A new approach for separating mixed model parameters:application to simultaneous inversion of earthquake source parameters

A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.

Testing the robustness of particle-based separation models for the magnetic separation of a complex skarn ore

Physical separation processes are best understood in terms of the behaviour of individual ore particles.Yet,while different empirical particle-based separation modelling approaches have been developed,their predictive performance has never been tested under variable process conditions.Here,we investigated the predictive performance of a state-of-the-art particle-based separation model under variable feed composition for a laboratory-scale magnetic separation of a skarn ore.Two scenarios were investigated:one in which the mass flow of the different processing streams could be measured and one in which it had to be estimated from data.In both scenarios,the predictive models were sufficiently general to predict the process outcomes of new samples of variable composition.Nevertheless,the scenario in which mass flow could be measured was4%more precise in predicting mass balances.The process behaviour of minerals present at concentrations above 0.1%by weight could be accurately predicted.Our findings indicate the potential use of this method to minimize the costs of metallurgical testwork while providing in-depth understanding of the recovery behaviour of individual ore particles.Moreover,the method may be used to establish powerful tools to forecast mineral recoveries for partly new ore types at a running mining operation.

Maneuvering target state estimation based on separate model-ing of target trajectory shape and dynamic characteristics

The state estimation of a maneuvering target,of which the trajectory shape is independent on dynamic characteristics,is studied.The conventional motion models in Cartesian coordinates imply that the trajectory of a target is completely determined by its dynamic characteristics.However,this is not true in the applications of road-target,sea-route-target or flight route-target tracking,where target trajectory shape is uncoupled with target velocity properties.In this paper,a new estimation algorithm based on separate modeling of target trajectory shape and dynamic characteristics is proposed.The trajectory of a target over a sliding window is described by a linear function of the arc length.To determine the unknown target trajectory,an augmented system is derived by denoting the unknown coefficients of the function as states in mileage coordinates.At every estimation cycle except the first one,the interaction(mixing)stage of the proposed algorithm starts from the latest estimated base state and a recalculated parameter vector,which is determined by the least squares(LS).Numerical experiments are conducted to assess the performance of the proposed algorithm.Simulation results show that the proposed algorithm can achieve better performance than the conventional coupled model-based algorithms in the presence of target maneuvers.

Modeling and identification for soft sensor systems based on the separation of multi-dynamic and static characteristics

Data-driven soft sensor is an effective solution to provide rapid and reliable estimations for key quality variables online. The secondary variables affect the primary variable in considerably different speed, and soft sensor systems exhibit multi-dynamic characteristics. Thus, the first contribution is improving the model in the previous study with multi-time-constant. The characteristics-separation-based model will be identified in substep way,and the stochastic Newton recursive(SNR) algorithm is adopted. Considering the dual-rate characteristics of soft sensor systems, the proposed model cannot be identified directly. Thus, two auxiliary models are first proposed to offer the intersample estimations at each update period, based on which the improved algorithm(DAM-SNR) is derived. These two auxiliary models function in switching mechanism which has been illustrated in detail. This algorithm serves for the identification of the proposed model together with the SNR algorithm, and the identification procedure is then presented. Finally, the laboratorial case confirms the effectiveness of the proposed soft sensor model and the algorithms.

FLUID DYNAMICS IN A GAS-STIRRED LADLE——A Separated Flow Model with Stochastical Trajectories

A separated flow model with stochastical trajectories has been developed to describe the fluid flow in a bubble stirred ladle.The bubble dispersion,turbulent characteristics and gas-liquid interactions can be predicted by this mathematical model.The bubble flow as a dispersed phase is treated in a Lagrangian frame of reference and the analysis of the turbulent flow for liquid phase is conducted in a Eulerian field.The interactions between bubbles and liquid phases are considered as a bubble source term in the control equation for a continuous phase. The Monte Carlo sampling method is used to determine the bubble trajectories.The homoge- neous flow model is also taken into consideration so that it can be compared with the sepa- rated flow model.Numerical predictions using a water model of a ladle show that the pre- dicted results of the separated flow model agree satisfactorily with the experimental results, but the prediction of the homogeneous flow model are not in good agreement with the experi- mental results.

Numerical modelling of storm surges in the Beibu Gulf with SCM

On the basis of 3-dimensional nonlinear hydrodynamical equations and by using the improved SCM the tides and storm surges induced by Typhoons 7109 and 8007 in the Beibu Gulf are simulated. In addition, the nonlinear interaction between the tide and storm surge in the gulf is discussed and some significant results are obtained.

Modeling of Coalescence and Separation of Liquid Droplets During Solidification of Immiscible Alloys

Directional solidification methods are being used f or in-situ production of metallic immiscible composites. A quantitative understa nding of the dynamic behavior and growth kinetics of the nucleated second phase during solidification is necessary to produce homogeneous dispersion in solidifi ed composites. This paper presents a mathematical model for describing the grow th of nucleated dispersed phase in the two-liquid phase region ahead of the sol idification front and the entrapment of these droplets by the moving solid-liqu id interface in vertical unidirectional solidification systems. The model has t wo components. A macro-heat transfer model for describing the temperature prof iles and the rate of advance of the solidification front. The dynamic behavior and coalescence and growth of nucleated droplets in the two-liquid phase region under the influence of effective gravity and thermocapillary forces were repres ented through the solution the droplet momentum and mass conservation equations in particle space. These two components of the models were coupled through a sp ecial algorithm for tracking the particle location and size with respect to movi ng solidification front in the solidification time scale. The model is used to study the particle size distribution in unidirectional solidified Zn-Bi hypermo notectic alloys at reduced gravity conditions. It has been found that the parti cle size and distribution in the solidified alloy depends on solidification rate and the ratio of effective gravity to thermocapillary forces. It was also foun d that uniform dispersion could only be obtained in a very narrow range of effec tive gravity values near zero gravity. The model predictions were compared agai nst experimental measurements obtained at different effective gravity conditions in a novel unidirectional solidification apparatus that uses electromagnetic fo rces to modulate gravitational forces. The model was found to reasonably predic t the experimentally measured particle size and distribution over the entire ran ge of effective gravity investigated as well as gravity conditions for settling and flotation of the second phase during solidification. The practical signific ance of these findings will be discussed.

THE SEPARATION OF LARGE VORTEXES AND THE CLOSED EQUATIONS OF TURBULENCE MODEL

This paper presents a new kind of everage for the loeally-generated large vortexes so that the physieal quantities of the locally-generated large vortexes and the external large vortexes canberigorously separated from the equal ions for the large vortexes proposed in a previous paper[1] To the equations for the two kinds of large vortexes, some auxiliary relations are introduced, and the value, of the length-scale lN of energy dissipation of the external large vortexes may he determined according to the actual circumstances of the disturbance of external sources. Thus the resulting equations of the second moments of turbulent velocity fluctuations for the two kinds of large vortexes can be made closed. Meanwhile, the corresponding coefficients of diffusion in the previous paper[1] are improved,Finally, a closed set of numerically-solvable equations of turbulence model are obtained.

On the impact of grinding conditions in the flotation of semi-soluble salt-type mineral-containing ores driven by surface or particle geometry effects?

Grinding and flotation processes are often studied independently, despite the well-established grinding influence on flotation performance, which affects not only particle size and thus liberation but also shape and leads to complex changes in pulp chemistry affecting the particle surface properties relevant for selective bubble attachment. Yet, no study jointly investigated these possible causes and many are limited to single mineral flotation. We relate grinding conditions to changes in pulp chemistry and particle surface properties and assess their impact on upgrading. We studied three non-sulfide ores with different feed grades and valuables: scheelite, apatite, and fluorite. These were dry-, wet-, and wet conditionedground before flotation in a laboratory mechanical cell. Results were evaluated with bulk-and particle-specific methodologies. The selectivity of the process is higher after dry grinding for the fluorite and apatite ores and irrelevant for the scheelite ore. Variations in flotation kinetics of individual particles associated to their size and shape are not sufficient to explain these results. The higher concentration of Ca2+and Mg2+observed in the pulp after wet grinding, altering particle surface properties, better explains the phenomenon. Additionally, we demonstrate how particle shape impacts are system specific and related to both entrainment and true flotation.

Dimensionality Reduction Using Optimized Self-Organized Map Technique for Hyperspectral Image Classification

The high dimensionalhyperspectral image classification is a challenging task due to the spectral feature vectors.The high correlation between these features and the noises greatly affects the classification performances.To overcome this,dimensionality reduction techniques are widely used.Traditional image processing applications recently propose numerous deep learning models.However,in hyperspectral image classification,the features of deep learning models are less explored.Thus,for efficient hyperspectral image classification,a depth-wise convolutional neural network is presented in this research work.To handle the dimensionality issue in the classification process,an optimized self-organized map model is employed using a water strider optimization algorithm.The network parameters of the self-organized map are optimized by the water strider optimization which reduces the dimensionality issues and enhances the classification performances.Standard datasets such as Indian Pines and the University of Pavia(UP)are considered for experimental analysis.Existing dimensionality reduction methods like Enhanced Hybrid-Graph Discriminant Learning(EHGDL),local geometric structure Fisher analysis(LGSFA),Discriminant Hyper-Laplacian projection(DHLP),Group-based tensor model(GBTM),and Lower rank tensor approximation(LRTA)methods are compared with proposed optimized SOM model.Results confirm the superior performance of the proposed model of 98.22%accuracy for the Indian pines dataset and 98.21%accuracy for the University of Pavia dataset over the existing maximum likelihood classifier,and Support vector machine(SVM).

Variable projection algorithms with sparse constraint for separable nonlinear models

Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.

A Multi-Level Authorization Based Tenant Separation Mechanism in Cloud Computing Environment

Separation issue is one of the most important problems about cloud computing security. Tenants should be separated from each other based on cloud infrastructure and different users from one tenant should be separated from each other with the constraint of security policies. Learning from the notion of trusted cloud computing and trustworthiness in cloud, in this paper, a multi-level authorization separation model is formally described, and a series of rules are proposed to summarize the separation property of this model. The correctness of the rules is proved. Furthermore, based on this model, a tenant separation mechanism is deployed in a real world mixed-critical information system. Performance benchmarks have shown the availability and efficiency of this mechanism.

Discriminant Analysis of the Linear Separable Data - Japanese 44 Cars

There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.

Progress on the Use of Stable Isotope Techniques in Catchment Hydrograph Separation: A Review

Hydrograph separation is a fundamental catchment descriptor,revealing information about sources of water in runoff generation processes. The water isotopes are ideal tracers in studying hydrological processes since the isotope fractionation produces a natural labeling effect within the hydrologic cycle. The water isotope technique has become one of effective means for investigating complex hydrologic system on a catchment scale. This paper reviews the progress on the use of stable water isotope techniques in catchment hydrograph separation in last decades. Also,the isotope mixing model for hydrograph separation and its uncertainties are explained in detail. In future research,there are three hot issues in the use of isotopic hydrograph separation（ IHS） ： integrating new approaches into IHS,calibration and verification of IHS model and IHS application in large river basins.

Development and comparison of local solar split models on the example ofCentral Europe

Solar radiation influences many and diverse fields like energy generation, agriculture and building operation.Hence, simulation models in these fields often rely on precise information about solar radiation. Measurementsare often restricted to global irradiance, whereby measurements of its single components, direct and diffuseirradiance, are sparse. However, information on both, the direct and diffuse irradiance, is necessary forsimulation models to work reliably. In this study, solar separation models are developed using 10-min trainingdata from two different locations in Austria. Direct horizontal irradiance is predicted via regressing the directfraction using several objective functions. The models are first trained on a data set including data from bothlocations, and evaluated regarding root mean squared deviation (RMSD), mean bias deviation (MBD), andcoefficient of determination (R2) on measured and estimated direct normal irradiance. The two best performing models are then selected for further analysis. This analysis comprises of an evaluation of the models per season,transferability of trained modes between two locations in Austria, a transferability and generalisability studyconducted for four more locations in Central Europe, and a comparison with the trusted Engerer model. Thesolar separation model with polynomial terms up to order three and Ridge regularisation outperforms thesecond model based a logistic term in combination with mixed quadratic terms as well as the Engerer model.

THE LINEAR SEPARATED FLOW MODEL FOR TWO－PHASI FLOW INSTABILITY IN BOILING CHANNELS

This paper presents linear separated model describing two-phase now instability. By employing the method of separated model and system control theory, dynamic system characteristic equations of describing two-phase flow instability are derived.It can be decided system stability depending on the characteristic value of characteristic equations. The calculated results agree well with the experimental data.

Gas-solids separation model of a novel FCC riser terminator device: super short quick separator (SSQS)

The gas flow field and the separation efficiency of a novel fluid catalytic cracking (FCC) riser terminal device, named as Super Short Quick Separator (SSQS), were studied. On the basis of above investigations, a section-lateral-mixing separation model was proposed, which included both the effect of inertia and structure of gas outlet on particles capture. After final modification, the results predicted with this model could be in good agreement with the cold experimental data. According to this model, the separation efficiency of SSQS is mainly influenced by the difference between the arc radius and the center pipe radius as well as the magnitude of particle tangential velocity.

Three-dimensional Numerical Simulation of Viscoelastic Phase Separation under Shear: the Roles of Bulk and Shear Relaxation Moduli

The morphological, dynamic and rheological characteristics in the viscoelastic phase separation（VPS） of sheared polymer solutions are investigated by three-dimensional（3D） numerical simulations of viscoelastic model. The simulations are accelerated by graphic process unit（GPU） to break through the limitation of computation power. Firstly, the morphological and dynamic characteristics of VPS under shear are presented by comparing with those in classic phase separation（CPS）. The results show that the phase inversion and phase shrink take place in VPS under shear. Then, the roles of bulk and shear relaxation moduli in VPS are investigated in details. The bulk relaxation modulus slows down the phase separation process under shear, but not affects the dynamic path of VPS. The dynamic path can be divided into three stages： freezing stage, growth stage and stable stage. The second overshoot phenomenon in the shear stress is observed, and explained by the breakdown and reform of string structures. The shear modulus affects morphology evolution in the late stage of VPS under shear.

Synergistic impacts of anthropogenic and biogenic emissions on summer surface O_3 in East Asia

A factor separation technique and an improved regional air quality model （RAQM） were applied to calculate synergistic contributions of anthropogenic volatile organic compounds （AVOCs）,biogenic volatile organic compounds （BVOCs） and nitrogen oxides （NOx） to daily maximum surface O3（O3DM） concentrations in East Asia in summer （June to August 2000）.The summer averaged synergistic impacts of AVOCs and NOx are dominant in most areas of North China,with a maximum of 60 ppbv,while those of BVOCs and NOx are notable only in some limited areas with high BVOC emissions in South China,with a maximum of 25 ppbv.This result implies that BVOCs contribute much less to summer averaged O3DM concentrations than AVOCs in most areas of East Asia at a coarse spatial resolution （1×1） although global emissions of BVOCs are much greater than those of AVOCs.Daily maximum total contributions of BVOCs can approach 20 ppbv in North China,but they can reach 40 ppbv in South China,approaching or exceeding those in some developed countries in Europe and North America.BVOC emissions in such special areas should be considered when O3 control measures are taken.Synergistic contributions among AVOCs,BVOCs and NOx significantly enhance O3 concentrations in the Beijing-Tianjin-Tangshan region and decrease them in some areas in South China.Thus,the total contributions of BVOCs to O3DM vary significantly from day to day and from location to location.This result suggests that O3 control measures obtained from episodic studies could be limited for long-term applications.

Study on the Splitting Methods for Separable Convex Optimization in a Unified Algorithmic Framework

It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality.Recently,we have proposed a unified algorithmic framework which can guide us to construct the solution methods for solving these monotone variational inequalities.In this work,we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago.In particular,exploiting this framework,we are able to give a very clear and elementary proof of the convergence of these solution methods.