Block Incremental Dense Tucker Decomposition with Application to Spatial and Temporal Analysis of Air Quality Data

How can we efficiently store and mine dynamically generated dense tensors for modeling the behavior of multidimensional dynamic data?Much of the multidimensional dynamic data in the real world is generated in the form of time-growing tensors.For example,air quality tensor data consists of multiple sensory values gathered from wide locations for a long time.Such data,accumulated over time,is redundant and consumes a lot ofmemory in its raw form.We need a way to efficiently store dynamically generated tensor data that increase over time and to model their behavior on demand between arbitrary time blocks.To this end,we propose a Block IncrementalDense Tucker Decomposition(BID-Tucker)method for efficient storage and on-demand modeling ofmultidimensional spatiotemporal data.Assuming that tensors come in unit blocks where only the time domain changes,our proposed BID-Tucker first slices the blocks into matrices and decomposes them via singular value decomposition(SVD).The SVDs of the time×space sliced matrices are stored instead of the raw tensor blocks to save space.When modeling from data is required at particular time blocks,the SVDs of corresponding time blocks are retrieved and incremented to be used for Tucker decomposition.The factor matrices and core tensor of the decomposed results can then be used for further data analysis.We compared our proposed BID-Tucker with D-Tucker,which our method extends,and vanilla Tucker decomposition.We show that our BID-Tucker is faster than both D-Tucker and vanilla Tucker decomposition and uses less memory for storage with a comparable reconstruction error.We applied our proposed BID-Tucker to model the spatial and temporal trends of air quality data collected in South Korea from 2018 to 2022.We were able to model the spatial and temporal air quality trends.We were also able to verify unusual events,such as chronic ozone alerts and large fire events.

Dynamic mode decomposition of the geomagnetic field over the last two decades

Earth’s magnetic field,which is generated in the liquid outer core through the dynamo action,undergoes changes on timescales of a few years to several million years,yet the underlying mechanisms responsible for the field variations remain to be elucidated.In this study,we apply a novel data analysis technique developed in fluid dynamics,namely the dynamic mode decomposition,to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available.The dominant dynamic modes are extracted by solving an eigen-value problem,so one can identify modes with periods longer than the time span of data.Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration,justifying the validity of applying the dynamic mode decomposition method to geomagnetic field.We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years,a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years.These modes are possibly related to magnetohydrodynamic waves in the Earth’s outer core.

A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

Application of Hankel Dynamic Mode Decomposition for Wide Area Monitoring of Subsynchronous Resonance

In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incident.This paper presents a Hankel dynamic mode decomposition(DMD)method to identify SSR parameters using synchrophasor data.The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors.It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes.Therefore,the SSR parameters can be calculated once the modal parameter is extracted.Compared with the existing method,the presented work has better dynamic performances as it requires much less data.Thus,it is more suitable for practical cases in which the SSR characteristics are timevarying.The effectiveness and superiority of the proposed method have been verified by both simulations and field data.

Parameters Identification for Extended Debye Model of XLPE Cables Based on Sparsity-Promoting Dynamic Mode Decomposition Method

To identify the parameters of the extended Debye model of XLPE cables,and therefore evaluate the insulation performance of the samples,the sparsity-promoting dynamicmode decomposition(SPDMD)methodwas introduced,aswell the basics and processes of its applicationwere explained.The amplitude vector based on polarization current was first calculated.Based on the non-zero elements of the vector,the number of branches and parameters including the coefficients and time constants of each branch of the extended Debye model were derived.Further research on parameter identification of XLPE cables at different aging stages based on the SPDMD method was carried out to verify the practicability of the method.Compared with the traditional differential method,the simulation and experiment indicated that the SPDMD method can effectively avoid problems such as the relaxation peak being unobvious,and possessing more accuracy during the parameter identification.And due to the polarization current being less affected by the measurement noise than the depolarization current,the SPDMD identification results based on the polarization current spectral line proved to be better at reflecting the response characteristics of the dielectric.In addition,the time domain polarization current test results can be converted into the frequency domain,and then used to obtain the dielectric loss factor spectrum of the insulation.The integral of the dielectric loss factor on a frequency domain can effectively evaluate the insulation condition of the XLPE cable.

Stability analysis for flow past a cylinder via lattice Boltzmann method and dynamic mode decomposition

A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.

Dynamical mode decomposition of Gurney flap wake flow

The present work uses dynamic mode decomposition(DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap.The physics of DMD is first introduced.Then the PIV-measured wake flow velocity field is decomposed into dynamical modes.The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency,wavelength and convection speed.It is observed that high-order dynamic modes convect faster than low-order modes;moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.

Crystalline Phase and Decomposition Dynamics of Aluminum Titanate at Different Temperature

The crystalline phase formed during aluminum titanate at 750-1300 ℃ as well as the relationship between its content change and decomposition dynamics was mainly discussed in this paper.Dynamical equation was established for calculating the reaction activation energy.It aimed at providing dynamics basic data for taking up necessary measures to inhibit the decomposition of aluminum titanate.Experimental results showed that aluminum titanate would decompose into TiO2 and corundum at 750-1300 ℃.Content of aluminum titanate would reduce with the increase of decomposition time,and the order of decomposition rates at different temperature was 1100 1200 1000 900 ℃.The decomposition was a chemical reaction with control steps,and could meet the first order reaction dynamic equation-F（G） = [（1-G）-2/3-1] = Kt.According to the calculation,rate constants of different decomposition reaction dynamic equations were K900 = 2.2×10-3,K1000 = 1.2×10-2,K1100 = 4×10-1 and K1200 = 1.5×10-1,and the reaction activation energy ΔGave = 203.21 KJ/mol.

Decomposition dynamic of higher plant pigments by HPLC analysis

The fate of the litter of dominant vegetation(willows and reeds) is one of the aspects studied in the frame of the project “Onderzoek Milieu Effecten Sigmaplan”. One of the questions to be considered is how long the litter stays within the estuary. In this paper, the time the leaf litter(Salix triandra and Phragmites australis) stayed in the Schelde estuary was studied by using plant pigment as biomarkers with HPLC application. After analyzing the original data from the incubation experiment described by Dubuison and Geers(1999), the decomposition dynamics patterns of pigments were analyzed and described, and these decomposition dynamics patterns were used as calibration patterns. By using Spearman Rank Order Correlation, the calibration patterns of the pigments which were significant(p<0.05) were grouped. In this way, several groups of the calibration patterns of pigment decomposition were achieved. The presence or absence of these groups of pigments (whether they can be detected or not from HPLC) was shown to be useful in determining the time the litter has stayed in the water. Combining data of DW and POC, more precise timing can be obtained.

Decomposition dynamics and ecological stoichiometry of Quercus acutissima and Pinus densiflora litter in the Grain to Green Program Area of northern China

Litter decomposition and ecological stoichiometry of nutrient release is an important part of material cycling and energy flow in forest ecosystems.In a study of the ecological stoichiometry and nutrient release during litter decomposition in a pine–oak forest ecosystem of the Grain to Green Program(GTGP)area of northern China,a typical pine and oak species(PDS:Pinus densiflora Sieb.,QAC:Quercus acutissima Carr.)were selected in the Taiyi Mountain study area.The ecological stoichiometry characteristics of carbon(C),nitrogen(N)and phosphorus(P)and litter decomposition dynamics were studied by field sampling and quantitative analyses.The results showed the following.(1)The decomposition dynamics of both litters was slow-fast-slow.The most important climatic factor affecting the litter decomposition rate from May to October was precipitation and temperature from November to April of the following year.(2)Throughout the 300-day study,in both litters,C of the two litters was released,N first accumulated and was then released,and P exhibited a release-accumulate-release pattern.(3)C:P was significantly higher than C:N and N:P(p<0.05);the C:N of PSD litter was higher than that of QAC(p<0.05),but the N:P of QAC litter was higher than that of PSD litter(p<0.05).The C:N of both litters was very high in the study area,indicating that the nutrient release ability during litter decomposition in the two typical pine–oak forest ecosystems was relatively weak;therefore,more attention should be paid to nitrogen-fixing species and mixed forests in the GTGP area of northern China.

Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil

The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.

Analysis of clearance flow of a fuel pump based on dynamical mode decomposition

The flow field structure within the clearances of turbomachinery is complex and diverse, exhibiting high-dimensional nonlinearity. How to accurately extract the main structures that affect the internal flow within the turbine from the complex clearance flow has always been a key issue. To explore the impact of the dynamic structure of the clearance flow on the mainstream region in a centrifugal pump, this study combines the dynamic mode decomposition (DMD) method to conduct a thorough analysis of the velocity and pressure pulsation frequencies in the multi-physics fields within the clearance. The study has identified the main characteristic structures under different physical conditions in the clearance and has established the relationship between the characteristic structure frequencies in different physical fields and the impeller frequency. The research indicates that the internal flow within the clearance affects the occurrence of vortices in the volute. Under design conditions, the velocity field within the clearance is primarily influenced by high-order harmonic frequencies of the impeller, and the pressure field is mainly affected by low-order harmonic frequencies of the impeller. This reflects the crucial influence of impeller frequency and inlet flow on the coherent structures within the clearance flow. The research results offer new insights and methods for analyzing complex internal flows in large turbomachinery.

Mode decomposition of a noise suppressed mixing layer

Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible version of proper orthogonal decomposition （POD） and dynamic mode decomposition （DMD） are employed to analyze the spatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and its uncontrolled counterpart. The analyses of POD indicate that the y-direction body force control mainly modify the most energetic spatial structures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies and corresponding mode structures, and the stability characteristics of each mode can be obtained from DMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modes emerging in uncontrolled flow within the frequency range （w 〈 0.4） are suppressed due to control, relevant spatial-temporal structures are also varied, which is coincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy for frequency components of ~ 〈 0.4 by weakening nonlinearities and regularizing corresponding dynamic structures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this study demon- strate that DMD can serve as an important supplement for POD in analyzing a time-resolved physical process.

Collaboration strategy for software dynamic evolution of multi-agent system

As the ability of a single agent is limited while information and resources in multi-agent systems are distributed, cooperation is necessary for agents to accomplish a complex task. In the open and changeable environment on the Internet, it is of great significance to research a system flexible and capable in dynamic evolution that can find a collaboration method for agents which can be used in dynamic evolution process. With such a method, agents accomplish tasks for an overall target and at the same time, the collaborative relationship of agents can be adjusted with the change of environment. A method of task decomposition and collaboration of agents by improved contract net protocol is introduced. Finally, analysis on the result of the experiments is performed to verify the improved contract net protocol can greatly increase the efficiency of communication and collaboration in multi-agent system.

A developed transient gas-liquid-solid flow model with hydrate phase transition for solid fluidization exploitation of marine natural gas hydrate reservoirs

The multiphase flow characteristic is one of the most concerning problems during solid fluidization exploitation of marine natural gas hydrate reservoirs.In this research,a new transient gas-liquid-solid multiphase flow model with hydrate phase transition was developed.Meanwhile,this model considered the coupling relationship among convective heat transfer,hydrate dynamic decomposition,and multi-phase flow.The model can simulate the change of flow pattern from solid-liquid to gas-liquid-solid flow,and describe the distribution character of volume fraction of phase,wellbore temperature and pressure,and hydrate decomposition rate during transportation.The simulation results indicate that the hydrate decomposition region in the wellbore gradually expands,but the hydrate decomposition rate gradually decreases during the solid fluidization exploitation of hydrate.When mining time lasts for 4 h,and the bottom hole pressure decreases by about 0.4 MPa.Increasing NaCl concentration in seawater helps expand hydrate decomposition regions and improves the wellbore hydrate decomposition rate.When the Nacl mass fraction in seawater reaches 15%,it will raise the hydrate decomposition regions to the whole wellbore.In addition,the higher the wellhead backpressure,the lower the decomposition area and decomposition rate of hydrate in the wellbore.When wellhead backpressure reaches 2 MPa,the volume fraction of gas near the wellhead will reduce to about 12%.This work is expected to provide a theoretical basis for the development of marine hydrate reservoirs.

Cross-shelf variation of internal tides west of the Dongsha Plateau in the northern South China Sea

We examine the cross-shelf variation of internal tides(ITs)west of the Dongsha Plateau in the northern South China Sea based on observations from 4 moorings deployed between August 2017 and September 2018.On the slope,the amplitude of diurnal baroclinic current ellipses are 5 times larger than that of barotropic currents.The baroclinic energy quickly dissipates during cross-shelf propagation,and barotropic currents become dominant on the shelf outside of the Zhujiang River Estuary,with the amplitude of semidiurnal barotropic current ellipses being 10 times larger than that of the baroclinic ones.Dynamic modal decomposition indicates the first baroclinic mode is dominant for both diurnal and semidiurnal ITs.The total horizontal kinetic energy(HKE)of the first three baroclinic modes shows spatiotemporal differences among the 4 moorings.On the slope,the HKE for diurnal ITs is stronger in summer and winter,but weaker in spring and autumn;for semidiurnal ITs there is a similar seasonal variation,but the HKE in winter is even stronger than that in summer.On the shallow shelf,both diurnal and semidiurnal ITs maintain a certain intensity in summer but almost disappear in winter.Further analysis shows that only the upper water column is affected by seasonal variation of stratification on the slope,variation of diurnal ITs is thus controlled by the semi-annual cycle of barotropic energy input from the Luzon Strait,while the incoherent baroclinic currents make a major contribution to the temporal variation of semidiurnal ITs.For the shelf region,the water column is well mixed in winter,and the baroclinic energy largely dissipates when ITs propagate to the shelf zone despite of a strong barotropic energy input from the Luzon Strait.

Practical Implementation and Operational Experience of Dynamic Mode Decomposition in Wide-area Monitoring Systems of Italian Power System

This study presents the assumptions and strategies for the practical implementation of the dynamic mode decomposition approach in the wide-area monitoring system of the Italian transmission system operator,Terna.The procedure setup aims to detect poorly damped interarea oscillations of power systems.Dynamic mode decomposition is a data-driven technique that has gained increasing attention in different fields;the proposed implementation can both characterize the oscillatory modes and identify the most influenced areas.This study presents the results of its practical implementation and operational experience in power system monitoring.It focuses on the main characteristics and solutions identified to reliably monitor the interarea electromechanical modes of the interconnected European power system.Moreover,conditions to issue an appropriate alarm in case of critical operating conditions are described.The effectiveness of the proposed approach is validated by its application in three case studies:a critical oscillatory event and a short-circuit event that occurred in the Italian power system in the previous years,and a 15-min time interval of normal grid operation recorded in March 2021.

Numerical analysis of the correlation between fluid dynamic modes and hydrodynamic noise in flows around a three-dimensional circular cylinder

The flow around a circular cylinder for Re=1000 is characterized by flow separation and Karman vortex street.The typical flow features can be captured to study the correlation between fluid fields and sound fields.In this paper,the three-dimensional circular cylinder is taken as the research object,and the probes of surface fluctuating pressure and far field sound pressure are arranged every 10°.The directional diagram and the coherence of fluctuating pressure and sound pressure are analyzed.The relationship between the flow mode and hydrodynamic noise is studied by using dynamic mode decomposition(DMD).The characteristics of the dipole and quadrupole sound source term of a long span cylinder are studied.The results show that at the angles between 30°–120°and 190°–350°,the fluctuating pressure contributes more to the generation of dipole sounds.The quadrupole sound source shows three-dimensional effects,which is more obvious in a cylinder with large spanwise length.

Effect of the vortical structures on the hydrodynamic performance of a pitching hydrofoil

The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost constant rate from 5° to 15° and then back to 5°, with the Reynolds number 4.4×10^(5) and the frequency 2 Hz. The results show that the main coherent structures around the pitching hydrofoil include small-scale laminar separation bubble (LSB), large-scale second vortex (SV) and trailing edge vortex (TEV) which are all vortical. The relationship between the vortical structure and the lift is investigated with the finite-domain impulse theory. It indicates that the major part of the lift is contributed by the LSB, whereas the shedding and the formation of the SV and TEV cause the fluctuation of the lift. The proper orthogonal decomposition (POD) method is applied to capture the most energetic modes, revealing that the LSB mode occupies a large amount of energy in the flow field. The dynamic mode decomposition (DMD) method accurately extracts the dominant frequency and modal characteristics, with the first mode corresponding to the mean flow, the second mode corresponding to the LSB structure and the third and fourth modes corresponding to the vortex shedding.

A transition prediction method for flow over airfoils based on high-order dynamic mode decomposition

This article presents a novel approach for predicting transition locations over airfoils,which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver.This approach combines Dynamic Mode Decomposition(DMD)with e^Ncriterion.The core idea is to use a spatial DMD analysis to extract the modes of unstable perturbations from a steady flowfield and substitute the local Linear Stability Theory(LST)analysis to quantify the spatial growth of Tollmien–Schlichting(TS)waves.Transition is assumed to take place at the stream-wise location where the most amplified mode’s N-factor reaches a prescribed threshold and a turbulence model is activated thereafter.To improve robustness,the high-order version of DMD technique(known as HODMD)is employed.A theoretical derivation is conducted to interpret how a spatial highorder DMD analysis can extract the growth rate of the unsteady perturbations.The new method is validated by transition predictions of flows over a low-speed Natural-Laminar-Flow(NLF)airfoil NLF0416 at various angles of attack and a transonic NLF airfoil NPU-LSC-72613.The transition locations predicted by our HODMD/e^Nmethod agree well with experimental data and compare favorably to those obtained by some existing methods■.It is shown that the proposed method is able to predict transition locations for flows over different types of airfoils and offers the potential for application to 3D wings as well as more complex configurations.