more than twice as much at 9. Again, in this case the Gaussian process out performed OLS regression. However, an RMSE of 4 does not mean the Gaussian process regression performed well. The average S for the 41 fuels is only 7.3, showing that having an RMSE of 4 is unsatisfactory. The poor prediction of S can also seen by considering the R2 coefficient of 0.5. This low correlation coefficient indicates poor model prediction. This poor prediction of S could be because the greedy kernel searching algorithm does not find globally optimal kernel for the Gaussian process. For the analysis presented here, the kernel searching algorithm was limited to two iterations: beyond two iterations, the number of hyperparameters increases and yet we did not see an improvement in accuracy. In almost all cases the final selected kernel is a linear combination of two base kernels: the Matern kernel (with nu=0.5,1.5, or 2.5) and the radial basis. This means that the magnitude of each kernel in the BiC (Equation 7) calculation is |G| = 4. 10


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Classification: candidate screening While it is interesting to consider the possibility of predicting a fuels RON and S values, a more pragmatic approach is to consider the possibility of screening fuels based on very small samples. This could reduce the number of candidates to explore using more traditional measurements that require larger fuel quantities. This leads us to the question of classifying a fuel’s RON and S. To try this approach, we select the following two criteria: • The fuel has a RON ≥ 90, • The fuel has a S ≥ 8. A RON of 90 and S of 8 are slightly above the average response values for all 41 fuels. For the classification problem, the response variable y is the class designation represented by a 0 or 1. Before performing the classification, one must choose how to label the classes. In our work, when classifying RON, we choose the classes RON ≥ 90 and RON < 90. For classifying S we choose the classes S ≥ 8 and S < 8. We represent the results in a confusion matrix. A confusion matrix splits the prediction results into four categories: True positive, True negative, False positive, False negative. The interpretation of these bins is as follows: if a fuel is placed into the True negative bin, it means the actual class is True (response = 1) but the response was predicted False (predicted response = 0). With perfect prediction, all fuels would be sorted into either the True positive or True negative bins. Figure 5 shows the confusion matrices for the Gaussian process classification with the kernel search algorithm. Again, we show side-by-side comparison between the Gaussian process classifier and the OLS linear classifier. As expected in light of the regression results, the Gaussian process classifier for RON performed well, with 95% correct classification. In addition, classification of S greater than 8 had a success rate of 85%. For comparison, the OLS linear classifier correctly classified the RON class for 85% of the fuels and only 73% of the fuels were correctly classified with respect to S. Figure 6 shows the classification results in greater detail.

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Figure 4: Leave one out cross validation regression prediction of RON (left column) and S (right column) given the experimental data. The top row is the Gaussian process regression with kernel search and the bottom row is OLS linear regression. For reference, the gray dotted line is the predicted octane number equals true octane number.

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Figure 5: Leave one out cross validation classification prediction of octane numbers given the experimental data: the left column shows RON prediction and right column shows S prediction. The top row is the Gaussian process classification with kernel search and the bottom row is ordinary least squares (OLS) linear classification. Figure A: Gaussian process RON classification, percent correct: 95%; Figure B: Gaussian process S classification, percent correct: 85%; Figure C: OLS linear classification, percent correct: 80%; and Figure D: OLS linear classification, percent correct: 73%.

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Figure 6: Gaussian process classifier with kernel searching algorithm. 95% correct RON classification and 85% correct S classification.

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Method verification and validation with synthetic data This section describes the performance of the analysis pipeline using synthetic data. The synthetic data consists of solutions to plug-flow reactor calculations using established kinetic mechanisms to obtain detailed speciation in plug-flow reactor calculations. In this dataset, 23 of the fuels are simulated and inputs to the analysis pipeline are the mole fractions of 2799 chemical species at seven temperatures in the same range as the experimental flowreactor measurements. Testing against synthetic data serves to address two questions. The first is if the GPR + kernel search method is effective in the absence of measurement error. The second is if there is additional information in detailed speciation beyond the MBMSobtained spectra that is useful in a screening context. The latter is of special interest, as it is possible to modify the apparatus to collect speciation data with a commensurate decrease in experimental throughput. While the results leave the question somewhat ambiguous, we can ascertain that the prediction improves with high-quality speciation data. Figures 7 and 8 shows the results of a classification exercise for RON > 90 and S> 8 using the simulated data. The classification using synthetic data also serves as validation of the accuracy of the chemical mechanism. While the simulation is notionally the ‘exact’ answer to the specified problem, there is still uncertainty in the chemical mechanism. The targets used were the published RON data from the literature so this is a demonstration that there is sufficient information in the products of flow reactor tests (numerical or experimental) to screen fuels for autoignition characteristics RON and S.

Figure 7: Gaussian process classification of RON greater than 90 and S greater than 8, with respect to the simulated data; 100% correct RON classification and 95% correct S classification. The synthetic dataset also provides an opportunity to easily compare the variation in 15


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Figure 8: Ordinary least squares linear classifier of RON > 90 and S > 8, with respect to the simulated data; 65% correct RON classification and 65% correct S classification. performance using separate testing and training sets where the test set includes multiple fuels (in contrast to ‘leave one out’ validation where the test set includes only a single fuel). In Figure 9, the regression results are shown for an ensemble of ways of partitioning the datasets. Since there are 23 fuels in the synthetic data, we choose a ‘leave 2 out’ methodology

Figure 9: Validation for separate training and tests sets on synthetic data. which gives a roughly 10%/90% testing/training data split. We then repeat this analysis 10 times, each with a different random partition of fuels to produce 10 different RON / S predictions for each fuel. The predicted values are the average over the 10 experiments. Indicating a shortcoming in the dataset set, which has only a single low RON entry, heptane is always predicted to have negative RON. When heptane is removed from the dataset the R2 terms jump to 0.99, 0.88 respectively for RON and S. The error bars for a given fuel 16


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represent plus or minus one standard deviation. As we can see, in most cases, the error bars are not visible, indicating that the predictions are largely insensitive to the test/training partitioning.

Conclusions Partial reaction of candidate fuels under highly dilute conditions appears to be a viable means of high throughput, small volume screening for autoignition characteristics. The relationship between the products observed under these pre-oxidation conditions and traditional autoignition characteristics expressed by octane measurements is complex and difficult to capture with linear models yet can be captured by more sophisticated machine learning models. Gaussian process regression with automated kernel search provides a basis for using this type of data to identify candidates likely to result in favorable characteristics with more in depth testing along with some consideration of the uncertainty in the identification. Extracting the probability of the predicted value exceeding some threshold fits naturally into the approach. Transformation of the raw data gathered—speciation resulting from a range of temperatures—into a single observable vector by integrating over temperature performs reasonably well. The approach also appears to be able to accomodate the non-trivial relationship between MBMS fragmentation patterns and speciation, enabling the use of MBMS AMU measurements directly as the input vector. Where the goal is not to extract detailed kinetic information but simply relate measurements to single valued characteristics this is convenient. Although more error prone, possibly due to the added complexity of the relationship to be captured by the model, MBMS data can be acquired at very high frequency and is a potential path to very high throughput screening small quantities, potentially 10s of µL, of candidate fuels.

Acknowledgement This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. This research was conducted as part of the CoOptimization of Fuels & Engines (Co-Optima) project sponsored by the U.S. Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy (EERE) Bioenergy Technologies and Vehicle Technologies Offices. Co-Optima is a collaborative project of multiple national laboratories initiated to simultaneously accelerate the introduction of affordable, scalable, and sustainable biofuels as well as high-efficiency, low-emission vehicle engines. Early stages of this work were supported by the Laboratory Directed Research and Development (LDRD) Program at the National Renewable Energy Laboratory. NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy operated by the Alliance for Sustainable Energy, LLC. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to 17


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publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.

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Screening fuels for autoignition with small volume experiments and

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