Random Sampling-High Dimensional Model Representation 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.

A new Bayesian probabilistic integration framework for hybrid uncertainty propagation

Efficient propagation of uncertainty is one of the most critical tasks for uncertainty quantification and reliable design in the presence of multi-source uncertainties. This work presents a new methodology framework, termed as “mixed imprecise probabilistic integration”, for efficient propagation of the uncertainties characterized by non-probabilistic models, imprecise probability models and precise probability models. In this paper, the mixed-high dimensional model representation combining the cut-high dimensional model representation and random sampling-high dimensional model representation is firstly proposed, which conserves all the advantages of these two methods. Secondly, the proposed method is realized by using mixed-high dimensional model representation and Bayesian inference. The estimations and the posterior variances of the proposed method are analytically derived of high accuracy. With the proposed method, all the three kinds of uncertainty models can be efficiently propagated with one set of function evaluations. The effectiveness of the proposed methods is demonstrated by three engineering examples.

Global sensitivity analysis of riveting parameters based on a random sampling-high dimensional model representation

The riveting process involves numerous parameters and complex problems, such as contact phenomena and material nonlinearity; therefore, it is challenging to accurately control the deformation of riveted parts by adjusting the riveting parameters. Therefore, this paper proposes a global sensitivity analysis method to determine the effects of riveting parameters on the maximum deformation of aeronautical thin-wall structures (ATWS). Considering the correlation among variables, the riveting parameters are used as input variables and the maximum deformations of ATWS are used as the output response to establish a high-precision second-order random sampling-high dimensional model representation response function. The structure and correlative sensitivity analysis method is then used to analyze the response function, and an importance ranking of the input variables is obtained to provide guidance for designs that reduce the riveting deformation of thin-walled plates.

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.

Applicability of high dimensional model representation correlations for ignition delay times of n-heptane/air mixtures

It is difficult to predict the ignition delay times for fuels with the two-stage ignition tendency because of the existence of the nonlinear negative temperature coefficient (NTC) phenomenon at low temperature regimes. In this paper, the random sampling-high dimensional model representation (RS-HDMR) methods were employed to predict the ignition delay times of n-heptane/air mixtures, which exhibits the NTC phenomenon, over a range of initial conditions. A detailed n-heptane chemical mechanism was used to calculate the fuel ignition delay times in the adiabatic constant-pressure system, and two HDMR correlations, the global correlation and the stepwise correlations, were then constructed. Besides, the ignition delay times predicted by both types of correlations were validated against those calculated using the detailed chemical mechanism. The results showed that both correlations had a satisfactory prediction accuracy in general for the ignition delay times of the n-heptane/air mixtures and the stepwise correlations exhibited a better performance than the global correlation in each subdomain. Therefore, it is concluded that HDMR correlations are capable of predicting the ignition delay times for fuels with two-stage ignition behaviors at low-to-intermediate temperature conditions.

Global sensitivity analysis for fiber reinforced composite fiber path based on D-MORPH-HDMR algorithm

This study presents a quantitative sensitivity analysis for the assessment of fiber reinforced composites (FRCs). Global sensitivity analysis (GSA) approach is based on the variance based method incorporating Random Sampling-High Dimensional Model Representation (RS-HDMR) expansion in which component functions are determined by diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression. The advantage of the D-MORPH regression lies in its capability to solve linear algebraic equations with a limited number of sample points. The main purpose is to investigate the influence of fiber path, regarded as the design variable, on the formability and structural performance of FRCs. Wherein, spring-back and load-carrying capacity are two meaningful problems to be addressed. Two typical FRCs are included that an L-shaped part with straight fiber path using autoclave manufacturing process and a variable stiffness composite cylindrical shell under pure bending. The work not only focuses on the ranking of design variables but also hopes to find out their interactions represented by the second order global sensitivity indexes. After being tested by three typical numerical functions, the GSA algorithm highlights that spring-back of FRC using autoclave manufacturing process is most sensitive to fiber orientation angles on plies close to the tool. And buckling performance of the VS cylinder is dominated by fiber orientation angles at compression/tension regions.

Structural damage identification: A random sampling-high dimensional model representation approach

Structural damage identification and quantification of damage using non-destructive methods are important aspects for any civil, mechanical and aerospace engineering structures. In this study, a novel damage identification algorithm has been developed using random sampling-high dimensional model representation approach. A global sensitivity analysis based on random sampling-high dimensional model representation is adopted for important parameter screening purpose. Three different structures (spring mass damper system, simply supported beam and fibre-reinforced polymer composite bridge deck) have been used for various single and multiple damage conditions to validate the proposed algorithm. The performance of this method is found to be quite satisfactory in the realm of damage detection in structures. The random sampling-high dimensional model representation-based approach for meta-model formation is particularly useful in damage identification as it works well when large numbers of input parameters are involved. In this study, two different optimization methods have been used and their relative capability to identify damage has been discussed. Performance of this damage identification algorithm under the influence of noise has also been addressed in this article.

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.

High Dimensional Model Representation With Principal Component Analysis

In engineering design, spending excessive amount of time on physical experiments or expensive simulations makes the design costly and lengthy. This issue exacerbates when the design problem has a large number of inputs, or of high dimension. High dimensional model representation (HDMR) is one powerful method in approximating high dimensional, expensive, black-box (HEB) problems. One existing HDMR implementation, random sampling HDMR (RS-HDMR), can build an HDMR model from random sample points with a linear combination of basis functions. The most critical issue in RS-HDMR is that calculating the coefficients for the basis functions includes integrals that are approximated by Monte Carlo summations, which are error prone with limited samples and especially with nonuniform sampling. In this paper, a new approach based on principal component analysis (PCA), called PCA-HDMR, is proposed for finding the coefficients that provide the best linear combination of the bases with minimum error and without using any integral. Several benchmark problems of different dimensionalities and one engineering problem are modeled using the method and the results are compared with RS-HDMR results. In all problems with both uniform and nonuniform sampling, PCA-HDMR built more accurate models than RS-HDMR for a given set of sample points.

Metamodelling with independent and dependent inputs

In the cases of computationally expensive models the metamodelling technique which maps inputs and outputs is a very useful and practical way of making computations tractable. A number of new techniques which improve the efficiency of the Random Sampling-High dimensional model representation (RS-HDMR) for models with independent and dependent input variables are presented. Two different metamodelling methods for models with dependent input variables are compared. Both techniques are based on a Quasi Monte Carlo variant of RS-HDMR. The first technique makes use of transformation of the dependent input vector into a Gaussian independent random vector and then applies the decomposition of the model using a tensored Hermite polynomial basis. The second approach uses a direct decomposition of the model function into a basis which consists of the marginal distributions of input components and their joint distribution. For both methods the copula formalism is used. Numerical tests prove that the developed methods are robust and efficient.

Global Sensitivity Analysis of the Regional Atmospheric Chemical Mechanism: An Application of Random Sampling-High Dimensional Model Representation to Urban Oxidation Chemistry

Chemical mechanisms play a crucial part for the air quality modeling and pollution control decision-making. Parameters in a chemical mechanism have uncertainties, leading to the uncertainties of model predictions. A recently developed global sensitivity analysis (SA) method based on Random Sampling-High Dimensional Model Representation (RS-HDMR) was applied to the Regional Atmospheric Chemical Mechanism (RACM) within a zero-dimensional photochemical model to highlight the main uncertainty sources of atmospheric hydroxyl (OH) and hydroperoxyl (HO(2)) radicals. This global SA approach can be applied as a routine in zero-dimensional photochemical modeling to comprehensively assess model uncertainty and sensitivity under different conditions. It also highlights the parameters to which the model is most sensitive during periods when the model/measurement OH and HO(2) discrepancies are greatest. Uncertainties in 584 model parameters were assigned for measured constituents used to constrain the model, for photolysis and kinetic rate coefficients, and for product yields of the reactions. With simulations performed for the hourly field data of two typical days, modeled and measured OH and HO(2) generally agree better for polluted conditions than for cleaner conditions, except during morning rush hour. Sensitivity analysis shows that the modeled OH and HO(2) depend most critically on the reactions of xylenes and isoprene with OH, NO(2) with OH, NO with HO(2), and internal alkenes with O(3) and suggests that model/measurement discrepancies in OH and HO(2) would benefit from a closer examination of these reactions.

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.

Identifying Biological Network Structure, Predicting Network Behavior, and Classifying Network State With High Dimensional Model Representation (HDMR)

This work presents an adapted Random Sampling - High Dimensional Model Representation (RS-HDMR) algorithm for synergistically addressing three key problems in network biology: (1) identifying the structure of biological networks from multivariate data, (2) predicting network response under previously unsampled conditions, and (3) inferring experimental perturbations based on the observed network state. RS-HDMR is a multivariate regression method that decomposes network interactions into a hierarchy of non-linear component functions. Sensitivity analysis based on these functions provides a clear physical and statistical interpretation of the underlying network structure. The advantages of RS-HDMR include efficient extraction of nonlinear and cooperative network relationships without resorting to discretization, prediction of network behavior without mechanistic modeling, robustness to data noise, and favorable scalability of the sampling requirement with respect to network size. As a proof-of-principle study, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various experimental perturbations. A comparison to network structure identified in the literature and through other inference methods, including Bayesian and mutual-information based algorithms, suggests that RS-HDMR can successfully reveal a network structure with a low false positive rate while still capturing non-linear and cooperative interactions. RS-HDMR identified several higher-order network interactions that correspond to known feedback regulations among multiple network species and that were unidentified by other network inference methods. Furthermore, RS-HDMR has a better ability to predict network response under unsampled conditions in this application than the best statistical inference algorithm presented in the recent DREAM3 signaling-prediction competition. RS-HDMR can discern and predict differences in network state that arise from sources ranging from intrinsic cell-cell variability to altered experimental conditions, such as when drug perturbations are introduced. This ability ultimately allows RS-HDMR to accurately classify the experimental conditions of a given sample based on its observed network state.

An efficient algorithm to accelerate the discovery of complex material formulations

The identification of complex multicomponent material formulations that possess specific optimal properties is a challenging task in materials discovery. The high dimensional composition space needs to be adequately sampled and the properties measured with the goal of efficiently identifying effective formulations. This task must also take into account mass fraction and possibly other constraints placed on the material components. Either combinatorial or noncombinatorial sampling of the composition space may be employed in practice. This paper introduces random sampling-high dimensional model representation (RS-HDMR) as an algorithmic tool to facilitate these nonlinear multivariate problems. RS-HDMR serves as a means to accurately interpolate over sampled materials, and simulations of the technique show that it can be very efficient. A variety of simulations is carried out modeling multicomponent-->property relationships, and the results show that the number of sampled materials to attain a given level of accuracy for a predicted property does not significantly depend on the number of components in the formulation. Although RS-HDMR best operates in the laboratory by guided iterative rounds of random sampling of the composition space along with property observation, the technique was tested successfully on two existing databases of a seven component phosphor material and a four component deNO(x) catalyst for reduction of NO with C(3)H(6).

Global Sensitivity Analysis for Systems with Independent and/or Correlated Inputs

The objective of a global sensitivity analysis is to rank the importance of the system inputs considering their uncertainty and the influence they have upon the uncertainty of the system output, typically over a large region of input space. This paper introduces a new unified framework of global sensitivity analysis for systems whose input probability distributions are independent and/or correlated. The new treatment is based on covariance decomposition of the unconditional variance of the output. The treatment can be applied to mathematical models, as well as to measured laboratory and field data. When the input probability distribution is correlated, three sensitivity indices give a full description, respectively, of the total, structural (reflecting the system structure) and correlative (reflecting the correlated input probability distribution) contributions for an input or a subset of inputs. The magnitudes of all three indices need to be considered in order to quantitatively determine the relative importance of the inputs acting either independently or collectively. For independent inputs, these indices reduce to a single index consistent with previous variance-based methods. The estimation of the sensitivity indices is based on a meta-modeling approach, specifically on the random sampling-high dimensional model representation (RS-HDMR). This approach is especially useful for the treatment of laboratory and field data where the input sampling is often uncontrolled.

Dissecting Enzyme Regulation by Multiple Allosteric Effectors: Nucleotide Regulation of Aspartate Transcarbamoylase

The enzyme aspartate transcarbamoylase (ATCase, EC 2.1.3.2 of Escherichia coli), which catalyzes the committed step of pyrimidine biosynthesis, is allosterically regulated by all four ribonucleoside triphosphates (NTPs) in a nonlinear manner. Here, we dissect this regulation using the recently developed approach of random sampling-high-dimensional model representation (RS-HDMR). ATCase activity was measured in vitro at 300 random NTP concentration combinations, each involving (consistent with in vivo conditions) all four NTPs being present. These data were then used to derive a RS-HDMR model of ATCase activity over the full four-dimensional NTP space. The model accounted for 90% of the variance in the experimental data. Its main elements were positive ATCase regulation by ATP and negative by CTP, with the negative effects of CTP dominating the positive ones of ATP when both regulators were abundant (i.e., a negative cooperative effect of ATP x CTP). Strong sensitivity to both ATP and CTP concentrations occurred in their physiological concentration ranges. UTP had only a slight effect, and GTP had almost none. These findings support a predominant role of CTP and ATP in ATCase regulation. The general approach provides a new paradigm for dissecting multifactorial regulation of biological molecules and processes.

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.