A reduced basis method based on a physics-informed machine learning framework is developed for efficient reduced-order modeling of parametrized partial differential equations (PDEs). A feedforward ...neural network is used to approximate the mapping from the time-parameter to the reduced coefficients. During the offline stage, the network is trained by minimizing the weighted sum of the residual loss of the reduced-order equations, and the data loss of the labeled reduced coefficients that are obtained via the projection of high-fidelity snapshots onto the reduced space. Such a network is referred to as physics-reinforced neural network (PRNN). As the number of residual points in time-parameter space can be very large, an accurate network – referred to as physics-informed neural network (PINN) – can be trained by minimizing only the residual loss. However, for complex nonlinear problems, the solution of the reduced-order equation is less accurate than the projection of high-fidelity solution onto the reduced space. Therefore, the PRNN trained with the snapshot data is expected to have higher accuracy than the PINN. Numerical results demonstrate that the PRNN is more accurate than the PINN and a purely data-driven neural network for complex problems. During the reduced basis refinement, the PRNN may obtain higher accuracy than the direct reduced-order model based on a Galerkin projection. The online evaluation of PINN/PRNN is orders of magnitude faster than that of the Galerkin reduced-order model.
•Physics-informed machine learning of reduced-order model without requirement of extra high-fidelity snapshots.•A PINN trained by minimizing the residual loss of the reduced-order equation.•A PRNN with improved accuracy obtained by adding the regression loss on the available high-fidelity snapshots data.•Higher accuracy of PRNN on small reduced basis than the direct reduced-order model based on a Galerkin projection.•PRNN as an accurate and efficient reduced-order modeling tool for general nonlinear problems.
Dimensionality reduction (DR) is an important way of improving the classification accuracy of a hyperspectral image (HSI). Graph learning, which can effectively reveal the intrinsic relationships of ...data, has been widely used in the case of HSIs. However, most of them are based on a simple graph to represent the binary relationships of data. An HSI contains complex high-order relationships among different samples. Therefore, in this article, we propose a hybrid-graph learning method to reveal the complex high-order relationships of the HSI, termed enhanced hybrid-graph discriminant learning (EHGDL). In EHGDL, an intraclass hypergraph and an interclass hypergraph are constructed to analyze the complex multiple relationships of a HSI. Then, a supervised locality graph is applied to reveal the binary relationships of a HSI which can form the complementarity of a hypergraph. Simultaneously, we also construct a weighted neighborhood margin model to boost the difference of samples from different classes. Finally, we design a DR model based on the intraclass hypergraph, the interclass hypergraph, the supervised locality graph, and the weighted neighborhood margin to improve the compactness of the intraclass samples and the separability of the interclass samples, and an optimal projection matrix can be achieved to extract the low-dimensional embedding features of the HSI. To demonstrate the effectiveness of the proposed method, experiments have been conducted on the Indian Pines, PaviaU, and HoustonU data sets. The experimental results show that EHGDL can generate better classification performance compared with some related DR methods. As a result, EHGDL can better reveal the complex intrinsic relationships of a HSI by the complementarity of different characteristics and enhance the discriminant performance of land-cover types.
Copper slag particles were prepared by rotary cup atomizer. Carbon-containing copper slag pellets were prepared by copper slag particles, carbon reductant, binder and slag former. The effects of six ...factors on reduction ratio of carbon-containing copper slag pellets were in accordance with the sequence of reaction temperature > the ratio of slag former > atmosphere > the types of reduction reductant > particle size of copper slag > the addition ratio of reductant, under experiment conditions. The optimum condition for direct reduction of carbon-containing copper slag pellets was that the reaction temperature was 1150℃, the ratio of slag former was 1∶0.4, atmosphere was CO2(50%)+N2(50%), the reductant was coal, particle size of copper slag was +0.425 mm and the addition ratio of reductant was 1.2∶1. On this condition, the reduction ratio of copper slag is 98.2%.
For the first time total structure determination of homoleptic alkynyl‐protected gold nanoclusters is reported. The nanoclusters are synthesized by direct reduction of PhC≡CAu, to give Au44(PhC≡C)28 ...and Au36(PhC≡C)24. The Au44 and Au36 nanoclusters have fcc‐type Au36 and Au28 kernels, respectively, as well as surrounding PhC≡C‐Au‐C2(Ph)Au‐C≡CPh dimeric “staples” and simple PhC≡C bridges. The structures of Au44(PhC≡C)28 and Au36(PhC≡C)24 are similar to Au44(SR)28 and Au36(SR)24, but the UV/Vis spectra are different. The protecting ligands influence the electronic structures of nanoclusters significantly. The synthesis of these two alkynyl‐protected gold nanoclusters indicates that a series of gold nanoclusters in the general formula Aux(RC≡C)y as counterparts to Aux(SR)y can be expected.
All alkynyl: The structure determinations of Au44(PhC≡C)28 and Au36(PhC≡C)24 are the first of homoleptic alkynyl‐protected gold nanoclusters. The structures are similar to those of Au44(SR)28 and Au36(SR)24, respectively, but the UV/Vis spectra are distinctly different.
As the European Union intensifies its response to the climate emergency, increased focus has been placed on the hard-to-abate energy-intensive industries. Primary among these is the steel industry, a ...cornerstone of the European economy and industry. With the emergence of new hydrogen-based steelmaking options, particularly through hydrogen direct reduction, the structure of global steel production and supply chains will transition from being based on low-cost coal resources to that based on low-cost electricity and therefore hydrogen production. This study examines the techno-economic options for three European countries of Germany, Spain, and Finland under five different steel supply chain configurations compared to local production. Results suggest that the high costs of hydrogen transportation make a European steelmaking supply chain cost competitive to steel produced with imported hydrogen, with local production costs ranging from 465 to 545 €/t of crude steel (CS) and 380–494 €/tCS for 2030 and 2040, respectively. Conversely, imports of hot briquetted iron and crude steel from Morocco become economically competitive with European supply chains. Given the capital and energy intensive nature of the steel industry, critical investment decisions are required in this decade, and this research serves to provide a deeper understanding of supply chain options for Europe.
•Hydrogen-based steelmaking in Europe can be cost competitive to coal-based routes.•European green steelmaking costs are competitive to hydrogen imports.•Hot briquetted iron imports would reduce steelmaking costs in Europe.•Investments in green steel this decade are crucial to steel defossilisation.
This study investigates the integration of water electrolysis technologies in fossil-free steelmaking via the direct reduction of iron ore followed by processing in an electric arc furnace (EAF). ...Hydrogen (H2) production via low or high temperature electrolysis (LTE and HTE) is considered for the production of carbon-free direct reduced iron (DRI). The introduction of carbon into the DRI reduces the electricity demand of the EAF. Such carburization can be achieved by introducing carbon monoxide (CO) into the direct reduction process. Therefore, the production of mixtures of H2 and CO using either a combination of LTE coupled with a reverse water-gas shift reactor (rWGS-LTE) or high-temperature co-electrolysis (HTCE) was also investigated. The results show that HTE has the potential to reduce the specific electricity consumption (SEC) of liquid steel (LS) production by 21% compared to the LTE case. Nevertheless, due to the high investment cost of HTE units, both routes reach similar LS production costs of approximately 400 €/tonne LS. However, if future investment cost targets for HTE units are reached, a production cost of 301 €/tonne LS is attainable under the conditions given in this study. For the production of DRI containing carbon, a higher SEC is calculated for the LTE-rWGS system compared to HTCE (4.80 vs. 3.07 MWh/tonne LS). Although the use of HTCE or LTE-rWGS leads to similar LS production costs, future cost reduction of HTCE could result in a 10% reduction in LS production cost (418 vs. 375 €/tonne LS). We show that the use of HTE, either for the production of pure H2 or H2 and CO mixtures, may be advantageous compared to the use of LTE in H2-based steelmaking, although results are sensitive to electrolyzer investment costs, efficiencies, and electricity prices.
•Reduction of iron ore with hydrogen using water electrolysis technologies.•Reduction in specific electricity consumption with high temperature electrolysis.•Addition of carbon in reduced iron using syngas produced with co-electrolysis.•Estimated cost of producing carbon-free and carbon containing liquid steel.•Electricity price and electrolyzer CAPEX are major parameters affecting cost of liquid steel.
In this study, the influence and mechanism of SiO2 on the gas-based direct reduction behavior of Hongge vanadium titanomagnetite pellet (HVTMP) by hydrogen-rich gases was investigated. Increasing ...SiO2 during the initial stage caused the reduction degree of HVTMP to initially increase and then decrease. At the later stage, SiO2 retarded the reduction, and this effect increased upon increasing the SiO2 addition. SiO2 caused the decrease of the metallization degree by forming hardly reducible Fe2SiO4 and hindering the further reduction of Fe2TiO4 to Fe. The size of metallic iron grains diminished gradually, and the boundary between the metallic iron phase and the slag phase became less obvious with the increase of SiO2 addition. Additionally, the number of metallic iron whiskers decreased, and the growth of metallic iron whiskers transformed from dispersed to close clusters, which decreased the reduction swelling. This study provides a theoretical and technical basis for the smelting of Hongge vanadium titanomagnetite in shaft furnaces by hydrogen-rich gases.
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•SiO2 decreased the rate of hydrogen-rich reduction.•The influence mechanism of SiO2 was revealed.•Increasing SiO2 significantly affected the microstructure.•SiO2 prevented the reduction swelling.
The present paper describes the direct reduction kinetics of industrial iron oxide pellets in various compositions of hydrogen and carbon monoxide. Different types of pellets with various percentages ...of total iron content and metal oxides were examined. They were reduced at different temperatures and pressure (700–1100 °C and 1–6 bar) in various atmosphere with different contents of hydrogen and carbon monoxide. The reduction behaviour was described in terms of time to reduction, rate of reduction and kinetics constant. All the obtained results were analysed through the employment of a commercial multi-objective optimization tool (modeFrontier) in order to precisely define the weight that each single parameter has on the reduction behaviour of the pellets. The performed analyses allowed also to correlate the different processing parameters and the pellets properties in order to define the kinetics conditions as well as the factors limiting the reduction process.
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•Both pellets properties and processing parameters largely influence the direct reduction.•It was precisely identified the effect of hydrogen on the improvement of kinetics reactions.•The weight of the different parameters on the kinetics of reduction were underlined.
An innovative technical route has been proposed to improve recycling efficiency of Ni and Fe from low-grade nickel laterite via the duplex process between direct reduction-magnetic separation and ...rotary kiln-electric furnace. The results indicated that the high‑nickel concentrates produced from direct reduction-magnetic separation process, which were combined with optimization of slag types can not only increase the grade of furnace burdens and decrease quantity of slag, but also improve the fluidity of slag and smelting efficiency as well as reduce the power consumption of smelting. For the industrial application of duplex process, a preferable stainless-steel master alloy with 10.02% Ni was obtained at a lower cost of 8420 RMB/t than that of 8731 RMB/t for a stainless-steel master alloy containing 8.14% Ni in conventional rotary kiln-electric furnace process, and the recovery of nickel also increased from 91.27% to 95.51%, which shows an obvious superiority for treating the low-grade nickel laterite.
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•An effective and economical way for processing low-grade nickel laterite was proposed.•The strengthening mechanism of DRMS-RKEF for recycling Ni and Fe was revealed.•The performance and prospect of DRMS-RKEF into industrial application were clarified.
The technological advancement in the communication and control infrastructure helps those smart households (SHs) that more actively participate in the incentive-based demand response (IBDR) programs. ...As the agent facilitating the SHs' participation in the IBDR program, load aggregators (LAs) need to comprehend the available SHs' demand response (DR) capacity before trading in the day-ahead market. However, there are few studies that forecast the available aggregated DR capacity from LAs' perspective. Therefore, this article proposes a forecasting model aiming to aid LAs forecast the available aggregated SHs' DR capacity in the day-ahead market. First, a home energy management system is implemented to perform optimal scheduling for SHs and to model the customers' responsive behavior in the IBDR program; second, a customer baseline load estimation method is applied to quantify the SHs' aggregated DR capacity during DR days; third, several features which may have significant impacts on the aggregated DR capacity are extracted and they are processed by principal component analysis; and finally, a support vector machine based forecasting model is proposed to forecast the aggregated SHs' DR capacity in the day-ahead market. The case study indicates that the proposed forecasting framework could provide good performance in terms of stability and accuracy.
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