Exponential Function Research Articles

Flame extension length and temperature profile beneath ceiling induced by endwall-attached fire inside compartment with lateral openings

This study experimentally investigated the fire characteristics of endwall-attached fire within the long-narrow compartment, including the flame extension and temperature profile. Experiments were conducted in a reduced scaled compartment featuring multiple lateral openings. Results show that the previous models of flame extension length and temperature rise in the literatures, whether for sidewall fires in tunnels or central fires in compartments with lateral openings, cannot predict the experimental data in this study. A new correlation is proposed for the flame extension length based on non-dimensional heat release rate. The longitudinal temperature profile generated by endwall-attached fires in compartment can be classified into three distinct regions related to the position of the lateral opening: temperature rapid decrease region, temperature slow decrease region, and backflow region at the end of the compartment. A model for the maximum temperature rise and a piecewise equation based on single exponential function for temperature decay profile are proposed, and these equations effectively correlate the experimental data. The findings of this study can deepen the understanding of fire dynamics within similar building structures and have value for the fire hazard assessment.

Power System Signal-Detection Method Based on the Accelerated Unsaturated Stochastic Resonance Principle

The classical bistable stochastic resonance algorithm has an inherent output saturation defect that restricts the amplitude of the output signal. This paper examines the causes of this phenomenon and its negative impact on the detection of weak signals. Proposing the Unsaturated Bistable Stochastic Resonance (UBSR) detection algorithm involves constructing a segmented potential function using a linear function to eliminate the effect of higher-order terms in the classical stochastic resonance algorithm. A new type of segmented potential function has been created by combining exponential and linear functions. This new function helps to eliminate the impact of higher-order terms in classical algorithms while also improving the noise immunity of the stochastic resonance system. This results in the development of the accelerated stochastic resonance (ASR) detection algorithm. In this paper, the Kramers escape rate and output signal-to-noise ratio of two improved stochastic resonance algorithms are theoretically derived and compared with the classical bistable stochastic resonance algorithms, and the proposed algorithms are able to effectively avoid the output saturation phenomenon and have more excellent detection performance under strong background noise.

Abundant soliton solutions on fractional Kraenkel Manna Merle model (FKMM) via new extended of generalized exponential rational function approach (GERFA)

In this paper, we use the generalized exponential rational function approach (GERFA) for constructing new solitary wave solutions for the fractional Kraenkel Manna Merle (FKMM) model, which is saturated ferromagnetic materials (MF) with a field outside that has very little conductivity, reflects the nonlinear of an ultrashort pulse. The proportional behavior of the suggested model is examined using the beta-derivative (BD). Through the use of this computational method, multiple types of solitons, such as kink, dark, anti-kink, periodic, bright, kink dark, kink bright, anti-kink dark, and anti-kink bright solitons, were obtained for (FKMM). Some of the revealed solutions’ 3D graphs are also employed in the numerical simulations. This investigation demonstrates the efficacy and simplicity of the offered strategy and the simple way to create many new solutions for different kinds of nonlinear partial differential equations, which have significant applications in the engineering and applied sciences. The findings show that the model theoretically has extraordinarily rich soliton structures.

On the Durability Performance of Two Adhesives to Be Used in Bonded Secondary Structures for Offshore Wind Installations.

The development of offshore wind farms requires robust bonding solutions that can withstand harsh marine conditions for the easy integration of secondary structures. This paper investigates the durability performance of two adhesives: Sikadur 30 epoxy resin and Loctite UK 1351 B25 urethane-based adhesive for use in offshore wind environments. Tensile tests on adhesive samples and accelerated aging tests were carried out under a variety of temperatures and environmental conditions, including both dry and wet conditions. The long-term effects of aging on adhesive integrity are investigated by simulating the operational life of offshore installations. The evolution of mechanical properties, studied under accelerated aging conditions, provides an important indication of the longevity of structures under normal conditions. The results show significant differences in performance between the two adhesives, highlighting their suitability for specific operating parameters. It should also be noted that for both adhesives, their exposure to different environments (seawater, distilled water, humid climate) over a prolonged period showed that (i) Loctite adhesive has a slightly faster initial uptake than Sikadur adhesive, but the latter reaches an asymptotic plateau with a lower maximum absorption rate than Loctite adhesive; and (ii) a progressive deterioration in the tensile properties occurred following an exponential function. Therefore, aging behavior results showed a clear correlation with the Arrhenius law, providing a predictive tool for the aging process and the aging process of the two adhesives followed Arrhenius kinetics. Ultimately, the knowledge gained from this study is intended to inform best practice in the use of adhesives, thereby improving the reliability and sustainability of the offshore renewable energy infrastructure.

On the effects of walking speed, crowd density and human-to-source distance on pollutant dispersion in indoor spaces

The effects of walking speed, crowd density and human-to-source distance on pollutant dispersion in two scaled room models are investigated using simultaneous planar laser-induced fluorescence and particle-image velocimetry techniques. For a small 3 m high room, where the length-scales of the people and room are comparable, the walking motions significantly influenced the macro room mean flow patterns. This has a strong effect on the scalar dispersion properties as the magnitudes of the advective scalar fluxes are often comparable or larger than the turbulent scalar fluxes. As such, the scalar dispersion properties are case specific. For a large 9 m high room, the walking motion influenced only the local mean flow field. The increase in walking speed and crowd density improves the efficiency in which the scalar is transported and mixed with fresh ambient fluid out of the measurement plane (i.e. along the direction of the motion), leading to scalar-free zones observed on the opposite side of the room from the ventilation outlet. The area of the scalar-free zone increases with an increase in the walking speed and crowd density. The advective scalar fluxes are more sensitive to the human motion than the turbulent components, and as the mixing efficiency improves, the advective fluxes show a greater weakening with increased distance from source. The concentration PDFs in the near-source region can be described by the exponential function where the expected value at the 99% percentile can be derived as C99/crms′=4.61, which agreed well with the experimental measurements of 4.1 to 5.9.

Analytical study of soliton dynamics in the realm of fractional extended shallow water wave equations

In this study, we use the Khater Method (KM) as an efficient analytical tool to solve (3+1)-dimensional fractional extended shallow water wave equations (FESWWEs) with conformable derivatives. The KM transforms fractional partial differential equations to ordinary differential equations (ODEs) via strategic variable transformation. Then, series-form solutions to these ODEs are proposed, which turn them into nonlinear algebraic systems. The solution to this set of algebraic equations yields shock travelling wave solutions expressed in hyperbolic, trigonometric, exponential, and rational functions. The study’s findings are corroborated by 2D, 3D, and contour graphs that show the changing patterns of the detected shock travelling waves. These findings have important significance for the discipline, offering vital insights into the intricate dynamics of FESWWEs. The effectiveness of KM is demonstrated by its capacity to produce varied solutions and contribute to a thorough knowledge of such complex phenomena.

P-S-N surfaces of lifting lug structure based on extremely small samples

Given the susceptibility of lifting lug structures to fatigue failure under heavy loads and the high cost associated with fatigue testing time, determining the P-S-N model with a limited sample size holds significance in engineering. Assuming that the logarithmic fatigue life of the lifting lug structure followed a normal distribution, this study utilized the gray model and Gaussian process regression optimized by a genetic algorithm to predict fatigue lives at equidistant stress amplitudes. In addition, the improved bootstrap method was used to expand the experimental extremely small samples. The findings demonstrate that incorporating the mean stress into the S-N curve of the exponential function and utilizing a polynomial to account for the segmented behavior proved highly advantageous in attaining a more accurate S-N model. The mean and standard deviation of logarithmic life at each stress level were assessed by the expanded samples, resulting in P-S-N surface fitting outcomes. This study contributes to the fatigue reliability analysis in situations with limited sample sizes.

Hydraulic conductivity of cement and fly ash stabilised clay mixes – Application to soil mixing techniques for seepage barrier construction

In-situ ground improvement techniques, namely, deep soil mixing, jet grouting, cutter soil mixing, and mass stabilisation are often utilized to improve the strength of soft grounds, and construct seepage barriers. Due to economic and environmental concerns, there is a global shift towards using industrial wastes such as fly ash (FA) from conventional binders such as ordinary Portland cement and lime. There is a plethora of literature on unconfined compressive strength (UCS) of cement-treated clays, and clays treated with fly ash-cement mixes with alkali activator (FCAA) binders. However, much remains unclear about the hydraulic conductivity of the FCAA-treated clays as low permeable hydraulic barrier systems. In this paper, the hydraulic conductivities of cement-treated and FCAA-treated clays are studied both quantitatively and qualitatively for different binder-content, FA:cement ratios, curing periods, and effective confining stress. The hydraulic conductivity of treated clay is measured by performing a series of accelerated permeability tests using a custom-fabricated triaxial system. The trends obtained from the measured hydraulic conductivity values are explained from the observations of X-ray diffraction analysis and scanning electron microscopy analysis. Results showed that the values of hydraulic conductivity for cement-treated clay were mostly higher than those of untreated clay. On the contrary, the hydraulic conductivities for the FCAA clay mixes were comparable to, or even lower than those for the untreated clay. The hydraulic conductivity reduced with the increase in effective confining stress; the influence of effective confining stress, however, became less substantial for 28 days curing period and higher cement-content (40 and 50 %). The relationships between the hydraulic conductivity, UCS, and water-binder (w/b) ratios were also determined for both cement-treated and FCAA-treated clays. The exponential function was found suitable to express the relationship between hydraulic conductivity and UCS of treated clays. In contrast, a strong logarithmic relationship was obtained for measured values of hydraulic conductivity and adopted w/b ratios. The results shall serve as a guide to adopting suitable binder-content or target UCS for achieving design hydraulic conductivity in ground improvement projects that involve cement and/or FCAA-treatment of clays.

Special Trans Function based exact expressions for the double and triple diode models of solar cells: Superior fitness, accuracy and convergence

Inspired by the fact that the Special Trans Function (STF) is more accurate than Lambert W function (LWF), this paper rigorously derives two types of STF-based exact expressions for the double-diode model (DDM) and triple-diode model (TDM) of solar cells. The former involves multi-STF (mSTF), while the latter contains single-STF (sSTF), bridging the remaining gap in describing the nonlinear I–V characteristic of solar cells using STF. The proposed mSTF and sSTF are closely linked with but different from the multi-Lambert W function (mLWF), single-LWF (sLWF) and implicit exponential function (IEF) based expressions, particularly in terms of fitness and parameter extraction. Through a fitness test involving 203 cases in the space of STF branch x∈R+, it was found that under the same parameter values, the proposed mSTF consistently outperforms in fitting the measured I–V data of various solar cell/modules, followed by the proposed sSTF, mLWF, sLWF, and finally IEF-based expression. Notably, all optimal STF branch x fall within the interval of x∈[0,6] rather than the preset x∈[0,20]. A normalized trust-region-reflective (NTRR) algorithm and a V-shaped selection strategy are developed to improve the parameter extraction of proposed mSTF and sSTF. Results from the derivative-dependent V-shaped NTRR algorithm and population-based Rcr-IJADE algorithm indicate that the proposed sSTF consistently achieves the highest accuracy and fastest convergence speed, followed by the mSTF, sLWF, mLWF and IEF-based expression. Moreover, the proposed sSTF exhibits fewer degeneracies from TDM to DDM compared to other expressions. Given these advantages, the proposed mSTF and sSTF show great promise for PV simulation and therefore deserve serious attention.

OSLD nanoDot characterization for carbon radiotherapy dosimetry

Objective. This study characterized optically-stimulated luminescent dosimeter (OSLD) nanoDots for use in a therapeutic carbon beam using the Imaging and Radiation Oncology Core (IROC) framework for remote output verification. Approach. The absorbed dose correction factors for OSLD (fading, linearity, beam quality, angularity, and depletion), as defined by AAPM TG 191, were characterized for carbon beams. For the various correction factors, the effect of linear energy transfer (LET) was examined by characterizing in both a low and high LET setting. Main results. Fading was not statistically different between reference photons and carbon, nor between low and high LET beams; thus, the standard IROC-defined exponential function could be used to characterize fading. Dose linearity was characterized with a linear fit; while low and high LET carbon linearity was different, these differences were small and could be rolled into the uncertainty budget if using a single linearity correction. A linear fit between beam quality and dose-averaged LET was determined. The OSLD response at various angles of incidence was not statistically different, thus a correction factor need not be applied. There was a difference in depletion between low and high LET irradiations in a primary carbon beam, but this difference was small over the standard five readings. The largest uncertainty associated with the use of OSLDs in carbon was because of the k Q correction factor, with an uncertainty of 6.0%. The overall uncertainty budget was 6.3% for standard irradiation conditions. Significance. OSLD nanoDot response was characterized in a therapeutic carbon beam. The uncertainty was larger than for traditional photon applications. These findings enable the use of OSLDs for carbon absorbed dose measurements, but with less accuracy than conventional OSLD audit programs.

Non-singular control strategies for a class of strict-feedback nonlinear time-delay systems

This paper focuses on the non-singular control for strict-feedback nonlinear time-delay systems. The boundedness of all the signals of the closed-loop system is rigorously proved by introducing a class of Lyapunov-Krasovskii functionals, including exponential functions. Besides, novel auxiliary functions with continuous derivatives are proposed to construct the control law to avoid the discontinuity of the virtual controllers. Besides, the amount of computation is reduced by applying the new auxiliary functions when the other control methods require loads of calculations for handling singular problems. In the end, numerical examples are given to validate the effectiveness of the proposed control scheme.

Estimation of Land Deformation and Groundwater Storage Dynamics in Shijiazhuang–Baoding–Cangzhou–Hengshui Using Multi-Temporal Interferometric Synthetic Aperture Radar

Groundwater resources are crucial to socio-economic development and the ecosystem, and over-extraction can cause the groundwater level to drop, deplete reserves, and trigger geological hazards like land subsidence. The North China Plain (NCP) has experienced both subsidence and groundwater depletion due to over-extraction in the past 70 years. In this study, we used MT-InSAR technology and ascending C-band Sentinel-1 SAR data from 2017 to 2023 to study land deformation in the junction area of Shijiazhuang–Baoding–Cangzhou–Hengshui. We identified multiple subsidence funnels with a maximum rate exceeding −150 mm/year and a total deformation surpassing 600 mm. Seasonal decomposition methods accurately separated seasonal signals in the time-series deformation and groundwater level data. An exponential function model applied to long-term deformation showed no significant decrease in subsidence in severely affected areas. By modeling seasonal deformation and seasonal groundwater levels, we determined the elastic skeletal storage coefficients (Ske) to be in the range of 1.02 × 10−3~6.53 × 10−3 in subsidence areas. We obtained the spatiotemporal evolution of the total groundwater storage (TGWS), irreversible ground storage (IGWS), and recoverable ground storage (RGWS). The TGWS and IGWS decreased annually while the RGWS increased, which is attributable to the implementation of the South-to-North Water Diversion Project (SNWDP) and the issuance of groundwater withdrawal policies in the NCP.

Impact of the thermal afterglow effect on infrared thermography data evaluation methods

In this work, the influence of the afterglow effects from a source impulse on commonly used data processing methods of infrared thermography (IRT), such as Pulsed Phase Thermography (PPT) and Thermographic Signal Reconstruction (TSR) was investigated. To resolve this issue, we propose the adoption of a modified mathematical model or an empirical function to approximate the flash lamp pulse, which we recorded during the test with a photodiode. Two models were evaluated: one consisting of a combination of exponential and power functions describing the entire pulse and a second, focusing only on the decreasing phase. The models were compared with well-established empirical functions, such as those of Degiovanni and Vageswar, using the widely known statistical scores R2adjusted and Akaike information criterion. The quantitative comparison revealed better fitting results for our proposed models. Additionally, we introduce an algorithm based on Hough transform-clustering for automated determination of the exact pulse length. Statistical analyses were performed to evaluate the reproducibility of the measured pulse shape. The results from applying the first model as pulse correction is compared to another widespread IR data treatment methodology, such as Modified Differential Absolute Contrast (MDAC). We also consider the impact of the afterglow effects on the Source Distribution Image (SDI). Two different specimens were used in the experiments: a homogeneous polymer sheet with blind holes as defects and an in-homogeneous plate made of carbon fiber reinforced polymer (CFRP) with artificial defects made from Tetrafluorethylen-Hexafluorpropylen-Copolymer (FEP) foil inserts. In both experiments a quantitative comparison was made using the Tanimoto criterion (TC), indicating an improved sensitivity. This work forms the basis for a faster and more reliable quantitative evaluation of experimental data, in particular algorithms for the automated detection and assessment of manufacturing defects or in-service damage will benefit from these results.

Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimating the scale parameter of the Weibull distribution. To evaluate their performance, we generate simulated datasets with different sample sizes and varying parameter values. A technique for pre-estimation shrinkage is suggested to enhance the precision of estimation. Simulation experiments proved that the Bayesian shrinkage estimator and shrinkage pre-estimation under the squared loss function method are better than the other methods because they give the least mean square error. Overall, our findings highlight the advantages of shrinkage Bayesian estimation methods for the proposed distribution. Researchers and practitioners in fields reliant on extreme value analysis can benefit from these findings when selecting appropriate Bayesian estimation techniques for modeling extreme events accurately and efficiently.

Vibration characteristics of a cylindrical sandwich shell with an FG auxetic honeycomb core and nanocomposite face layers subjected to supersonic fluid flow

In this paper, the flutter analysis is studied for a cylindrical sandwich shell subjected to external supersonic fluid flow. The sandwich shell consists of a re-entrant auxetic honeycomb (AH) core made of functionally graded materials (FGMs) which is covered with two polymeric face layers enriched with either carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), or graphene oxide powders (GOPs). The volume fraction (percentage) of the ceramic phase in the functionally graded auxetic honeycomb (FGAH) core varies from zero at the inner surface to one at the outer one based on either power-law function (P-FGM), exponential function (E-FGM), or sigmoid function (S-FGM). It is assumed that the nanofillers are distributed uniformly inside the face layers. The first-order shear deformation theory (FSDT) and the piston theory are employed to provide the mathematical models of the shell and the aerodynamic pressure, respectively. The governing equations and boundary conditions are derived via Hamilton’s principle. An exact solution is performed in the circumferential direction via harmonic trigonometric functions (sine and cosine) and an approximate solution is performed in the axial direction utilizing the differential quadrature method (DQM). The natural frequencies and corresponding damping ratios are attained through the presented semi-analytical solution and the impacts of several factors on the natural frequencies and the critical aerodynamic pressure of the shell are examined. These factors the type of the FGM, the material index, and inclined angle of the cells in the FGAH core, the thickness of the FGAH core, the type and mass fraction of the nanofillers in the nanocomposite face layers, and boundary conditions.

Investigation of effects of impeller geometry on the spatial distribution of turbulent field and micro-mixing performance in a stirred reactor equipped with multiple impellers

There are few studies on the effects of spatial distribution of hydrodynamics on the micro-mixing in stirred reactors. In this work, a statistical approach is introduced to quantitatively assess the spatial distributions of hydrodynamic parameters, using the turbulent dissipation rate as an example. According to the results, the effects of impeller geometry and angular velocity on the turbulent dissipation rate can be well described in terms of the volume-averaged values and spatial distribution functions. In the present study, a more uniform distribution of the turbulent dissipation rate is achieved by the multiple impellers with an inclinational angle of 15° at the same rotational speed. However, increasing the inclinational angle can decrease the volume-averaged value. The cumulative percentage of area-averaged turbulent dissipation rate is well modeled by an exponential function. The effects of impeller types on the meso- and micro-mixing processes are also investigated. It is found that the micro-mixing process has more significant influences than the meso-mixing process in the bottom region and near the free surface. The effects of impeller types on the micro-mixing performance are further investigated using the Villermaux–Dushman reaction system, both experimentally and numerically. An empirical correlation that considers the spatial distribution of turbulent parameters for the reaction rate of I2 synthesis is proposed. The results show that the predictions of segregation index, which represents micro-mixing performance, are improved by a numerical model coupled with the new reaction rate model.

Lump Kink interactional and breather-type waves solutions of (3+1)-dimensional shallow water wave dynamical model and its stability with applications

The shallow water equations are used to describe the behavior of water waves in various shallow regions such as coastal areas, lakes, rivers, etc. These equations are derived by making simplifying assumptions about the water depth relative to the wavelength of the waves. In this paper, the generalized exponential rational function method (gERFM) is used to construct novel wave solutions of the (3+1)-dimensional shallow water wave ((3+1)-dSWW) dynamical model. These solutions encompass distinct kinds of waves, such as solitary waves, solitons, Kink and anti-kink solitons, lump Kink interactional waves, traveling breathers-type waves and multi-peak solitons. The dynamical behavior of these wave solutions is discussed, examining the influence of free parameters on the resulting wave shapes. Furthermore, to provide a scientific elucidation of the obtained results, the solutions are presented graphically, making it easy to distinguish the dynamical features, which have practical implications in different areas of applied sciences and engineering. The stability of this dynamical model is revealed via modulational instability analysis, signifying that all analytical results are stable. The obtained results show that the given technique is universal and efficient. Through comparing the projected technique with the existing techniques, the obtained results demonstrate that the given technique is universal, pithy and efficient.

Exact solitary wave propagations for the stochastic Burgers’ equation under the influence of white noise and its comparison with computational scheme

In this manuscript, the well-known stochastic Burgers’ equation in under investigation numerically and analytically. The stochastic Burgers’ equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results. The existence of results is shown by the help of Schauder fixed point theorem. For the approximate results the proposed stochastic finite difference scheme is constructed. The analysis of the proposed scheme is analyzed by presented the consistency and stability of scheme. The consistency is checked under the mean square sense while the stability condition is gained by the help of Von-Neumann criteria. Meanwhile, the stochastic exact solutions are constructed by using the generalized exponential rational function method. These exact stochastic solutions are obtained in the form of hyperbolic, trigonometric and exponential functions. Mainly, the comparison of both numerical and exact solutions are analyzed via simulations. The unique physical problems are constructed from the newly constructed soliton solutions to compare the numerical results with exact solutions under the presence of randomness. The 3D and line plots are dispatched that are shown the similar behavior by choosing the different values of parameters. These results are the main innovation of this study under the noise effects.

Simple mathematical model for predicting COVID-19 outbreaks in Japan based on epidemic waves with a cyclical trend

BackgroundSeveral models have been used to predict outbreaks during the COVID-19 pandemic, with limited success. We developed a simple mathematical model to accurately predict future epidemic waves.MethodsWe used data from the Ministry of Health, Labour and Welfare of Japan for newly confirmed COVID-19 cases. COVID-19 case data were summarized as weekly data, and epidemic waves were visualized and identified. The periodicity of COVID-19 in each prefecture of Japan was confirmed using time-series analysis and the autocorrelation coefficient, which was used to investigate the longer-term pattern of COVID-19 cases. Outcomes using the autocorrelation coefficient were visualized via a correlogram to capture the periodicity of the data. An algorithm for a simple prediction model of the seventh COVID-19 wave in Japan comprised three steps. Step 1: machine learning techniques were used to depict the regression lines for each epidemic wave, denoting the “rising trend line”; Step 2: an exponential function with good fit was identified from data of rising straight lines up to the sixth wave, and the timing of the rise of the seventh wave and speed of its spread were calculated; Step 3: a logistic function was created using the values calculated in Step 2 as coefficients to predict the seventh wave. The accuracy of the model in predicting the seventh wave was confirmed using data up to the sixth wave.ResultsUp to March 31, 2023, the correlation coefficient value was approximately 0.5, indicating significant periodicity. The spread of COVID-19 in Japan was repeated in a cycle of approximately 140 days. Although there was a slight lag in the starting and peak times in our predicted seventh wave compared with the actual epidemic, our developed prediction model had a fairly high degree of accuracy.ConclusionOur newly developed prediction model based on the rising trend line could predict COVID-19 outbreaks up to a few months in advance with high accuracy. The findings of the present study warrant further investigation regarding application to emerging infectious diseases other than COVID-19 in which the epidemic wave has high periodicity.

Facial Recognition and Classification of Terracotta Warriors in the Mausoleum of the First Emperor Using Deep Learning

Abstract. The facial features of the Terracotta Warriors unearthed from the Mausoleum of the First Emperor of Qin are authentic depictions of the appearance of soldiers from the same period. Recognizing facial features to classify the Terracotta Warriors is one of the crucial aspects of archaeological research. Due to limitations in the collection of facial samples from the Terracotta Warriors, an enhanced SqueezeNet model is proposed for deep learning facial recognition. The FaceNet backbone feature extraction network has been improved by replacing the initial 7×7 convolution kernel with three 3×3 convolution kernels. The model's feature extraction layer is composed of alternating convolution layers, pooling layers, Fire modules, and pooling layers, with the introduction of an exponential function to smooth the shape of the loss function. Finally, facial classification of 295 Terracotta Warriors is accomplished using Agglomerative Clustering. The model demonstrates a facial recognition accuracy of 95.6%, showing a respective improvement of 4.1% and 2.8% compared to the classical SqueezeNet and Inception_ResNetV1 models. This approach better meets the requirements for facial recognition and classification of Terracotta Warriors, providing intelligent and efficient technical support for technological archaeology.