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

This work presents the random sampling - high dimensional model representation (RS-HDMR) algorithm for identifying complex bionetwork structures from multivariate data. RS-HDMR describes network interactions through a hierarchy of input-output (IO) functions of increasing dimensionality. Sensitivity analysis based on the calculated RS-HDMR component functions provides a statistically interpretable measure of network interaction strength, and can be used to efficiently infer network structure. Advantages of RS-HDMR include the ability to capture nonlinear and cooperative realtionships among network components, the ability to handle both continuous and discrete relationships, the ability to be used as a high-dimensional IO model for quantitative property prediction, and favorable scalability with respect to the number of variables. To demonstrate, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various perturbations. The resultant analysis identified the network structure comparable to that reported in the literature and to the results from a previous Bayesian network (BN) analysis. The IO model also revealed several nonlinear feedback and cooperative mechanisms that were unidentified through BN analysis.

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

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.

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.

Hybrid high dimensional model representation (HHDMR) on the partitioned data

Based on the high dimensional model representation (HDMR) and Monte Carlo simulation (MCS), this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models. The HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. Once the limit state function is defined by using the HDMR, the failure probability can be obtained by using the MCS without increasing computational efforts. 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 HDMR are both high in terms of series system and parallel system, the accuracy can be acceptable with respect to series system, and the accuracy can not be acceptable with respect to parallel system.

Any engineering structure under the action of various internal and external factors like changes in the material properties, inadequate design, faulty construction, deterioration due to malfunctioning are susceptible to damages. In the past, many methods have attempted to identify damage by solving an inverse problem, which inevitably needs an analytical model. However, often the construction of these analytical model requires considerable effort in building a mathematical framework with acceptable level of accuracy and reliability which makes these approaches less attractive. To circumvent this complexity, this work presents a computationally efficient approach in structural damage identification using high dimensional model representation.

Uncertainty propagation (UP) of the frequency response is essential for the robust design of viscoelastic damping structures. One challenge in solving this problem is enormous computation cost from the UP analysis. This paper aims to develop a novel computational effective method based on the combination of the adaptive sparse grid collocation (ASGC) method and the high dimensional model representation (HDMR) technique to evaluate the variability of the frequency response of viscoelastic damping structures. First, a well-validated layer-wise finite element method is employed to model the viscoelastic damping structures. The direct frequency response (DFR) method is utilized to calculate the response. Then, a modified adaptive strategy using expectation increments as the sampling indicator is proposed for cost-effective sparse grid construction. Lastly, high dimensional model representation (HDMR) technique is introduced to address the difficulty in moderate and high random dimensional situations. Two numerical examples are provided to assess the performances of the proposed method. Variations in constitutive parameters of viscoelastic material and thicknesses of the viscoelastic layer are considered. Numerical results show that, compared to the original high-dimensional ASGC method and Monte Carlo Simulation (MCS), the proposed method accurately predicts the variability of frequency responses and significantly improves the computational efficiency.

Affine transformational HDMR and linearised rational least squares approximation

The effects of parametric uncertainties in simulations of a reactive plume using a Lagrangian stochastic model

This paper presents recently developed Enhanced Multivariance Product Representation (EMPR) method for multivariate functions. EMPR disintegrates a multivariate function to components which are respectively constant, univariate, bivariate and so on in ascending multivariance. Although the EMPR method has the same philosophy with the High Dimensional Model Representation (HDMR) method, it has been proposed to get better quality than HDMR’s with the help of the support functions. For this purpose, we investigate the EMPR truncation qualities with respect to the selection of the support functions. The obtained results and a number of numerical implementations to show the efficiency of the method are also given in this paper.

A comparative assessment of efficient uncertainty analysis techniques for environmental fate and transport models: application to the FACT model

High Dimensional Model Representation (HDMR) method does not have the random data partitioning capability because of its nature. This paper focuses on how we can bring the random data partitioning feature to the HDMR method by virtue of the fluctuation free approximation method for the multivariate interpolation problems. The main aim of this work is to construct the universal fluctuation free matrix and to determine the best eigenvalues and the corresponding eigenvectors needed in our new method for partitioning the given multivariate random data through the HDMR method.

This work focuses on the development of a multivariate function approximating method by using quartic Transformational High Dimensional Model Representation (THDMR). The method uses the target function’s image under a quartic transformation for High Dimensional Model Representation(HDMR) instead of the function’s itself.

Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions