Semi-empirical Prediction Model Research Articles

A semi-empirical model for online real-time control of NOX generation in diesel engines

Diesel NOX emission control is the main control content of diesel engines. Real-time high-precision NOX emission prediction model is the basic guarantee for (1) Diesel combustion management, (2) SCR after-treatment control, (3) OBD system. Existing models that rely exclusively on physical processes or data-driven artificial intelligence models fail to meet real-time requirements, while MAP look-up table-based models are poorly adapted and require extensive experiments for calibration. In this study, a new semi-empirical model for NOX emission prediction was developed, and the variables of the model were identified as exhaust temperature, engine speed, injected fuel mass flow rate, air intake mass flow rate, and exhaust oxygen mass flow rate, taking into account the mechanism of NOX generation in diesel engines as well as the requirement of real-time and direct measurability of the variables for on-line control. The influence of each variable on NOX was analyzed, the model structure of the NOX prediction model was determined, and the parameters of the prediction model were identified by least squares. The model is applied to real operating vehicles for validation and compared with a previous semiempirical model taken from the literature, and the results show that the overall accuracy of the proposed model is improved. Finally, the effect of variable uncertainty on the proposed model was assessed and it was found that the relative uncertainty in predicting NOX emissions ranged between 0 and 8% for sensor accuracies of [Formula: see text] and [Formula: see text] for exhaust temperature and intake air mass flow, respectively, suggesting that the sensor accuracy has a significant effect on the uncertainty of the model.

Machine learning based prediction models for uniaxial ratchetting of extruded AZ31 magnesium alloy

The detrimental effect of ratchetting on the fatigue life of materials requires precise prediction models to guarantee the safety of engineering structures. This study focuses on predicting the uniaxial ratchetting of extruded AZ31 magnesium (Mg) alloy using machine learning (ML) based approaches. At first, the evolution and deformation mechanisms of ratchetting are summarized based on the existing experimental results of the Mg alloy. Subsequently, a semi-empirical prediction model, tailored for engineering applications, is developed to describe the evolution of ratchetting strain. Then, a pure data-driven ML based prediction model is proposed to overcome the shortcoming existed in the semi-empirical model and improve the prediction accuracy to the uniaxial ratchetting of the Mg alloy. Finally, a physics-informed ML based model, incorporating the physical information derived from the semi-empirical one, is proposed to further enhance its prediction accuracy and generalization ability. The comparison with correspondent experimental data demonstrates that the proposed physics-informed ML based model exhibits high prediction accuracy and generalization ability.

A practical semi-empirical model for predicting the SoH of lithium-ion battery: A novel perspective on short-term rest

In this paper, the semi-empirical battery degradation prediction model proposed considers electrochemical degradation characteristics and represents degradation effects under various conditions, including different states of charge (SoC) areas. This model is specifically designed to address degradation during cycling and short-term rest periods in lithium-ion batteries using liquid electrolytes. Cycle aging incorporates the impact of solid electrolyte interphase (SEI) growth, a known dominant factor, and the model for short-term resting periods captures potential aging impacts on subsequent cycles due to internal material concentration gradients, moving away from the traditionally used calendar life approach. The derivation of the model presented in this paper is based on 14 data sets under different SoC conditions and 8 data sets under various Crates, explaining the degradation effects at 10 % SoC intervals and three different Crate points. Moreover, the model's performance was validated through capacity prediction for two data sets experimented with dynamic operational schedules of actual energy storage systems (ESS), including various conditions. The results showed a root mean square error (RMSE) of 0.564 and a mean absolute percentage error (MAPE) of 0.346. The superiority of this model is demonstrated by comparing its performance with four other types of degradation models derived through the same process in the validation data.

Development of a semi-empirical physical model for transient NOx emissions prediction from a high-speed diesel engine.

With emissions regulations becoming increasingly restrictive and the advent of real driving emissions limits, control of engine-out NOx emissions remains an important research topic for diesel engines. Progress in experimental engine development and computational modelling has led to the generation of a large amount of high-fidelity emissions and in-cylinder data, making it attractive to use data-driven emissions prediction and control models. While pure data-driven methods have shown robustness in NOx prediction during steady-state engine operation, deficiencies are found under transient operation and at engine conditions far outside the training range. Therefore, physics-based, mean value models that capture cyclic-level changes in in-cylinder thermo-chemical properties appear as an attractive option for transient NOx emissions modelling. Previous experimental studies have highlighted the existence of a very strong correlation between peak cylinder pressure and cyclic NOx emissions. In this study, a cyclic peak pressure-based semi-empirical NOx prediction model is developed. The model is calibrated using high-speed NO and NO2 emissions measurements during transient engine operation and then tested under different transient operating conditions. The transient performance of the physical model is compared to that of a previously developed data-driven (artificial neural network) model, and is found to be superior, with a better dynamic response and low (<10%) errors. The results shown in this study are encouraging for the use of such models as virtual sensors for real-time emissions monitoring and as complimentary models for future physics-guided neural network development.

Predictive thermodynamic model for solvent extraction of Iron(III) by tri-n-butyl phosphate (TBP) from chloride media

Hydrometallurgical processes are crucial to reducing the environmental impact of metal recovery, yet dealing with iron impurities is a major challenge. This paper presents a semi-empirical predictive thermodynamic model for iron removal from chloride media by solvent extraction with tri-n-butyl phosphate (TBP). This model is built upon the OLI mixed-solvent electrolyte framework (OLI-MSE). It goes beyond traditional thermodynamic models by incorporating the non-ideality of both the aqueous and organic phases in a single, chemistry-based thermodynamic model. On top of the OLI-MSE framework lies the chemical model that depicts the extraction of Fe(III) by forming an ion pair between the FeCl4– anion and protonated TBP (TBPH+) in the organic phase. The iron(III)-containing ion pair in the organic phase is further stabilized by interactions with neutral TBP molecules. Developing the model required modeling the Fe(III) – chloride chemistry in the aqueous phase, optimizing the HCl extraction model, and fitting the parameters between FeCl4–, TBPH+, and TBP to experimental solvent extraction data. The resulting thermodynamic model can predict the solvent extraction of iron(III) from complex feed solutions by TBP in aliphatic diluents at all concentrations up to undiluted TBP. It can be used to calculate the equilibrium energies and composition, and the species present at equilibrium.

Semi-empirical model for abrasive particle velocity prediction in abrasive waterjet based on momentum transfer efficiency

AbstractAbrasive waterjet (AWJ) is a technology that removes a target material with an abrasive accelerated by ultra-high-pressure water. Recently, its application for rock excavations in civil and geotechnical engineering has increased. AWJ excavation performance is affected by the abrasive velocity formed by momentum transfer during mixing and acceleration. The abrasive velocity varies owing to changes in the abrasive flow rate, focusing tube diameter, and focusing tube length. In this study, the momentum transfer efficiency (MTE) according to the abrasive flow rate and focusing tube geometry was investigated by a numerical analysis to better understand the multiphase flow inside the AWJ system. The MTE was defined based on the theoretical relationship between the abrasive velocity ratio and focusing tube factor, and evaluated through the empirical relationship between the water stiffness and focusing tube length. The optimal abrasive flow rate for generating efficient MTE was approximately 15 g/s, which enabled economical and effective acceleration of abrasive particles. Accordingly, a prediction model based on the derived MTE was developed for the final abrasive velocity generated at the tip of the focusing tube. Using the prediction model, it is possible to evaluate the comprehensive relationship between various AWJ parameters. Based on the prediction model, the abrasive–water flow ratio to generate the optimal abrasive velocity was 0.83. The developed prediction model provides guidelines for selecting the optimal focusing tube geometry and applying an economical abrasive flow rate when designing an AWJ system.

A semi-empirical and multi-variable model for prediction of capacity loss in lithium-ion batteries: Considering cycling and performance time degradations

The lifetime of a lithium-ion battery (LIB) is primarily influenced by several key factors including time (number of charge-discharge cycles and performance time), temperature, and current rate (C-rate). In this study, a semi-empirical model is employed to predict the lifetime of LIBs by incorporating these variables. Previous models mainly neglect the influence of performance time on LIB capacity loss. However, our analysis reveals that adding performance time parameter significantly improves the model's accuracy. Additionally, the present model investigates the relationship between the functions of the semi-empirical model and factors such as temperature and C-rate, thereby improving the precision of the model's predictions. The experiments are conducted at several temperatures (25, 35, and 45 °C), each subjected to three current rates of 0.5C, 1 C, and 1.5C to develop the models. The proposed model for estimating LIB capacity loss consists of two terms that account for the impacts of cycling and performance time. The optimization findings indicate that both temperature and current rate have an impact on the cycling term. However, the term of performance time has temperature functions. Validation tests of the model are conducted at 25 °C-0.8C and 45 °C-1.7C. There is a perfect agreement between the model results and the experimental data. Using this model, it is possible to predict the lifetime of LIB with a relative error of less than 2%. Furthermore, this error diminishes as the number of cycles increases. Moreover, the proposed model allows for a quantitative evaluation of the individual contributions of cycling or performance time to the total LIB capacity loss. The results reveal that when the LIB undergoes more cycles, the proportion of capacity loss ascribed to performance time increases, while the proportion assigned to cycling declines. This indicates that the electrochemical processes responsible for the gradual capacity loss, which have no relationship to cycling, happen more rapidly during the LIB's operation.

Fatigue Life Prediction for Injection-Molded Carbon Fiber-Reinforced Polyamide-6 Considering Anisotropy and Temperature Effects.

The effects of anisotropy and temperature of short carbon fiber-reinforced polyamide-6 (CF-PA6) by the injection molding process were investigated to obtain the static and fatigue characteristics. Static and fatigue tests were conducted with uniaxial tensile and three-point bending specimens with various fiber orientations at temperatures of 40, 60, and 100 °C. The anisotropy caused by the fiber orientations along a polymer flow was calculated using three software connecting analysis sequences. The characteristics of tensile strength and fatigue life can be changed by temperature and anisotropy variations. A semi-empirical strain-stress fatigue life prediction model was proposed, considering cyclic and thermodynamic properties based on the Arrhenius equation. The developed model had a good agreement with an R2 = 0.9457 correlation coefficient. The present fatigue life prediction of CF-PA6 can be adopted when designers make suitable decisions considering the effects of temperature and anisotropy.

Experimentally-verified thermal-electrochemical simulations of a cylindrical battery using physics-based, simplified and generalised lumped models

The parameterisation for fully physics-based, simplified, and semi-empirical electrochemical-thermal coupled models for prediction of the core temperature of a cylindrical 21,700 cell are addressed in this paper for the first time. When compared to fully physics-based models, the semi-empirical approaches require fewer input parameters overall, simplifying the necessary experimental values and reducing the burden on the battery management system. There are roughly 40 and 30 parameters needed for a Doyle-Fuller-Newman (DFN) and a single particle, respectively. The generalised lumped electrochemical-thermal model, in contrast, requires ten input and three fitting parameters. The present work, aimed at thermal management challenges, couples these electrochemical models with a 2D-axisymmetric heat transfer model to compare qualities such as computational time, accuracy, generalisation, high fidelity, and experimental parameterisations required. The core temperature and voltage predictions for a 21,700 NMC/Si-Graphite cell has been made using coupled thermal-electrochemical models that are accurate (voltage and core temperature standard deviations: 38-130 mV and 0.24–0.79 K) and have a quick response (computation time: 18–262 s).The electrochemical and thermal parameterisation for the models were conducted using the experimental measurements at 1C, 0.3, and 0.7C-rates. Measurements are the core temperature made with a fiber optic sensing system and voltage curves using a battery cycler. For the single particle and P2D models, electrode diffusivities (both negative and positive) are adjusted to calibrate the models. For the single particle model, the results revealed that the core temperature and voltage standard deviations were 0.6 K and 0.13 V, respectively. Depending on the number of mesh, computational times were between 16 and 262 s. For the P2D model, the core temperature and cell voltage standard deviations were found to be 0.038 V and 0.7 K, respectively. Each simulation takes between 27 and 52 s. This is an increase of 189 % over the time required to compute a previously developed lumped model, for which the voltage and core temperature had 0.12 V and 0.8 K standard deviations. P2D simulations in the literature take between 21 and 43 times longer than simulations in the current P2D model. For the generalised lumped model, only the 1C-rate discharge results are used in the calibration, and a generalisation test has been conducted by using a full discharge-charge curve for the first time. The results showed that the change in standard deviations of core temperature (within 21 %) and voltage (within 31 %) are acceptable when a discharge-calibrated model used for full-cycle validations.

Integrated a Fused Silica Capillary Cell and In Situ Raman Spectroscopy for Determining the Solubility of CO2 in n-Decane and n-Decane + n-Hexane System

Understanding the solubility of CO2 is critical for implementing CO2-enhanced oil recovery (CO2-EOR). In this work, the solubility of CO2 in n-decane in a temperature range between 303.15 K and 353.15 K and pressures up to 15 MPa was measured using a fused silica capillary cell with in situ Raman spectroscopy. A semi-empirical CO2 solubility prediction model was obtained according to the experimental results. In order to improve the solubility of CO2 in n-decane, the solubility of CO2 in n-decane and co-solvent n-hexane (3% wt) mixture was also comparatively investigated. The results indicated that the solubility of CO2 in n-decane was 1.6355~64.0084 mol/kg. The data from the prediction model were in good agreement with the experimental data, and the mean relative deviation was 3.65%, indicating that the prediction model could be used to predict the solubility of CO2 in n-decane under different conditions. The solubility of CO2 in n-decane + n-hexane system ranged from 1.0127 mol/kg to 65.7286 mol/kg. It was found that, under low-pressure conditions, the addition of co-solvent n-hexane did not enhance the solubility of CO2, while it had a certain enhancement effect on the dissolution of CO2 under high-pressure conditions. As the temperature increased from 303.15 K to 353.15 K, the enhancement efficiency of the solubility of CO2 also increased from 1.34~2.05% to 8.17~9.82%, and the average enhancement efficiency increased from 1.74% to 9.00%. This study provides more CO2 solubility data for CO2-EOR.

A Prediction Method of Compacted Rock Hydraulic Permeability Based on the MGEMTIP Model

The permeability of the fluid-bearing rock is an important parameter for reservoir prediction. The Kozeny-Carman (K-C) formulation based on electrical measurements effectively characterizes the permeability-resistivity relationship of rocks with a single mineral composition or high porosity. The complex pore structure and mineral composition of compacted reservoirs affect induced polarization (IP) characteristics, indirectly limiting the applicability of conventional electrical K-C models. The permeability of fluid-bearing rocks is an important parameter for reservoir prediction. The theoretical chargeability of the modified generalized effective medium theory of induced polarization (MGEMTIP) model includes the effects of various conductive minerals. Due to the disconnection assumption of the disturbed medium in the MGEMTIP, there is a significant difference between the theoretical chargeability and the measured chargeability, and the difference is a sensitive parameter of rock permeability. A semi-empirical reservoir permeability prediction model is proposed based on the MGEMTIP. Theoretically and experimentally, the prediction model based on MGEMTIP is compared with the two electrical K-C models. Under the condition that the rock does not contain low-resistivity minerals, the prediction model based on MGEMTIP is theoretically equivalent to the K-C model. The experimental results show that this prediction model is more suitable for low-porosity and low-permeability rocks containing low-resistivity minerals, and the prediction results can be effectively restricted to the same order of magnitude. From the perspective of differences between model assumptions and natural rocks, the prediction model provides a semi-empirical relationship between complex mineral IP characteristics and permeability. Combined with the geological information of the survey area, the permeability prediction model can provide a theoretical basis for reservoir permeability prediction based on electromagnetic exploration.

A novel semi-empirical model for lifetime prediction of gravity based ceramic filter and permeability estimation

A novel semi-empirical model for lifetime prediction of gravity based ceramic filter and permeability estimation

Operating life assessment of a carbon fibre brush seal through endurance testing

While brush seals have been studied for almost forty years, carbon fibre brush seals have only recently drawn interest for their excellent leakage performance, combined with low friction. Their suitability for oil sealing applications has been acknowledged in the aeronautical field, specifically for civil aircraft gas turbine engines. This paper focuses on the endurance of optimally designed brush seals in an environment simulating the bearing chamber working conditions. They underwent a wide range of differential pressures and rotational speeds in long runs ranging from 100 to 300 h. A semi-empirical performance prediction model was developed based on these results, allowing estimation of the leakage performance beyond the recorded data. In addition, the presence of lubrication oil largely increases seal life, despite initial leakage performance degradation due to hydrodynamic lift. Finally, a visual inspection with a high precision microscope revealed uprooting of the carbon fibres. This phenomenon may well be the biggest cause of performance degradation, rather than fibre material losses, which were ultimately deemed unquantifiable.

Mesoscale effect on droplet formation in a step-emulsification microdevice with parallel microchannels

The monodispersity of droplet generation in parallel microchannels is critical for particle synthesis, chemical reactions, and separations. The mesoscale concept of compromise in competition is critical to reveal complex changes in the dominant mechanisms during droplet formation. In this paper, the uniformity and fluid distribution mechanism of droplet generation in a step-emulsification microdevice with 10 parallel microchannels are investigated by a high-speed camera. It is found that the spontaneous breakup of droplets dominated by interface tension is conducive to the uniform generation of droplets, and the feedback effect of droplet swarms in the cavity reduce the monodispersity of droplets. The pressure drop model in parallel microchannels is constructed. Compromise in competition between microchannels in energy storage phenomenon is analyzed, and the influence of hydrodynamic feedback effect of droplet swarms and the compromise in competition on fluid distribution is explained. The dripping region are improved through the strategy of expelling the droplet swarms by gravity, and droplets with coefficients of variation below 2% are prepared. Finally, a semi-empirical prediction model of droplet size is established.

Fatigue Life Prediction Methodology of Hot Work Tool Steel Dies for High-Pressure Die Casting Based on Thermal Stress Analysis

High-pressure die casting (HPDC) can produce precise geometries in a highly productive manner. In this paper, the failure location and cycles were identified by analyzing the fatigue behavior of the die subjected to repeated thermal stress. An energy-based semi-empirical fatigue life prediction model was developed to handle the complex stress history. The proposed model utilizing mean stress, amplitudes of stress, and strain was calculated by one-way coupling numerical analysis of computational fluid dynamics (CFD) and finite element analysis (FEA). CFD temperature results of the die differed from the measured results by 2.19%. The maximum stress distribution obtained from FEA was consistent with the actual fracture location, demonstrating the reliability of the analytical model with a 2.27% average deviation between the experimental and simulation results. Furthermore, the model showed an excellent correlation coefficient of R2 = 97.6%, and its accuracy was verified by comparing the calculated fatigue life to the actual die breakage results with an error of 20.6%. As a result, the proposed model is practical and can be adopted to estimate the fatigue life of hot work tool steels for various stress and temperature conditions.

An Advanced Prediction Model for Underwater Noise Emissions of Ships

_ The aim of this paper is to investigate the relationship between design and operational ship parameters with respect to radiated underwater noise and to develop a semiempirical noise prediction model that includes the dominant noise contributors present on merchant vessels. The model is based on Dietrich Wittekind’s prediction model and on underwater noise measurements with related Automatic Identification System (AIS) data. Additionally, the noise contribution of a two-stroke engine is investigated using structure-borne noise measurements and Finite Element Methods (FEM). The updated model can be used to assess the expected underwater noise emissions induced by ship traffic in a specific sea area based on AIS data and as a basis to produce noise maps. In conclusion, the prediction model will work as a useful tool to help understanding the noise contributors, their sensitivity on ships speed, and their impact in a defined environment. Introduction When discussing emissions in shipping, the focus is mainly reduced to greenhouse gases and pollutants. In the meantime, ships have been recognized as the most common source of anthropogenic noise emission in the oceans (Tournadre 2014). The dominant components of shipping noise are propeller cavitation, as well as the vibration of the hull caused by the power plant (Zou et al. 2003; Wittekind 2014). An increase in ship traffic and larger ship sizes are responsible for the steady rise in ambient noise, especially at low frequencies (Andrew et al. 2002). Several studies identified an increase of noise by 3 dB per decade. In other words, noise emissions double every 10 years as observed between the 1960s and 1990s (Andrew et al. 2002).

Prediction Model of Dynamic Resilient Modulus of Unsaturated Modified Subgrade under Multi-Factor Combination

The objective of this research is to solve the problem of the lack of prediction methods and basis for the long-term road performance of oil shale residue-modified soil in seasonally frozen regions. This paper summarizes and expands the resilient modulus prediction methods in the related literature. Based on the measured soil–water characteristic curve (SWCC) of the compacted modified soil and the trend characteristics of dynamic resilient modulus under freeze–thaw cycles, a semi-empirical prediction model is proposed. This model was used to quantitatively forecast the resilient modulus of unsaturated modified subgrade soil after the freeze–thaw cycle in a seasonal permafrost region. The applicability and accuracy of the method were verified by dynamic resilient modulus tests of the oil shale residue-modified soil under various freeze–thaw cycles and moisture content. The results show that the model has a high degree of fit to the experimental data and is more suitable for predicting the dynamic resilient modulus of modified soil under the change of moisture and the freeze–thaw cycle compared to the existing models.

Modeling the acoustic behavior of stepwise gradient porous structures

Spatial property gradients can significantly enhance the noise reduction potential of porous structures. However, predicting the acoustic behavior of structures with gradient microstructures continues to remain a challenge. For porous structures with controlled periodic microstructures, researchers have recently demonstrated the use of a multiscale asymptotic method to extract the acoustic transport properties necessary for use in semi-empirical predictive models. Here, we propose the adaptation of this method to enable the modeling of porous absorbers with stepwise property gradients. The unit cell of the chosen microstructure is modeled in COMSOL Multiphysics and the acoustic transport properties are extracted using the multiscale method. The extracted properties are then used to formulate the transfer matrix of each unit cell. The global sound absorption and transmission loss behavior of the stepwise gradient structures are further predicted by combining the appropriate local transfer matrices. Our results show that the integration of the unit cell and transfer matrix methods provides a robust way of predicting the acoustic behavior of stepwise gradient porous structures with various combinations of layer thicknesses and geometries. The method provides a computationally efficient method to model such structures and can further the development of porous structures with application-specific acoustical properties.

Empirical modelling of shear behavior of oil contaminated sand - geogrid interface

ABSTRACT Based on the experimental studies, a semi empirical predictive model has been presented and discussed in this paper to simulate the interface shear behavior of used diesel engine oil (UDEO) contaminated (0%, 2%, 4%, 6% and 8%) sand and geogrids. Experiments were conducted in a standard large-scale direct shear apparatus, which demonstrated that when the oil content increases from 0% to 8%, there is a drop in shear strength at the interface, with a marginal strain hardening trend. While the peak friction angle decreased as the UDEO content increased, the apparent cohesion showed an increasing trend. In addition to UDEO content, the normal stress is also an influencing parameter in the interface shear behavior. In order to simulate the interface shear behavior, a best-fit semi-empirical hyperbolic model has been suggested from the observed data using least square error method. The proposed model showed an excellent agreement with the experimentally observed behavior for both sand–sand and sand–geogrid interface.

Evaluation of the compressive-strength reducing behavior of concrete containing rubber aggregate

It is well known that the toughness and freeze-thaw resistance of concrete can be improved by rubber aggregate (RA) while it significantly reduces the compressive strength. In this study, a simple semi-empirical prediction model of strength reduction factor (SRF) for rubberized concrete (RuC) is proposed to evaluate the compressive-strength reducing behavior of RuC. The model takes the volume fraction of RA as an independent variable and can be used to quantitatively describe the influence of different composition factors on compressive strength. In addition, a database containing more than 321 groups of reported experimental results is established to validate the proposed model. The main influencing factors of SRF are also clarified, including the content, particle size, surface property and replacement method of RA. According to the above factors, scientific classification and statistical fitting analysis are carried out on the database to determine the model parameter b. It is found that the proposed SRF model has good universality and predictability, which can be used to guide the mix design of RuC.