Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

Proper orthogonal decomposition based seismic source wavefield reconstruction for finite element reverse time migration

The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.

Reaction Rate Models for the Thermal Decomposition of Ibuprofen Crystals

Kinetics of the decomposition of racemic ibuprofen crystals were studied by non-isothermal analysis. Thermogravimetric analysis revealed that ibuprofen is thermally stable up to 152.6°C and the initial loss of mass was due to evaporation only. Activation energy, pre-exponential factor, activation entropy and Gibbs free energy for the decomposition of ibuprofen were determined using the integral method of Coats-Redfern (CR). Geometrical contraction models were found to be the best fits. The Arrheinus equation for the thermal decomposition of ibuprofen is k = (1.1 × 107) e–79125/RT sec–1.

Vehicle-Bridge Interaction Simulation and Damage Identification of a Bridge Using Responses Measured in a Passing Vehicle by Empirical Mode Decomposition Method

To prevent early bridge failures, effective Structural Health Monitoring (SHM) is vital. Vibration-based damage assessment is a powerful tool in this regard, as it relies on changes in a structure’s dynamic characteristics as it degrades. By measuring the vibration response of a bridge due to passing vehicles, this approach can identify potential structural damage. This dissertation introduces a novel technique grounded in Vehicle-Bridge Interaction (VBI) to evaluate bridge health. It aims to detect damage by analyzing the response of passing vehicles, taking into account VBI. The theoretical foundation of this method begins with representing the bridge’s superstructure using a Finite Element Model and employing a half-car dynamic model to simulate the vehicle with suspension. Two sets of motion equations, one for the bridge and one for the vehicle are generated using the Finite Element Method, mode superposition, and D’Alembert’s principle. The combined dynamics are solved using the Newmark-beta method, accounting for road surface roughness. A new approach for damage identification based on the response of passing vehicles is proposed. The response is theoretically composed of vehicle frequency, bridge natural frequency, and a pseudo-frequency component related to vehicle speed. The Empirical Mode Decomposition (EMD) method is applied to decompose the signal into its constituent parts, and damage detection relies on the Intrinsic Mode Functions (IMFs) corresponding to the vehicle speed component. This technique effectively identifies various damage scenarios considered in the study.

A unified Minorization-Maximization approach for estimation of general mixture models

The mixed distribution model is often used to extract information from heteroge-neous data and perform modeling analysis.When the density function of mixed distribution is complicated or the variable dimension is high,it usually brings challenges to the parameter es-timation of the mixed distribution model.The application of MM algorithm can avoid complex expectation calculations,and can also solve the problem of high-dimensional optimization by decomposing the objective function.In this paper,MM algorithm is applied to the parameter estimation problem of mixed distribution model.The method of assembly and decomposition is used to construct the substitute function with separable parameters,which avoids the problems of complex expectation calculations and the inversion of high-dimensional matrices.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Parallel Computing of a Climate Model on the Dawn 1000 by Domain Decomposition Method

In this paper the parallel computing of a grid-point nine-level atmospheric general circulation model on the Dawn 1000 is introduced. The model was developed by the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (CAS). The Dawn 1000 is a MIMD massive parallel computer made by National Research Center for Intelligent Computer (NCIC), CAS. A two-dimensional domain decomposition method is adopted to perform the parallel computing. The potential ways to increase the speed-up ratio and exploit more resources of future massively parallel supercomputation are also discussed.

Modified version of three-component model-based decomposition for polarimetric SAR data

A new hybrid Freeman/eigenvalue decomposition based on the orientation angle compensation and the various extended volume models for polarimetric synthetic aperture radar(PolSAR) data are presented. There are three steps in the novel version of the three-component model-based decomposition.Firstly, two special unitary transform matrices are applied on the coherency matrix for deorientation to decrease the correlation between the co-polarized term and the cross-polarized term.Secondly, two new conditions are proposed to distinguish the manmade structures and the nature media after the orientation angle compensation. Finally, in order to adapt to the scattering properties of different media, five different volume scattering models are used to decompose the coherency matrix. These new conditions pre-resolves man-made structures, which is beneficial to the subsequent selection of a more suitable volume scattering model.Fully PolSAR data on San Francisco are used in the experiments to prove the efficiency of the proposed hybrid Freeman/eigenvalue decomposition.

Eigen-Space Decomposition(ESD)Method for the Design of Internal Model Controller(IMC)from Noisy Input and Output Plant Data

A novel approach to design Internal Model Controller(IMC)is proposed in this paper directly from measuredinput and output plant data,which are assumed to becontaminated by measurement noise.In order to avoidthe complicated structure-identification problem inmost cases,two Finite Impulse Response(FIR)modelsare taken to represent the plant model and the internalmodel controller respectively.Taking account of mea-surement noise both in the plant input and its output,anESD based Total Least Squares(TLS)solution is appliedfor the unbiased identification of the plant model and itsinverse model,the latter constitutes the internal modelcontroller according to the principle that the internalmodel controller approximates the inverse dynamics ofthe plant model.Simulations are given for a testifica-tion.

Hybrid Model Based on Wavelet Decomposition for Electricity Consumption Prediction

The effective supply of electricity is the basis of ensuring economic development and people's normal life. It is difficult to store electricity, as leading to the production and consumption must be completed simultaneously. Therefore, it is of great significance to accurately predict the demand for electricity consumption for the production planning of electricity and the normal operation of the society. In this paper, a hybrid model is constructed to predict the electricity consumption in China. The structural breaks test of monthly electricity consumption in China from January 2010 to December 2016 is carried out by using the structural breaks unit root test. Based on the existence of structura breaks, the electricity consumption data are decomposed into low-frequency and high-frequency components by wavelet model, and the separated low frequency signal and high frequency signal are predicted by autoregressive integrated moving average(ARIMA) and nonlinear autoregressive neural network(NAR), respectively. Therefore the wavelet-ARIMA-NAR hybrid model is constructed. In order to compare the effect of the hybrid model, the structural time series(STS) model is applied to predicting the electricity consumption. The results of prediction error test show that the hybrid model is more accurate for electricity consumption prediction.

Preliminaries for a New Mathematical Framework for Modelling Tumour Growth Using Stress State Decomposition Technique

The main goal of the present paper is to present a mathematical framework for modelling tumour growth based on stress state decomposition technique (SSDT). This is a straightforward extension of the model for multi-phase nonsaturated soil consolidation with pollutant transport presented by the authors and may be regarded as an alternative to classical frameworks based on TCAT theory. In this preliminary work, the Representative Volume Element (RVE) for tumour is proposed along with its comparison with the corresponding one for soils modelling developed formerly by the authors. Equations standing for tumour phase are flawlessly brought into correspondence with those of gaseous phase in the soil problem showing that a similar task may be carried out for the remainders phases taking part in both RVEs. Furthermore, stresses induced by nonlinear saturation and permeability dependence on suction for soil interstitial fluids transport finds its counterpart on the contact between the cancer cell membrane and interstitial fluids rendering a higher primary variables coupling degree than what was attained in TCAT theory. From these preliminaries assessments, it may be put forward that likewise the stress state decomposition procedure stands for an alternative for modelling multi-phase nonsaturated soil consolidation with pollutant transport;it does for modelling cancer as well.

Wavelet Decomposition Impacts on Traditional Forecasting Time Series Models

This investigative study is focused on the impact of wavelet on traditional forecasting time-series models,which significantly shows the usage of wavelet algorithms.Wavelet Decomposition(WD)algorithm has been combined with various traditional forecasting time-series models,such as Least Square Support Vector Machine(LSSVM),Artificial Neural Network(ANN)and Multivariate Adaptive Regression Splines(MARS)and their effects are examined in terms of the statistical estimations.The WD has been used as a mathematical application in traditional forecast modelling to collect periodically measured parameters,which has yielded tremendous constructive outcomes.Further,it is observed that the wavelet combined models are classy compared to the various time series models in terms of performance basis.Therefore,combining wavelet forecasting models has yielded much better results.

Analysis of a Residual Model for the Decomposition of Polarimetric SAR Data

Accurate estimation of the double-bounce scattering fd and surface scattering fs coefficients with Freeman-Durden decomposition is still difficult. This difficulty arises because overestimation of the volume scattering energy contribution Pv leads to negative values for fd and fs. A generalized residual model is introduced to estimate fd and fs. The relationship between Pv and the residual model is analyzed. Eigenvalues computed from the residual model must be positive to explain physical scattering mechanisms. The authors employ a new volumetric scattering model to minimize Pv as calculated by several decomposition methods. It is concluded that decreasing Pv can help reduce negative energy. This conclusion is validated using actual polarimetric SAR data.

Mathematical modelling of a biofilm: The Adomian decomposition method

A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement.

Analysis and Forecasting COVID-19 Outbreak in Pakistan Using Decomposition and Ensemble Model

COVID-19 has caused severe health complications and produced a substantial adverse economic impact around the world.Forecasting the trend of COVID-19 infections could help in executing policies to effectively reduce the number of new cases.In this study,we apply the decomposition and ensemble model to forecast COVID-19 confirmed cases,deaths,and recoveries in Pakistan for the upcoming month until the end of July.For the decomposition of data,the Ensemble Empirical Mode Decomposition(EEMD)technique is applied.EEMD decomposes the data into small components,called Intrinsic Mode Functions(IMFs).For individual IMFs modelling,we use the Autoregressive Integrated Moving Average(ARIMA)model.The data used in this study is obtained from the official website of Pakistan that is publicly available and designated for COVID-19 outbreak with daily updates.Our analyses reveal that the number of recoveries,new cases,and deaths are increasing in Pakistan exponentially.Based on the selected EEMD-ARIMA model,the new confirmed cases are expected to rise from 213,470 to 311,454 by 31 July 2020,which is an increase of almost 1.46 times with a 95%prediction interval of 246,529 to 376,379.The 95%prediction interval for recovery is 162,414 to 224,579,with an increase of almost two times in total from 100802 to 193495 by 31 July 2020.On the other hand,the deaths are expected to increase from 4395 to 6751,which is almost 1.54 times,with a 95%prediction interval of 5617 to 7885.Thus,the COVID-19 forecasting results of Pakistan are alarming for the next month until 31 July 2020.They also confirm that the EEMD-ARIMA model is useful for the short-term forecasting of COVID-19,and that it is capable of keeping track of the real COVID-19 data in nearly all scenarios.The decomposition and ensemble strategy can be useful to help decision-makers in developing short-term strategies about the current number of disease occurrences until an appropriate vaccine is developed.

Modeling Microbial Decomposition in Real 3D Soil Structures Using Partial Differential Equations

Partial Differential Equations (PDEs) have been already widely used to simulate various complex phenomena in porous media. This paper is one of the first attempts to apply PDEs for simulating in real 3D structures. We apply this scheme to the specific case study of the microbial decomposition of organic matter in soil pore space. We got a 3D geometrical representation of the pore space relating to a network of volume primitives. A mesh of the pore space is then created by using the network. PDEs system is solved by free finite elements solver Freefem3d in the particular mesh. We validate our PDEs model to experimental data with 3D Computed Tomography (CT) images of soil samples. Regarding the current state of art on soil organic matter decay models, our approach allows taking into account precise 3D spatialization of the decomposition process by a pore space geometry description.

Restarted Adomian Decomposition Method for Solving Volterra’s Population Model

In this paper, we used an efficient algorithm to obtain an analytic approximation for Volterra’s model for population growth of a species within a closed system, called the Restarted Adomian decomposition method (RADM) to solve the model. The numerical results illustrate that RADM has the good accuracy.

Simplified Models to Describe Transport and Decomposition of Ozone in a Bubble Column

The understanding of ozonation in bubble columns is the first step to describe this process for organic and inorganic pollutants in water medium in this equipment.This paper developed mathematical models for decomposition of ozone in liquid phase,with analytical solution for zero,first and second-orders kinetics for different pH values,with and without gaseous phase mass transfer effect in the ozone transfer to the liquid phase.The results models are satisfactory when compared with experimental data,and indicate the importance to consider such effects.

Factor decomposition analysis of energy efficiency change based on modified structural model:A case of Xinjiang

In order to find the dominant factor of energy efficiency change, this paper uses the modified structural model to analyze energy efficiency change from 1990 to 2012 in Xinjiang. The result shows that the energy efficiency increase is largely due to energy technological innovation especially by the industrial sector, and the contribution from structural shift is limited. Therefore, we should vigorously support energy-saving technological progress in the industrial sector and develop the modern service industries with lower energy consumption, in order to realize the goal of improving energy efficiency.

Research on Qualitative Model Decomposition

Qualitative reasoning uses incomplete knowledge to compute a description of the possible behaviors for dynamic systems. A standard qualitative simulation（QSIM） algorithm frequently results in a large number of incomprehensible behavioral descriptions and the simulation for complex systems frequently is intractable. Two model de- composition methods are proposed in this paper to eliminate or decrease the insujficiency of this algorithm. Using a directed graph to represent the qualitative model, the strongly connected graph based theory and genetic algorithm based model decomposition are proposed to decompose the model. A new simple system model is reconstructed by subgraphs and causal relations when the system directed graph is decomposed completely. Each sub-graph is viewed as a separate system and will be simulated separately, and the simulation result of causally upstream subsystem is used to constrain the behavior of downstream subsystems. The model decomposition algorithm provides a promising paradigm for qualitative simulation whose complexity is driven by the complexity of the problem specification rather than the inference mechanism used.