Numerical Engine Research Articles

A Pressure Projection Scheme With Near‐Spectral Accuracy for Nonhydrostatic Flow in Domains With Open Boundaries

AbstractWe describe a pressure projection scheme for the simulation of incompressible flow in cubic domains with open boundaries based on fast Fourier transforms. The scheme is implemented in flow_solve, a numerical code designed for process studies of rotating, density‐stratified flow. The main algorithmic features of the open‐boundary code are the near‐spectral accuracy of the discrete differentiation and a dynamic two‐dimensional domain decomposition that scales efficiently to large numbers of processors. The simulated flows are not required to be periodic or to satisfy symmetry conditions at the open boundaries owing to the use of mixed series expansions combining cosine and singular Bernoulli polynomial basis functions. These expansions facilitate the imposition of inhomogeneous boundary conditions and allow the code to be used for offline, one‐way nesting within an arbitrarily embedded subdomain of a larger scale simulation. The projection scheme is designed to exploit a simple and powerful numerical engine: inversion of Poisson's equation with homogeneous Neumann boundary conditions using fast cosine transforms. Here, we describe the mathematical transformations used to accommodate the imposition of space‐ and time‐varying boundary conditions. The utility of the approach for process studies and for nesting within submesoscale‐resolving ocean models is demonstrated with simulations of wind‐driven near‐inertial waves in the upper ocean.

Investigating dynamic characteristics and thermal-lag phenomenon in a thermal-lag engine using a CFD-mechanism dynamics model

Thermal-lag engines (TLE) are external combustion engines with a single piston that offer the potential for reduced maintenance and production costs compared to traditional Stirling engines. Despite these promising prospects, studies on the physical behavior of this engine type remain limited. In this study, three novelties are presented: (1) a novel computational fluid dynamics-mechanism dynamics (CFDMD) model with high complexity for the TLE; (2) an analysis of the work generation in relation to the phase difference between pressure and volume; and (3) an analysis of the thermal-lag phenomenon based on the full spectrum of the phase difference between temperatures and piston position. In the CFDMD model, there are two key components: a computational fluid dynamics (CFD) model that captures the temporal evolution of the three-dimensional thermo-fluid fields and a mechanism dynamics model that solves the transient dynamics of the crank-drive mechanism. The CFDMD model effectively simulates the complex interplay between the thermodynamic behavior of the working gas and the dynamic behavior of the engine mechanism. The study additionally investigates the temporal evolution of the engine speed and examines its dynamic behavior. The influence of parameters, including crank radius, heating temperature, and initial crank angle, on shaft power and brake thermal efficiency is thoroughly explored. To gain a profound understanding of the indicated work generation mechanism and the thermal-lag phenomenon, the discrete Fourier transform provides full spectra of the periodic quantities of interest generated by the CFDMD model. It is found that the numerical average engine speed at different heating temperatures and torques from the CFDMD model is in good agreement with the experimental data, with a maximum difference of 140 rpm. The shaft power decreases from 19.8 to 5.3 W, while brake thermal efficiency increases from 4.5 to 7.7% as the initial crank angle varies from −90° to 90°. The first-oscillation phase differences between pressure and volume are close to 180°, decrease as the heating capacity is raised, and dominate the swelling of the PV diagrams. Only the first harmonic oscillation of the heater temperature exhibits the thermal-lag phenomenon.

Structurally Optimized Neural Fuzzy Modeling for Model Predictive Control

This paper investigates the local linear model tree (LOLIMOT), a typical neural fuzzy model, in the multiple-input-multiple-output model predictive control (MPC). In the conventional LOLIMOT, the structural parameters including centres and variances of its Gaussian kernels are set based on equally dividing the input data space. In this paper, after the structural parameters are initially obtained from the input space partition, they are optimized by the gradient descent search, from which the space partitions are further adjusted. This makes it better for the model structure to fit the input data statistics, leading to improved modelling performance with small model size. The MPC based on the proposed structurally optimized LOLIMOT is then implemented and verified with both numerical and diesel engine plants. Validation results show that the proposed MPC has significantly better controlling performance than the MPC based on the conventional LOLIMOT, making it an attractive solution in practice.

DISCREPANCY MODELING FOR MODEL CALIBRATION WITH MULTIVARIATE OUTPUT

This paper explores the application of the Kennedy and O'Hagan (KOH) Bayesian framework to the calibration of physics models with multivariate outputs by formulating the problem in a dimension-reduced subspace. The approach in the KOH framework is to calibrate the physics model parameters simultaneously to the parameters of an additive discrepancy (model error) function. It is a known issue that such discrepancy functions may result in non-identifiability between the model parameters and discrepancy function parameters. Three main approaches to avoid this problem have been considered in the literature: (i) careful definition of the parameter priors based on extensive knowledge of the problem physics, (ii) separating the calibration process into more than a single step (referred to as a modular or sequential solution), or (iii) choosing functions that are less flexible than a Gaussian process (GP). By transformation of the problem into a dimension-reduced principal components (PC) space [using PC analysis (PCA)], we explore a fourth approach to this problem. Advantages are dimension reduction of the calibration problem due to fewer outputs, simplified discrepancy functions and priors, and feasibility for the simultaneous solution approach. The additive discrepancy method is limited in the case of future predictions with the model; thus, we instead suggest how the results may be used for model diagnostic purposes. The methods are demonstrated on a simple numerical example and gas turbine engine heat transfer model.

Distributed primal outer approximation algorithm for sparse convex programming with separable structures

This paper presents the distributed primal outer approximation (DiPOA) algorithm for solving sparse convex programming (SCP) problems with separable structures, efficiently, and in a decentralized manner. The DiPOA algorithm development consists of embedding the recently proposed relaxed hybrid alternating direction method of multipliers (RH-ADMM) algorithm into the outer approximation (OA) algorithm. We also propose two main improvements to control the quality and the number of cutting planes that approximate nonlinear functions. In particular, the RH-ADMM algorithm acts as a distributed numerical engine inside the DiPOA algorithm. DiPOA takes advantage of the multi-core architecture of modern processors to speed up optimization algorithms. The proposed distributed algorithm makes practical the solution of SCP in learning and control problems from the application side. This paper concludes with a performance analysis of DiPOA for the distributed sparse logistic regression and quadratically constrained optimization problems. Finally, the paper concludes with a numerical comparison with state-of-the-art optimization solvers.

Investigation of the Behaviors of Methanol Spray Impingement and Wall Wetting

Port fuel injection is an important technical route in methanol engines. To obtain a theoretical basis for injector arrangement and injection strategy development in methanol engines, an optimal experimental platform based on diffuse back-illumination and the refractive index matching method (RIM) was designed and built in this study. The experiments on the behavior of low-pressure methanol spray-wall impingement and wall film were carried out and the influence of the three boundary conditions of spray distance (Dimp), wall temperature (Twall), and injection pressure (Pinj) were analyzed comprehensively. Results showed that with the increase of Dimp, the overall shape of spray before impinging the wall changed from conical to cylindrical. The impinging spray height Hi and impinging spray width Wi increased with the decrease of Dimp and the increase of Pinj. Adhesive fuel film mass Mf increased with the increase of Dimp due to the decrease of kinetic energy during wall impact. In addition, the increase of the wall temperature Twall reduced Mf due to evaporation, but when Twall reached 423 K, Mf rebounded due to the Leidenfrost effect. The results of this study are helpful to improve the accuracy of the numerical methanol engine model.

Computational investigation of ammonia-hydrogen peroxide blends in HCCI engine mode

The potential use of hydrogen peroxide as an ignition promoter to enable the use of ammonia in compression ignition engines is explored in the current study. A simplified numerical HCCI engine model within the Chemkin Pro suite is employed. The numerical investigation reveals that the proposed use of hydrogen peroxide is significantly more advantageous against the more conventional method of preheating the intake charge to achieve ignition, whilst using a glow plug. In particular, the IMEP, power and torque exhibit an increase greater than 65% along with a spectacular decrease of NOx emissions reaching in certain cases a 9-fold decrease. The thermal efficiency exhibits a more moderate, yet non-negligible increase, around 5%. Generally, the incremental increase of hydrogen peroxide leads to the increase of the IMEP, power and torque as well as the maximum temperature and, hence, NOx emissions. These increases are largely linear with the hydrogen peroxide addition. Finally, the introduction of hydrogen peroxide leads to a two-stage ignition process, where the first ignition stage was found to be instrumental to the control of the ignition process, and, therefore, the system’s efficiency. Further research is required to substantiate further the feasibility and the the limitations of the proposed technology which can enable the rapid decarbonization of heavy duty applications, such as marine ships and trucks.

Accurate automatic object 4D tracking in digital in-line holographic microscopy based on computationally rendered dark fields

Building on Gabor seminal principle, digital in-line holographic microscopy provides efficient means for space–time investigations of large volumes of interest. Thus, it has a pivotal impact on particle tracking that is crucial in advancing various branches of science and technology, e.g., microfluidics and biophysical processes examination (cell motility, migration, interplay etc.). Well-established algorithms often rely on heavily regularized inverse problem modelling and encounter limitations in terms of tracking accuracy, hologram signal-to-noise ratio, accessible object volume, particle concentration and computational burden. This work demonstrates the DarkTrack algorithm—a new approach to versatile, fast, precise, and robust 4D holographic tracking based on deterministic computationally rendered high-contrast dark fields. Its unique capabilities are quantitatively corroborated employing a novel numerical engine for simulating Gabor holographic recording of time-variant volumes filled with predefined dynamic particles. Our solution accounts for multiple scattering and thus it is poised to secure an important gap in holographic particle tracking technology and allow for ground-truth-driven benchmarking and quantitative assessment of tracking algorithms. Proof-of-concept experimental evaluation of DarkTrack is presented via analyzing live spermatozoa. Software supporting both novel numerical holographic engine and DarkTrack algorithm is made open access, which opens new possibilities and sets the stage for democratization of robust holographic 4D particle examination.

Experimental and numerical engine cycle setup for a dual fuel hydrogen, methane, and hythane with diesel to assess the effect of water injection and nozzle geometry

AbstractIn this study, the potential of gaseous fuels such as hydrogen, methane, and hythane in combination with diesel fuel is assessed in a closed loop thermodynamic framework. An experimental test is conducted with basic diesel fuel and then the model is configured based on the realistic one‐cylinder diesel engine to evaluate the robustness and reliability of the simulation. The model is accurate in terms of in‐cylinder pressure, temperature, and heat release rate within the 3% error band. In principle, three blend cases of diesel50%—methane50%, diesel50%—hydrogen50%, and diesel50%—hythane50% are compared with baseline neat diesel from engine performance to emissions characteristics. For hythane and hydrogen‐involved fuels, the 10% water injection effect is analyzed as well to damp the high flammability and ignition intensity of hydrogen. The findings indicate that the entropy generation in hythane and hydrogen is markedly higher than in diesel case, while water injection can slightly decrease the entropy amount. It is shown that D50H50 has more fuel consumption in higher nozzle diameter (28% at 1 mm hole diameter), while in lower nozzle size range pure diesel fuel consumption dominates. The results revealed that D50Hy40W10 is particularly effective for elevated torque at lower nozzle hole values since the steam contributes toward maximized pressure and the exerted force. The increase of the nozzle number resulted in the CO content increase in the exhaust with the burning temperature reduction.

Lattice kinetic model of 3D flow characterization in core samples via synchrotron X-ray micro-tomography

Flow characterization using more accurate and robust numerical engine in the natural domains is a demanding subject in underground related surveys for an optimized performance. Primarily, we employed a more precise insight into constructing a proper three-dimensional rock model, the XCT. Representative samples were scanned with a synchrotron Micro-Tomography beamline. The reconstructed volumes were analyzed using iMorph and the fluid flow simulated by employing the novel Constant Speed Kinetic Lattice model (CSKM).In this approach, the 4D Fourier series have been employed to simulate 3D fluid flow taking into account thermodynamic consistency. Considering the recently proposed entropic model of Burg and Tsallis, the extended Boghosian distribution function model was substituted by the recently proposed 4D CSKM with Tsallis entropy, incorporating a new developed forcing term through modified Exact Difference Method (EDM). Compared earlier research, the results reveal more accuracy in making flow parameters consistent with the porous-media-related physical phenomena.

Evaluation of flux trapping moat position on AQFP cell performance

With recent advances in InductEx and the TetraHenry numerical engine, it is now possible to analyze the coupling of trapped flux in moats to superconductor circuit structures. Here we show the analysis of moat position in the layout of an adiabatic quantum-flux-parametron (AQFP) buffer cell on the coupling to critical inductors such as the load inductor. This inductor is often carefully laid out to balance current flow and cancel out stray coupling between clock and dc current excitation lines. We investigate the effect of trapped flux that couples asymmetrically to the circuit—either due to the moat position and shape or due to only one of a symmetrical duo of moats being filled with a trapped fluxon—on circuit operating margin and performance. We conclude with suggestions on moat placement to reduce the chances of circuit failure when fluxons are trapped in the moats.

Estimation of layer coefficients of cubipod homogeneous low-crested structures using physical and numerical model placement tests

Homogeneous low-crested structures (HLCSs) on hard seabed are designed to protect beaches and regenerate coral reefs. The height of a HLCS depends on the placement grid which determines the crest freeboard, wave transmission and concrete consumption. In real seafloor conditions, it is not easy to define feasible placement grids for HLCSs on uneven sea bottoms. In this study, the parameters of the numerical model Bullet Physics Engine (BPE) are calibrated and validated using the results of small-scale physical model placement tests of five-layer Cubipod HLCSs on horizontal rigid bottom. The BPE model showed a low sensitivity to variations in the calibrated parameters; the numerical model estimated the layer coefficients with global mean relative errors of 1.04% and 1.39% in the triangular and rectangular placements grids, respectively. Once the numerical model was calibrated, new numerical and physical model tests on a 4% rigid bottom slope were compared for validation. A five-layer Cubipod HLCS on a 4% bottom slope was simulated using the BPE numerical model showing a global mean relative error of 2.75% compared to the small-scale physical model tests. A good agreement was found between numerical and physical model tests of five-layer Cubipod HLCSs on both horizontal as well as 4% rigid bottom slope. The BPE numerical model was found a suitable tool to estimate the structure height of HLCSs and to optimize placement grids of HLCSs on real cases with hard sea bottom.

Parallel simulation of cyber-physical systems

Model-based design (MBD) in systems engineering is a well-accepted technique to abstract, analyze, verify, and validate complex systems. In MBD, we design a mathematical model of the system to virtually execute and test systems via model simulations to understand the system dynamics better. Computing model simulations has their challenges; one is to ensure that the simulation trajectory preserves the model semantics. Besides, computing many simulation trajectories over a long time-horizon must be time efficient for rapid respond to system engineers. In this work, we address these challenges in simulating models of cyber-physical systems (CPS), particularly systems possessing mixed discrete–continuous dynamics. We focus on the subclass of CPS’s hybrid automata models, where Jump predicates are restricted to polygonal constraints and present a numerical simulation engine that can efficiently compute many random simulations in parallel by exploiting the parallel computing capability in modern multicore processors. Our simulation engine implements a lock-free parallel breadth-first-search (BFS)-like algorithm and is implemented in the model-checking tool XSpeed. In addition, an application of our simulation engine in property verification of CPS models has been illustrated on two benchmarks. Some model coverage metrics have been defined that users of the tool can specify to set the desired thoroughness of testing with simulations. We demonstrate the performance gains of our simulation engine over SpaceEx and CORA, the modern model checkers and simulators for affine hybrid systems.

A hybrid time-frequency domain method to predict insertion loss of intake system.

A hybrid time-frequency domain method for predicting insertion loss (IL) of intake systems is investigated with detailed evaluation and optimization in terms of acoustic performance and intake efficiency for an automotive engine intake system. Instead of progressively coupling of both domain variables, as in the existing hybrid methods, the proposed method uses frequency-domain source impedance to characterize the acoustic source, and a time-domain method to analyze the acoustic transmission. A simplified equation is derived to predict IL using noise reduction (NR) and acoustic impedance Zl rather than four-pole transfer matrices as used in the traditional frequency-domain method and hybrid-domain method. The NR and Zl of intake systems calculated by the time-domain method are used to predict IL for the first time. This hybrid method has advantages of requiring no numerical engine model while considering the convective and dissipative effect of intake flow on a complex intake system. The predicted ILs of a quarter-wavelength tube and an optimized air cleaner were validated with the measured results. The proposed method and results are applicable and useful to the design of an intake system at an early stage of engine development.

Experiment and simulation investigation on energy management of a gasoline vehicle and hybrid turbocharger optimization based on equivalent consumption minimization strategy

The experiment and simulation investigation of vehicle energy management (VEM) were carried out on a passenger car equipped with a turbocharged gasoline engine. The research results show that the vehicle takes on the characteristic of overcharge under urban conditions to guarantee the power by sacrificing economy. Exhaust energy after catalytic converter and the greater circulation heat transfer loss that account for more than one-third of total energy under New European Driving Cycle (NEDC) are wasted without being used, which indicates that the tested vehicle has great potential for recovering the waste heat. To solve these problems, the VEM model coupled multiple physical fields was developed and calibrated. Original turbocharger was reformed to hybrid turbocharger with the aid of simulation model, and its optimal control strategy based on equivalent consumption minimization strategy (ECMS) was designed. The one-dimensional numerical engine model was introduced into algorithms, which opens new windows for the development of VEM optimization strategies. After the transformation of hybrid turbocharger, the overcharge phenomenon under urban driving cycle has been eliminated. The main contribution to fuel saving comes from the reduction of pumping loss and alternator power consumption. The energy saving rate of hybrid turbocharger in different driving cycles ranges from 1% to 5%, which is mainly affected by the deterioration degree of overcharge on the economy of original machine and the characteristics of regeneration conditions in different driving cycles.

Development and validation of a novel quasi-dimensional combustion model for un-scavenged prechamber gas engines with numerical simulations and engine experiments

Lean-burn gas engines equipped with an un-scavenged prechamber have proven to reduce nitrogen oxides (NOx) emissions and fuel consumption, while mitigating combustion cycle-to-cycle fluctuations and unburned hydrocarbon (UHC) emissions. However, the performance of a prechamber gas engine is largely dependent on the prechamber design, which has to be optimised for the particular main chamber geometry and the foreseen engine operating conditions. Optimisation of such complex engine components relies partly on computationally efficient simulation tools, such as quasi and zero-dimensional models, since extensive experimental investigations can be costly and time-consuming. This article presents a newly developed quasi-dimensional (Q-D) combustion model for un-scavenged prechamber gas engines, which is motivated by the need for reliable low order models to optimise the principle design parameters of the prechamber. Our fundamental aim is to enhance the predictability and robustness of the proposed model with the inclusion of the following: (i) Formal derivation of the combustion and flow submodels via reduction of the corresponding three-dimensional models. (ii) Individual validation of the various submodels. (iii) Combined use of numerical simulations and experiments for the model validation. The resulting model shows very good agreement with the numerical simulations and the experiments from two different engines with various prechamber geometries using a set of fixed calibration parameters.

(Invited) Experimentally-Driven Numerical Investigations of High-Voltage GaN HEMTs

In this talk, we will report on an ongoing investigation of the performance of GaN HEMT devices over their life-cycle from first activation through long-term operation. Of particular interest is also a device’s response to repeating high-voltage cycling and even to external stress events, such as an electromagnetic pulse. It has been previously established that a HEMT’s electrical performance can be ascertained by examining its thermal behavior. Therefore, deep submicron resolution thermoreflectance (TR) temperature imaging is used to measure the temperature profile of the exposed surface features of the device, which are mainly the source and drain metal contacts as well as the GaN channel region. The TR thermography (TRTG) method is based on detecting changes in surface reflectivity (ΔR) that result from changes in local surface temperature (ΔT). The relationship between the changes in reflectivity and temperature is linear to first-order effects, and is typically referred to as the coefficient of thermoreflectance (CTR). As expected, this coefficient depends on the material and the wavelength of light, but also on any transparent layers (e.g., passivation) in the optical path between the first reflective surface and the sensor where the light is collected. Therefore, the success of a TR measurement requires that the surface of interest exhibit both a high reflective index and be thermally-reflective, i.e., have a good value of CTR. By using a near ultra-violet source to illuminate the device under test (DUT), the GaN is rendered opaque, thus ensuring that the obtained temperature fields are those of the GaN surface and not an integrated average over multiple semi-transparent layers. However, the presence of the field-plate obstructs imaging access to the gate where the peak temperatures are expected. Therefore, this investigation couples the measurements to 3D computations in order to produce temperature fields that would otherwise be inaccessible to direct measurement.Both quasi-steady-state and transient temperature fields of the GaN HEMTs are obtained at different activation power levels and an experimental assessment is made with regard to the electrical activation limits and the thermal self-heating. In addition to the measurements, thermal computations are performed using a self-adaptive, multi-scale, numerical simulation engine. The 3D transient thermal model is then driven by the experimentally-obtained temperature maps to provide a more detailed and device-specific interpretation of the coupled electro-thermal effect of the field-plates on reducing the temperature and increasing the break-down voltage. Moreover, the full 3D thermal model also helps provide physically-accurate temperature fields of regions of critical channel regions, where the heat sources are located, and where localized hotspots that are hidden underneath field-plates are inaccessible to optical measurement approaches. The attached figure contains two temperature fields, numerical on the left and experimental on the right. These results are representative of the type of useful data that can be obtained from the computational and measurement techniques. The presentation will additionally include the results of the coupling of the two approaches and the insights that can be gained, especially for those features that are optically inaccessible.

Experimental and numerical investigation of the Advanced Fuel Ignition Delay Analyzer (AFIDA) constant-volume combustion chamber as a research platform for fuel chemical kinetic mechanism validation

Advanced combustion engine strategies that can offer increased efficiency and reduced emissions are enabled by numerical engine combustion simulations, requiring accurate chemical kinetic mechanism input. The Advanced Fuel Ignition Delay Analyzer (AFIDA) device can perform high quality, repeatable measurements of ignition delay (ID) times using small fuel quantities with high throughput. The AFIDA experiments involve liquid fuel injection into the heated and pressurized constant-volume chamber, producing an autoignition delay resulting from a combination of physical mixing and chemical kinetic processes, a complexity which makes the development of complementary numerical models necessary for the development and validation of chemical kinetic mechanisms. Modeling the device based on a homogenous approximation with reduced primary reference fuel (PRF) mechanism shows up to 75% error in the modeled vs. observed autoignition delay data for n-heptane and iso-octane at 10 bar (ɸ = 1.2–0.8) and 20 bar (ɸ = 0.6–0.4) over 973–648 K, whereas the use of a computational fluid dynamics (CFD) model reduces the discrepancy to within 25%. The homogenous approximation error is greatest for conditions where the observed ignition delay is short and the system is not sufficiently mixed (<30 ms), providing guidance to select a homogenous reactor vs. CFD modeling approach based upon desired accuracy. Experimental 20 bar iso-octane ID results show a larger magnitude of negative temperature coefficient chemistry compared to numerical results, indicating possible deficiencies in the PRF chemical kinetic mechanism. This characterization demonstrates the AFIDA as a capable research platform for chemical kinetic model development and validation.

Integrating Models and Remote Sensing Data for Distributed Glacier Mass Balance Estimation

This article presents an approach to improve the estimation of the glacier mass balance (GMB) of six selected alpine glaciers in the European Alps. This is achieved by combining three complementary data sources: hydroclimatological model, remote sensing (RS) data, and ground measurements. The hydroclimatological model provides spatially distributed mass balances. RS supplies spatially distributed surface characteristics. The ground point measurements provide the mass balance at the local scale. The combination of these data sources allows us to improve the spatial resolution of the model output and its GMB estimates. We used the alpine multiscale numerical distributed simulation engine model (AMUNDSEN), which considers the processes of accumulation and ablation of snow and ice for the area of the entire glacier (with a given spatial and temporal resolution). In the proposed integration approach, we first compute the deviations between the GMB simulation (afforded by the hydroclimatological model) and the ground measurements. Then, the RS data are used to define a feature space (which objectively characterizes the glacier surface properties). The method estimates the adjustment required to the model, for each unlabeled sample, leveraging on its neighboring labeled samples in the feature space. This allows us to apply similar adjustment to samples sharing similar glacier surface conditions. Experimental results show that the proposed integration approach achieves an average root-mean-square error of 460 mm (compared to 732 and 661 mm obtained by the hydroclimatological model and the standard regression models, typically used for parameters estimation).

Local Linear Model Tree with Optimized Structure

This paper investigates the local linear model tree (LOLIMOT) with optimized structure. The performance of the LOLIMOT model depends on how the neurons are constructed. In the typical LOLIMOT model, the number of neurons is initially set as one and starts to increase by repeatedly splitting an existing neuron into two equal ones until the required performance is achieved. Because the equal split of a neuron is not optimal, a large model size is often necessary for required performance, leading to high complexity and strong overfitting. In this paper, we propose a gradient-decent-search-based algorithm to optimally split an existing neuron into two new ones. Based on both numerical data and simulated engine data, through the evaluation of optimized structure, the effectiveness of proposed method has been verified.