Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.

A Review on Sources,Extractions and Analysis Methods of a Sustainable Biomaterial:Tannins

Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly to substitute petroleum-based products.They are a definite class of sustainable materials of the forestry industry.They have been in operation for hundreds of years to manufacture leather and now for a growing number of applications in a variety of other industries,such as wood adhesives,metal coating,pharmaceutical/medical applications and several others.This review presents the main sources,either already or potentially commercial of this forestry by-materials,their industrial and laboratory extraction systems,their systems of analysis with their advantages and drawbacks,be these methods so simple to even appear primitive but nonetheless of proven effectiveness,or very modern and instrumental.It constitutes a basic but essential summary of what is necessary to know of these sustainable materials.In doing so,the review highlights some of the main challenges that remain to be addressed to deliver the quality and economics of tannin supply necessary to fulfill the industrial production requirements for some materials-based uses.

LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

A comparison study on structure-function relationship of polysaccharides obtained from sea buckthorn berries using different methods:antioxidant and bile acid-binding capacity

In this study,the structural characters,antioxidant activities and bile acid-binding ability of sea buckthorn polysaccharides(HRPs)obtained by the commonly used hot water(HRP-W),pressurized hot water(HRP-H),ultrasonic(HRP-U),acid(HRP-C)and alkali(HRP-A)assisted extraction methods were investigated.The results demonstrated that extraction methods had significant effects on extraction yield,monosaccharide composition,molecular weight,particle size,triple-helical structure,and surface morphology of HRPs except for the major linkage bands.Thermogravimetric analysis showed that HRP-U with filamentous reticular microstructure exhibited better thermal stability.The HRP-A with the lowest molecular weight and highest arabinose content possessed the best antioxidant activities.Moreover,the rheological analysis indicated that HRPs with higher galacturonic acid content and molecular weight showed higher viscosity and stronger crosslinking network(HRP-C,HRP-W and HRP-U),which exhibited stronger bile acid binding capacity.The present findings provide scientific evidence in the preparation technology of sea buckthorn polysaccharides with good antioxidant and bile acid binding capacity which are related to the structure affected by the extraction methods.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.

NEGATIVE NORM LEAST-SQUARES METHODS FOR THE INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS

The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method

In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP un-certainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20%are added to these original factors for con-structing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron(MLP),support vector machine(SVM)and random forest(RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2)With the proportions of random errors increasing from 5%to 20%,the LSP uncertainty increases continuously.(3)The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4)The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5)The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide sus-ceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Robustness Study and Superior Method Development and Validation for Analytical Assay Method of Atropine Sulfate in Pharmaceutical Ophthalmic Solution

Background: The robustness is a measurement of an analytical chemical method and its ability to contain unaffected by little with deliberate variation of analytical chemical method parameters. The analytical chemical method variation parameters are based on pH variability of buffer solution of mobile phase, organic ratio composition changes, stationary phase (column) manufacture, brand name and lot number variation;flow rate variation and temperature variation of chromatographic system. The analytical chemical method for assay of Atropine Sulfate conducted for robustness evaluation. The typical variation considered for mobile phase organic ratio change, change of pH, change of temperature, change of flow rate, change of column etc. Purpose: The aim of this study is to develop a cost effective, short run time and robust analytical chemical method for the assay quantification of Atropine in Pharmaceutical Ophthalmic Solution. This will help to make analytical decisions quickly for research and development scientists as well as will help with quality control product release for patient consumption. This analytical method will help to meet the market demand through quick quality control test of Atropine Ophthalmic Solution and it is very easy for maintaining (GDP) good documentation practices within the shortest period of time. Method: HPLC method has been selected for developing superior method to Compendial method. Both the compendial HPLC method and developed HPLC method was run into the same HPLC system to prove the superiority of developed method. Sensitivity, precision, reproducibility, accuracy parameters were considered for superiority of method. Mobile phase ratio change, pH of buffer solution, change of stationary phase temperature, change of flow rate and change of column were taken into consideration for robustness study of the developed method. Results: The limit of quantitation (LOQ) of developed method was much low than the compendial method. The % RSD for the six sample assay of developed method was 0.4% where the % RSD of the compendial method was 1.2%. The reproducibility between two analysts was 100.4% for developed method on the contrary the compendial method was 98.4%.

Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method

In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.

Application of neural network model coupling with the partial least-squares method for forecasting watre yield of mine

Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.