High Dimensional Model Representation Research Articles

DeepEMPR: coffee leaf disease detection with deep learning and enhanced multivariance product representation

Plant diseases threaten agricultural sustainability by reducing crop yields. Rapid and accurate disease identification is crucial for effective management. Recent advancements in artificial intelligence (AI) have facilitated the development of automated systems for disease detection. This study focuses on enhancing the classification of diseases and estimating their severity in coffee leaf images. To do so, we propose a novel approach as the preprocessing step for the classification in which enhanced multivariance product representation (EMPR) is used to decompose the considered image into components, a new image is constructed using some of those components, and the contrast of the new image is enhanced by applying high-dimensional model representation (HDMR) to highlight the diseased parts of the leaves. Popular convolutional neural network (CNN) architectures, including AlexNet, VGG16, and ResNet50, are evaluated. Results show that VGG16 achieves the highest classification accuracy of approximately 96%, while all models perform well in predicting disease severity levels, with accuracies exceeding 85%. Notably, the ResNet50 model achieves accuracy levels surpassing 90%. This research contributes to the advancement of automated crop health management systems.

An advanced high dimensional model representation approach for internal combustion engine modeling and optimization

This work introduces an efficient data-driven approach for engine performance modeling and optimization. A highly accurate and robust high-dimensional model representation (HDMR) surrogate model is developed based on the dataset generated from a coupled KIVA4-CHEMKIN Ⅱ software. The HDMR model is integrated with a multi-objective optimization algorithm, enabling the automatic identification of optimal combustion strategies. Results suggest that the constructed HDMR model is able to accurately predict the engine performance and exhaust gas emissions with negligible CPU costs. Moreover, the model effectively identifies optimal engine operating conditions, leading to enhanced fuel efficiency.

Structural integrity assessment of CANDU pressure tubes using Sobol indices for global sensitivity analysis

CANDU11CANDU is a registered trademark of Atomic Energy of Canada Limited. reactors are a channel-type design where up to 480 zirconium alloy pressure tubes (PTs) act as the reactor pressure boundary. Fitness-for-service standards such as CSA N285.8 (CSA Group, 2015) have been established to prescribe the requirements of pressure tube evaluations to maintain their integrity throughout their lifetime. Probabilistic leak-before-break (LBB) assessments can be used in evaluations to demonstrate that the likelihood of a flaw growing past the stability point while undetected (or before a safe shutdown can be achieved) is below regulatory limits. The assessments typically require a ranking of model parameters based on their influence. The ranking process traditionally uses expert judgment and local sensitivity analysis methods. There has been recent interest in implementing global methods for LBB assessments as they can manage large numbers of variables and extensive sampling spaces. However, their adoption is hindered by the computational cost of the models involved.The current study proposes a method for performing global sensitivity parameter rankings during probabilistic LBB assessments. The study is the continuation of the CANDU nuclear power plant (NPP) pressure tube (PT) case study in El Bouzidi et al., (2024) where a probabilistic approach was implemented in RAVEN (Rabiti and Alfonsi, 2019) to estimate whether the probability of unstable crack growth in PTs is within acceptable limits. This follow-up work proposes surrogate modeling using a high-dimensional model representation to derive Sobol indices and establish a parameter influence ranking. The methodology is demonstrated in a Monte Carlo simulation campaign of a pressure tube inlet rolled joint. The implemented approach successfully identified and quantified critical parameters of the model while efficiently ranking and quantifying the interactions between input variables.

A pointwise weighting prediction variance–high-dimensional model representation model-based global optimization approach for ship hull parametric design

Ship hull optimization techniques based on computer-aided design/computational fluid dynamics can effectively enhance the efficiency and stability of ship designs, with significant application prospects. To enhance the potential of ship hull optimization, increasing design variable dimensionality is essential, but can cause a significant increase in hydrodynamic simulations. To reduce simulations required for high-dimensional ship hull optimization, a new surrogate method, pointwise weighting prediction variance–high-dimensional model representation (PWPV-HDMR), which uses pointwise weighting prediction variance (PWPV) to aggregate different a priori assumptions, is developed. Moreover, a differential evolution algorithm is used to identify promising hull design parameters, using the PWPV-HDMR model instead of costly simulation as the fitness function. The proposed approach is tested on the hydrostatic resistance optimization of KRISO Container Ship. The results show that PWPV-HDMR outperforms kriging-HDMR, with a better resistance optimization effect, illustrating the effectiveness of the PWPV-HDMR-based global optimization approach in discovering promising ship hull parameters.

A point mapping strategy-based sparse grid integration method for statistical moments estimation and structural reliability analysis

The high-order moment-based method is an attractive non-intrusive approach for structural reliability analysis, while it remains a challenge to strike a balance between accuracy, efficiency, and versatility in estimating statistical moments of performance functions. In this paper, a point mapping strategy-based sparse grid integration (SGI) method is proposed for statistical moment estimation and structural reliability analysis, with improved efficiency while ensuring the accuracy. Firstly, a point mapping strategy (PMS) is developed based on the adaptive high dimensional model representation (HDMR), by which the traditional SGI is reconstructed as a sum of multiple integrations over the sparse grid point sets with different effective dimensions. With this new form of SGI, the estimation of statistical moments only requires the evaluation of the performance function at a small number of necessary reference points, once the effects of some interaction terms are negligible. The validity and feasibility of the proposed PMS-based SGI method for statistical moments estimation are verified by several numerical examples. Then, the proposed method is applied to structural reliability analysis with the aid of an improved maximum entropy method. Two engineering examples are investigated, including the strength failure problem of tubular tower K-shape connection joints and the fatigue failure problem of a marine riser resulting from the vortex-induced vibration (VIV). The results indicate that the proposed method provides a better trade-off between accuracy and efficiency in evaluating the first four order statistical moments and structural failure probability compared to conventional methods.

Uncertainty Quantification in SAR Induced by Ultra-High-Field MRI RF Coil via High-Dimensional Model Representation.

As magnetic field strength in Magnetic Resonance Imaging (MRI) technology increases, maintaining the specific absorption rate (SAR) within safe limits across human head tissues becomes challenging due to the formation of standing waves at a shortened wavelength. Compounding this challenge is the uncertainty in the dielectric properties of head tissues, which notably affects the SAR induced by the radiofrequency (RF) coils in an ultra-high-field (UHF) MRI system. To this end, this study introduces a computational framework to quantify the impacts of uncertainties in head tissues' dielectric properties on the induced SAR. The framework employs a surrogate model-assisted Monte Carlo (MC) technique, efficiently generating surrogate models of MRI observables (electric fields and SAR) and utilizing them to compute SAR statistics. Particularly, the framework leverages a high-dimensional model representation technique, which constructs the surrogate models of the MRI observables via univariate and bivariate component functions, approximated through generalized polynomial chaos expansions. The numerical results demonstrate the efficiency of the proposed technique, requiring significantly fewer deterministic simulations compared with traditional MC methods and other surrogate model-assisted MC techniques utilizing machine learning algorithms, all while maintaining high accuracy in SAR statistics. Specifically, the proposed framework constructs surrogate models of a local SAR with an average relative error of 0.28% using 289 simulations, outperforming the machine learning-based surrogate modeling techniques considered in this study. Furthermore, the SAR statistics obtained by the proposed framework reveal fluctuations of up to 30% in SAR values within specific head regions. These findings highlight the critical importance of considering dielectric property uncertainties to ensure MRI safety, particularly in 7 T MRI systems.

Uncertain vibration response of vehicles passing through barricades based on approximate models

In vibration analysis, a vehicle system encounters dimensionality issues due to its high-dimensional uncertain parameters. An approximate model offers a viable solution for analyzing such uncertain responses. This study introduces an efficient approximate model, called PCE-HDMR, which is founded on the Legendre Polynomial Chaos Expansion (PCE) and High-Dimensional Model Representation (HDMR). Specifically, the Legendre PCE in interval space is employed to delineate the lower and upper bounds of uncertain responses. At the same time, the HDMR is harnessed to develop a high-dimensional uncertainty model that approximates the dynamic response. To demonstrate the application of PCE-HDMR, a model for a vehicle with interval parameters was constructed using a 9-DOF dynamics model for testing. In this framework, all stiffness and damping parameters are treated as interval uncertainty parameters. The numerical results validate the effectiveness of the proposed method for high-dimensional uncertain parameters, demonstrating that PCE-HDMR outperforms Monte Carlo simulation (MCS) in terms of efficiency. This study advances an effective interval uncertainty analysis approach for assessing vehicle performance, particularly when dealing with high-dimensional interval uncertainty parameters. The proposed method serves as a viable alternative for interval analysis and subsequent optimization design for complex vehicle systems characterized by high-dimensional uncertain parameters.

An efficient data-driven approach for modeling and optimization of reactivity-controlled compression ignition engine fueled with polyoxymethylene dimethyl ethers and hydrogen

This paper presents an efficient data-driven approach for optimizing the utilization of PODEn and hydrogen in reactivity-controlled compression ignition (RCCI) engines. A novel high dimensional model representation (HDMR) technique is adopted to construct a highly accurate surrogate model for the RCCI engine based on the dataset generated by a detailed CFD model that has been calibrated against experimental data. The HDMR model is then coupled with Non-dominated Sorting Genetic Algorithm III (NSGA III), a multi-objective genetic algorithm, to search for the optimal operating conditions where the RCCI engine fueled by PODEn and H2 achieves the highest combustion performance. Results suggest that the constructed HDMR model is highly accurate, being able to predict the engine performance within milliseconds. The coupled HDMR-NSGA III approach successfully identifies the optimal engine operating condition, which significantly improves the combustion performance and reduces pollutant emissions compared with the base condition.

High dimensional model representation median filter for removing salt and pepper noise

High dimensional model representation median filter for removing salt and pepper noise

A novel kriging-improved high-dimensional model representation metamodelling technique for approximating high-dimensional problems

Aiming to address the issue of the ‘curse of dimensionality’ encountered in approximating high-dimensional problems using surrogate-based methods, high-dimensional model representation (HDMR), decomposing the high-dimensional problem into summands of different-order component functions, has been widely studied. To reduce the computational demands of the current HDMR metamodelling techniques, an improved high-dimensional model representation framework (iHDMR) is presented, taking full advantage of the relationships between the first-order and second-order component functions in the Cut-HDMR theory. then, a novel metamodelling technique, termed kriging (KRG)-iHDMR, is implemented by integrating the kriging technique and the suggested surface-axes alternating sampling strategy into the iHDMR framework. The accuracy and efficiency of KRG-iHDMR are demonstrated by various numerical and engineering examples with different dimensions. Finally, an optimization problem of the multi-stage solid launch vehicle propulsion system is introduced to verify the engineering feasibility of the KRG-iHDMR metamodelling technique.

Identification and modelling of parameters for the information-physical-social convergence characteristics of user-side flexible resources

The use of flexible resource information on the user side helps to increase system efficiency. Power system power variation becomes more pronounced with the access to renewable resources. Therefore, the study proposes a parameter identification and modeling method for the physical and social integration characteristics of flexible resource information on the user side. Taking the user’s air conditioning load as the object, the thermal dynamic model of the air conditioning building is constructed using equivalent thermal parameters, and the variable frequency air conditioning load is embedded in the battery model. The model parameter identification is carried out using high-dimensional model expression technology. According to the experimental data, in options 2 and 3, the system operator makes power purchases based on the storage status of the lithium battery or virtual battery, increasing the number of power purchases when the price of electricity is low and decreasing the number of power purchases when the price of electricity is high. This effectively reduces the system operator’s electricity costs. The error of multiple linear regression modelling varies widely, with relative errors up to 0.75 and an average relative error of 15.1%. The relative error of modelling based on the high-dimensional model expression technique is in the range of 0 to 0.2, with an average relative error of 5.5%. The results show that compared with multiple linear regression models, high-dimensional model representation technology has higher modeling accuracy and can accurately identify the parameters of the air conditioning load aggregation model, solving the problem of difficult parameter calculation in the practical application of the air conditioning load aggregation model, and providing technical support for power system regulation.

Stochastic analysis of thin beams and plates incorporating von-Kármán nonlinear strains using meshless method

The current paper proposes methods for stochastic meshless analysis of thin beams and plates, by considering von-Kármán nonlinear strains. Here, Young’s modulus is assumed to have a spatial variation over the domain and is modeled as a homogeneous random field. Further, it is discretized utilizing moving least square based shape functions. Gaussian and lognormal properties are presumed to model the randomness related to Young’s modulus. Element-free Galerkin method is used as the meshless tool. The present study suggests employing perturbation method if the quantities of interest are limited to the first or second probabilistic moments of the responses. The nonlinear equations in the proposed perturbation formulations are solved using Newton-Raphson iterative scheme for finding out the deterministic part of the response, as well as its initial two derivatives with respect to random variables. Additionally, if there is an interest in higher probabilistic moments, probability density functions, cumulative distribution functions, and so forth, the study proposes a method using high-dimensional model representation (HDMR) in the meshless framework. In HDMR, the nonlinear connection between input variables and the output response is represented in terms of hierarchical correlated function expansions. These hierarchical functions are approximated over the response values evaluated using deterministic analysis on selected number and combinations of control points of random variables involved. Lagrange interpolation method is employed for the construction of response surfaces. Unlike Monte Carlo simulation (MCS) which needs numerous deterministic nonlinear analyses to be performed during each simulation, HDMR requires only a few deterministic nonlinear analyses to construct the component functions. Hence, simulations performed on the reduced order models of high-dimensional response can be used to estimate the probabilistic moments as well as density functions and cumulative distributions of response, with high computational efficiency compared to MCS. The probabilistic moments and distributions produced for a range of coefficient of variation of input random field up to 30%, for both the normal and lognormal input random fields are compared with those provided by crude MCS on the system of equations and are observed to be matching well.

Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations.

We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general, high-dimensional model representations of potential energy surfaces. For this purpose, we extend the vDMRG framework to support vibrational Hamiltonians expressed in the so-called n-mode second-quantization formalism. The resulting n-mode vDMRG method offers full flexibility with respect to both the functional form of the PES and the choice of the single-particle basis set. We leverage this framework to apply, for the first time, vDMRG based on an anharmonic modal basis set optimized with the vibrational self-consistent field algorithm on an on-the-fly constructed PES. We also extend the n-mode vDMRG framework to include excited-state-targeting algorithms in order to efficiently calculate anharmonic transition frequencies. We demonstrate the capabilities of our novel n-mode vDMRG framework for methyloxirane, a challenging molecule with 24 coupled vibrational modes.

Uncertainty assessment method for thermal runaway propagation of lithium-ion battery pack

To some extent, the thermal runaway issue pertaining to lithium-ion battery still present challenging problems, to put the safety-related issue under control in high-power and high-energy applications. One of these challenging issues relates to the underpinning stochastic uncertainties associated with thermal runaway propagation. Therefore, this study proposes a methodology to evaluate the uncertainty of thermal runaway propagation in Li-ion battery modules. Firstly, a numerical thermal runaway propagation model is developed for phase change material-based thermal management system and verified by experiments. Subsequently, the Adaptive Kriging High-dimensional model representation method is employed to construct a surrogate model, followed by global sensitivity analysis to evaluate the impact of six different influencing factors on thermal runaway propagation. Finally, the random fluctuation of the critical factors affecting thermal runaway propagation is integrated to analyze and quantify the uncertainty. The results show that the state of charge, the thermal conductivity of phase change material, and inter-cell spacing are critical factors affecting thermal runaway propagation. With the system parameters proposed in this paper, the critical state of charge range that significantly impacts the uncertainty of thermal runaway propagation is approximately 40% to 55%. The analysis of the propagation results and the cell temperature indicates that the highest level of uncertainty occurs at around 45% state of charge. In this case, the thermal runaway propagation is significantly impacted by changes in key factors, and the battery temperature exhibits high fluctuation levels. Furthermore, although there is a 59% likelihood of no propagation, the potential damage to all batteries becomes exceedingly significant once thermal runaway propagation occurs. The method proposed in this study effectively evaluates the uncertainty of thermal runaway propagation in battery systems. It identifies the causes of the uncertainty, which can be used to implement effective suppression measures to enhance safety.

Parametric study of square dome-shaped kirigami folded structure for blast mitigation

This paper explores the potential of using Square Dome-shaped Kirigami (SDK) structures as a core component in cladding systems for blast mitigation. The study aims to assess the effectiveness of the SDK foldcore in reducing the impact of blast loading and to determine the optimal geometry of the SDK foldcore for enhanced blast mitigation using High Dimensional Model Representations (HDMR). A nonlinear finite element analysis with the ABAQUS software package has been carried out to investigate the blast mitigation capacity. The model is subjected to a quasi-static compression test to simulate the crushing effect, and the results are used to calibrate the simulation with the experimental data from the literature. Four different levels of blast loading conditions are applied to evaluate the blast resistance of the system. The structural response of the SDK foldcore is compared to that of a traditional Square Honey Comb (SHC) core with the same relative density under the same blast loading conditions. The peak load transmitted by the SDK foldcore is much more consistent than the SHC core, even under different blast loading conditions. SDK foldcore significantly improves energy absorption, resulting in better performance in mitigating the effects of blast loading. Additionally, a mathematical model using HDMR is created to assess the performance of the SDK foldcore using geometric parameters as input variables. The HDMR model enables the generation of numerous alternative design solutions, allowing designers to select the most optimal geometry for the SDK foldcore.

A geometric sensitivity study for the aerodynamics of a strut-braced airframe

A global sensitivity analysis method, the adaptive-cut high-dimensional model representation method (HDMR) is considered to evaluate the impact of geometrical changes of a ultra-high aspect ratio strut-braced wing configuration on the aerodynamic performance. A data-driven reduced order model based on Proper Orthogonal Decomposition is used to keep the computational cost of the analysis at a manageable level. The airframe configuration is described using 7 geometrical parameters, which comprise the design space. The geometrical parameters are decomposed and analysed across their whole range of values by the HDMR to assess their influence on the Drag coefficient, Lift coefficient and Lift-to-Drag ratio of the aircraft. These results form the basis for a qualitative exploration of the aerodynamics of such airframes further augmented by high-fidelity CFD simulations. Results show that the sweep angle of the wing is the dominant parameter in terms of Drag due to changes in shock wave intensity. Changes in the wing root chord also implicitly affect the local geometry at the wing-strut junction, which influences the blockage effect and thus the intensity of the shock waves at the junction. Lift is affected primarily by the twist of the wing. Overall, the strut is shown to have significant effects on the performance of the aircraft design due to the presence of strong shock waves at the wing-strut junction and interference effects.

Experiment and simulation of hydrogen oxidation in a high-pressure turbulent flow reactor

Hydrogen oxidation has a complex dependence on pressure. Despite the well-known, reverse S-shape explosion limits, variation of hydrogen oxidation reactivity with pressure has rarely been investigated in a quantitative manner, particularly in the peninsula between the second and third ignition branches when the overall reactivity is low. This work investigates hydrogen oxidation in a turbulent flow reactor at 10 to 48 bar with an inlet temperature of 950 K and an equivalence ratio of 0.03–0.05, which complements our recent study at 1–8 bar in the same reactor (Lu et al. Proc. Combust. Inst. 2021, 243–250). The elevated pressures show a weak promoting effect, in contrast to the strong inhibiting effect at lower pressures in crossing the second ignition branch. Analyzing the hydrogen consumption rates across the pressure range revealed that the reactivity remains at a low level and is barely affected by pressure between 2 and 20 bar, suggesting the existence of a broad low-reactivity valley on the temperature–pressure plane which could be potentially important for practical applications.The measured species-time concentrations, combined with ignition delays selected from the literature, are used to develop a new hydrogen oxidation model focusing on hydrogen autoignition behavior. A comprehensive review of elementary reactions incorporating the latest updates for the rate coefficients is conducted to determine the prior uncertainties. A global optimization method incorporating random sampling and high-dimensional model representation is used to identify the most sensitive reactions and to constrain their uncertainty with the selected experimental targets. An optimized model is then obtained which shows excellent agreement with hydrogen autoignition experiments.

CFD Uncertainty Quantification using PCE–HDMR: Exemplary Application to a Buoyancy-Driven Mixing Process

For the investigation of uncertainties in high dimensional spaces of computationally expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are needed. These methods should provide accurate and efficient High-Dimensional Model Representations of stochastic results using a reasonable number of calculations. Therefore, the PCE–HDMR approach (Polynomial Chaos Expansion–High-Dimensional Model Representation) is utilized to qualify appropriate UQ methods for large-scale computations in the field of Computational Fluid Dynamics. This technique is a combination of Cut-HDMR, a hierarchical decomposition modeling approach, with PCE. To demonstrate its effectiveness, the PCE–HDMR methodology in conjunction with complementary modeling techniques is applied for the UQ analysis of a buoyancy-driven mixing process between two miscible fluids within the Differentially Heated Cavity of aspect ratio 4. The results include a thorough probabilistic representation of time-dependent response quantities that comprehensively describe the mixing process. The stochastic models are derived from Large Eddy Simulations using PCE–HDMR and the Sparse Grid Method, which serves as a reference for the results from PCE–HDMR. The results show that PCE–HDMR provides accurate statistics of the modeled time-dependent stochastic processes and shows good agreement with the reference results. Thus, PCE–HDMR indicates great potential for UQ of technical-scale computations due to its efficiency and flexibility in the construction of stochastic models.

High Dimensional Model Representation Approach for Prediction and Optimization of the Supercritical Water Gasification System Coupled with Photothermal Energy Storage

Supercritical water gasification (SCWG) coupled with solar energy systems is a new biomass gasification technology developed in recent decades. However, conventional solar-powered biomass gasification technology has intermittent operation issues and involves multi-variable characteristics, strong coupling, and nonlinearity. To solve the above problems, firstly, a solar-driven biomass supercritical water gasification technology combined with a molten salt energy storage system is proposed in this paper. This system effectively overcomes the intermittent problem of solar energy and provides a new method for the carbon-neutral process of hydrogen production. Secondly, the high dimensional model representation (HDMR) approach, as a surrogate model, was used to predict the production and lower heating value of syngas developed in Aspen Plus, which were validated using experimental data obtained from the literature. The ultimate analysis of biomass, temperature, pressure, and biomass-to-water ratio (BWR) were selected as input variables for the model. The non-dominated sorted genetic algorithm II (NSGA II) was considered to maximize the gasification yield of H2 and the LHV of syngas in the SCWG process for five different types of biomass. Firstly, the results showed that HDMR models demonstrated high performance in predicting the mole fraction of H2, CH4, CO, CO2, gasification yield of H2, and lower heating value (LHV) with R2 of 0.995, 0.996, 0.997, 0.996, 0.999, and 0.995, respectively. Secondly, temperature and BWR were found to have significant effects on SCWG compared to pressure. Finally, the multi-objective optimization results for five different types of biomass are discussed in this paper. Therefore, these operating parameters can provide an optimal solution for increasing the economics and characteristics of syngas, thus keeping the process energy efficient.

Seismic fragility of non-ductile RC frames for pounding risk assessment

Building structures subjected to seismic excitation tend to vibrate with a unique set of dynamic characteristics, such as natural frequencies, fundamental mode shapes etc. In series-configured structural systems, a difference in such characteristics induces a phase difference between the structures’ oscillations, leading to structural collisions or pounding. Pounding often becomes a cause of catastrophic failures, hence an accurate estimation of structural integrity with respect to pounding is of paramount importance. This study aims to examine different fragility curve development methodologies available in the literature to assess the seismic performance of adjacent Reinforced Concrete (RC) structures subjected to structural pounding. The study primarily focuses on displacement-based fragility curves for the highly critical floor-to-column interactions of an eight-storey non-ductile RC frame, non-eccentrically adjacent to a three-storey rigid RC frame having different storey heights. Nonlinear time–history analyses have been performed to simulate pounding, and fragility curves have been generated using five methodologies. The direct Monte-Carlo Simulation technique has been used to benchmark against the obtained results to identify the suitability of each fragility assessment technique. Results indicate that even though there is no effect of the choice of assessment methodology on the estimated risk at low performance levels and intensity measures, the disparity becomes clearly visible at higher levels. The study presents alternate ways of developing accurate fragility curves by keeping in mind the need for computational efficiency without compromising the accuracy of results. The High Dimensional Model Representation meta-model is found to efficiently represent target pounding fragilities while incurring minimal computational costs.