Multi-block Model Research Articles

On the Global Linear Convergence of the ADMM with MultiBlock Variables

The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems. In particular, the ADMM can solve convex programs that minimize the sum of $N$ convex functions whose variables are linked by some linear constraints. While the convergence of the ADMM for $N=2$ was well established in the literature, it remained an open problem for a long time whether the ADMM for $N \ge 3$ is still convergent. Recently, it was shown in [Chen et al., Math. Program. (2014), DOI 10.1007/s10107-014-0826-5.] that without additional conditions the ADMM for $N\ge 3$ generally fails to converge. In this paper, we show that under some easily verifiable and reasonable conditions the global linear convergence of the ADMM when $N\geq 3$ can still be ensured, which is important since the ADMM is a popular method for solving large-scale multiblock optimization models and is known to perform very well in practice even when $N\ge 3$. Our study aims to offer an explanation for this phenomenon.

Simplified multi-block constitutive model predicting earthquake-induced landslide triggering and displacement along slip surfaces of saturated sand

Slopes consisting of saturated sand have recently moved down-slope tens or hundreds of meters under the action of earthquakes. This paper presents a simplified but accurate method predicting the triggering and displacement of such landslides. For this purpose, a simplified constitutive model simulating soil response of saturated sands along slip surfaces is proposed and validated. Then, this constitutive model is coupled with the multi-block sliding system model to predict the triggering and displacement of such slides. The multi-block model considers a general mass sliding on a trajectory which consists of n linear segments. The steps needed to apply this method are described in detail. The method was applied successfully to predict the triggering, the motion and the final configuration of the well-documented (a) Higashi Takezawa, (b) Donghekou and (c) Nikawa earthquake-induced slides.

Quantitative Analysis of Lavender (<i>Lavandula angustifolia</i>) Essential Oil Using Multiblock Data from Infrared Spectroscopy

Near-infrared and mid-infrared spectroscopies were currently used to analyze natural compounds. During the last ten years various multiblocks methods were developed such as Concatenated PLS, Hierarchical-PLS (H-PLS), and MultiBlock-PLS (MB-PLS). These three algorithms were used to analyze 55 lavender (Lavandula angustifolia) essential oil samples. The results obtained were compared to the ones obtained respectively in NIR and MIR ranges. The accuracies of the models depend on the spectroscopic technique, pretreatment and the PLS methods. The results showed that the choice of the factor numbers used to build the multiblock models was the most important parameter for the H-PLS and MB-PLS methods.

Progressive multi-block modelling for enhanced fault isolation in batch processes

A multi-block progressive modelling approach is proposed for enhanced fault isolation in batch processes. The unfolding of batch data typically leads to matrices with a large number of columns and this complicates contribution analysis. In order to rapidly focus fault isolation in batch processes, it would be desirable to employ multi-block modelling techniques. Multi-block model such as consensus principal component analysis (CPCA) can produce multiple monitoring charts for sub-blocks and block loadings and block scores can be obtained which can represent unique behaviour of each sub-block. CPCA model uses super score which is the same as score from normal principal component analysis (PCA) model and it does not produce enhanced monitoring performance. Multi-block PCA (MBPCA) model using block score for model calculation can represent sub-blocks’ character but block scores are obtained from super loading so it may not be the best way to describe sub-blocks. A new MBPCA model is proposed for better expression of each sub-block. Through progressive modelling and contribution analysis, variables related to or affected by the fault, as well as the associated time information, are gradually identified. This enables a fault propagation path being established. The proposed method is applied to a benchmark simulated penicillin production process, PenSim.

Global, local and unique decompositions in OnPLS for multiblock data analysis

OnPLS is an extension of O2PLS that decomposes a set of matrices, in either multiblock or path model analysis, such that each matrix consists of two parts: a globally joint part containing variation shared with all other connected matrices, and a part that contains locally joint and unique variation, i.e. variation that is shared with some, but not all, other connected matrices or that is unique in a single matrix.A further extension of OnPLS suggested here decomposes the part that is not globally joint into locally joint and unique parts. To achieve this it uses the OnPLS method to first find and extract a globally joint model, and then applies OnPLS recursively to subsets of matrices that contain the locally joint and unique variation remaining after the globally joint variation has been extracted. This results in a set of locally joint models. The variation that is left after the globally joint and locally joint variation has been extracted is (by construction) not related to the other matrices and thus represents the strictly unique variation in each matrix. The method's utility is demonstrated by its application to both a simulated data set and a real data set acquired from metabolomic, proteomic and transcriptomic profiling of three genotypes of hybrid aspen. The results show that OnPLS can successfully decompose each matrix into global, local and unique models, resulting in lower numbers of globally joint components and higher intercorrelations of scores. OnPLS also increases the interpretability of models of connected matrices, because of the locally joint and unique models it generates.

Multiblock modeling for complex preference study. Application to European preferences for smoked salmon

The aim of the paper is to propose an alternative method to external preference mapping for the case of complex data where explanatory variables are organized in meaningful blocks. We propose an innovative method in the multiblock modeling framework, called multiblock Redundancy Analysis. The interest and relevance of this method is illustrated on the basis of a European consumer preference study for cold-smoked salmon. The study aims at explaining six homogeneous clusters of preference with explanatory parameters organized in five thematic blocks related to physico-chemical measurements, microbiological characterization, appearance attributes, odor/flavor characterization and texture descriptors. Overall indexes and graphical displays associated with different interpretation levels are proposed to sort the key drivers of preference by order of priority at the variables and at the block level. On the basis of these data, multiblock Redundancy Analysis is also compared to standard preference mapping in terms of model quality; the best model is here associated with the multiblock method.

Multi-block lattice Boltzmann simulations of solute transport in shallow water flows

We report a two-dimensional multi-block lattice Boltzmann model for solute transport in shallow water flows, which is developed based on the advection–diffusion equation for mass transport and the shallow water equations for the flows. A weighting factor is included in the centered scheme for improved accuracy. The model is firstly verified by simulating three benchmark tests: wind-driven circulation in a dish-shaped lake, jet-forced flow in a circular basin, and flow formed by two parallel streams containing different uniform concentrations at the same constant velocity; and then it is applied to a practical wind-induced flow, Baiyangdian Lake, which is characterized by irregular geometries and complex bathymetries. The numerical results have shown that the model is able to produce accurate and detailed results for both water flows and solute transport, which is attractive, especially for flows in narrow zones of practical terrains and certain areas with largely varying pollutant concentrations.

Object-oriented modeling for three-dimensional multi-block systems

This paper presents an object-oriented computer model for three-dimensional multi-block systems based on the object-oriented programming (OOP) technique. The intricate structures of rock systems are deciphered by implementing an object-oriented analysis (OOA), and a universal class library is developed using an object-oriented design (OOD). The geometries of a multi-block system are created by cutting a computational domain into element-blocks and then combining the element-blocks into complex-blocks (convex or concave). The established multi-block system model would be available for various discontinuum-based methods. A computer program, BLKLAB, is developed based on the proposed method, and a case study is performed on a large-scale, underground, water-tight oil depot.

Numerical investigation of centerline curvature effects on a compact S-shaped intake

Taking into account stealth, structure and maintenance, ultra-compact S-shaped intake has been widely used in modern vehicles. In this paper a series of steady numerical simulation were carried out to investigate the complex flow mechanism in s-shaped intake, particular attention was given to examining the effect of centerline curvature on the performance and flowfield of an ultra-compact S-shaped intake. In order to validate the multi-block model, the computational results for Royal Aircraft Establishment intake 2129-M2129 which had modest centerline curvature distribution were corrected with available experimental test data. The numerical simulation results agreed fairly well with the experimental data, and the computational method was then used to investigate the effects of different centerline curvature distributions on performance and flow field in compact S-shaped intake. Detailed analyses of the flow visualization had exposed the different flow topologies between the cases with different centerline curvature. It was found that different centerline curvature distributions changed the initial location and the size of separation bubble, as well as the strength of two counter-rotating vortices at the entrance of engine.

A sensitivity analysis of low salinity habitats simulated by a hydrodynamic model in the Manatee River estuary in Florida, USA

This paper presents a sensitivity study of simulated availability of low salinity habitats by a hydrodynamic model for the Manatee River estuary located in the southwest portion of the Florida peninsula. The purpose of the modeling study was to establish a regulatory minimum freshwater flow rate required to prevent the estuarine ecosystem from significant harm. The model used in the study was a multi-block model that dynamically couples a three-dimensional (3D) hydrodynamic model with a laterally averaged (2DV) hydrodynamic model. The model was calibrated and verified against measured real-time data of surface elevation and salinity at five stations during March 2005–July 2006. The calibrated model was then used to conduct a series of scenario runs to investigate effects of the flow reduction on salinity distributions in the Manatee River estuary. Based on simulated salinity distribution in the estuary, water volumes, bottom areas and shoreline lengths for salinity less than certain predefined values were calculated and analyzed to help establish the minimum freshwater flow rate for the estuarine system.The sensitivity analysis conducted during the modeling study for the Manatee River estuary examined effects of the bottom roughness, ambient vertical eddy viscosity/diffusivity, horizontal eddy viscosity/diffusivity, and ungauged flow on the model results and identified the relative importance of these model parameters (input data) to the outcome of the availability of low salinity habitats. It is found that the ambient vertical eddy viscosity/diffusivity is the most influential factor controlling the model outcome, while the horizontal eddy viscosity/diffusivity is the least influential one.

Dynamic Decision and Data-Driven Strategies for the Optimal Management of Subsurface Geo-Systems

Effective geo-system management involves understanding of the interplay between surface entities (e.g., locations of injection and production wells in an oil reservoir) and appropriately effecting subsurface characteristics. This in turn requires efficient integration of complex numerical models of the environment, optimization procedures, and decision making processes. The dynamic, data-driven application systems (DDDAS) paradigm offers a promising framework to address this requirement. To achieve this goal, we have developed advanced multi-physics, multi-scale, and multi-block numerical models and autonomic systems software for dynamic, data-driven applications systems. This work has enabled a new generation of data-driven, interactive and dynamically adaptive strategies for subsurface characterization and management. These strategies have been applied to different aspects of subsurface management in strategically important application areas, including simulation-based optimization for the optimal oil well placement and the data-driven management of the Ruby Gulch Waste Repository. This paper summarizes the key outcomes and achievements of our work, as well as reports ongoing and future activities focused on uncertainty estimation and characterization.

Modeling and Optimization of a Tablet Manufacturing Line

This paper investigates an approach to modeling and optimizing an industrial tablet manufacturing line for different API and excipient formulations. Multi-block partial lease square (PLS) models are built from historical data on a given class of drug products. The data blocks consisted of data on the mass fractions of API and 11 excipients used in the different formulations, the roller compaction process variables, the tablet press settings and the measured final product quality attributes (tablet weight, hardness, and disintegration time). More than 400 runs are used in the modeling. The multi-block PLS models are first used to show which process blocks and which variables in each of the process blocks are most influential on the product quality variables. An optimization is then performed in the latent variable space of the PLS model to find the optimal combination of settings to use for the critical to quality roller compaction and tablet press variables in order to achieve the desired final tablet properties for a specified drug formulation. This optimization can be used to set up the tableting line prior to running a new formulation or can be used in an on-line mode for making small corrections to the operation of the tablet presses in response to small variations in formulations, raw material properties, and roller compaction operation.

Multiblock redundancy analysis: interpretation tools and application in epidemiology

AbstractFor the purpose of exploring and modeling the relationships between a dataset Y and several datasets () measured on the same individuals, multiblock Partial Least Squares is a regression technique which is widely used, particularly in process monitoring, chemometrics and sensometrics. In the same vein, a new multiblock method, called multiblock Redundancy Analysis, is proposed. It is introduced by maximizing a criterion that reflects the objectives to be addressed. The solution of this maximization problem is directly derived from the eigenanalysis of a matrix. In addition, this method is related to other multiblock methods. Multiblock modeling methods provide to the user a large spectrum of interpretation indices for the investigation of the relationships among variables and among datasets. They are related to the criterion to maximize and therefore directly derived from the maximization problem under consideration. The interest of multiblock Redundancy Analysis and the associated interpretation tools are illustrated using a dataset in the field of veterinary epidemiology. Copyright © 2011 John Wiley & Sons, Ltd.

Multiblock modelling to assess the overall risk factors for a composite outcome

Research in epidemiology may be concerned with assessing risk factors for complex health issues described by several variables. Moreover, epidemiological data are usually organized in several blocks of variables, consisting of a block of variables to be explained and a large number of explanatory variables organized in meaningful blocks. Usual statistical procedures such as generalized linear models do not allow the explanation of a multivariate outcome, such as a complex disease described by several variables, with a single model. Moreover, it is not easy to take account of the organization of explanatory variables into blocks. Here we propose an innovative method in the multiblock modelling framework, called multiblock redundancy analysis, which is designed to handle most specificities of complex epidemiological data. Overall indices and graphical displays associated with different interpretation levels are proposed. The interest and relevance of multiblock redundancy analysis is illustrated using a dataset pertaining to veterinary epidemiology.

The Impact of Debt Management Policies on Borrowing Costs Incurred by U.S. State Governments

This study empirically examines the impact of debt management policies on borrowing costs incurred by U.S. state governments when issuing debt in the municipal bond market. Based on positive political theory and the benefit principle of taxation, it is proposed that states that adhere to best practice debt management policies transmit signals to the credit ratings, investment community and taxpayers that the government should meet its obligations in a timely manner, resulting in lower debt costs. As a result of a multi-block multivariate regression model the implication of adhering to debt policies aimed at promoting transparency results in a borrowing cost savings in terms of true interest cost (TIC) of close to $8,000 for every $1,000,000 of debt issued (-.769, p<.10). However a comprehensive debt policy is not a significant indicator of borrowing costs. These results suggest a product of a pull push process between the economic forces of the bond market on one hand and politics on the other, pulling the administrative function toward efficiency in the former and democratic values of responsiveness and transparency in the latter. The problem lies in policies that respond to the bond market but virtually exclude any other community interest in policy making. It is recommended that openness in government and allowing taxpayers to understand government services are essential goals in ensuring responsible citizen oversight and providing taxpayers the opportunity to be less likely to propose restrictive initiatives or force dramatic political or management changes through the electoral process or bond referenda.

Correction for Geometry Changes during Motion of Sliding-Block Seismic Displacement

The sliding-block model is often used for the prediction of permanent coseismic displacements of natural slopes and earth structures. This model assumes motion in an inclined plane but does not consider the decrease in inclination of the sliding soil mass as a result of its downward motion, which is the usual condition in the field. The paper studies the above effect and proposes an empirical equation correcting the predictions of the sliding-block model. The investigation is performed by using a recently developed multiblock model. The equation correcting the predictions of the sliding-block model depends on the slip length, the difference in inclinations of the upper and lower part of the slip surface, the seismic displacement predicted by the sliding-block model and the maximum value of the applied horizontal acceleration.

Multiblock-Based Qualitative and Quantitative Spectral Calibration Analysis

In this article, an improved spectral calibration and statistical analysis approach is proposed. Having realized the multiplicity of underlying spectral characteristics and their different effects on the quality of interpretation and prediction, the major task lies in how to qualify and quantify the descriptor−quality relationship more meaningfully over different wavelength subspaces. The underlying spectral information can be explored more comprehensively by a spectral subspace separation and multiblock modeling strategy. Unlike the specific purpose of quality predictions over different spectral subspaces, systematic information in both descriptor and quality spaces is decomposed into different parts under the control of different between-set relationships. Closely related variations and irrelevant ones are discriminated and evaluated separately, where, in particular, the orthogonal variations, as important systematic information, are quantified in specific model parameters, even though they are not predictive. In this way, the approach well tracks the wavelength-varying underlying characteristics, takes full advantage of underlying variations in both X and Y spaces, and allows for a more meaningful interpretation of the between-set relationship. This article theoretically and experimentally illustrates the efficiency of the proposed method in qualitative and quantitative spectral calibration analysis.

Fundamentals of migrating multi-block lattice Boltzmann model for immiscible mixtures in 2D geometries

This paper proposes an extension scheme for the application of the single phase multi-block lattice Boltzmann method (LBM) to the multiphase Gunstensen model, in which the grid is refined in a specific part of the domain where a fluid–fluid interface evolves, and the refined grid is free to migrate with the suspended phase in the flow direction. The method is applicable to single and multiphase flows, and it was demonstrated by simulating a benchmark single phase flow around a 2D asymmetrically placed cylinder in a channel and for investigating the shear lift of 2D neutrally buoyant drop in a parabolic flow.

Migrating multi-block lattice Boltzmann model for immiscible mixtures: 3D algorithm development and validation

The lattice Boltzmann method (LBM) has emerged as a powerful numerical fluid solver especially in the areas of multi-component and multi-phase mixtures. However the LBM uses the particle velocity for the determination of the model time step required by the Courant–Friedrichs–Lewy (CFL) stability condition. This degrades the LBM efficiency, when compared with standard CFD solvers which use instead the macroscopic velocity for the CFL requirements. This paper discusses the development and validation of a 3D migrating multi-block model aiming at the acceleration of the LBM solution. The proposed algorithm is especially applicable to the Gunstensen multi-component model, in which a fine grid block engulfs the fluid–fluid interface and migrates with it. This increases the efficiency of the LBM since less iteration steps are required in areas of marginal interest, and it enables a better interface resolution because the fluid interface is always covered with finer grid. The method was demonstrated by simulating the case of a 3D rising bubble in infinite medium, in which the model results for the bubble terminal velocity were in good agreement with a semi-analytical solution, and the produced shapes fitted very well an experimental shape regime map.

Assessment of adaptive focused acoustics versus manual vortex/freeze-thaw for intracellular metabolite extraction from Streptomyces lividans producing recombinant proteins using GC-MS and multi-block principal component analysis

We compared the gas chromatography-mass spectrometry (GC-MS) metabolite profiles of mouse tumour necrosis factor alpha (mTNF-alpha) secreting Streptomyces lividans TK24 to the non-secreting wild type and the wild type harbouring the empty pIJ486 plasmid by multi-block principal component analysis (PCA). The multi-block PCA model successfully identified peaks that were statistically different between the protein secreting and non-secreting strains, and at the same time also uncovered the efficiency of intracellular metabolite extraction by an ultrasonic adaptive focused acoustics (AFA) technique compared to a manual vortex/freeze-thaw method. Fifty-one metabolites were significantly different between the three biological strains and 17 of these were abundant in the mTNF-alpha secreting strain compared to the non-secreting strains. No significant differences in the number of detected metabolite peaks were observed between the two extraction techniques. However, from the loadings of the multi-block PCA model, as well as univariate statistical analysis, we observed that the relative peak response ratios to the internal standard of 10 metabolites were higher for the AFA extraction, suggesting a more efficient recovery of these metabolites than achieved with the manual vortex/freeze thaw method.