High-precision Finite Element Research Articles

Maximum displacement prediction model for steel beams with hexagonal web openings under impact loading based on artificial neural networks

The estimation of the maximum displacement of steel beams with hexagonal web openings under impact loads is crucial for the anti-impact design of structures. The dynamic characteristics are complex, and the maximum displacement can be obtained experimentally, although the time cost, and expense of such experiments are high. In this context, a 6-5-1 artificial neural network model based on the Levenberg-Marquardt backpropagation algorithm was developed, incorporating 5-fold cross-validation techniques. Due to limited experimental data, 324 high-precision finite element models were created in bulk using Python-based ABAQUS software scripts to provide additional numerical data, and 26 specimens were designed for drop hammer tests to validate the finite element models. The artificial neural network model on the test data yielded a mean squared error of 0.0268, a mean absolute error of 0.0014, and a coefficient of determination value of 0.9806, with samples having an error of less than 10% comprising 77.16% of the total samples. Using Garson’s algorithm, the contribution of input features was estimated, and a full parameter analysis of the proposed model was conducted. The results indicate that the most significant factor is the impact mass, which accounts for 37.58%. When the impact mass increased from 530 kg to 630 kg, the maximum displacement of Q235 surged by 93.75%. The factor with the least impact is the opening spacing, accounting for 2%, with an average increase in maximum displacement of only 3.45%. Finally, ANN-based equations that can be used as design tools are established.

Seismic collaborative reliability analysis for a slope considering spatial variability base on optimized subset simulation

Seismic reliability analysis of actual slopes considering the spatial variability of soil materials is crucial. However, for the discretization of large-scale random fields, high-precision finite element analysis and analysis of small failure probability events, the random analysis of slopes under seismic loads is inefficient. To address this situation, this study proposes a collaborative reliability analysis framework based on the modified linear estimation method (MLEM) and optimized subset simulation (OSS). First, the random field of the uncertain parameters of the Jinping-I left bank slope model is efficiently discretized by the MLEM, and a sensitivity analysis is carried out. Then, considering the adoption of different degrees of cross-correlation of the sensitive random parameters, the OSS method is used to perform random finite element analysis on the coarse mesh model. Finally, the fine mesh samples are obtained according to the response conditioning method (RCM). The MLEM is used to ensure the consistency of the two sets of random fields, and the seismic failure probability and reliability index of the slope under different cross-correlation coefficients of uncertain parameters are obtained. The results suggest that the degree of cross-correlation of parameters has a great influence on the seismic reliability of the slope. Considering that the shear strength parameters of geotechnical materials are often negatively correlated, the fine analysis based on a fine model is necessary.

Data-driven initial peak crushing force prediction of hybrid tubes

Accurately predicting the initial peak crushing force (IPCF) of the CFRP/metal hybrid structure is of great significance for the high-efficiency energy absorption of energy-absorbing elements and ordered deformation of combined energy-absorbing devices. Due to the significant differences in material properties between CFRP and metal and the high complexity of cross-sectional shape, a combined method of machine learning and mechanism analysis is proposed for predicting the IPCF of CFRP/Al hybrid energy-absorbing tube. First, a high-precision finite element model validated by the axial and oblique experiments is conducted to generate the dataset for predictive analysis. Second, a sample space through the design of experiment (DOE) is established for data fitting between structural parameters and IPCF based on traditional response surface model (RSM). It is found that traditional RSM method can successfully predict the IPCF of the single-cell hybrid tube, but cannot effectively predict the IPCF of the multi-cell tube due to the strong coupling effect between inner and outer plates. To address the issue of the lack of accurate correspondence between structural parameters and IPCFs in multi-cell hybrid tube, the indicator of relative density is proposed to characterize complex cross-sectional features. Surprisingly, there is a strong correlation between relative density and IPCF where multi-cell tubes with the same relative density have almost the same IPCF. Third, different artificial neural networks (ANN) are trained by a pre-simulated IPCF database of CFRP/Al hybrid energy-absorbing tube depending on the parameter characterization scheme based on mechanism analysis. In order to enhance the network's performance, the optimal configuration parameters of the neural network, including the number of layers and nodes, are ascertained through a combination of K-fold cross-validation and the Grid Search method. As a result, compared with the traditional RSM and Kriging model, the IPCF of CFRP/Al hybrid energy-absorbing tube can be predicted in small samples with high accuracy using the optimal ANN model. Finally, Through the comparative analysis of the IPCF of hybrid tubes with reported multi-cell configurations, it is found that the prediction model proposed in this paper has good generalization ability, which can be used to predict more complex types of multi-cell tube configurations. The present study offers important suggestions for the overall control of multi-materials hybrid energy-absorbing tube and the ordered deformation of combined energy-absorbing devices.

Effects of prestressing wire corrosion on the load response law and bearing capacity of PCCP

The corrosion of prestressed steel wires plays a crucial role in the failure of prestressed concrete cylinder pipes (PCCP). To explore the load-bearing response of prestressed steel wire corroded PCCP and the impact of prestressed steel wire corrosion on the load-bearing capacity of PCCP, a high-precision finite element model of buried PCCP with prestressed steel wire corrosion was established, and a bearing test was conducted based on this model. The results show that the corrosion of prestressed steel wires has the greatest impact on the mortar protective layer and outer core concrete, and the corrosion point at the waist of the pipe is the most detrimental to the pipeline. In addition, as the degree of corrosion of the steel wire increases, the mortar protective layer and outer core concrete at the corrosion point first crack under the action of compressive stress and internal water pressure. Finally, it was verified that the constructed bearing capacity model of PCCP with different corrosion points had high accuracy and could be used to predict the bearing capacity of corroded pipelines. This article can provide theoretical support for the structural safety monitoring and repair of PCCP in service.

Tensile Failure Behaviors of Adhesively Bonded Structure Based on In Situ X-ray CT and FEA.

Adhesive bonding plays a pivotal role in structural connections, yet the bonding strength is notably affected by the presence of pore defects. However, the invisibility of interior pores severely poses a challenge to understanding their influence on tensile failure behaviors under loading. In this study, we present a pioneering investigation into the real-time micro-failure mechanisms of adhesively bonded structures using in situ X-ray micro-CT. Moreover, the high-precision finite element analysis (FEA) of stress distribution is realized by establishing the real adhesive layer model based on micro-CT slices. The findings unveil that pores induce stress concentration within the adhesive layer during the tensile process, with stress levels significantly contingent upon pore sizes rather than their specific shapes. Consequently, larger pores initiate and propagate cracks along their paths, ultimately culminating in the failure of adhesively bonded structures. These outcomes serve as a significant stride in elucidating how pore defects affect the bonding performance of adhesively bonded structures, offering invaluable insights into their mechanisms.

Optimal design of rotor structure for vibration and noise reduction in electric vehicle generator

In order to reduce the vibration noise of an extended-range electric vehicle (EREV) generator, an optimization method based on changing the rotor structure is proposed in this paper. Firstly, the specific optimization scheme is determined by theoretical and simulation analysis to perform skew pole segmentation of the rotor, while using an eccentric pole arc design to determine the optimal parameters with the target of cogging torque. Then, in order to verify the feasibility of the scheme, the main performance of the generator before and after the optimization is analyzed, including radial electromagnetic force wave, counter-electromotive force (counter EMF), electromagnetic torque, and rotor strength. Finally, a high-precision finite element model of the generator was established, the vibration acceleration, as well as the sound pressure level before and after optimization, were calculated, and a noise test was completed. The results show that the optimized scheme significantly weakened the cogging torque of the generator, while reducing the radial electromagnetic force wave and counter EMF distortion rate to a certain extent, and finally significantly improved the vibration and noise performance of the generator.

Finite element analysis of the mechanical properties of sheet- and skeleton-gyroid Ti6Al4V structures produced by laser powder bed fusion

Additive manufacturing, and laser powder bed fusion (L-PBF) in particular, can produce complex geometric components with high resolution, and is very suitable for manufacturing lightweight triple periodic minimal surface (TPMS) structures to achieve lightweight. With regard to the two forms of the same structure, most of the previous studies focused on sheet-TPMS, but lacked the understanding of the difference between skeleton-TPMS and sheet-TPMS structures. In order to explore the characteristics of these two structures and provide theoretical support for the development of lightweight structure design, this paper compares the manufacturing performance and defect distribution of skeleton-gyroid (GSK) and sheet-gyroid structures (GSH). It employs high-precision finite element analysis (FEA) prediction and experimental verification to compare comprehensively the mechanical properties, failure behavior and energy absorption characteristics of the two structures. The results show that, compared to GSK, the larger specific surface area of GSH leads to more unmelted powder and draping adhesion, without affecting its higher stiffness and strength. Moreover, the more stable failure mode of GSH leads to more gentle stress platform stage and superior energy absorption performance. The results predicted by simulation are highly consistent with the experimental results. This improved understanding allows better prediction of the mechanical properties of the specimens using the Gibson–Ashby theory, which can reduce the experimental cost and time, and improve the resource consumption of TPMS structural performance research. This study can open new possibilities for the design and application of TPMS structures.

Research on Seismic Performance and Reinforcement Methods for Self-Centering Rocking Steel Bridge Piers

To study the seismic performance of self-centering circular-section rocking steel bridge piers whose functions can be restored after an earthquake, a high-precision finite element (FE) analysis model of such a bridge piers was established. The hysteresis behavior of concrete-infilled and hollow rocking steel bridge piers was compared. In response to the characteristics of the local deformation of the wall plates and elliptical deformation of the bottom surface, two reinforcement methods for the pier bottom, namely thickening the wall plate and adding longitudinal stiffeners in the plastic zone of the pier bottom, were proposed. The pseudo static analysis of bridge piers was carried out considering the effects of overall design parameters and reinforcement parameters of the pier bottom. The results indicate that the FE model used in this paper can obtain accurate horizontal load-displacement curves of rocking steel bridge piers. The hysteresis curves of the rocking steel bridge piers and infilled concrete rocking steel bridge piers is close, and directly using hollow steel bridge piers can improve the economic efficiency of the design. Compared to adding longitudinal stiffeners, the reinforcement form of thickened wall plates at the pier bottom has a better effect in improving the seismic performance of bridge piers. The reinforcement of the pier bottom has little effect on the energy dissipation capacity of the bridge pier, but it helps to reduce residual displacement and improve lateral stiffness.

Accuracy of a Recent Regularized Nuclear Potential.

F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [Gygi J. Chem. Theory Comput. 2023, 19, 1300-1309.]. This potential V(r) is determined by inverting the Schrödinger equation for the wave function Ansatz ϕ(r) = exp[-h(r)]/√π with h(r) = r erf(ar) + b exp(-a2r2), where a and b are parameters. Gygi fixes b by demanding ϕ to be normalized, with the value b(a) depending on the strength of the regularization controlled by a. We begin this work by re-examining the determination of b(a) and find that the original 10-decimal tabulations of Gygi are only correct to 5 decimals, leading to normalization errors in the order of 10-10. In contrast, we show that a simple 100-point radial quadrature scheme not only ensures at least 10 correct decimals of b but also leads to machine-precision level satisfaction of the normalization condition. Moreover, we extend Gygi's plane-wave study by examining the accuracy of V(r) with high-precision finite element calculations with Hartree-Fock and LDA, GGA, and meta-GGA functionals on first- to fifth-period atoms. We find that although the convergence of the total energy appears slow in the regularization parameter a, orbital energies and shapes are indeed reproduced accurately by the regularized potential even with relatively small values of a, as compared to results obtained with a point nucleus. The accuracy of the potential is furthermore studied with s-d excitation energies of Sc-Cu as well as ionization potentials of He-Kr, which are found to converge to sub-meV precision with a = 4. The findings of this work are in full support of Gygi's contribution, indicating that all-electron plane-wave calculations can be accurately performed with the regularized nuclear potential.

Modelling and simulation of high- and low-speed impact damage of lithium batteries for light and small UAVs

In this study, the high- and low-speed impact damage of lithium batteries for light and small UAVs was investigated through the combination of experimental and simulation methods. A high-precision finite element model of the lithium battery was built, impact compression tests were performed for battery cells and battery modules to investigate the mechanical behavior of the lithium battery under the low-speed impact. In addition, the failure parameters of the lithium battery model were modified through battery cells and battery modules impact compression tests. In this paper, we designed and implemented a battery modules air cannon impact test on aluminum plates. The results achieved using the target impact simulation model of lithium batteries were compared with the results of the lithium battery target impact test. The peak strain error was obtained as 5.1%, the error of the back abrupt deformation of the aluminum plate after the target impact test was found as 5.67%, and the error of the approximate circle diameter of the aluminum plate crater reached 2.23%. The numerical simulation results of the lithium battery target impact were well consistent with the results of the target impact test, thus verifying the accuracy of the lithium battery finite element model built in this study under the high-speed impact. As revealed by the results, when the fall impact speed was higher than the normal flight speed of the UAV, the protective effect of the external battery box on the internal battery cell was found to decrease rapidly; the higher the impact speed, the more serious the damage of the internal single lithium battery would be, thus suggesting that the lithium battery under the high-speed impact would have a high risk of explosion and fire.

Study of mechanical properties of cylinder under transient multi-physical field coupling conditions

The use of lightweight metal cylinders is of great significance to artillery weapon systems in terms of significant mass reduction, service life extension, power consumption reduction and operational effectiveness. Based on the load conditions provided by the classical internal ballistic theory, a high precision finite element model is solved by the explicit integration algorithm with central difference. The results show that the maximum stress of the thin-walled cylinder increases linearly with the increase of the initial clearance, while the maximum extraction force increases first and then decreases, while the influence of temperature on the extraction force cannot be ignored. Therefore, the design of the initial gap between the thin-walled cylinder and the thick-walled cylinder should be designed to ensure that the maximum stress of the thin-walled cylinder does not exceed the maximum permissible stress and to meet the minimum extraction force, while choosing the correct extraction timing can effectively reduce the extraction force.

Free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams

PurposeThis study aimed to solve the engineering problem of free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams. The accurate identification of the crack damage depth, number and location depends on high-precision frequency and vibration mode solutions; therefore, it is critical to obtain these reliable solutions. The high-precision finite element method for the free vibration of cracked beams needs to be developed to grasp and control error information in the conventional solutions and the non-uniform mesh generation near the cracks. Moreover, the influence of multi-crack damage on the natural frequency and vibration mode of a circularly curved beam needs to be detected.Design/methodology/approachA scheme for cross-sectional damage defects in a circularly curved beam was established to simulate the depth, location and the number of multiple cracks by implementing cross-section reduction induced by microcrack damage. In addition, the h-version finite element mesh adaptive analysis method of the Timoshenko beam was developed. The superconvergent solution of the vibration mode of the cracked curved beam was obtained using the superconvergent patch recovery displacement method to determine the finite element solution. The superconvergent solution of the frequency was obtained by computing the Rayleigh quotient. The superconvergent solution of the eigenfunction was used to estimate the error of the finite element solution in the energy norm. The mesh was then subdivided to generate an improved mesh based on the error. Accordingly, the final optimised meshes and high-precision solution of natural frequency and mode shape satisfying the preset error tolerance can be obtained. Lastly, the disturbance behaviour of multi-crack damage on the vibration mode of a circularly curved beam was also studied.FindingsNumerical results of the free vibration and damage disturbance of cracked curved beams with cracks were obtained. The influences of crack damage depth, crack damage number and crack damage distribution on the natural frequency and mode of vibration of a circularly curved beam were quantitatively analysed. Numerical examples indicate that the vibration mode and frequency of the beam would be disturbed in the region close to the crack damage, and a greater crack depth translates to a larger frequency change. For multi-crack beams, the number and distribution of cracks also affect the vibration mode and natural frequency. The adaptive method can use a relatively dense mesh near the crack to adapt to the change in the vibration mode near the crack, thus verifying the efficacy, accuracy and reliability of the method.Originality/valueThe proposed combination of methodologies provides an extremely robust approach for free vibration of beams with cracks. The non-uniform mesh refinement in the adaptive method can adapt to changes in the vibration mode caused by crack damage. Moreover, the proposed method can adaptively divide a relatively fine mesh at the crack, which is applied to investigating free vibration under various curved beam angles and crack damage distribution conditions. The proposed method can be extended to crack damage detection of 2D plate and shell structures and three-dimensional structures with cracks.

Research on Determining Elastic-Plastic Constitutive Parameters of Materials from Load Depth Curves Based on Nanoindentation Technology.

It is of great significance for structural design and engineering evaluation to obtain the elastic-plastic parameters of materials. The inverse estimation of elastic-plastic parameters of materials based on nanoindentation technology has been applied in many pieces of research, but it has proved to be difficult to determine the elastic-plastic properties of materials by only using a single indentation curve. A new optimal inversion strategy based on a spherical indentation curve was proposed to obtain the elastoplastic parameters (the Young's modulus E, yield strength σy, and hardening exponent n) of materials in this study. A high-precision finite element model of indentation with a spherical indenter (radius R = 20 µm) was established, and the relationship between the three parameters and indentation response was analyzed using the design of experiment (DOE) method. The well-posed problem of inverse estimation under different maximum indentation depths (hmax1 = 0.06 R, hmax2 = 0.1 R, hmax3 = 0.2 R, hmax4 = 0.3 R) was explored based on numerical simulations. The results show that the unique solution with high accuracy can be obtained under different maximum press-in depths (the minimum error was within 0.2% and the maximum error was up to 1.5%). Next, the load-depth curves of Q355 were obtained by a cyclic loading nanoindentation experiment, and the elastic-plastic parameters of Q355 were determined by the proposed inverse-estimation strategy based on the average indentation load-depth curve. The results showed that the optimized load-depth curve was in good agreement with the experimental curve, and the optimized stress-strain curve was slightly different from the tensile test, and the obtained parameters were basically consistent with the existing research.

High-Accuracy Finite Element Model Updating a Framed Structure Based on Response Surface Method and Partition Modification

In this paper, a finite element model updating (FEMU) method is proposed based on the response surface model (RSM) and genetic algorithm (GA) to establish a high-precision finite element (FE) model of space station scientific experiment racks. First, the fine solid and mixed FE models are established, respectively, and a comparison of the modal test results is conducted. Then, an orthogonal experimental design is used to analyze the significance of the parameters, and the variables to be modified are determined. The design parameters are sampled via the Latin hyperbolic method and are substituted into the FE model to obtain the modal parameters of the scientific experiment rack. The mapping relationship between the design and modal parameters is fitted by constructing the Kriging function, and the RSM is established. The design parameters of the scientific experiment rack are optimized via GA, and the initial FE model is updated, which has the advantage of improving the computing efficiency. Finally, the updated FE model of the experiment rack is verified by frequency sweep and random vibration tests. The experimental results show that the proposed approach has high precision and computing efficiency, and compared with the test results, the modal frequency errors of the updated model are within 5%, and the vibration response errors under random excitation of the updated model are within 7%.

Structural Dynamic Model Updating with Automatic Mode Identification Using Particle Swarm Optimization

Dynamic model-updating methods are a useful tool for obtaining high-precision finite element (FE) models. However, when using such methods to update a model, there will be problems with incompleteness and mode switching. To overcome these problems, this paper proposes a structural dynamic model-updating with an automatic mode-identification method. In this method, a mode-identification index is established based on image-similarity recognition to identify the consistency between FE and experimental mode shapes, and particle swarm optimization is introduced to update the model. In addition, to reduce the computational time, Latin hypercube sampling is employed to perform probability statistics of the switching range of the concerned mode orders, and the orders of mode identification are reduced according to the statistics results. In this paper, the proposed method was validated by model-updating of a square plate. The natural frequencies and mode shapes of the plate were obtained by experimental modal analysis and used as the updating objectives of the FE model. In addition, the boundary condition of the plate was simplified by a series of springs, which were used as updating parameters along with material properties and dimensions. Finally, the FE model of the plate was updated by the present method, and the results indicate that the objective function error of the updated FE model was successfully reduced from 14.31% to 1.05%, which proves that the proposed model-updating method is effective and feasible.

Numerical prediction of Joule heating effect in electric hot incremental sheet forming

Since the deformation region involves the interaction of electric-thermal-force coupling in electric hot incremental sheet forming, the numerical simulation of the forming process is unusually difficult. Currently, the thermal-force coupling method is adopted to simulate approximately the whole forming process, and the Joule heating effect is often ignored. Therefore, the numerical simulation of the Joule heating effect is especially significant for the prediction accuracy of forming process. In this paper, a novel numerical simulation method considering electric-thermal-force parameters was proposed to update the thermal-force condition of the forming region instantly. Meanwhile, the model of contact thermal conductance was established, combining geometrical and electric-thermal parameters. Then a high-precision finite element model was obtained to predict the Joule heating effect of the forming region. In addition to this, the impact of thermal superposition on forming temperature was further analyzed, and a modified model of contact thermal conductance was established in electric hot incremental sheet forming.

Micro-fracture behaviors of needled short-chopped fiber reinforced phenolic aerogel composites based on in-situ X-ray micro-CT

Needled short-chopped fiber reinforced phenolic aerogel composites (PAC) are the most promising thermal protection materials for space applications. However, the complex microstructures deriving from the irregular needling yarns severely limits the revealing of their fracture mechanisms. Herein, for the first time, the micro-fracture behaviors of PAC are innovatively revealed using in-situ X-ray micro-CT under tensile loading. Furthermore, the high-precision finite element analysis of stress evolution is realized by establishing PAC model based on the micro-CT slices. The results indicate that the needling yarns will result in the enrichment of resin aerogel, leading to the stress concentration and micro-cracks initiation during loading. And the needling yarns can effectively hinder the separation and orientation of short-chopped fibers and retard the stress transmission between fibers and matrix, which are the main strengthening mechanisms of PAC. The present results will give references for revealing the fracture mechanisms of composites enhanced by needled fibers.

Interactive software for processing and modeling oil well resistivity logs as part of a two-dimensional interpretation approach

Resistivity well logging is widely used to identify reservoir rocks and evaluate their oil potential. However, the integral nature of the rock response to the field excited by the logging tool leads to the fact that the tool signal opposite the target formation is influenced by a well filled with drilling fluid, overlying sediments, drilling fluid filtrate invasion into the formation, etc. Today's widespread methods of resistivity logs interpretation are based on excessive simplifications, which in complex conditions leads to errors in determining the oil saturation coefficient of the target reservoir, costs of testing water-saturated intervals and missing the potentially promising reservoirs. The paper presents the results of developing new interactive software for working with well logging data and geoelectric model of the environment, focused on a 2D approach to interpreting resistivity logs. The use of a 2D axisymmetric geoelectric model of the medium as a base allows one to correctly take into account the above factors when interpreting practical data. Original realization of user interaction with geoelectric model of near-wellbore space takes into account the features of 2D approach to resistivity logs interpretation and provides convenience of work with multilayer models. The computing server AlondraCore integrated with the software supports resistivity logs simulation using two types of forward problem solvers: high-precision finite-element and fast neural network-based ones. The finite-element algorithms provide high log simulation accuracy with the ability to adjust the tool parameters. On the other hand, the neural network-based algorithms provide fast solution of forward problems for common logging tools.

ТРЕУГОЛЬНЫЙ КОНЕЧНЫЙ ЭЛЕМЕНТ С ШЕСТЬЮ СТЕПЕНЯМИ СВОБОДЫ В УЗЛЕ

The work is devoted to obtaining the stiffness matrix of a high-precision, flat finite element with 6 degrees of freedom in the node, for solving plane elasticity problems by the finite element method.
 The scientific literature describes higher order elements. However, the theoretical results of these studies are quite far from their practical application. This paper gives a very detailed derivation of the stiffness matrix of a high-precision finite element. Similarly, a stiffness matrix of a tetrahedral finite element with 12-degree-of-freedom node can be obtained. To test the obtained stiffness matrix, a program based on the FEM was written, with the help of which the cantilever beam is calculated. The error in calculating displacements is only 0.22%.
 Conclusion: the stiffness matrix presented in the paper can be used with great success in numerical methods for calculating the stress-strain state.

Hybrid intelligent modeling approach for online predicting and simulating surface temperature of HVs

Online prediction as well as online simulation of surface temperature will play a significant role in flight safety of future near space hypersonic vehicles (HVs). But it still remains a classical scientific problem both in thermodynamics and aerospace science. In view of the complex HV structure and complex heat conduction procedure, three-dimensional numerical simulation is too inefficient for online prediction, while current rapid computation methods cannot meet the requirement of accuracy. Therefore, a hybrid intelligent dynamic modeling approach is proposed to estimate the surface temperature of HV with the combination of mechanism equations, test data and intelligent modeling technology. A simplified model based on a mechanism equation and experimental formulas is presented for predicting or simulating transient heat conduction procedure efficiently, while a case-based reasoning (CBR) algorithm is developed to estimate two uncertain coefficients in the simplified model. Furthermore, a support vector regression (SVR)-based model is developed to compensate the modeling error. With the data both from high-precision finite element computation and from real-world HV thermal protection experiments, a number of comparative simulations demonstrate the effectiveness of the proposed hybrid intelligent modeling approach.