巧建“模”,妙激趣——例谈给数学知识建“模”

将抽象的数学知识和枯燥的数学学习活动用简单、生动、鲜明、具体的形象,通过直观性语言和感性化材料的辅助来展开数学问题的思维活动。使学生从具体可感的形象中,把理论与形象融为一体,完成从生动直观到抽象思维的飞跃。即借助比喻、类比、模拟、描绘等艺术手法,给学生以感性认识,使学生形成生动的表象或产生丰富的联想从而掌握难以理解的抽象原理、概念、公式和定理,使学生对客观事物的特点和规律有了更进一步的认识。这一方法便是给数学知识适当建＂模＂。给数学知识适当建＂模＂,在保证教学科学性的前提下,千方百计追求趣味性、生动性、形象性和实效性,能诱发学生的学习兴趣,帮助学生更好更快地领悟和掌握知识。

3D Printing with a 5-Axis FDM Printer Using Bézier Techniques

In the last decade,3D printing,especially fused deposition modeling(FDM),has revolutionized manufacturing with intricate designs.Traditional 3-axis FDM printers face challenges with complex geometries,but 5-axis versions offer more design freedom.However,it requires specialized strategies.This research presents a model for 5-axis FDM printers using Bézier curves with an algorithm to enhance print quality.The result shows significant accuracy improvements,especially for curve-based tasks.In addition,this study deepens the understanding of 5-axis FDM technology,setting a solid basis for further research and potentially refining manufacturing methods.

Gated Neural Network-Based Unsteady Aerodynamic Modeling for Large Angles of Attack

Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.

Non-cooperative Space Target Estimation Algorithm Without Prior Information Dependence Based on Temporal Line of Sight Constraint

Under single-satellite observation,the parameter estimation of the boost phase of high-precision space noncooperative targets requires prior information.To improve the accuracy without prior information,we propose a parameter estimation model of the boost phase based on trajectory plane parametric cutting.The use of the plane passing through the geo-center and the cutting sequence line of sight(LOS)generates the trajectory-cutting plane.With the coefficient of the trajectory cutting plane directly used as the parameter to be estimated,a motion parameter estimation model in space non-cooperative targets is established,and the Gauss-Newton iteration method is used to solve the flight parameters.The experimental results show that the estimation algorithm proposed in this paper weakly relies on prior information and has higher estimation accuracy,providing a practical new idea and method for the parameter estimation of space non-cooperative targets under single-satellite warning.

Dynamic evaluation of digital and green development policies based on text mining of the PMC framework

Aiming to identify policy topics and their evolutionary logic that enhance the digital and green development(dual development)of traditional manufacturing enterprises,address weaknesses in current policies,and provide resources for refining dual development policies,a total of 15954 dual development-related policies issued by national and various departmental authorities in China from January 2000 to August 2023 were analyzed.Based on topic modeling techniques and the policy modeling consistency(PMC)framework,the evolution of policy topics was visualized,and a dynamic assessment of the policies was conducted.The results show that the digital and green development policy framework is progressively refined,and the governance philosophy shifts from a“regulatory government”paradigm to a“service-oriented government”.The support pattern evolves from“dispersed matching”to“integrated symbiosis”.However,there are still significant deficiencies in departmental cooperation,balanced measures,coordinated links,and multi-stakeholder participation.Future policy improvements should,therefore,focus on guiding multi-stakeholder participation,enhancing public demand orientation,and addressing the entire value chain.These steps aim to create an open and shared digital industry ecosystem to promote the coordinated dual development of traditional manufacturing enterprises.

Simulation of Start-Up Process of Turbofan Engine Based on Full-State Characteristics of Fan

Difficulties in obtaining component characteristics in the sub-idle state of rotor constrain the simulation capabilities of ground and windmill start-up processes for turbofan engines.This paper proposes a backbone feature method based on conventional characteristics parameters to derive the full-state characteristics of fan.The application of the fan’s full-state characteristics in component-level model of turbofan engine enables zero-speed iterative simulation for ground start-up process and windmill simulation for windmill start-up process,thereby improving the simulation capability of sub-idle state during turbofan engine start-up.

Data Analysis and Modeling of Fiber Optic Gyroscope Drift

A data gathering system is designed for the interferometric fiber optic gyroscope (IFOG) of land strapdown inertial system. IFOG is tested and the testing curve is given. The test data of IFOG are analyzed with Allan variance method and each error coefficient is identified. Furthermore, a random drift error model for IFOG is built by the method of time series analysis. The conclusion provides supports for improving IFOG design and compensating for errors of IFOG in practice.

Modeling and Simulation of the Characteristics of Pneumatic Cushion Cylinders

The analysis of the characteristics of the cushion process of the pneumatic cushion cylinder is presented, and the nonlinear model of pneumatic cushion cylinders is built in the form of nonlinear differential equations. Besides, through the simulation of the pressure in the cushion chamber, the characteristics of the pneumatic cushion cylinder are obtained, which helps to understand the performance of the pneumatic cushion cylinder and improve or design the better cushion structure.

Three-dimensional orebody modelling and intellectualized longwall mining for stratiform bauxite deposits

Acoupled biharmonic spline and linear interpolation algorithm was proposed to create a three-dimensional smooth deposit model with minimal curvature containing grade and position data. To obtain the optimal technical parameters, such as cuttingheight and drum diameter, a virtual longwall mining procedure was modelled by simulating the actual fully mechanized longwall mining process. Based on the above work, a bauxite deposit in a longwall mining panel was modelled by scattered grade data from ores sampled on the entry wall. The deposit was then demarcated by industrial indexes and sliced according to the virtual longwallmining procedure. The results show that the proposed interpolation algorithm can depict the stratiform structure of bauxite depositsand that the uncovered bauxite deposit has high proportions of high-grade and rich ore. The ranges of optimal cutting height and drum diameters are 1.72-2.84 m and 1.42-1.72 m, respectively. Finally, an intellectualized longwall mining procedure was designed to guide the mining process with the lowest dilution and loss rates.

Dynamic analysis and optimization of car's body-in-white based on superelement approach

An approach based on the superelement theory is proposed, and it is applied to model the car's body-in-white as well as to dynamic simulation and optimization. This approach can improve the calculation speed and do the dynamic optimization among substructures respectively in the car's body design. To meet the car's design of harshness, a dynamic optimal design model, based on the mean square of vertical displacement response at two points of the car floor, is proposed. Satisfactory results are achieved.

Reconstructing DEM using TLS point cloud data and NURBS surface

Underground coal mining inevitably results in land surface subsidence.Acquiring information on land surface subsidence is important in the detection of surface change.However,conventional data acquisition techniques cannot always retrieve information on whole subsidence area.This study focuses on the reconstruction of a digital elevation model（DEM） with terrestrial laser scanning（TLS） point cloud data.Firstly,the methodology of the DEM with terrestrial 3-dimensional laser scanning is introduced.Then,a DEM modeling approach that involves the application of curved non-uniform rational B-splines（NURBS） surface is put forward.Finally,the performance of the DEM modeling approach with different surface inverse methods is demonstrated.The results indicate that the DEM based on the point cloud data and curved NURBS surface can achieve satisfactory accuracy.In addition,the performance of the hyperbolic paraboloid appears to be better than that of the elliptic paraboloid.The reconstructed DEM is continuous and can easily be integrated into other programs.Such features are of great importance in monitoring dynamic ground surface subsidence.

A rock-physical modeling method for carbonate reservoirs at seismic scale

Strong heterogeneity and complex pore systems of carbonate reservoir rock make its rock physics model building and fluid substitution difficult and complex. However, rock physics models connect reservoir parameters with seismic parameters and fluid substitution is the most effective tool for reservoir prediction and quantitative characterization. On the basis of analyzing complex carbonate reservoir pore structures and heterogeneity at seismic scale, we use the gridding method to divide carbonate rock into homogeneous blocks with independent rock parameters and calculate the elastic moduli of dry rock units step by step using different rock physics models based on pore origin and structural feature. Then, the elastic moduli of rocks saturated with different fluids are obtained using fluid substitution based on different pore connectivity. Based on the calculated elastic moduli of rock units, the Hashin-Shtrikman-Walpole elastic boundary theory is adopted to calculate the carbonate elastic parameters at seismic scale. The calculation and analysis of carbonate models with different combinations of pore types demonstrate the effects of pore type on rock elastic parameters. The simulated result is consistent with our knowledge of real data.

Modeling customer satisfaction for bus rapid transit in Changzhou, China

This paper aims to develop a customer satisfaction model for bus rapid transit （BRT）. Both the socio-economic and travel characteristics of passengers were considered to be independent variables. Changzhou BRT was taken as an example and on which on-board surveys were conducted to collect data. Ordinal logistic regression （OLR） was used as the modeling approach. The general OLR-based procedure for modeling customer satisfaction is proposed and based on which the customer satisfaction model of Changzhou BRT is developed. Some important findings are concluded： Waiting sub-journey affects customer satisfaction the most, riding sub- journey comes second and arriving station sub-journey has relatively fewer effects. The availability of shelter and benches at stations imposes heavy influence on customer satisfaction. Passengers＇ socio-economic characteristics have heavy impact on customer satisfaction.

Approximation Property of the Modified Elman Network

A new type of recurrent neural network is discussed, which provides the potential for modelling unknown nonlinear systems. The proposed network is a generalization of the network described by Elman, which has three layers including the input layer, the hidden layer and the output layer. The input layer is composed of two different groups of neurons, the group of external input neurons and the group of the internal context neurons. Since arbitrary connections can be allowed from the hidden layer to the context layer, the modified Elman network has more memory space to represent dynamic systems than the Elman network. In addition, it is proved that the proposed network with appropriate neurons in the context layer can approximate the trajectory of a given dynamical system for any fixed finite length of time. The dynamic backpropagation algorithm is used to estimate the weights of both the feedforward and feedback connections. The methods have been successfully applied to the modelling of nonlinear plants.

Experiments and modeling of double-peak precipitation hardening and strengthening mechanisms in Al-Zn-Mg alloy

The aim of the present work is to develop a model for simulating double-peak precipitation hardening kinetics in Al-Zn-Mg alloy with the simultaneous formation of different types of precipitates at elevated temperatures based on the modified Langer-Schwartz approach. The double aging peaks are present in the long time age-hardening curves of Al-Zn-Mg alloys. The physically-based model, while taking explicitly into account nucleation, growth, coarsening of the new phase precipitations and two strengthening mechanisms associated with particle-dislocation interaction （shearing and bypassing）, was used for the analysis of precipitates evolution and precipitation hardening during aging of Al-Zn-Mg alloy. Model predictions were compared with the measurements of Al-Zn-Mg alloy. The systematic and quantitative results show that the predicted hardness profiles of double peaks via adding a shape dependent parameter in the growth equation for growth and coarsening generally agree well with the measured ones. Two strengthening mechanisms associated with particle-dislocation interaction （shearing and bypassing） were considered operating simultaneously in view of the particle size-distribution. The transition from shearing to bypassing strengthening mechanism was found to occur at rather early stage of the particle growth. The bypassing was found to be the prevailing strengthening mechanism in the investigated alloys.

ANALYSIS OF UN-COINCIDE COORDINATE ERROR IN SINGLE-AXIS ROTATING FIBER OPTIC STRAP-DOWN INERTIAL NAVIGATION SYSTEM

The un-coincide coordinate error in the single-axis rotating fiber optic strap-down inertial navigation system（SINS） is analyzed. Firstly, a rotating modulation technology is presented for SINS. The method provides the enhanced property of SINS when using the same-leveled inertial measurement units. Then, the rotating struc- ture modification is derived and augmented to resolve the un-modulated error-accumulated problem. As the insuf- ficient machine processing, the horizontal and the vertical errors on the machine surface are inevitable, and the in- volved coordinates are difficult to get the exact coincident. So, two major kinds of coordinate situation are stud- ied. The equivalent error models on gyro and acceleration outputs are built for each situation, and the impact is analyzed for compensation. The part of attitude and position error models caused by the built angle-rate error is established to calculate the un-eoincident impact. Considering these conditions of different gyro accuracy and mo- tion states simultaneously, numerical simulations are implemented. Results indicate that the SINS modulation ac- curacy is seriously affected by the combined factors on gyro accuracy and motion conditions.

GEOMETRIC MODELING OF GENERATING-MANUFACTURED SPIRAL BEVEL GEARS BASED ON CUTTING SIMULATION

A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.

Tomographic velocity inversion for ADCIGs in areas with a rugged surface

Pre-stack depth migration velocity analysis is one of the key techniques influencing image quality. As for areas with a rugged surface and complex subsurface, conventional prestack depth migration velocity analysis corrects the rugged surface to a known datum or designed surface velocity model on which to perform migration and update the velocity. We propose a rugged surface tomographic velocity inversion method based on angle-domain common image gathers by which the velocity field can be updated directly from the rugged surface without static correction for pre-stack data and improve inversion precision and efficiency. First, we introduce a method to acquire angle-domain common image gathers （ADCIGs） in rugged surface areas and then perform rugged surface tornographic velocity inversion. Tests with model and field data prove the method to be correct and effective.

Prosthetic modeling for femoral head based on ellipsoid fitting

A novel modeling method which can restore the shape of the femoral head with collapse induced by ischemic necrosis is proposed. First, sequential tomograms of the hip are obtained from a CT scan; secondly, an accurate and automatic method is used to extract the profile of the acetabulum; thirdly, a hybrid method is utilized to gather fiducial marks on the acetabulum; fourthly, bulky error sampling points are removed. Finally, an ellipsoid fitting method is used to fit the ellipsoid model of the femoral head. Two male sufferers with different necrosis extents are chosen as experimental subjects for contrastive simulation. Fifty cases of different ages （from 25 to 79 years old） are utilized for statistical comparisons of matching errors. The prosthetic models highly resemble the primary shape of the femoral head in health. This new method provides not only a theoretical model for accurate operation position fixing in an orthopaedics clinic, but it is also an innovative practical means for the individual manufacture of artificial femoral heads.

Gas sand distribution prediction by prestack elastic inversion based on rock physics modeling and analysis

Seismic inversion is one of the most widely used technologies for reservoir prediction. Many good results have been obtained but sometimes it fails to differentiate the lithologies and identify the fluids. However, seismic prestack elastic inversion based on rock physics modeling and analysis introduced in this paper is a significant method that can help seismic inversion and interpretation reach a new quantitative （or semi-quantitative） level from traditional qualitative interpretation. By doing rock physics modeling and forward perturbation analysis, we can quantitatively analyze the essential relationships between rock properties and seismic responses and try to find the sensitive elastic properties to the lithology, porosity, fluid type, and reservoir saturation. Finally, standard rock physics templates （RPT） can be built for specific reservoirs to guide seismic inversion interpretation results for reservoir characterization and fluids identification purpose. The gas sand distribution results of the case study in this paper proves that this method has unparalleled advantages over traditional post-stack methods, by which we can perform reservoir characterization and seismic data interpretation more quantitatively and efficiently.