Fit To Data Sets Research Articles

Factorial Invariance in a Repeated Measures Design: An Application to the Study of Person-Organization Fit

An important methodological concern of any research based on a person-environment (P-E) fit approach is the operationalization of the fit, which imposes some measurement requirements that are rarely empirically tested with statistical methods. Among them, the assessment of the P and E components along commensurate dimensions is possibly the most cited one. This paper proposes to test the equivalence across the P and E measures by analyzing the measurement invariance of a multi-group confirmatory factor analysis model. From a methodological point of view, the distinct aspect of this approach within the context of P-E fit research is that measurement invariance is assessed in a repeated measures design. An example illustrating the procedure in a person-organization (P-O) fit dataset is provided. Measurement invariance was tested at five different hierarchical levels: (1) configural, (2) first-order factor loadings, (3) second-order factor loadings, (4) residual variances of observed variables, and (5) disturbances of first-order factors. The results supported the measurement invariance across the P and O measures at the third level. The implications of these findings for P-E fit studies are discussed.

Equilibrium two-parameter isotherms of acid dyes sorption by activated carbons: Study of residual errors

The adsorption of two acid dyes Acid Black 1 (AB1) and Acid Blue 113 (AB113) onto mesoporous granular pine-cone derived activated carbon and the adsorption of three acid dyes Acid Black 80 (AB80), Acid Red 114 (AR114) and Acid Yellow 117 (AY117) onto microporous Granular Activated Carbon (GAC) type F400, from aqueous solution, has been studied in a batch system. Seven two-parameter isotherm models – Langmuir, Freundlich, Dubinin–Radushkevich, Temkin, Halsey, Jovanovic and Harkins–Jura – were used to correlate the experimental data. Adsorption isotherm modeling shows that the interaction of dye with activated carbon surface is by localized monolayer adsorption. In order to determine the best fit isotherm for each system, nine error analysis methods, namely, chi-square ( χ 2), log-likelihood ( G 2), residual root mean square error (RMSE), sum of the squares of the errors (ERRSQ), composite functional error (HYBRD), derivative of Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of absolute error (EABS) and average percentage error (APE) were used to evaluate the data. In order to facilitate decision making for the best fit data set, a procedure of normalizing and combining the error results was adopted producing a “sum of the normalized errors” for each parameter set from which the “lowest normalized error set” is selected.

Robust Sequential Data Modeling Using an Outlier Tolerant Hidden Markov Model

Hidden Markov (chain) models using finite Gaussian mixture models as their hidden state distributions have been successfully applied in sequential data modeling and classification applications. Nevertheless, Gaussian mixture models are well known to be highly intolerant to the presence of untypical data within the fitting data sets used for their estimation. Finite Student's t-mixture models have recently emerged as a heavier-tailed, robust alternative to Gaussian mixture models, overcoming these hurdles. To exploit these merits of Student's t-mixture models in the context of a sequential data modeling setting, we introduce, in this paper, a novel hidden Markov model where the hidden state distributions are considered to be finite mixtures of multivariate Student's t-densities. We derive an algorithm for the model parameters estimation under a maximum likelihood framework, assuming full, diagonal, and factor-analyzed covariance matrices. The advantages of the proposed model over conventional approaches are experimentally demonstrated through a series of sequential data modeling applications.

Average seasonal changes in chlorophyll a in Icelandic waters

Abstract Guðmundsson, K., Heath, M. R., and Clarke, E. D. 2009. Average seasonal changes in chlorophyll a in Icelandic waters. – ICES Journal of Marine Science, 66: 2133–2140. The standard algorithms used to derive sea surface chlorophyll a concentration from remotely sensed ocean colour data are based almost entirely on the measurements of surface water samples collected in open sea (case 1) waters which cover ∼60% of the worlds oceans, where strong correlations between reflectance and chlorophyll concentration have been found. However, satellite chlorophyll data for waters outside the defined case 1 areas, but derived using standard calibrations, are frequently used without reference to local in situ measurements and despite well-known factors likely to lead to inaccuracy. In Icelandic waters, multiannual averages of 8-d composites of SeaWiFS chlorophyll concentration accounted for just 20% of the variance in a multiannual dataset of in situ chlorophyll a measurements. Nevertheless, applying penalized regression spline methodology to model the spatial and temporal patterns of in situ measurements, using satellite chlorophyll as one of the predictor variables, improved the correlation considerably. Day number, representing seasonal variation, accounted for substantial deviation between SeaWiFS and in situ estimates of surface chlorophyll. The final model, using bottom depth and bearing to the sampling location as well as the two variables mentioned above, explained 49% of the variance in the fitting dataset.

Linear and non-linear T– S models for the eastern North Atlantic from Argo data: Role of surface salinity observations

Linear and non-linear empirical models for salinity (S) are estimated from the Argo temperature (T) and salinity (delayed) data. This study focuses on the reconstruction of salinity in the upper 1200 m of the eastern North Atlantic Ocean, a region characterized by the presence of many different water masses. While previous studies have found it necessary to split this region by boxes to fit different polynomial models in each box, a unique model valid for the entire region is fitted here. Argo profiles are randomly distributed on two sets: one for fitting the models and one for testing them. Non-linear regressions are built using neural networks with a single hidden layer and the fitting data set is further divided into two subsets: one for adjusting the coefficients (training data) and one for early stopping of the fitting (validation data). Our results indicate that linear regressions perform better than the climatologic T– S relationship, but that non-linear regressions perform better than the linear ones. Non-linear training using a three-data subsets strategy successfully prevents overfitting even when networks with 90 neurons in the hidden layer are being trained. While the presence of local minima may complicate the generalization of non-linear models to new data, network committees (created by training the same network from different random initial weights) are shown to better reproduce the test data. Several predictors are tested, and the results show that geographical, or surface, information does provide significant information. These results highlight the potential applications of future satellite missions measuring sea-surface salinity to reconstruct, when combined with temperature profiles, vertical salinity profiles.

Estimating a Nonlinear Mixed Volume-age Model with and without Taking into Account Serially-correlated Errors: Differences and Implications

In this study we estimated a lodgepole pine (Pinus contorta var. latifolia Engelm.) volume-age model with and without taking into account serially-correlated errors arisen from permanent sample plots. The estimations were based on the first-order (FO) and first-order conditional expectation (FOCE) methods of the nonlinear mixed model technique. Among the correlated error structures considered, the spatial power structure was found to be the most appropriate. Model predictions were obtained and evaluated on model fitting data, as well as on independent validation data collected from a different ecoregion. Results showed that the model estimated with the independent and identically distributed (iid) error structure performed much better than the model estimated with the correlated error structure. This is true on both model fitting and validation data sets, and for both FO and FOCE methods. It implies that, if the main purpose of a study is to develop models for predictions, there is no real benefit to consider more elaborate and complex error structures to account for the correlated errors. The iid error structure is a sound choice for dealing with correlated errors under the nonlinear mixed model framework.

Mechanistic Model for the Reclamation of Industrial Wastewaters Using Algal−Bacterial Photobioreactors

A mechanistic model describing the steady-state biodegradation of inhibitory pollutants by algal-bacterial consortia in enclosed chemostat photobioreactors was developed. The modelwasthenvalidated againstexperimentaldataonsalicylate removal by a Chlorella Sorokiniana/Ralstonia basilensis consortium cultivated without external O2 supplied in an enclosed chemostat photobioreactor under various conditions of photon flux radiation, salicylate inlet concentrations, temperatures, and hydraulic retention times (HRT). A satisfactory fit of experimental data was achieved in both the fitting and validation data sets (11% of average relative error). The model was thus capable of describing satisfactorily the influence of the HRT and the combined increase of light input and temperature on salicylate removal efficiency (RE). The potential inhibitory effect of salicylate was considered into the model structure based on the influence of salicylate concentration on microalgae photosynthetic activity. Only four adjustable parameters were necessary when using this modeling approach, which significantly reduces the number of experimental kinetic and stoichiometric coefficients needed for process description. Variables such as reactor geometry and light absorption characteristics of the biomass were grouped into a single parameter, which highly simplifies photobioreactor modeling. Being based on stoichiometric, thermodynamic, and mass balances analysis, this model can be extended to the removal of any organic pollutant in industrial wastewaters and to any photobioreactor configuration. It therefore provides an important tool to assess the feasibility of pollutant biodegradation under full photosynthetic oxygenation (i.e., no external O2 supply) and to optimize photobioreactors by establishing the conditions under which complete pollutant removal can be achieved. The model herein developed also provides a tool to better understand the complex relationships between microalgae, bacteria, light, and pollutant concentration, which will promote the development of algal-bacterial processes as a cost-effective alternative for wastewater reclamation and algae production from wastewater.

Applications and comparison of six methods for predicting parameters of the Weibull function in unthinned Picea glauca plantations

The objectives of this study were (1) to compare six methods for predicting parameters of the Weibull probability density function (PDF) for diameter at breast height (dbh) distribution in the unthinned white spruce plantations in eastern Canada with respect to their applicability, and (2) to evaluate their predictive abilities in terms of error index (EI) and Kolmogorov–Smirnov (K-S) statistic. The reasons for undertaking this study were (1) there are no available models for the dbh distributions of the studied species and (2) to determine the best method for projecting dbh distributions of white spruce plantations. A total of 113 sample plots which consisted of the commonly measured stand-level variables [stand age (A), site index at 25-year base age (SI), average height of dominant and co-dominant trees (H d), and stand density (SD)] and associated diameter frequency distributions were used in this study. Of all the six prediction methods, the moment-based and percentile-based parameter recovery approach (PRM and PCT), maximum likelihood estimation regression (MLER), cumulative distribution function regression (CDFR) and parameter prediction method (PPM) were able to be applied for adequately modeling the diameter frequency distributions for the data sets used in this study. The moment-percentile estimation hybrid method (HYBM) performed the poorest. PCT was most highly recommended as it had the consistently lowest EI and K-S statistic values for both fit and validation data sets. Therefore, the dbh distributions for white spruce plantations could be predicted at a point over time using the established methods here, especially the PCT method, from the stand variables (A, SI, H d, SD).

Hermite variational implicit surface reconstruction

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit volume model which fits the data points and normal constraints. Compared with variational implicit surfaces, we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs, the proposed method only needs to solve an n×n positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets.

Optimum operating conditions for a water purification process integrated to a heat transformer with energy recycling using neural network inverse

Artificial neural network inverse (ANNi) is applied to calculate the optimal operating conditions on the coefficient of performance (COP) for a water purification process integrated to an absorption heat transformer with energy recycling. An artificial neural network (ANN) model is developed to predict the COP which was increased with energy recycling. This ANN model takes into account the input and output temperatures for each one of the four components (absorber, generator, evaporator, and condenser), as well as two pressures and LiBr + H 2O concentrations. For the network, a feedforward with one hidden layer, a Levenberg–Marquardt learning algorithm, a hyperbolic tangent sigmoid transfer function and a linear transfer function were used. The best fitting training data set was obtained with three neurons in the hidden layer. On the validation data set, simulations and experimental data test were in good agreement ( R > 0.99). This ANN model can be used to predict the COP when the input variables (operating conditions) are well known. However, to control the COP in the system, we developed a strategy to estimate the optimal input variables when a COP is required from ANNi. An optimization method (the Nelder–Mead simplex method) is used to fit the unknown input variable resulted from the ANNi. This methodology can be applied to control on-line the performance of the system.

Software quality analysis by combining multiple projects and learners

When building software quality models, the approach often consists of training data mining learners on a single fit dataset. Typically, this fit dataset contains software metrics collected during a past release of the software project that we want to predict the quality of. In order to improve the predictive accuracy of such quality models, it is common practice to combine the predictive results of multiple learners to take advantage of their respective biases. Although multi-learner classifiers have been proven to be successful in some cases, the improvement is not always significant because the information in the fit dataset sometimes can be insufficient. We present an innovative method to build software quality models using majority voting to combine the predictions of multiple learners induced on multiple training datasets. To our knowledge, no previous study in software quality has attempted to take advantage of multiple software project data repositories which are generally spread across the organization. In a large scale empirical study involving seven real-world datasets and seventeen learners, we show that, on average, combining the predictions of one learner trained on multiple datasets significantly improves the predictive performance compared to one learner induced on a single fit dataset. We also demonstrate empirically that combining multiple learners trained on a single training dataset does not significantly improve the average predictive accuracy compared to the use of a single learner induced on a single fit dataset.

Artificial neural network for the evaluation of CO2 corrosion in a pipeline steel

This paper presents a predictive model for the determination of different types of corrosion by using electrochemical impedance spectroscopy curves and artificial neural network. This proposed model obtains predictions for three different types of corrosion by using Nyquist impedance curves from four input variables: inhibitor concentration, time of exposure, and the real and imaginary experimental component of these curves. The model takes into account the variations of inhibitor concentration over steel to decrease the corrosion rate. For the network, the Levenberg–Marquardt learning algorithm, the hyperbolic tangent sigmoid transfer function and the linear transfer function were used. The best fitting training data set was obtained with five neurons in the hidden layer, which made possible to predict satisfactory efficiency (R > 0.99). On the validation of the data set, simulations and theoretical data tests were in good agreement (R > 0.9905). The developed model can be used for the determination of the type of curves related to the nature phenomena and rate of corrosion at the metal surface.

Prediction of brightness and surface area kinetics during coffee roasting

The amount of heat transferred to green coffee beans is essential in the coffee roasting. During this process, several parameters can be used as indicators to determine the degree of roasting (color, aroma, volume, bean temperature). Consequently, two predictive models, using artificial neural networks, are proposed to determine the quality of coffee roasting. A bean brightness model took account of bean temperature (simulated by a physical model) and roasting time. A second model predicting the bean surface area, focused on roasting air temperature and roasting time. The color changes affecting coffee beans during the process were studied experimentally in a pilot roaster equipped with a CCD video camera and a lighting system consisting of two small optic fiber spotlights. Arabica green coffee beans of Colombian origin were roasted using different air temperatures (190, 200, 210, … 300 °C), for 10 min. Two separate feedforward networks with one hidden layer were used to brightness and surface kinetics. The best fitting training data set was obtained using three neurons in the hidden layer, which enable prediction of brightness and bean surface kinetics with an accuracy that was at least as good as the experimental error, over the entire experimental range. Using the validation data set, simulations and experimental data were in good agreement ( R 2 > 0.98). This study showed that real-time simulations were possible so that the roasting process could be stopped when the simulated brightness was similar to a target fixed by the roast master. The model thus developed could contribute to the on-line estimation of product quality, thus providing a parameter to control coffee roasting.

Investigation of mouldability for feedstocks used powder injection moulding

In this study performed experimental and theoretical analysis of mouldability for feedstocks used powder injection moulding. This study covers two main subjects: (i) The experimental analysis: The barrel temperature, injection pressure and flow rate are factors for powder injection moulding (PIM). Powder–binder mixture using as feedstock as feedstock in PIM requires a little more attention and sensitivity. Obtaining the balance among with pressure, temperature and especially flow rate are the most important in aspect of undesirable conclusions such as powder–binder separation, sink marks and crack in moulded party structure. In this study; available feed stocks using in PIM were injected in three different cavities which consist of zigzag form, constant cross section and stair form (in five different thicknesses) mouldability them are measured. Because of difference between material and binder measured lengths were different. These were measured as 533 mm, 268 mm, 211 mm and 150 mm in advanced materials trade mark Fe-2Ni, BASF firm Catamould AO-F, FN02, 316L stainless steel, respectively. (ii) The theoretical analysis: The use of artificial neural network (ANN) has been proposed to determine the mouldability for feedstocks using in powder injection moulding using results of experimental analysis. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained with three and four neurons in the hidden-layer, which made it possible to predict yield length with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found the R 2 values are 0.999463, 0.999445, 0.999574 and 0.999593for Fe-2Ni, BASF firm Catamould AO-F, FN02, 316L stainless steel, respectively. Similarly, these values for testing data are 0.999129, 0.999666, 0.998612 and 0.997512, respectively. As seen from the results of mathematical modeling, the calculated yield length are obviously within acceptable uncertainties.

Modelling of residual stresses in the shot peened material C-1020 by artificial neural network

This study consists of two cases: (i) The experimental analysis: Shot peening is a method to improve the resistance of metal pieces to fatigue by creating regions of residual stress. In this study, the residual stresses induced in steel specimen type C-1020 by applying various strengths of shot peening, are investigated using the electrochemical layer removal method. The best result is obtained using 0.26 mm A peening strength and the stress encountered in the shot peened material is −276 MPa, while the maximum residual stress obtained is −363 MPa at a peening strength of 0.43 mm A. (ii) The mathematical modelling analysis: The use of ANN has been proposed to determine the residual stresses based on various strengths of shot peening using results of experimental analysis. The back-propagation learning algorithm with two different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained with four neurons in the hidden layer, which made it possible to predict residual stress with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found the R 2 values are 0.996112 and 0.99896 for annealed before peening and shot peened only, respectively. Similarly, these values for testing data are 0.995858 and 0.999143, respectively. As seen from the results of mathematical modelling, the calculated residual stresses are obviously within acceptable uncertainties.

COP prediction for the integration of a water purification process in a heat transformer: with and without energy recycling

A predictive model for a water purification process integrated in an absorption heat transformer, using an artificial neural network, is proposed in order to obtain on-line predictions of the coefficient of performance (COP). This model takes into account the input and output temperatures for each one of the four components (absorber, generator, evaporator, and condenser), as well as two pressure parameters of the absorption heat transformer and LiBr+H 2O concentrations. Two separate feedforward networks with one hidden layer were used to predict the COP values which increased with energy recycling, and the COP values without energy recycling, respectively. For the networks, the Levenberg-Marquardt learning algorithm, the hyperbolic tangent sigmoid transfer-function and the linear transfer-function were used. The best fitting training data set was obtained with three neurons in the hidden layer, which made it possible to predict COP with accuracy at least as good as that of the experimental error over the whole experimental range. On the validation data set, simulations and experimental data test were in good agreement ( R 2 >0.99). The developed models can be used for a reliable on-line state estimation and control of a water purification process integrated in an absorption heat transformer.

Improving Software Quality Prediction by Noise Filtering Techniques

Accuracy of machine learners is affected by quality of the data the learners are induced on. In this paper, quality of the training dataset is improved by removing instances detected as noisy by the Partitioning Filter. The fit dataset is first split into subsets, and different base learners are induced on each of these splits. The predictions are combined in such a way that an instance is identified as noisy if it is misclassified by a certain number of base learners. Two versions of the Partitioning Filter are used: Multiple-Partitioning Filter and Iterative-Partitioning Filter. The number of instances removed by the filters is tuned by the voting scheme of the filter and the number of iterations. The primary aim of this study is to compare the predictive performances of the final models built on the filtered and the un-filtered training datasets. A case study of software measurement data of a high assurance software project is performed. It is shown that predictive performances of models built on the filtered fit datasets and evaluated on a noisy test dataset are generally better than those built on the noisy (un-filtered) fit dataset. However, predictive performance based on certain aggressive filters is affected by presence of noise in the evaluation dataset.

Experimental and Theoretical Investigations of Mouldability for Feedstocks Used in Powder Injection Moulding

Experimental and theoretical analyses of mouldability for feedstocks used in powder injection moulding are performed. This study covers two main analyses. (i)The experimental analysis: the barrel temperature, injection pressure, and flow rate are factors for powder injection moulding (PIM). Powder-binder mixture used as feedstock in PIM requires a little more attention and sensitivity. Obtaining the balance among pressure, temperature, and especially flow rate is the most important aspect of undesirable conclusions such as powder-binder separation, sink marks, and cracks in moulded party structure. In this study, available feedstocks used in PIM were injected in three different cavities which consist of zigzag form, constant cross-section, and stair form (in five different thicknesses) and their mouldability is measured. Because of the difference between material and binder, measured lengths were different. These were measured as 533 mm, 268 mm, 211 mm, and 150 mm in advanced materials trade marks Fe–2Ni, BASF firm Catamould A0-F, FN02, and 316L stainless steel, respectively. (ii)The theoretical analysis: the use of artificial neural network (ANN) has been proposed to determine the mouldability for feedstocks used in powder injection moulding using results of experimental analysis. The back-propagation learning algorithm with two different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained with three and four neurons in the hidden layer, which made it possible to predict yield length with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found that theR2values are 0.999463, 0.999445, 0.999574, and 0.999593 for Fe–2Ni, BASF firm Catamould A0-F, FN02, and 316L stainless steel, respectively. Similarly, these values for testing data are 0.999129, 0.999666, 0.998612, and 0.997512, respectively. As seen from the results of mathematical modeling, the calculated yield lengths are obviously within acceptable uncertainties.

Determination of residual stresses based on heat treatment conditions and densities on a hybrid (FLN2-4405) powder metallurgy steel using artificial neural network

This paper presents a new approach based on artificial neural networks (ANNs) to determine the residual stresses in PM steel based nickel (FLN2-4405). This study consists of two cases: (i) The experimental analysis: The measurements of residual stresses were carried out by electrochemical layer removal technique. The values and distributions of residual stresses occurring in PM steel processed under various densities (6.8, 7.05, 7.2 and 7.4 g/cm 3) and heat treatment conditions (sintered at 2050 °F, sintered at 2300 °F, quenching-tempered, and sinter-hardened) were determined. In most of the experiments, tensile residual stresses were recorded in surface of samples. The residual stress distribution on the surface of the PM steels is affected by the heat treatment conditions and density. Maximum values of residual stresses on the surface were observed sinter hardened condition and 7.4 g/cm 3 density. (ii) The mathematical modeling analysis: The use of ANN has been proposed to determine the residual stresses based on heat treatment conditions and densities in PM steel using results of experimental analysis. The back propagation learning algorithm with two different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained with four and five neurons in the hidden layer, which made it possible to predict residual stress with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found the R 2 values are 0.999244, 0.999025, 0.999664 and 0.999322 for sintered at 2050 °F, sintered at 2300 °F, quenching-tempered, and sinter-hardened, respectively. Similarly, these values for testing data are 0.998354, 0.99706, 0.999607 and 0.999205, respectively. As seen from the results of mathematical modeling, the calculated residual stresses are obviously within acceptable uncertainties.

Comparative study of mathematical and experimental analysis of spark ignition engine performance used ethanol–gasoline blend fuel

This study consists of two cases: (i) The experimental analysis: Ethanol obtained from biomass can be used as a fuel in spark ignition engines. As renewable energy source ethanol, due to the high octane number, low emissions and high engine performance is preferred alternative fuel. First stage of this study, ethanol–unleaded gasoline blends (E10, E20, E40 and E60) were tested in a single cylinder, four-stroke spark ignition and fuel injection engine. The tests were performed by varying the ignition timing, relative air–fuel ratio (RAFR) and compression ratio at a constant speed of 2000 rpm and at wide open throttle (WOT). Effect of ethanol–unleaded gasoline blends and tests variables on engine torque and specific fuel consumption were examined experimentally. (ii) The mathematical modeling analysis: The use of ANN has been proposed to determine the engine torque and specific fuel consumption based on the ignition timing, RAFR and compression ratio at a constant speed of 2000 rpm and at WOT for different fuel densities using results of experimental analysis. The back-propagation learning algorithm with two different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained Levenberg–Marquardt (LM) algorithm with five neurons in the hidden layer, which made it possible to the engine torque and specific fuel consumption with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found the R 2 values are 0.999996 and 0.999991 for, the engine torque and specific fuel consumption, respectively. Similarly, these values for testing data are 0.999977 and 0.999915, respectively. As seen from the results of mathematical modeling, the calculated engine torque and specific fuel consumption are obviously within acceptable uncertainties.