Underdetermined Model Research Articles

Using calibrated minimum input models to predict retrofit performance on residential dwellings

Accurate energy models for existing buildings depend on the appropriate calibration of a large number of unknown parameters against detailed monitoring data. This process typically requires significant computational effort and often produces an underdetermined model. Simplifying the model by reducing unknown parameters can alleviate these challenges. This study assesses whether a previously introduced minimum input method, which uses a subset of significant parameters for simplified calibration, can predict post-retrofit performance. The paper compares the predictive power of this new method with conventional calibration, using post-retrofit monitored data from three social housing dwellings. Results indicate that minimum input models achieve significant improvements in retrofit prediction from uncalibrated models and can outperform conventionally calibrated models. On average, minimum input models reduced CVRMSE by 5.6% from baseline, slightly less than the 6.3% improvement from full calibration. Our results support simplified calibration as a viable alternative for predicting thermal performance from residential retrofits.

Quantum Particle Swarm Optimization Extraction Algorithm Based on Quantum Chaos Encryption

Considering the highly complex structure of quantum chaos and the nonstationary characteristics of speech signals, this paper proposes a quantum chaotic encryption and quantum particle swarm extraction method based on an underdetermined model. The proposed method first uses quantum chaos to encrypt the speech signal and then uses the local mean decomposition (LMD) method to construct a virtual receiving array and convert the underdetermined model to a positive definite model. Finally, the signal is extracted using the Levi flight strategy based on kurtosis and the quantum particle swarm optimization optimized by the greedy algorithm (KLG-QPSO). The bit error rate and similarity coefficient of the voice signal are extracted by testing the source voice signal SA1, SA2, and SI943 under different SNR, and the similarity coefficient, uncertainty, and disorder of the observed signal and the source voice signal SA1, SA2, and SI943 verify the effectiveness of the proposed speech signal extraction method and the security of quantum chaos used in speech signal encryption.

Radioactive Depth Marker Emplacement and Survey for Early Subsurface Geomechanical Model Calibration: Learnings from a Successful Ultra-HPHT Deployment

Summary Ultra-high-pressure high-temperature (uHPHT) reservoirs undergo extreme pressure depletion during their production life cycle. This results in significant reservoir compaction and consequent overburden subsidence with major consequences for wellbore mechanical integrity, safety, and field economics. However, the use of underdetermined geomechanical models to accurately predict compaction-induced stress/strain changes on wellbores and its consequences during production time results in significant residual uncertainty. One method of measuring compaction-induced stress/strain changes in wellbore is by the emplacement and measurement of radioactive markers. Although it is long established in normal pressure reservoirs, it is rare in uHPHT projects. The Culzean uHPHT gas-condensate field is located in the UK Central North Sea. To constrain geomechanical model compaction uncertainty, radioactive markers were deployed. The objective was to accurately acquire preproduction baseline measurements and subsequent changes through periodic measurements during production life. These accurate wellbore measurements would then be compared with the geomechanical model to help calibrate predicted to actual compaction. By doing so, the objective is to enable better informed decisions regarding well and field management. The Culzean uHPHT radioactive marker project comprised a planning phase and a preproduction safe deployment including a baseline survey phase. Subsequent repeat measurements are planned during field production life. The emplacement and surveying of the subsurface radioactive markers for compaction monitoring in uHPHT reservoirs is a high value but nontrivial operation. In addition, much knowledge and experience of the methodology has been lost. This paper contributes to published literature by describing the successful emplacement and monitoring of subsurface radioactive markers on Culzean and aims to capture learnings and knowledge for future workers. Early detailed planning coupled with extensive testing is key to successful deployment. Timely engagement of all stakeholders and ensuring all decisions are aligned with safety and environmental considerations also contribute to realization of the project aims.

A Sparse Model of Guided Wave Tomography for Corrosion Mapping in Structure Health Monitoring Applications

To improve the reconstruction image spatial resolutions of ultrasonic guided wave ray tomography, a sparse model, based on the differences between the inspected and original slowness of the ultrasonic guided waves propagating in the plate-like or pipe-like materials, is first proposed in this paper. Unlike the conventional ultrasonic guided wave tomography whose reconstruction image resolutions are limited by an underdetermined linear model, analyses show that our new model, although it is also underdetermined, can give the optimal solution of the reconstruction image when the constraints on the sparsity of the slowness difference distribution are valid. The reason for the validation of the sparse constraints on the corrosions of the materials is explained. Based on our new model, a least absolute shrinkage and selection operator (LASSO) approach to do the thickness change mapping of a structure health monitoring (SHM) application is then formulated. Analyses also show that the visible artifacts can be avoided using our method, and the spatial resolutions of reconstruction image by our approach can further be improved by increasing the number of grids in the calculation. The approach is validated by experimental work on an aluminum plate. It is also shown that compared to the conventional ray tomography, the presented method can achieve a relatively high spatial resolution, with good suppression of artifacts.

Sufficient condition for exact support recovery of sparse signals through greedy block coordinate descent

In the underdetermined model Y ^ = A X + N , where X is a K-group sparse matrix (i.e. it has no more than K non-zero rows), the matrix A may be also perturbed. Theoretically, a more relaxed condition means that fewer measurements are required to ensure sparse recovery. In this study, a relaxed sufficient condition is proposed for greedy block coordinate descent (GBCD) under total perturbations based on the restricted isometry property in order to guarantee that the support of X is recovered. We also show that GBCD fails in a more general case when 1 / ( K + 1 ) ≤ δ K + 1 < 1 .

An Improved Analysis for Support Recovery With Orthogonal Matching Pursuit Under General Perturbations

Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for recovering the support of a sparse signal x from the underdetermined model $\text {y}=\text {A}\text {x}$ . In practice, we should analyze the performance of OMP under general perturbations, which means that both y and A are perturbed. In this paper, under general perturbations, we present necessary and sufficient conditions for the exact support recovery with the OMP. We also discuss the performance of OMP for recovering $\alpha $ strongly decaying sparse signals. Typically, in the noise-free case, we show that the upper bound of our sufficient condition is unrelated with $K$ and is a sharp bound. Furthermore, we establish sufficient conditions for the recovery of OMP, which can guarantee that the recovery is in the order of the signal entries’ magnitude.

Catchment tomography - An approach for spatial parameter estimation

The use of distributed-physically based hydrological models is often hampered by the lack of information on key parameters and their spatial distribution and temporal dynamics. Typically, the estimation of parameter values is impeded by the lack of sufficient observations leading to mathematically underdetermined estimation problems and thus non-uniqueness. Catchment tomography (CT) presents a method to estimate spatially distributed model parameters by resolving the integrated signal of stream runoff in response to precipitation. Basically CT exploits the information content generated by a distributed precipitation signal both in time and space. In a moving transmitter-receiver concept, high resolution, radar based precipitation data are applied with a distributed surface runoff model. Synthetic stream water level observations, serving as receivers, are assimilated with an Ensemble Kalman Filter. With a joint state-parameter update the spatially distributed Manning's roughness coefficient, n, is estimated using the coupled Terrestrial Systems Modelling Platform and the Parallel Data Assimilation Framework (TerrSysMP-PDAF). The sequential data assimilation in combination with the distributed precipitation continuously integrates new information into the model, thus, increasingly constraining the parameter space. With this large amount of data included for the parameter estimation, CT reduces the problem of underdetermined model parameters. The initially biased Manning's coefficients spatially distributed in two and four fixed parameter zones are estimated with errors of less than 3% and 17%, respectively, with only 64 model realizations. It is shown that the distributed precipitation is of major importance for this approach.

Improved analysis of SP and CoSaMP under total perturbations

Practically, in the underdetermined model y=A x, where x is a K sparse vector (i.e., it has no more than K nonzero entries), both y and A could be totally perturbed. A more relaxed condition means less number of measurements are needed to ensure the sparse recovery from theoretical aspect. In this paper, based on restricted isometry property (RIP), for subspace pursuit (SP) and compressed sampling matching pursuit (CoSaMP), two relaxed sufficient conditions are presented under total perturbations to guarantee that the sparse vector x is recovered. Taking random matrix as measurement matrix, we also discuss the advantage of our condition. Numerical experiments validate that SP and CoSaMP can provide oracle-order recovery performance.

A Blind Recognition Algorithm for Real Orthogonal STBC MC-CDMA Underdetermined Systems Based on LPCA and SCA

This paper proposes a blind recognition algorithm for real orthogonal space---time block code multi-carrier code division multiple access (OSTBC MC-CDMA) underdetermined systems based on Laplacian potential clustering algorithm (LPCA) and sparse component analysis. In our work, the received signal first has been constructed to satisfy the instantaneous underdetermined model, where the mixing matrix (virtual channel matrix) includes the information of space---time block code. The virtual channel matrix is then can be separated by using the LPCA. We show that, for OSTBC, the correlation matrix of virtual channel matrix is a diagonal matrix, while with non-OSTBC (NOSTBC) signal, such correlation matrix of virtual channel matrix was not. According to this property, two characteristic parameters of correlation matrix of virtual channel matrix are extracted, such as sparsity and energy ratio of non-main and main diagonal elements. In recognition process, the energy ratio will be used in pre-decision step, thus it avoids the influence of noise and making sure that the correlation matrix of virtual channel matrix is a diagonal matrix for OSTBC. The last decision will be done through comparing sparsity parameter with the number of transmitted symbols, where the sparsity parameter of OSTBC will be equal the number of transmitted symbols and the such parameter of NOSTBC will not. Simulation results demonstrate the effectiveness of the proposed algorithm.

Impact-force sparse reconstruction from highly incomplete and inaccurate measurements

The classical l2-norm-based regularization methods applied for force reconstruction inverse problem require that the number of measurements should not be less than the number of unknown sources. Taking into account the sparse nature of impact-force in time domain, we develop a general sparse methodology based on minimizing l1-norm for solving the highly underdetermined model of impact-force reconstruction. A monotonic two-step iterative shrinkage/thresholding (MTWIST) algorithm is proposed to find the sparse solution to such an underdetermined model from highly incomplete and inaccurate measurements, which can be problematic with Tikhonov regularization. MTWIST is highly efficient for large-scale ill-posed problems since it mainly involves matrix-vector multiplies without matrix factorization. In sparsity frame, the proposed sparse regularization method can not only determine the actual impact location from many candidate sources but also simultaneously reconstruct the time history of impact-force. Simulation and experiment including single-source and two-source impact-force reconstruction are conducted on a simply supported rectangular plate and a shell structure to illustrate the effectiveness and applicability of MTWIST, respectively. Both the locations and force time histories of the single-source and two-source cases are accurately reconstructed from a single accelerometer, where the high noise level is considered in simulation and the primary noise in experiment is supposed to be colored noise. Meanwhile, the consecutive impact-forces reconstruction in a large-scale (greater than 104) sparse frame illustrates that MTWIST has advantages of computational efficiency and identification accuracy over Tikhonov regularization.

Introducing Socio-Political Regimes in Economic Development Models: Historical Simulations on Agrarian Reform for India and Chile

The paper starts with a basic undetermined model that specifies four principle actors: landlords, peasants, the non-agricultural sector, and the government. Peasants and landlords are assumed to behave differently according to their own separate institutional attitudes, production function, savings and consumption patterns, tax and interest rates, and so forth. The novelty of the approach lies in adapting the basic undetermined model to applied models that represent different configurations of the socio-political power structure, i.e., configurations in which the sole dominant actor is the landlords group, or the peasants, or the non-agriculturalists, while the other actors are followers. Government policy is supposed to operate within the prescribed socio-political structural constraints imposed by the leader group. In adapting the basic model to fit, and be applied, to different sociopolitical situations, the procedure followed is to convert the basic underdetermined model into a determinate model by exogenously fixing perceived target variables by the leading actor. The paper applies the model to a socio-political system characterized by a landlord-leader configuration, i.e. rural India of the 1960’s, and explores policy alternatives for the ‘soft state’ in the Indian context. The paper presents also an application to Chile under the Allende regime where the proposed confiscatory reforms corresponded closely with a peasant platform. The applied model predicted grave costs of the proposed reforms for all other actors in Chile; suggesting that substantive opposition to the proposed reforms was inevitable.

On interpretation of protein X‐ray structures: Planarity of the peptide unit

Pauling's mastery of peptide stereochemistry-based on small molecule crystal structures and the theory of chemical bonding-led to his realization that the peptide unit is planar and then to the Pauling-Corey-Branson model of the α-helix. Similarly, contemporary protein structure refinement is based on experimentally determined diffraction data together with stereochemical restraints. However, even an X-ray structure at ultra-high resolution is still an under-determined model in which the linkage among refinement parameters is complex. Consequently, restrictions imposed on any given parameter can affect the entire structure. Here, we examine recent studies of high resolution protein X-ray structures, where substantial distortions of the peptide plane are found to be commonplace. Planarity is assessed by the ω-angle, a dihedral angle determined by the peptide bond (C-N) and its flanking covalent neighbors; for an ideally planar trans peptide, ω = 180°. By using a freely available refinement package, Phenix [Afonine et al. (2012) Acta Cryst. D, 68:352-367], we demonstrate that tightening default restrictions on the ω-angle can significantly reduce apparent deviations from peptide unit planarity without consequent reduction in reported evaluation metrics (e.g., R-factors). To be clear, our result does not show that substantial non-planarity is absent, only that an equivalent alternative model is possible. Resolving this disparity will ultimately require improved understanding of the deformation energy. Meanwhile, we urge inclusion of ω-angle statistics in new structure reports in order to focus critical attention on the usual practice of assigning default values to ω-angle constraints during structure refinement.

Perturbation Analysis of Greedy Block Coordinate Descent Under RIP

Practically, in the underdetermined model Y = AX, where X is a K-group sparse matrix (i.e., it has no more than K nonzero rows), both Y and A could be totally perturbed. In this paper, based on restricted isometry property, for the greedy block coordinate descent algorithm, a sufficient condition of exact recovery is presented under the total perturbations, to guarantee that the support of the sparse matrix X is recovered exactly. It is pointed out that there exists some case satisfying our condition, but not the mutual coherence condition. We also discuss the upper bound of our sufficient condition.

Sparse Representation for Brain Signal Processing: A tutorial on methods and applications

In many cases, observed brain signals can be assumed as the linear mixtures of unknown brain sources/components. It is the task of blind source separation (BSS) to find the sources. However, the number of brain sources is generally larger than the number of mixtures, which leads to an underdetermined model with infinite solutions. Under the reasonable assumption that brain sources are sparse within a domain, e.g., in the spatial, time, or time-frequency domain, we may obtain the sources through sparse representation. As explained in this article, several other typical problems, e.g., feature selection in brain signal processing, can also be formulated as the underdetermined linear model and solved by sparse representation. This article first reviews the probabilistic results of the equivalence between two important sparse solutions?the 0-norm and 1-norm solutions. In sparse representation-based brain component analysis including blind separation of brain sources and electroencephalogram (EEG) inverse imaging, the equivalence is related to the recoverability of the sources. This article also focuses on the applications of sparse representation in brain signal processing, including components extraction, BSS and EEG inverse imaging, feature selection, and classification. Based on functional magnetic resonance imaging (fMRI) and EEG data, the corresponding methods and experimental results are reviewed.

An Ecological Network Analysis of nitrogen cycling in the Laurentian Great Lakes

As water moves through the Laurentian Great Lakes system, it experiences a steep gradient in physical and chemical conditions between oligotrophic Lake Superior and eutrophic Lake Erie, likely affecting stocks and flows of nitrogen (N) across these lakes. We used published rates, supplemented by measurements conducted during a series of research cruises from 2010 to 2012, to construct three coupled 4-compartment N models for Lakes Superior, Huron, and Erie. Linear Inverse Modeling was used to identify plausible solutions to this model, and subsequent analysis focused on the most parsimonious model solution. For the most parsimonious model solution, we used Ecological Network Analysis (ENA) to analyze N flow and cycling in this steady-state model, and to examine the ultimate source of the N removed via denitrification within each lake. We also calculated denitrification efficiencies for each lake (the fraction of N removed through denitrification relative to all N exported) for 10,000 possible solutions to the underdetermined model. The average path length of N atoms in Lake Superior was 47.4, compared to 25.7 in Lake Huron and 15.2 in Lake Erie. Lake Superior's long (191 years) hydrologic residence time and relatively high N cycling rates allow for N atoms to have multiple opportunities to enter the sediment N pool and ultimately be removed through denitrification. Despite having a low areal denitrification rate, Lake Superior had a higher denitrification efficiency (86±1%; mean±95% CI) compared to Lake Huron (64±12%), and Lake Erie (48±7%). This long residence time also makes Lake Superior highly sensitive to changes in loading rates and internal processes, probably contributing to the steady nitrate rise over the past century.

Blind Source Separation of Underdetermined Mixtures Based on Local Mean Decomposition and Conjugate Gradient Algorithm

Most of the existing underdetermined blind source separation (BSS) approaches assume that the source signals are strictly or partially sparse. This paper, however, presents a new BSS method in underdetermined mixing situation for non- sparse signals. The proposed method first introduces the local mean decomposition algorithm into the BSS problem to rebuild some extra mixing signals. Such signals are then combined with the initial mixtures such that the underdetermined BSS problem is transformed to a determined one and the difficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and the newly formed determined BSS problem, the minimum mutual information principle is employed as the BSS cost function. A conjugate gradient learning algorithm is then derived for training the separating matrix. In each update step of the algorithm, the term of score function is estimated by a kernel function estimation algorithm. The simulation results have demonstrated the efficacy of the proposed underdetermined BSS method.  Index Terms—Blind source separation, underdetermined model, local mean decomposition, conjugate gradient

A variational Bayes spatiotemporal model for electromagnetic brain mapping

In this article, we present a new variational Bayes approach for solving the neuroelectromagnetic inverse problem arising in studies involving electroencephalography (EEG) and magnetoencephalography (MEG). This high-dimensional spatiotemporal estimation problem involves the recovery of time-varying neural activity at a large number of locations within the brain, from electromagnetic signals recorded at a relatively small number of external locations on or near the scalp. Framing this problem within the context of spatial variable selection for an underdetermined functional linear model, we propose a spatial mixture formulation where the profile of electrical activity within the brain is represented through location-specific spike-and-slab priors based on a spatial logistic specification. The prior specification accommodates spatial clustering in brain activation, while also allowing for the inclusion of auxiliary information derived from alternative imaging modalities, such as functional magnetic resonance imaging (fMRI). We develop a variational Bayes approach for computing estimates of neural source activity, and incorporate a nonparametric bootstrap for interval estimation. The proposed methodology is compared with several alternative approaches through simulation studies, and is applied to the analysis of a multimodal neuroimaging study examining the neural response to face perception using EEG, MEG, and fMRI.

Use of Prior Information for Calibration of River Roughness

River roughness calibration usually is an underdetermined model for lack of hydrological information, and its calibrated results may deviate from the true solution seriously. Using prior information is an effective way to regularize inverse problems, which can make the calibrated results reasonable and improve the stability of numerical calculation. A robust model, which takes account of river roughness smooth matrix and error minimization, is developed on the basis of the prior information that the spatial distribution of river roughness is smooth. In the computing example of a river network, cases are tested about the uniqueness of solution, numerical stability, and reliability. The results show that the present model can calibrate river roughness effectively with high numerical stability and reliable results.

Combining Economic Forecasts by Using a Maximum Entropy Econometric Approach

ABSTRACTThis paper explores the use of a maximum entropy econometric approach to combine forecasts when the small amount of information available does not allow the use of regression procedures since a dimensionality problem arises. This approach has its roots in information theory and builds on the entropy information measures and the classical maximum entropy principle, which was developed to recover information from underdetermined models. More specifically, we use the maximum entropy econometric approach for the measure of Shannon and we also propose its extension to the quadratic uncertainty measure. The experimental results over a pool of forecasts referring to Spanish inflation show some improvements when compared with equally weighted combined forecasting. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Dimension reduction: Additional benefit of an optimal filter for independent component analysis to extract event-related potentials

The present study addresses benefits of a linear optimal filter (OF) for independent component analysis (ICA) in extracting brain event-related potentials (ERPs). A filter such as the digital filter is usually considered as a denoising tool. Actually, in filtering ERP recordings by an OF, the ERP’ topography should not be changed by the filter, and the output should also be able to be modeled by the linear transformation. Moreover, an OF designed for a specific ERP source or component may remove noise, as well as reduce the overlap of sources and even reject some non-targeted sources in the ERP recordings. The OF can thus accomplish both the denoising and dimension reduction (reducing the number of sources) simultaneously. We demonstrated these effects using two datasets, one containing visual and the other auditory ERPs. The results showed that the method including OF and ICA extracted much more reliable components than the sole ICA without OF did, and that OF removed some non-targeted sources and made the underdetermined model of EEG recordings approach to the determined one. Thus, we suggest designing an OF based on the properties of an ERP to filter recordings before using ICA decomposition to extract the targeted ERP component.