Random Sampling-High Dimensional Model Research Articles

Comprehensive influence of uncertainty propagation of chemical kinetic parameters on laminar flame speed prediction: a case study of dimethyl ether

The uncertainties existing in the parameters of chemical kinetic models have a non-negligible influence on the model predictions. It is necessary to conduct a quantitative uncertainty analysis to explore the influence of each parameter on chemical mechanism predictions. To comprehensively consider the effect of the uncertainties of reaction rate parameters, thermodynamic parameters, and transport parameters on model predictions, local sensitivity analysis, local-sensitivity-based uncertainty analysis (LSUA), and random-sampling high dimensional model representation (RS-HDMR) method were coupled to investigate the uncertainty propagation of the chemical kinetic parameters to the calculated laminar flame speed of dimethyl ether under a wide range of conditions using a detailed mechanism. First, the uncertainty analysis was conducted using the local sensitivity analysis and the LSUA method under a wide range of operating conditions to identify the important operating conditions and chemical kinetic parameters. It is found that the prediction uncertainty of laminar flame speed is more obvious under the conditions of high dilution ratio, high pressure, and large equivalence ratio than that under other conditions. According to the results of LSUA, the prediction uncertainty is mainly from the reaction rate coefficients and thermodynamic data. Then, the uncertainty propagation from the significant parameters to the calculated laminar flame speed under important conditions was analysed using the RS-HDMR method. To reduce the huge computational cost of the RS-HDMR method, the backpropagation artificial neural network was employed. The RS-HDMR results indicate that the reaction H + O2 = O + OH has the highest sensitivity coefficient under the whole investigated conditions, which is different from the results using the LSUA method. The non-linear relationship between the rate coefficient and the predicted laminar flame speed is responsible for the discrepancy. Furthermore, it is found that the sensitivity coefficient of the input parameters strongly depends on the operating conditions.

Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general method

We present an implementation for the RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression) method. The method builds representations of multivariate functions with lower-dimensional terms, either as an expansion over orders of coupling or using terms of only a given dimensionality. This facilitates, in particular, recovering functional dependence from sparse data. The method also allows for imputation of missing values of the variables and for a significant pruning of the useful number of HDMR terms. It can also be used for estimating relative importance of different combinations of input variables, thereby adding an element of insight to a general machine learning method, in a way that can be viewed as extending the automatic relevance determination approach. The capabilities of the method and of the associated Python software tool are demonstrated on test cases involving synthetic analytic functions, the potential energy surface of the water molecule, kinetic energy densities of materials (crystalline magnesium, aluminum, and silicon), and financial market data.

Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for Multivariate Function Representation: Application to Molecular Potential Energy Surfaces.

We present an approach combining a representation of a multivariate function using subdimensional functions with machine learning based representation of component functions: Random sampling high dimensional model representation Gaussian process regression (RS-HDMR-GPR). The use of Gaussian process regressions to represent component functions allows nonparametric (unbiased) representation and the possibility to work only with functions of desired dimensionality, obviating the need to build an expansion over orders of coupling. All component functions are determined from a single set of samples. The method is tested by fitting six- and 15-dimensional potential energy surfaces (PES) of polyatomic molecules as well as by computing vibrational spectra for a four-atomic molecule.

An Innovative Methodology for Online Surrogate-Based Model Updating of Historic Buildings Using Monitoring Data

ABSTRACT Structural Health Monitoring (SHM) based on Automated Operational Modal Analysis (A-OMA) has gained increasing importance in the conservation of heritage structures over recent decades. In this context, finite element model updating techniques using modal data constitute a commonly used approach for damage identification. Nevertheless, the large number of simulations usually involved in the associated minimization problem hinders the application to real-time condition assessment. This is especially critical for historic buildings, where the modelling of complex geometries involves large computational burdens. Alternatively, surrogate models offer an efficient solution to replace computationally demanding numerical models and so perform continuous model updating. In this light, this paper presents a surrogate-based model updating approach for online assessment of historic buildings and its application to a medieval masonry tower, the Sciri Tower in Perugia (Italy). Using modal properties identified by A-OMA, the proposed approach allows the continuous fitting of certain damage-sensitive parameters of the structure. To do so, three different surrogate models are considered, including the quadratic response surface method, Kriging, and Random Sampling High-Dimensional Model Representation, and their effectiveness is compared from an SHM perspective. The reported results demonstrate the suitability of the proposed methodology for tracking the temperature-dependent intrinsic properties of the tower.

A global sensitivity analysis-assisted sequential optimization tool for plant-fin heat sink design

Purpose This study aims to suggest and develops a global sensitivity analysis-assisted multi-level sequential optimization method for the heat transfer problem. Design/methodology/approach Compared with other surrogate-assisted optimization methods, the distinctive characteristic of the suggested method is to decompose the original problem into several layers according to the global sensitivity index. The optimization starts with the several most important design variables by the support vector regression-based efficient global optimization method. Then, when the optimization process progresses, the filtered design variables should be involved in optimization one by one or the setting value. Therefore, in each layer, the design space should be reduced according to the previous optimization result. To improve the accuracy of the global sensitivity index, a novel global sensitivity analysis method based on the variance-based method incorporating a random sampling high-dimensional model representation is introduced. Findings The advantage of this method lies in its capability to solve complicated problems with a limited number of sample points. Moreover, to enhance the reliability of optimum, the support vector regression-based global efficient optimization is used to optimize in each layer. Practical implications The developed optimization tool is built by MATLAB and can be integrated by commercial software, such as ABAQUS and COMSOL. Lastly, this tool is integrated with COMSOL and applied to the plant-fin heat sink design. Compared with the initial temperature, the temperature after design is over 49°. Moreover, the relationships among all design variables are also disclosed clearly. Originality/value The D-MORPH-HDMR is integrated to obtain the coupling relativities among the design variables efficiently. The suggested method can be decomposed into multiplier layers according to the GSI. The SVR-EGO is used to optimize the sub-problem because of its robustness of modeling.

Higher-order sensitivity analysis of a final repository model with discontinuous behaviour using the RS-HDMR meta-modeling approach

Sensitivity analysis is considered a useful tool for determining sensitivities and assessing uncertainties of computational models, which is critical for the performance assessment of final repository models. One group of methods of sensitivity analysis is variance-based methods, which can identify sensitivities of individual parameters and parameter interactions. This is done via computation of Sobol’ sensitivity indices of first and higher orders.Models describing complex physical systems can behave in a highly nonlinear, non-monotonic or even discontinuous manner. Many methods of sensitivity analysis perform poorly or even fail completely on such models. In former investigations with a model of this kind, we could not identify any method capable of calculating reliably second- or higher-order sensitivity indices.This paper demonstrates that the Random-Sampling High Dimensional Model Representation (RS-HDMR) meta-modelling approach is able to compute efficiently sensitivity indices of the first, second and total orders for a complex, highly nonlinear model describing the long-term behaviour of a final repository for low- and intermediate-level radioactive waste, and that the results are consistent and plausible. The efficiency of the RS-HDMR approach in computing sensitivity indices of the first order is compared to that of two other methods: EASI and the State-Dependent-Parameter (SDP) meta-modelling approach.

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.

Accelerate global sensitivity analysis using artificial neural network algorithm: Case studies for combustion kinetic model

Global sensitivity and uncertainty analyses have attracted more and more attention in recent combustion kinetic studies. However, the high computational cost hinders their application in complex kinetic models. In order to accelerate the convergence speed, the artificial neural networks (ANN) methodology is applied into two widely used quantitative sensitivity analysis methods in the present work, i.e. the Sobol' sensitivity estimation and the random sampling high dimensional model representations (RS-HDMR). An ANN is constructed and trained using original model samples, which can then be used as a surrogate model to generate numerous samples for a global sensitivity analysis with Sobol' sensitivity estimation or RS-HDMR. It is shown that the ANN greatly reduces computational costs for estimating Sobol' sensitivity indices. The performances of the proposed ANN based HDMR method (ANN-HDMR) have been tested by a widely used analytical function (Sobol' g-function) and two practical models in combustion (master equation kinetic model and reaction kinetic model). The results show that the ANN-HDMR only needs a few tenths of original samples in the sensitivity analysis of master equation kinetic model and premixed H2/O2 ignition model. The ANN-HDMR is a kind of double-layer surrogate model which couples the advantage of ANN for fast convergence and RS-HDMR for direct sensitivity indices calculation, and thus it exhibits better performance in convergence and stability comparing with the commonly used RS-HDMR.

Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling

In this paper, the parameter selection capabilities of the group method of data handling (GMDH) as an inductive self-organizing modelling method are used to construct sparse random sampling high dimensional model representations (RS-HDMR), from which the Sobol’s first and second order global sensitivity indices can be derived. The proposed method is capable of dealing with high-dimensional problems without the prior use of a screening technique and can perform with a relatively limited number of function evaluations, even in the case of under-determined modelling problems. Four classical benchmark test functions are used for the evaluation of the proposed technique.

Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses

The precise inflammatory role of the cytokine interleukin (IL)-6 and its utility as a biomarker or therapeutic target have been the source of much debate, presumably due to the complex pro- and anti-inflammatory effects of this cytokine. We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamics of endotoxin (lipopolysaccharide; LPS)-induced acute inflammation and associated whole-animal damage/dysfunction (a proxy for the health of the organism), along with the inflammatory mediators tumor necrosis factor (TNF)-α, IL-6, IL-10, and nitric oxide (NO). The model was partially calibrated using data from endotoxemic C57Bl/6 mice. Herein, we investigated the sensitivity of the area under the damage curve (AUCD) to the 51 rate parameters of the ODE model for different levels of simulated LPS challenges using a global sensitivity approach called Random Sampling High Dimensional Model Representation (RS-HDMR). We explored sufficient parametric Monte Carlo samples to generate the variance-based Sobol’ global sensitivity indices, and found that inflammatory damage was highly sensitive to the parameters affecting the activity of IL-6 during the different stages of acute inflammation. The AUCIL6 showed a bimodal distribution, with the lower peak representing healthy response and the higher peak representing sustained inflammation. Damage was minimal at low AUCIL6, giving rise to a healthy response. In contrast, intermediate levels of AUCIL6 resulted in high damage, and this was due to the insufficiency of damage recovery driven by anti-inflammatory responses from IL-10 and the activation of positive feedback sustained by IL-6. At high AUCIL6, damage recovery was interestingly restored in some population of simulated animals due to the NO-mediated anti-inflammatory responses. These observations suggest that the host׳s health status during acute inflammation depends in a nonlinear fashion on the magnitude of the inflammatory stimulus, on the host׳s propensity to produce IL-6, and on NO-mediated downstream responses.

Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation

Global uncertainty and sensitivity analysis is used to study the propagation of uncertainties in fundamental theoretical parameters through to uncertainties in the predicted temperature and pressure dependent phenomenological rate coefficients. Predictions are obtained from ab initio transition state theory based master equation calculations. The fundamental parameters for these rate predictions include barrier heights, well depths, vibrational frequencies, collision frequency, and energy transfer parameters. A random sampling high-dimensional model representation (HDMR) approach is used to perform the global sensitivity analysis. This approach determines the predicted distributions of the phenomenological rate coefficients based on a quasi-random sample of the fundamental parameters within their uncertainty range. Sensitivity analysis then identifies the main parameters which contribute to variance in the predicted distributions. Here the approach is applied to a study of the oxidation of the propyl radical, employing the parameters derived in our recent theoretical study. We find rates at 3σ variances that typically differ from the most frequent values by factors of 4–6, with the uncertainties decreasing with increasing temperature. For the well skipping reactions there are more parameters that contribute significantly to the variance, the second-order sensitivities are greater, and the uncertainties increased with increasing pressure. For the other reactions, the uncertainties tend to decrease with increasing pressure.

Regularized random-sampling high dimensional model representation (RS-HDMR)

High Dimensional Model Representation (HDMR) is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input–output system behavior. HDMR is based on a hierarchy of component functions of increasing dimensions. The Random-Sampling High Dimensional Model Representation (RS-HDMR) is a practical approach to HDMR utilizing random sampling of the input variables. To reduce the sampling effort, the RS-HDMR component functions are approximated in terms of a suitable set of basis functions, for instance, orthonormal polynomials. Oscillation of the outcome from the resultant orthonormal polynomial expansion can occur producing interpolation error, especially on the input domain boundary, when the sample size is not large. To reduce this error, a regularization method is introduced. After regularization, the resultant RS-HDMR component functions are smoother and have better prediction accuracy, especially for small sample sizes (e.g., often few hundred). The ignition time of a homogeneous H2/air combustion system within the range of initial temperature, 1000 < T 0 < 1500 K, pressure, 0.1 < P < 100 atm and equivalence ratio of H2/O2, 0.2 < R < 10 is used for testing the regularized RS-HDMR.

A random-sampling high dimensional model representation neural network for building potential energy surfaces

We combine the high dimensional model representation (HDMR) idea of Rabitz and co-workers [J. Phys. Chem. 110, 2474 (2006)] with neural network (NN) fits to obtain an effective means of building multidimensional potentials. We verify that it is possible to determine an accurate many-dimensional potential by doing low dimensional fits. The final potential is a sum of terms each of which depends on a subset of the coordinates. This form facilitates quantum dynamics calculations. We use NNs to represent HDMR component functions that minimize error mode term by mode term. This NN procedure makes it possible to construct high-order component functions which in turn enable us to determine a good potential. It is shown that the number of available potential points determines the order of the HDMR which should be used.

Optimizing Genetic Circuits by Global Sensitivity Analysis

Artificial genetic circuits are becoming important tools for controlling cellular behavior and studying molecular biosystems. To genetically optimize the properties of complex circuits in a practically feasible fashion, it is necessary to identify the best genes and/or their regulatory components as mutation targets to avoid the mutation experiments being wasted on ineffective regions, but this goal is generally not achievable by current methods. The Random Sampling—High Dimensional Model Representation (RS-HDMR) algorithm is employed in this work as a global sensitivity analysis technique to estimate the sensitivities of the circuit properties with respect to the circuit model parameters, such as rate constants, without knowing the precise parameter values. The sensitivity information can then guide the selection of the optimal mutation targets and thereby reduce the laboratory effort. As a proof of principle, the in vivo effects of 16 pairwise mutations on the properties of a genetic inverter were compared against the RS-HDMR predictions, and the algorithm not only showed good consistency with laboratory results but also revealed useful information, such as different optimal mutation targets for optimizing different circuit properties, not available from previous experiments and modeling.

Simulating bioremediation of uranium-contaminated aquifers; uncertainty assessment of model parameters

Bioremediation of trace metals and radionuclides in groundwater may require the manipulation of redox conditions via the injection of a carbon source. For example, after nitrate has been reduced, soluble U(VI) can be reduced simultaneously with other electron acceptors such as Fe(III) or sulfate to U(IV), which may precipitate as a solid (uraninite). To simulate the numerous biogeochemical processes that will occur during the bioremediation of trace-metal-contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled mass balance equations, accounting for advection, hydrodynamic dispersion, and a kinetic formulation of the biological or chemical transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and trace metal contaminants of interest, uranium in this study. This set of equations is solved numerically, using a finite difference approximation. The redox conditions of the domain are characterized by estimating the pE, based on the concentration of the dominant terminal electron acceptor and its corresponding reduced species. This pE and the concentrations of relevant species are then used by a modified version of MINTEQA2, which calculates the speciation/sorption and precipitation/dissolution of the species of interest under equilibrium conditions. Kinetics of precipitation/dissolution processes are described as being proportional to the difference between the actual and calculated equilibrium concentration. A global uncertainty assessment, determined by Random Sampling High Dimensional Model Representation (RS-HDMR), was performed to attain a phenomenological understanding of the origins of output variability and to suggest input parameter refinements as well as to provide guidance for field experiments to improve the quality of the model predictions. By decomposing the model output variance into its different input contributions, RS-HDMR can identify the model inputs with the most influence on various model outputs, as well as their behavior pattern on the model output. Simulations are performed to illustrate the effect of biostimulation on the fate of uranium in a saturated aquifer, and to identify the key processes that need to be characterized with the highest accuracy prior to designing a uranium bioremediation scheme.