Low rank optimization for efficient deep learning:making a balance between compact architecture and fast training

Deep neural networks(DNNs)have achieved great success in many data processing applications.However,high computational complexity and storage cost make deep learning difficult to be used on resource-constrained devices,and it is not environmental-friendly with much power cost.In this paper,we focus on low-rank optimization for efficient deep learning techniques.In the space domain,DNNs are compressed by low rank approximation of the network parameters,which directly reduces the storage requirement with a smaller number of network parameters.In the time domain,the network parameters can be trained in a few subspaces,which enables efficient training for fast convergence.The model compression in the spatial domain is summarized into three categories as pre-train,pre-set,and compression-aware methods,respectively.With a series of integrable techniques discussed,such as sparse pruning,quantization,and entropy coding,we can ensemble them in an integration framework with lower computational complexity and storage.In addition to summary of recent technical advances,we have two findings for motivating future works.One is that the effective rank,derived from the Shannon entropy of the normalized singular values,outperforms other conventional sparse measures such as the?_1 norm for network compression.The other is a spatial and temporal balance for tensorized neural networks.For accelerating the training of tensorized neural networks,it is crucial to leverage redundancy for both model compression and subspace training.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

A Perturbation Analysis of Low-Rank Matrix Recovery by Schatten p-Minimization

A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.

Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption

Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.

Improving bubble-particle attachment during the flotation of low rank coal by surface modification

Based on the problems caused by many oxygen-containing functional groups and poor floatability on the surface of low rank coal,the characteristics of low rank coal were analyzed systematically by means of scanning electron microscopy(SEM),X-ray diffraction(XRD)and X-Ray photoelectron spectroscopy(XPS)techniques.The bubble-particle induction time was used to determine the characterization of the bubble-particle attachment,and the bubble-particle attachment of low rank coal modified by soaking the coal samples in an acid or alkaline solution was analyzed.The floatability of the modified coal surface was verified by flotation tests.The results show that the particle size of 0.125–0.074 mm of the coal sample exhibited better bubble-particle attachment characteristics.The small bubble,the larger approach velocity of bubble and the larger bubble deformation were more helpful to enhance the bubbleparticle attachment.For an acid solution,the smaller the p H was and the longer the soaking time was,the better the floatability of the coal sample and the higher the combustible material recovery were.The combustible material recovery of low rank coal was increased to 78.79%by soaking the sample in an acid solution of pH=0 for 180 min.On the contrary there was a best concentration for the alkaline solution.

Influence of heating rate on reactivity and surface chemistry of chars derived from pyrolysis of two Chinese low rank coals

A series of char samples were derived from pyrolysis of two typical low-rank coals in China(Shengli lignite and Shenmu bituminous coal) at low, medium and fast heating rates, respectively, to the same pyrolysis temperature 750 °C. Then these chars were characterized by means of thermogravimetric analysis and Fourier transform infrared spectrometer with the aim to investigate the influence of heating rate in pyrolysis process on gasification reactivity and surface chemistry of them. Besides, a homogeneous model was used to quantitatively analyze the activation energy of gasification reaction. The results reveal that Shengli lignite and its derived chars behave higher gasification reactivity and have less content of oxygen functional groups than Shenmu coal and chars. Meanwhile, chars derived from Shengli lignite at 50 °C/min and Shenmu coal at 200 °C/min have the greatest gasification reactivity, respectively. The oxygen functional groups in Shengli lignite are easily thermo-decomposed, and they are less affected by the heating rate, while that in Shenmu coal have a significant change with the variation of heating rate.In addition, there is no good correlation between the change of oxygen functional groups and that of the gasification reactivity of the derived chars from pyrolysis at different heating rates.

The mechanism and products for co-thermal extraction of biomass and low-rank coal with NMP

The high-value utilization of low-rank coal would allow for expanding energy sources,improving energy efficiencies,and alleviating environmental issues.In order to use low-rank coal effectively,the hypercoals(HPCs)were co-extracted from two types of low-rank coal and biomass via N-methyl-2-purrolidinone(NMP)under mild conditions.The structures of the HPCs and residues were characterized by proximate and ultimate analysis,Raman spectra,and Fourier transform infrared(FT-IR)spectra.The carbon structure changes within the raw coals and HPCs were discussed.The individual thermal dissolution of Xibu(XB)coal,Guandi(GD)coal,and the biomass demonstrated that the biomass provided the lowest thermal dissolution yield Y1 and the highest thermal soluble yield Y2 at 280℃,and the ash content of three HPCs decreased as the extraction temperature rose.Co-thermal extractions in NMP at various coal/biomass mass ratios were performed,demonstrating a positive synergic effect for Y2 in the whole coal/biomass mass ratios.The maximum value of Y2 was 52.25wt% for XB coal obtained with a XB coal/biomass of 50wt% biomass.The maximum value of Y2 was 50.77wt% for GD coal obtained with a GD coal/biomass of 1:4.The difference for the optimal coal/biomass mass ratios between XB and GD coals could be attributed to the different co-extraction mechanisms for this two type coals.

Resistivity response to the porosity and permeability of low rank coal

Laojunmiao coal samples from the eastern Junggar basin were studied to understand the relationship between coal resistivity and the physical parameters of coal reservoirs under high temperatures and pressures.Specifically,we analysed the relationship of coal resistivity to porosity and permeability via heating and pressurization experiments.The results indicated that coal resistivity decreases exponentially with increasing pressure.Increasing the temperature decreases the resistivity.The sensitivity of coal resistivity to the confining pressure is worse when the temperature is higher.The resistivity of dry coal samples was linearly related to φ~m.Increasing the temperature decreased the cementation exponent(m).Increasing the confining pressure exponentially decreases the porosity.Decreasing the pressure increases the resistivity and porosity for a constant temperature.Increasing the temperature yields a quadratic relationship between the resistivity and permeability for a constant confining pressure.Based on the Archie formula,we obtained the coupling relationship between coal resistivity and permeability for Laojunmiao coal samples at different temperatures and confining pressures.

Co-pyrolysis characteristics and interaction route between low-rank coals and Shenhua coal direct liquefaction residue

To reasonably utilize the coal direct liquefaction residue(DLR), contrasting research on the co-pyrolysis between different low-rank coals and DLR was investigated using a TGA coupled with an FT-IR spectrophotometer and a fixed-bed reactor. GC–MS, FTIR, and XRD were used to explore the reaction mechanisms of the various co-pyrolysis processes. Based on the TGA results, it was confirmed that the tetrahydrofuran insoluble fraction of DLR helped to catalyze the conversion reaction of lignite. Also, the addition of DLR improved the yield of tar in the fixed-bed, with altering the composition of the tar. Moreover, a kinetic analysis during the co-pyrolysis was conducted using a distributed activation energy model. The co-pyrolysis reactions showed an approximate double-Gaussian distribution.

Separation and analysis of six fractions in low temperature coal tar by column chromatography

The low temperature coal tar(CT)is taken as the raw material,and the extraction and column chromatography are used for detailed and accurate characterization in this paper.The n-heptane soluble fraction(CT-HS)and insoluble fraction(CT-HI)were obtained by n-heptane Soxhlet extraction.The extraction rate of CT-HS reached 92.79%(mass),which indicated that there are few heavy compounds in it.Further,different solvents(methylbenzene,benzene,ethyl acetate,methylbenzene-ethanol)were used to elute CT-HS by chromatographic column to obtain five fractions(saturates,aromatics,heteroatoms,phenolics and resins,named CT-SA,CT-AR,CT-HE,CT-PH,CT-RE,respectively).The yields of CTSA,CT-AR,CT-HE,CT-PH,CT-RE are 42.12%,10.43%,2.19%,9.50%and 6.63%(mass),respectively.Gas chromatography-mass spectrometry analysis of eluting components show that alkanes are the main components in CT,followed by polycyclic aromatics,and the corresponding fractions are CT-SA and CT-AR,respectively.The relative content of aliphatics in CT-SA is 76.93%,and the relative content of aromatics in CT-AR is 75.05%.This separation technology effectively separates and enriches different components in CT,and the activation energy required for the pyrolysis process of a single eluting fraction is lower than that of CT,which is expected to provide an important reference for the separation,analysis and conversion of complex oil products such as coal-oil co-processing products,coal tar and other complex heavy carbon oil products.

Investigation of Low Rank Coal Gasification in a Two-Stage Downdraft Entrained-Flow Gasifier

Low-rank coal contains more inherent moisture, high alkali metals (Na, K, Ca), high oxygen content, and low sulfur than high-rank coal. Low-rank coal gasification usually has lower efficiency than high-rank coal, since more energy has been used to drive out the moisture and volatile matters and vaporize them. Nevertheless, Low-rank coal comprises about half of both the current utilization and the reserves in the United States and is the largest energy resource in the United States, so it is worthwhile and important to investigate the low-rank coal gasification process. In this study, the two-stage fuel feeding scheme is investigated in a downdraft, entrained-flow, and refractory-lined reactor. Both a high-rank coal (Illinois No.6 bituminous) and a low-rank coal (South Hallsville Texas Lignite) are used for comparison under the following operating conditions: 1) low-rank coal vs. high-rank coal, 2) one-stage injection vs. two-stage injection, 3) low-rank coal with pre-drying vs. without pre-drying, and 4) dry coal feeding without steam injection vs. with steam injection at the second stage. The results show that 1) With predrying to 12% moisture, syngas produced from lignite has 538 K lower exit temperature and 18% greater Higher Heating Value (HHV) than syngas produced from Illinois #6. 2) The two-stage fuel feeding scheme results in a lower wall temperature (around 100 K) in the lower half of the gasifier than the single-stage injection scheme. 3) Without pre-drying, the high inherent moisture content in the lignite causes the syngas HHV to decrease by 27% and the mole fractions of both H2 and CO to decrease by 33%, while the water vapor content increases by 121% (by volume). The low-rank coal, without pre-drying, will take longer to finish the demoisturization and devolatilization processes, resulting in delayed combustion and gasification processes.

Combustion characteristics of semicokes derived from pyrolysis of low rank bituminous coal

Various semicokes were obtained from medium-low temperature pyrolysis of Dongrong long flame coal.The proximate analysis,calorific value and Hardgrove grindability index(HGI) of semicokes were determined,and the ignition temperature,burnout temperature,ignition index,burnout index,burnout ratio,combustion characteristic index of semicokes were measured and analyzed using thermogravimetry analysis(TGA).The effects of pyrolysis temperature,heating rate,and pyrolysis time on yield,composition and calorific value of long flame coal derived semicokes were investigated,especially the influence of pyrolysis temperature on combustion characteristics and grindability of the semicokes was studied combined with X-ray diffraction(XRD) analysis of semicokes.The results show that the volatile content,ash content and calorific value of semicokes pyrolyzed at all process parameters studied meet the technical specifications of the pulverized coal-fired furnaces(PCFF) referring to China Standards GB/T 7562-1998.The pyrolysis temperature is the most influential factor among pyrolysis process parameters.As pyrolysis temperature increases,the yield,ignition index,combustion reactivity and burnout index of semicokes show a decreasing tend,but the ash content increases.In the range of 400 and 450 °C,the grindability of semicokes is rational,especially the grindability of semicokes pyrolyzed at 450 °C is suitable.Except for the decrease of volatile content and increase of ash content,the decrease of combustion performance of semicokes pyrolyzed at higher temperature should be attributed to the improvement of the degree of structural ordering and the increase of aromaticity and average crystallite size of char.It is concluded that the semicokes pyrolyzed at the temperature of 450 °C is the proper fuel for PCFF.

Structure and production fluid flow pattern of post-fracturing high-rank coal reservoir in Southern Qinshui Basin

Field geological work, field engineering monitoring, laboratory experiments and numerical simulation were used to study the development characteristics of pore-fracture system and hydraulic fracture of No.3 coal reservoir in Southern Qinshui Basin. Flow patterns of methane and water in pore-fracture system and hydraulic fracture were discussed by using limit method and average method. Based on the structure model and flow pattern of post-fracturing high-rank coal reservoir, flow patterns of methane and water were established. Results show that seepage pattern of methane in pore-fracture system is linked with pore diameter, fracture width, coal bed pressure and flow velocity. While in hydraulic fracture, it is controlled by fracture height, pressure and flow velocity. Seepage pattern of water in pore-fracture system is linked with pore diameter, fracture width and flow velocity. While in hydraulic fracture, it is controlled by fracture height and flow velocity. Pores and fractures in different sizes are linked up by ultramicroscopic fissures, micro-fissures and hydraulic fracture. In post-fracturing high-rank coal reservoir, methane has level-three flow and gets through triple medium to the wellbore; and water passes mainly through double medium to the wellbore which is level-two flow.

Geological characteristics and exploration breakthroughs of coal rock gas in Carboniferous Benxi Formation,Ordos Basin,NW China

To explore the geological characteristics and exploration potential of the Carboniferous Benxi Formation coal rock gas in the Ordos Basin,this paper presents a systematic research on the coal rock distribution,coal rock reservoirs,coal rock quality,and coal rock gas features,resources and enrichment.Coal rock gas is a high-quality resource distinct from coalbed methane,and it has unique features in terms of burial depth,gas source,reservoir,gas content,and carbon isotopic composition.The Benxi Formation coal rocks cover an area of 16×104km^(2),with thicknesses ranging from 2 m to 25 m,primarily consisting of bright and semi-bright coals with primitive structures and low volatile and ash contents,indicating a good coal quality.The medium-to-high rank coal rocks have the total organic carbon(TOC)content ranging from 33.49%to 86.11%,averaging75.16%.They have a high degree of thermal evolution(Roof 1.2%-2.8%),and a high gas-generating capacity.They also have high stable carbon isotopic values(δ13C1of-37.6‰to-16‰;δ13C2of-21.7‰to-14.3‰).Deep coal rocks develop matrix pores such as gas bubble pores,organic pores,and inorganic mineral pores,which,together with cleats and fractures,form good reservoir spaces.The coal rock reservoirs exhibit the porosity of 0.54%-10.67%(averaging 5.42%)and the permeability of(0.001-14.600)×10^(-3)μm^(2)(averaging 2.32×10^(-3)μm^(2)).Vertically,there are five types of coal rock gas accumulation and dissipation combinations,among which the coal rock-mudstone gas accumulation combination and the coal rock-limestone gas accumulation combination are the most important,with good sealing conditions and high peak values of total hydrocarbon in gas logging.A model of coal rock gas accumulation has been constructed,which includes widespread distribution of medium-to-high rank coal rocks continually generating gas,matrix pores and cleats/fractures in coal rocks acting as large-scale reservoir spaces,tight cap rocks providing sealing,source-reservoir integration,and five types of efficient enrichment patterns(lateral pinchout complex,lenses,low-amplitude structures,nose-like structures,and lithologically self-sealing).According to the geological characteristics of coal rock gas,the Benxi Formation is divided into 8 plays,and the estimated coal rock gas resources with a buried depth of more than 2000 m are more than 12.33×10^(12)m^(3).The above understandings guide the deployment of risk exploration.Two wells drilled accordingly obtained an industrial gas flow,driving the further deployment of exploratory and appraisal wells.Substantial breakthroughs have been achieved,with the possible reserves over a trillion cubic meters and the proved reserves over a hundred billion cubic meters,which is of great significance for the reserves increase and efficient development of natural gas in China.

Carbon monoxide adsorptive capability of low rank coal's maceral

The centrifugal separation with gravity experiment was made for getting every pure macerals like inertinite and vitrinite,and the isothermal adsorption tests of pure mac- eral are carried out at 30,40,50,55,60,65℃,respectively,after analyzing the proximate element and maceral of coal samples,which was aimed to study the CO adsorptive capa- bility of every maceral of low rank coal at difference temperature and pressure.The results show that the adsorption isotherm of CO can be described by Langmuir equation because it belongs to the Type I adsorption isotherm at low temperature(T≤50℃),and the tem- perature effect on coal adsorption is greater than of pressure in lower temperature and pressure area;what's more,the relationship is linear between the coal adsorption quantity of CO and the pressure at high temperature(T>50℃),it can be described by Henry equation(Q=KP),which increases with pressure.Both temperature and pressure has great influence on CO adsorptive capability of low rank coals,especially the temperature's effect is so very complex that the mechanism need to study further.At the same time,the volatile matter,inertinite,oxygen-function groups and negative functional groups are high popu- larly in low rank coal samples,especially,the content of hydroxide(-OH) has great influ- ence on CO adsorption in that the inertinite has stronger effect than vitrinite on adsorptive capability of low rank coal samples,the result is same to the research on CH4 adsorption.

Pore Characteristics of Vitrain and Durain in Low Rank Coal Area

The low rank coalbed methane (CBM) has great potential for exploration and development in China, but its exploitation level is low at present stage. The pores are the storage space of CBM, so recognizing its structural characteristics has very important practical significance for the development of CBM. The samples of No. 4 and upper No. 4 coalbed in Dafosi were selected to carry out the analysis of mercury injection test, nitrogen adsorption test and scanning electron microscopy to study the different lithotypes of the pore structure, pore throat distribution and fracture character of low rank coal reservoir. The results showed that micropore of low rank coal in Dafosi relatively developed and the pore volume of vitrain was equivalent to durain. The pore throat of durain was larger than vitrain, the connectivity was better and the fissures were more developed. The percolation capacity and reservoir performance of upper No. 4 coal was better than No. 4 coal. Generally, the potential of exploration and development of upper No. 4 coal in the study area was better than that of No. 4, and the developed area of durain was more beneficial for the development of CBM.