High Dimensional Model Representation Method Research Articles

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.

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.

High dimensional model representation for flood fragility analysis of highway bridge

Climate changes and global warming have increased the frequency and severity of rains, hence the vulnerability of structures due to floods. Bridges are the most affected components of the transportation infrastructure affected by floods. Analysis in a probabilistic framework is required for reliable performance assessments of bridges. However, the detailed performance assessment of bridges requires consideration of the uncertainties in geometry, material properties, and flood loading. The random structural responses due to flood loading can be obtained by stochastic analysis; conventionally, this is carried out using Monte Carlo Simulations (MCS). Due to the high computational cost required for MCS, non-statistical methods like High Dimensional Model Representation (HDMR) can be a feasible alternative to MCS. The present study is an application of the HDMR method to develop metamodels for the flood response of the highway bridge, considering the uncertainties. The structural responses due to flood at the sampling points of the HDMR are obtained by conducting finite element analysis. The HDMR could predict the random bridge responses due to flood loading fairly well compared to other popular response surface methods (like Central Composite Design, Box Behnken Design, and Full Factorial Design) with significantly fewer simulations. HDMR provides a flood response metamodel, as a function of the sensitive random parameters, with a substantial reduction in the computational effort. The efficiency of the HDMR method can be attributed to the ability of HDMR to model the nonlinear flood responses in terms of the statistical properties of random variables. The metamodels for the pier drifts developed are further utilized to generate flood fragility curves. The HDMR metamodels are found to simplify the fragility computations.

An adaptive augmented radial basis function–high-dimensional model representation method for structural engineering optimization

A new engineering optimization approach using an adaptive metamodeling method is developed and studied. The adaptive metamodels are based on a high-dimensional model representation framework, and the high-dimensional model representation component functions are created using radial basis functions or augmented radial basis functions. The proposed optimization approach starts with an explicit first-order augmented radial basis function–high-dimensional model representation metamodel, before a numerical optimization algorithm is applied. In each subsequent iteration, an additional sample point is found, and a high-order high-dimensional model representation component function is created and added to the first-order augmented radial basis function–high-dimensional model representation metamodel. The accuracy of the augmented radial basis function–high-dimensional model representation metamodel is improved in an adaptive manner, especially in the neighborhood of the optimal design point. Several numerical examples are solved to demonstrate the method, including a practical three-dimensional reinforced concrete high-rise building structure. The proposed approach works well, and the convergence of the optimal solutions for each of the examples is obtained within a few adaptive iterations.

On a High-Dimensional Model Representation method based on Copulas

This article provides an alternative to High-Dimensional Model Representation using a Copula approximation of an unknown functional form. We apply our methodology in the context of an extensive Monte Carlo study and to a sample of large US commercial banks. In the Monte Carlo experiment, the approximations errors of the Copula approach are small and behave randomly. In our empirical application, we find that the Copula Approximation performs much better, in terms of Bayes factors for model comparison, compared to High-Dimensional Model Representation, which, in turn, provides better results when compared with standard flexible functional forms, like the translog, the minflex Laurent, and the Generalized Leontief, or a Multilayer Perceptron. Moreover, the choice of approximation has significant implications for productivity and its components (returns to scale, technical inefficiency, technical change, and efficiency change).

Shape optimization for blended-wing–body underwater glider using an advanced multi-surrogate-based high-dimensional model representation method

To deal with shape optimization for the blended-wing-body underwater glider (BWBUG), a multi-surrogate-based optimization method using high-dimensional model representation with a score-based infill criterion (MSIC-HDMR) is presented. In this algorithm, multiple surrogate models are constructed to alleviate the prediction uncertainty. A score-based infill criterion is proposed to obtain new samples and a reduced space is used to improve accuracy of the optimization results. Simultaneously, mean square errors of the individual surrogate models for infill points are calculated to determine which surrogate is suitable for the component terms. 20 numerical examples are used to verify the practicability of the proposed MSIC-HDMR, and the results show that the proposed algorithm has remarkable performance on all the test problems. Finally, the optimization method based on MSIC-HDMR is applied to shape optimization of the BWBUG, and the lift-to-drag ratio of the BWBUG is improved by 3.3009% with the proposed MSIC-HDMR.

Fragility curves production by seismic improvement of the high-dimensional model representation method

PurposeIn the absence of random variables, random variables are generated by the Monte Carlo (MC) simulation method. There are some methods for generating fragility curves with fewer nonlinear analyses. However, the accuracy of these methods is not suitable for all performance levels and peak ground acceleration (PGA) range. This paper aims to present a method through the seismic improvement of the high-dimensional model representation method for generating fragility curves while taking advantage of fewer analyses by choosing the right border points.Design/methodology/approachIn this method, the values of uncertain variables are selected based on the results of the initial analyses, the damage limit of each performance level or according to acceptable limits in the design code. In particular, PGAs are selected based on the general shape of the fragility curve for each performance limit. Also, polynomial response functions are estimated for each accelerogram. To evaluate the accuracy, fragility curves are estimated by different methods for a single degree of freedom system and a reinforced concrete frame.FindingsThe results indicated that the proposed method can not only reduce the computational cost but also has a higher accuracy than the other methods, compared with the MC baseline method.Originality/valueThe proposed response functions are more consistent with the actual values and are also congruent with each performance level to increase the accuracy of the fragility curves.

High-dimensional model representation-based global sensitivity analysis and the design of a novel thermal management system for lithium-ion batteries

Abstract Thermal management is indispensable to the lithium-ion battery packs utilized in electrical vehicles. In this study, a novel air-cooling-based battery thermal management system with the heat fins-assisted phase change material/expanded graphite structure is proposed. After verification of the accuracy of the thermal model based on experimental measurements, numerical studies are performed on a battery submodule. All the results are obtained at an ambient temperature of 25 °C. Considering the complexity of the multi-physics modeling, a Kriging-based high-dimensional model representation method is employed to perform the global sensitivity analysis with relatively low computational effort. The results reveal the influence of the design variables on the thermal performance of the proposed cooling system. Moreover, this method reveals the correlations between the design variables, which reduce the dimensions of the given problem and improve the computational efficiency during optimization. Finally, a series of simulation-based tests is performed to validate the superiority of the optimal cooling system under realistic and extreme operation conditions. The comparison results show that this system can effectively improve the thermal behavior of the battery, and this cooling system after optimization provides much better cooling efficiency in alleviating the temperature increase and reducing the temperature difference of the batteries within the battery packs compared to the original one.

Stochastic response of reinforced concrete buildings using high dimensional model representation

Dynamic responses of structures are random in nature due to the uncertainties in geometry, material properties, and loading. The random dynamic responses can be represented fairly well by stochastic analysis. The methods used for stochastic analysis can be grouped into statistical and non-statistical approaches. Although statistical approaches like Monte Carlo simulation is considered as an accurate method for the stochastic analysis, computationally less intensive yet efficient, simplified non-statistical methods are necessary as an alternative. The present study is an evaluation of a relatively new non-statistical metamodel-based approach known as, High Dimensional Model Representation, with reference to existing response surface methods such as Central Composite Design, Box Behnken Design, and Full Factorial Design, in a dynamic response analysis. The geometry of a reinforced concrete frame is chosen to conduct free vibration and nonlinear dynamic analysis to study the stochastic responses using High Dimensional Model Representation method. This method was found to provide results as good as other methods with less computational effort with regard to the selected case studies.

Investigation of the effect of correlated uncertain rate parameters via the calculation of global and local sensitivity indices

Applications of global uncertainty methods for models with correlated parameters are essential to investigate chemical kinetics models. A global sensitivity analysis method is presented that is able to handle correlated parameter sets. It is based on the coupling of the Rosenblatt transformation with an optimized Random Sampling High Dimensional Model Representation method. The accuracy of the computational method was tested on a series of examples where the analytical solution was available. The capabilities of the method were also investigated by exploring the effect of the uncertainty of rate parameters of a syngas–air combustion mechanism on the calculated ignition delay times. Most of the parameters have large correlated sensitivity indices and the correlation between the parameters has a high influence on the results. It was demonstrated that the values of the calculated total correlated and final marginal sensitivity indices are independent of the order of the decorrelation steps. The final marginal sensitivity indices are meaningful for the investigation of the chemical significance of the reaction steps. The parameters belonging to five elementary reactions only, have significant final marginal sensitivity indices. Local sensitivity indices for correlated parameters were defined which are the linear equivalents of the global ones. The results of the global sensitivity analysis were compared with the corresponding results of local sensitivity analysis for the case of the syngas–air combustion system. The same set of reactions was indicated to be important by both approaches.

A new unbiased metamodel method for efficient reliability analysis

Metamodel method is widely used in structural reliability analysis. A main limitation of this method is that it is difficult or even impossible to quantify the model uncertainty caused by the metamodel approximation. This paper develops an improved metamodel method which is unbiased and highly efficient. The new method formulates a probability of failure as a product of a metamodel-based probability of failure and a correction term, which accounts for the approximation error due to metamodel approximation. The correction term is constructed and estimated using the Markov chain simulation. An iterative scheme is further developed to adaptively improve the accuracy of the metamodel and the associated correction term. The accuracy and efficiency of the new metamodel method is illustrated and compared with the classical Kriging metamodel and high dimensional model representation methods using a number of numerical and structural examples.

High dimensional model representation constructed by support vector regression. I. Independent variables with known probability distributions

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing high dimensional input-output system behavior. In practice, the HDMR component functions are each approximated by an appropriate basis function expansion. This procedure often requires many input-output samples which can restrict the treatment of high dimensional systems. In order to address this problem we introduce svr-based HDMR to efficiently and effectively construct the HDMR expansion by support vector regression (SVR) for a function \(f(\mathbf{x})\). In this paper the results for independent variables sampled over known probability distributions are reported. The theoretical foundation of the new approach relies on the kernel used in SVR itself being an HDMR expansion (referred to as the HDMR kernel ), i.e., an ANOVA kernel whose component kernels are mutually orthogonal and all non-constant component kernels have zero expectation. Several HDMR kernels are constructed as illustrations. While preserving the characteristic properties of HDMR, the svr-based HDMR method enables efficient construction of high dimensional models with satisfactory prediction accuracy from a modest number of samples, which also permits accurate computation of the sensitivity indices. A genetic algorithm is employed to optimally determine all the parameters of the component HDMR kernels and in SVR. The svr-based HDMR introduces a new route to advance HDMR algorithms. Two examples are used to illustrate the capability of the method.

Sensitivity analysis and probabilistic re-entry modeling for debris using high dimensional model representation based uncertainty treatment

Well-known tools developed for satellite and debris re-entry perform break-up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. The treatment of uncertainties associated with the re-entry of a space object requires a probabilistic approach. A Monte Carlo campaign is the intuitive approach to performing a probabilistic analysis, however, it is computationally very expensive. In this work, we use a recently developed approach based on a new derivation of the high dimensional model representation method for implementing a computationally efficient probabilistic analysis approach for re-entry. Both aleatoric and epistemic uncertainties that affect aerodynamic trajectory and ground impact location are considered. The method is applicable to both controlled and un-controlled re-entry scenarios. The resulting ground impact distributions are far from the typically used Gaussian or ellipsoid distributions.

Automated embolic signal detection using adaptive gain control and classification using ANFIS.

This work proposes an automated system for real-time high-accuracy detection of cerebral embolic signals (ES) to couple with transcranial Doppler ultrasound (TCD) devices in diagnosing a risk of stroke. The algorithm employs Adaptive Gain Control (AGC) approach to capture suspected ESs in real-time. Then, Adaptive Wavelet Packet Transform (AWPT) and Fast Fourier Transform (FFT) are used to extract from them features most efficiently representing ES, which determined by Sequential Feature Selection technique. Extracted feature vectors from the suspected ESs are later determined whether they are of an ES or non-ES interval by Adaptive Neuro-Fuzzy Inference System (ANFIS) based classifier. The effectiveness of the developed system was evaluated over 19 subjects going under procedures generating solid and gaseous emboli. The results showed that the proposed algorithm yielded 91.5% sensitivity, 90.0% specificity, and 90.5% accuracy. Cross validations were performed 20 times on both the proposed algorithm and the High Dimensional Model Representation (HDMR) method (the most efficient algorithm to date) and their performances were compared. Paired t-test difference showed that the proposed algorithm outperformed the HDMR method, in both detection accuracy [t(19, 0.01) = 132.2073, p ~ 0] and sensitivity [t(19, 0.01) = 131.4676, p ~ 0] at 90.0% specificity, suggesting promising potential as a medical support system in ES monitoring of various clinical settings.

Investigation of the effect of correlated uncertain rate parameters on a model of hydrogen combustion using a generalized HDMR method

The High Dimensional Model Representation (HDMR) method has been applied in several previous studies to obtain global sensitivity indices of uncorrelated model parameters in combustion systems. However, the rate parameters of combustion models are intrinsically correlated and therefore uncertainty analysis methods are needed that can handle such parameters. A generalized HDMR method is presented here, which uses the Rosenblatt transformation on a correlated model parameter sample to obtain a sample of independent parameters. The method provides a full set of both correlated and marginal sensitivity indices. Ignition delay times predicted by an optimized hydrogen–air combustion model in stoichiometric mixtures near the three explosion limits are investigated with this new global sensitivity analysis tool. The sensitivity indices which account for all the correlated effects of the rate parameters are shown to dominate uncertainties in the model output. However, these correlated indices mask the individual influence of parameters. The final marginal uncorrelated sensitivity indices for individual parameters better indicate the change of importance of homogeneous gas phase and species wall-loss reactions as the pressure is increased from above the first explosion limit to above the third limit. However, these uncorrelated indices are small and whilst they provide insights into the dominant chemical and physical processes of the model over the range of conditions studied, the correlations between parameters have a very significant effect. The implications of this result on model tuning will be discussed.

A high-dimensional design optimisation method for centrifugal impellers

The metamodel-based design optimisation (MBDO) method has been gaining increasing popularity in the field of turbomachinery design. Nevertheless, the ‘curse of dimensionality’ remains a formidable obstacle for the application of MBDO in high-dimensional design problems, which, in the context of turbomachinery design, are problems with at least 10 design variables, if expensive simulations such as computational fluid dynamics are required. To address this issue, the present study proposes to utilise a novel high-dimensional model representation (HDMR) method to support the process of MBDO and applies it to the design optimisation of a centrifugal impeller. A total of 15 geometrical design variables and three performance objectives are considered in the optimisation. In particular, the HDMR method is assisted by support vector regression (SVR) metamodels to explicitly represent the relationships between design variables and performance objectives. Apart from high metamodelling accuracy and efficiency, the SVR-HDMR metamodelling technique enables designers to refine design space as well as to identify correlations between design variables during the metamodelling process. Analysis of the final optimisation results show that a reduced hub-line curvature, a negative rake angle, a positive splitter blade lean angle and an increased splitter blade inlet angle are beneficial for enhancing efficiency of this impeller. This work provides valuable references for further high-dimensional design optimisation of turbomachine components.

Weight optimization in HDMR with perturbation expansion method

High dimensional model representation method forms an effective divide-and-conquer method used for the truncated representation of a multivariate function, having N independent variables, in terms of certain number ( $$<$$ 2 $$^N$$ ) of less variate functions. The main aim of this method is not to use all these functions in the representation and to obtain an approximation to the given problem. This results in a need of having a good convergence performance just as it is expected in the other numerical methods. This work aims to increase the convergence rate of HDMR approximation by optimizing the weight function, which appears in the method as Prof. Rabitz suggested first, with the help of the perturbation expansion and fluctuationlessness theory. This work also includes a computational procedure with the help of a testing function to better understand the steps of the proposed method.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in each subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques.

A Method of Multi-Failure Models Based on Response Surfaces Method-High Dimensional Model Representation on Structural Reliability Analysis

The response surface method (RSM) is widely adopted for structural reliability analysis because of its numerical efficiency. However, the RSM is time consuming for large-scale applications and sometimes shows large errors in the calculation of the sensitivity of the reliability index with respect to random variables. In order to overcome these problems, this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models which is based on the high dimensional model representation (HDMR) and response surface method (RSM).Once the limit state function is defined, the design point can be found by using HDMR method, through which the response surface can be established to calculate the failure probability. The series and parallel system are considered in this paper, a numerical example is presented to demonstrate the efficiency and the accuracy of the proposed method. It is shown that the efficiency of the RSM-HDMR are both high in terms of series system and parallel system.

A polynomial based algorithm for detection of embolism

The Transcranial Doppler ultrasound can be used to detect asymptomatic circulating cerebral emboli. Emboli indicate particles that can plug the arterial system. Asymptomatic emboli signals help to discover critical stroke events by taking the embolus activities into consideration. Cerebral emboli detection is searched deeply in the literature. But none of them proposed a polynomial method to generalize the solution of the emboli detection. High Dimensional Model Representation (HDMR) philosophy is an effective way of generating an analytical model for a given multivariate data modeling problem, that is, HDMR can be used in constructing a general polynomial model for detecting embolism. In this study, emboli related data set was collected from $$35$$ 35 different patients. HDMR based methods and various data mining techniques were used to detect emboli through that data set. The Euclidean Matrix Based Indexing HDMR method has an important superiority in terms of generating a polynomial model which can then be used in other emboli detection problems without a training process. The method also shows satisfactory results in generalizing the emboli characteristics when compared with the other methods.