Discrete multi-step phase hologram for high frequency acoustic modulation

Acoustic holograms can recover wavefront stored acoustic field information and produce high-fidelity complex acoustic fields. Benefiting from the huge spatial information that traditional acoustic elements cannot match, acoustic holograms pursue the realization of high-resolution complex acoustic fields and gradually tend to high-frequency ultrasound applications. However, conventional continuous phase holograms are limited by three-dimensional(3D) printing size, and the presence of unavoidable small printing errors makes it difficult to achieve acoustic field reconstruction at high frequency accuracy. Here, we present an optimized discrete multi-step phase hologram. It can ensure the reconstruction quality of image with high robustness, and properly lower the requirement for the 3D printing accuracy. Meanwhile, the concept of reconstruction similarity is proposed to refine a measure of acoustic field quality. In addition, the realized complex acoustic field at 20 MHz promotes the application of acoustic holograms at high frequencies and provides a new way to generate high-fidelity acoustic fields.

Adaptive Multi-Step Evaluation Design With Stability Guarantee for Discrete-Time Optimal Learning Control

This paper is concerned with a novel integrated multi-step heuristic dynamic programming(MsHDP)algorithm for solving optimal control problems.It is shown that,initialized by the zero cost function,MsHDP can converge to the optimal solution of the Hamilton-Jacobi-Bellman(HJB)equation.Then,the stability of the system is analyzed using control policies generated by MsHDP.Also,a general stability criterion is designed to determine the admissibility of the current control policy.That is,the criterion is applicable not only to traditional value iteration and policy iteration but also to MsHDP.Further,based on the convergence and the stability criterion,the integrated MsHDP algorithm using immature control policies is developed to accelerate learning efficiency greatly.Besides,actor-critic is utilized to implement the integrated MsHDP scheme,where neural networks are used to evaluate and improve the iterative policy as the parameter architecture.Finally,two simulation examples are given to demonstrate that the learning effectiveness of the integrated MsHDP scheme surpasses those of other fixed or integrated methods.

Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

Virtual Machine Consolidation with Multi-Step Prediction and Affinity-Aware Technique for Energy-Efficient Cloud Data Centers

Virtual machine(VM)consolidation is an effective way to improve resource utilization and reduce energy consumption in cloud data centers.Most existing studies have considered VM consolidation as a bin-packing problem,but the current schemes commonly ignore the long-term relationship between VMs and hosts.In addition,there is a lack of long-term consideration for resource optimization in the VM consolidation,which results in unnecessary VM migration and increased energy consumption.To address these limitations,a VM consolidation method based on multi-step prediction and affinity-aware technique for energy-efficient cloud data centers(MPaAF-VMC)is proposed.The proposed method uses an improved linear regression prediction algorithm to predict the next-moment resource utilization of hosts and VMs,and obtains the stage demand of resources in the future period through multi-step prediction,which is realized by iterative prediction.Then,based on the multi-step prediction,an affinity model between the VM and host is designed using the first-order correlation coefficient and Euclidean distance.During the VM consolidation,the affinity value is used to select the migration VM and placement host.The proposed method is compared with the existing consolidation algorithms on the PlanetLab and Google cluster real workload data using the CloudSim simulation platform.Experimental results show that the proposed method can achieve significant improvement in reducing energy consumption,VM migration costs,and service level agreement(SLA)violations.

Banach空间中Mann-Ishikawa迭代和Multi-Step迭代的等价性问题

本文研究了一致光滑Banach空间中迭代算法等价性的问题.利用泛函分析的方法,获得了广义强连接Φ伪压缩算子在具误差的修正的Mann-Ishikawa迭代和具误差的修正的multi-step迭代下收敛等价性的结果,推广了目前的相关结果.

Strategies for multi-step-ahead available parking spaces forecasting based on wavelet transform

A new methodology for multi-step-ahead forecasting was proposed herein which combined the wavelet transform(WT), artificial neural network(ANN) and forecasting strategies based on the changing characteristics of available parking spaces(APS). First, several APS time series were decomposed and reconstituted by the wavelet transform. Then, using an artificial neural network, the following five strategies for multi-step-ahead time series forecasting were used to forecast the reconstructed time series: recursive strategy, direct strategy, multi-input multi-output(MIMO) strategy, DIRMO strategy(a combination of the direct and MIMO strategies), and newly proposed recursive multi-input multi-output(RECMO) strategy which is a combination of the recursive and MIMO strategies. Finally, integrating the predicted results with the reconstructed time series produced the final forecasted available parking spaces. Three findings appear to be consistently supported by the experimental results. First, applying the wavelet transform to multi-step ahead available parking spaces forecasting can effectively improve the forecasting accuracy. Second, the forecasting resulted from the DIRMO and RECMO strategies is more accurate than that of the other strategies. Finally, the RECMO strategy requires less model training time than the DIRMO strategy and consumes the least amount of training time among five forecasting strategies.

Nonlinear system PID-type multi-step predictive control

A compound neural network was constructed during the process of identification and multi-step prediction. Under the PID-type long-range predictive cost function, the control signal was calculated based on gradient algorithm. The nonlinear controller’s structure was similar to the conventional PID controller. The parameters of this controller were tuned by using a local recurrent neural network on-line. The controller has a better effect than the conventional PID controller. Simulation study shows the effectiveness and good performance.

A hybrid decomposition-boosting model for short-term multi-step solar radiation forecasting with NARX neural network

Due to global energy depletion,solar energy technology has been widely used in the world.The output power of the solar energy systems is affected by solar radiation.Accurate short-term forecasting of solar radiation can ensure the safety of photovoltaic grids and improve the utilization efficiency of the solar energy systems.In the study,a new decomposition-boosting model using artificial intelligence is proposed to realize the solar radiation multi-step prediction.The proposed model includes four parts:signal decomposition(EWT),neural network(NARX),Adaboost and ARIMA.Three real solar radiation datasets from Changde,China were used to validate the efficiency of the proposed model.To verify the robustness of the multi-step prediction model,this experiment compared nine models and made 1,3,and 5 steps ahead predictions for the time series.It is verified that the proposed model has the best performance among all models.

Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network

This paper proposes a co-evolutionary recurrent neural network （CERNN） for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by coevolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets： the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series.

Accurate Multi-Site Daily-Ahead Multi-Step PM_(2.5)Concentrations Forecasting Using Space-Shared CNN-LSTM

Accurate multi-step PM_(2.5)(particulate matter with diameters≤2.5 um)concentration prediction is critical for humankinds’health and air populationmanagement because it could provide strong evidence for decisionmaking.However,it is very challenging due to its randomness and variability.This paper proposed a novel method based on convolutional neural network(CNN)and long-short-term memory(LSTM)with a space-shared mechanism,named space-shared CNN-LSTM(SCNN-LSTM)for multi-site dailyahead multi-step PM_(2.5)forecasting with self-historical series.The proposed SCNN-LSTM contains multi-channel inputs,each channel corresponding to one-site historical PM_(2.5)concentration series.In which,CNN and LSTM are used to extract each site’s rich hidden feature representations in a stack mode.Especially,CNN is to extract the hidden short-time gap PM_(2.5)concentration patterns;LSTM is to mine the hidden features with long-time dependency.Each channel extracted features aremerged as the comprehensive features for future multi-step PM_(2.5)concentration forecasting.Besides,the space-shared mechanism is implemented by multi-loss functions to achieve space information sharing.Therefore,the final features are the fusion of short-time gap,long-time dependency,and space information,which enables forecasting more accurately.To validate the proposed method’s effectiveness,the authors designed,trained,and compared it with various leading methods in terms of RMSE,MAE,MAPE,and R^(2)on four real-word PM_(2.5)data sets in Seoul,South Korea.The massive experiments proved that the proposed method could accurately forecast multi-site multi-step PM_(2.5)concentration only using self-historical PM_(2.5)concentration time series and running once.Specifically,the proposed method obtained averaged RMSE of 8.05,MAE of 5.04,MAPE of 23.96%,and R^(2)of 0.7 for four-site daily ahead 10-hourPM_(2.5)concentration forecasting.

Chaotic time series multi-step direct prediction with partial least squares regression

Considering chaotic time series multi-step prediction, multi-step direct prediction model based on partial least squares （PLS） is proposed in this article, where PLS, the method for predicting a set of dependent variables forming a large set of predictors, is used to model the dynamic evolution between the space points and the corresponding future points. The model can eliminate error accumulation with the common single-step local model algorithm~ and refrain from the high multi-collinearity problem in the reconstructed state space with the increase of embedding dimension. Simulation predictions are done on the Mackey-Glass chaotic time series with the model. The satisfying prediction accuracy is obtained and the model efficiency verified. In the experiments, the number of extracted components in PLS is set with cross-validation procedure.

Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.

Attention-based spatio-temporal graph convolutional network considering external factors for multi-step traffic flow prediction

Traffic flow prediction is an important part of the intelligent transportation system. Accurate multi-step traffic flow prediction plays an important role in improving the operational efficiency of the traffic network. Since traffic flow data has complex spatio-temporal correlation and non-linearity, existing prediction methods are mainly accomplished through a combination of a Graph Convolutional Network (GCN) and a recurrent neural network. The combination strategy has an excellent performance in traffic prediction tasks. However, multi-step prediction error accumulates with the predicted step size. Some scholars use multiple sampling sequences to achieve more accurate prediction results. But it requires high hardware conditions and multiplied training time. Considering the spatiotemporal correlation of traffic flow and influence of external factors, we propose an Attention Based Spatio-Temporal Graph Convolutional Network considering External Factors (ABSTGCN-EF) for multi-step traffic flow prediction. This model models the traffic flow as diffusion on a digraph and extracts the spatial characteristics of traffic flow through GCN. We add meaningful time-slots attention to the encoder-decoder to form an Attention Encoder Network (AEN) to handle temporal correlation. The attention vector is used as a competitive choice to draw the correlation between predicted states and historical states. We considered the impact of three external factors (daytime, weekdays, and traffic accident markers) on the traffic flow prediction tasks. Experiments on two public data sets show that it makes sense to consider external factors. The prediction performance of our ABSTGCN-EF model achieves 7.2%–8.7% higher than the state-of-the-art baselines.

Effects of yttrium addition and aging on mechanical properties of AA2024 fabricated through multi-step stir casting

The effects of yttrium and artificial aging on AA2024 alloy were investigated.The developed samples were further subjected to artificial aging at 190℃for 1-10 h with an interval of 1 h.The metallurgical characterization was done by scanning electron microscope and X-ray diffraction.The mechanical characterization like hardness and tensile strength of the samples was done using computerized Vickers hardness testing machine and universal testing machine.The microstructures revealed that addition of yttrium refined theα(Al)matrix and led to the formation of Al-Cu-Y intermetallic in the shape of Chinese script which strengthened the samples.Compared to the base metal,samples with yttrium addition showed better mechanical properties.The sample reinforced with 0.3 wt.%yttrium showed the highest mechanical properties with the hardness of 66 HV,UTS of 223 MPa,YS of 180 MPa,and elongation of 20.9%.The artificially aged samples showed that the peak hardening of all the samples took place within 5 h of aging at 190℃with Al2 Cu precipitation.Aging changed the intermetallic from Chinese script to the fibrous form.The optimum amount of yttrium addition to AA2024 was found to be 0.3 wt.%.

Damping of Oblique Ocean Waves by a Vertical Porous Structure Placed on a Multi-step Bottom

Oblique ocean wave damping by a vertical porous structure placed on a multi-step bottom topography is studied with the help of linear water wave theory. Some portion of the oblique wave, incident on the porous structure, gets reflected by the multi-step bottom and the porous structure, and the rest propagates into the water medium following the porous structure. Two cases are considered： first a solid vertical wall placed at a finite distance from the porous structure in the water medium following the porous structure and then a special case of an unbounded water medium following the porous structure. In both cases, boundary value problems are set up in three different media, the first medium being water, the second medium being the porous structure consisting ofp vertical regions-one above each step and the third medium being water again. By using the matching conditions along the virtualvertical boundaries, a system of linear equations is deduced. The behavior of the reflection coefficient and the dimensionless amplitude of the transmitted progressive wave due to different relevant parameters are studied. Energy loss due to the propagation of oblique water wave through the porous structure is also carried out. The effects of various parameters, such as number of evanescent modes, porosity, friction factor, structure width, number of steps and angle of incidence, on the reflection coefficient and the dimensionless amplitude of the transmitted wave are studied graphically for both cases. Number of evanescent modes merely affects the scattering phenomenon. But higher values of porosity show relatively lower reflection than that for lower porosity. Oscillation in the reflection coefficient is observed for lower values of friction factor but it disappears with an increase in the value of friction factor. Amplitude of the transmitted progressive wave is independent of the porosity of the structure. But lower value of friction factor causes higher transmission. The investigation is then carried out for the second case, i.e., when the wall is absent. The significant difference between the two cases considered here is that the reflection due to a thin porous structure is very high when the solid wall exists as compared to the case when no wall is present. Energy loss due to different porosity, friction factor, structure width and angle of incidence is also examined. Validity of our model is ascertained by matching it with an available one.

A Content-Aware Bitrate Selection Method Using Multi-Step Prediction for 360-Degree Video Streaming

A content-aware multi-step prediction control(CAMPC)algorithm is proposed to determine the bitrate of 360-degree videos,aim⁃ing to enhance the quality of experience(QoE)of users and reduce the cost of video content providers(VCP).The CAMPC algorithm first em⁃ploys a neural network to generate the content richness and combines it with the current field of view(FOV)to accurately predict the probability distribution of tiles being viewed.Then,for the tiles in the predicted viewport which directly affect QoE,the CAMPC algorithm utilizes a multi-step prediction for future system states,and accordingly selects the bitrates of multiple subsequent steps,instead of an instantaneous state.Meanwhile,it controls the buffer occupancy to eliminate the impact of prediction errors.We implement CAMPC on players by building a 360-degree video streaming platform and evaluating other advanced adaptive bitrate(ABR)rules through the real network.Experimental results show that CAMPC can save 83.5%of bandwidth resources compared with the scheme that completely transmits the tiles outside the viewport with the Dynamic Adaptive Streaming over HTTP(DASH)protocol.Besides,the proposed method can improve the system utility by 62.7%and 27.6%compared with the DASH official and viewport-based rules,respectively.

Influence of a multi-step process on the thickness reduction error of sheet metal in a flexible rolling process

Flexible rolling is a forming process based on thickness reduction, and the precision of thickness reduction is the key factor affecting bending deformation. The major purpose of the present work is to solve the problem of bending deformation error caused by insufficient thickness reduction. Under the condition of different rolling reductions with the same sheet thickness and the same thickness reduction with different sheet thicknesses, the thickness reduction error of sheet metal is analyzed. In addition, the bending deformation of sheet metal under the same conditions is discussed and the influence of the multi-step forming process on the thickness reduction error is studied. The results show that, under the condition of the same sheet thickness, the thickness reduction error increases with increasing rolling reduction because of an increase in work hardening. As rolling reduction increases, the longitudinal bending deformation decreases because of the decrease of the maximum thickness difference. Under the condition with the same thickness reduction, the thickness reduction error increases because of the decrease of the rolling force with increasing sheet thickness. As the sheet thickness increases, the longitudinal bending deformation increases because of the increase in the maximum thickness difference. A larger bending deformation is divided into a number of small bending deformations in a multi-step forming process, avoiding a sharp increase in the degree of work hardening; the thickness reduction error is effectively reduced in the multi-step forming process. Numerical simulation results agree with the results of the forming experiments.

Lagrangian simulation of multi-step and rate-limited chemical reactions in multi-dimensional porous media

Management of groundwater resources and remediation of groundwater pollution require reliable quantification of contaminant dynamics in natural aquifers, which can involve complex chemical dynamics and challenge traditional modeling approaches. The kinetics of chemical reactions in groundwater are well known to be controlled by medium heterogeneity and reactant mixing, motivating the development of particle-based Lagrangian approaches. Previous Lagrangian solvers have been limited to fundamental bimolecular reactions in typically one-dimensional porous media. In contrast to other existing studies, this study developed a fully Lagrangian framework, which was used to simulate diffusion-controlled, multi-step reactions in one-, two-, and three-dimensional porous media. The interaction radius of a reactant molecule, which controls the probability of reaction, was derived by the agent-based approach for both irreversible and reversible reactions. A flexible particle tracking scheme was then developed to build trajectories for particles undergoing mixing-limited, multi-step reactions. The simulated particle dynamics were checked against the kinetics for diffusion-controlled reactions and thermodynamic wellmixed reactions in one-and two-dimensional domains. Applicability of the novel simulator was further tested by(1) simulating precipitation of calcium carbonate minerals in a two-dimensional medium, and(2) quantifying multi-step chemical reactions observed in the laboratory. The flexibility of the Lagrangian simulator allows further refinement to capture complex transport affecting chemical mixing and hence reactions.

Impact of user influence on information multi-step communication in a micro-blog

User influence is generally considered as one of the most critical factors that affect information cascading spreading. Based on this common assumption, this paper proposes a theoretical model to examine user influence on the information multi-step communication in a micro-biog. The multi-steps of information communication are divided into first-step and non-first-step, and user influence is classified into five dimensions. Actual data from the Sina micro-blog is collected to construct the model by means of an approach based on structural equations that uses the Partial Least Squares （PLS） technique. Our experimental results indicate that the dimensions of the number of fans and their authority significantly impact the information of first-step conxrnunication. Leader rank has a positive impact on both first-step and non-first-step communication. Moreover, global centrality and weight of friends are positively related to the information non-first-step communication, but authority is found to have much less relation to it.

Bending Properties of GCr15 Steel Guide Rail under the Multi-step Loading

To analyze the bending properties of GCr15 steel guide rail based on the elastic-plastic theory, the novel bending loading method consisting of multi-step loading and corresponding unloading was applied in three specimens with different cross section shape and different heat treatment condition. According to the experimental results, using numerical calculation software program and the numerical simulation with finite element analysis （FEA）, the relationships among the maximal load and displacement on cross section shape with each step bend loading, the loading stroke with the heat treatment condition, and the loading stroke with cross section shape were gained, and also those curves were discussed qualitatively. Finally, the contrast results between the numerical simulation and experiment were carried out to study the influence about the multi-step loading on specimen. It is put forward that enlightenment for the straightening stroke in the precision linear guide rail manufacture process.