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The authors propose to estimate a varying coefficient panel data model with different smoothing variables and fixed effects using a two-step approach. The pilot step estimates the varying coefficients by a series method. We then use the pilot estimates to perform a one-step backfitting through local linear kernel smoothing, which is shown to be oracle efficient in the sense of being asymptotically equivalent to the estimate knowing the other components of the varying coefficients. In both steps, the authors remove the fixed effects through properly constructed weights. The authors obtain the asymptotic properties of both the pilot and efficient estimators. The Monte Carlo simulations show that the proposed estimator performs well. The authors illustrate their applicability by estimating a varying coefficient production frontier using a panel data, without assuming distributions of the efficiency and error terms.

This paper aims to propose a three-phase interpenetrating continua model for the numerical simulation of water waves and porous structure interaction.

In contrast with one-fluid formulation or multi-component methods, each phase has its own characteristics, density, velocity, etc., and each point is occupied by all phases. First, the porous structure is modelled as a phase of continua with a penalty force adding on the momentum equation, so the conservation of mass is guaranteed without source terms. Second, the adaptive unstructured mesh modelling with P1DG-P1 elements is used here to decrease the total number of degree of freedom maintaining the same order of accuracy.

Several benchmark problems are used to validate the model, which includes the Darcy flow, classical collapse of water column and water column with a porous structure. The interpenetrating continua model is a suitable approach for water wave and porous structure interaction problem.

The interpenetrating continua model is first applied for the water wave and porous structure interaction problem. First, the structure is modelled as phase of non-viscous fluid with penalty force, so the break of the porous structure, porosity changes can be easily embedded for further complex studies. Second, the mass conservation of fluids is automatically satisfied without special treatment. Finally, adaptive anisotropic mesh in space is employed to reduce the computational cost.

The cumulative sum (Cusum) operator, also referred to as accumulating generation operator, is the fundamental of grey system models and proves to be successful in various real-world applications. This paper aims to uncover the advantages of the Cusum operator from a parameter estimation perspective, i.e. comparing integral matching with classical gradient matching.

Grey system models are represented as a state space form to investigate the effect of measurement errors on estimation performance; subsequently, gradient matching and integral matching are respectively formulated to estimate parameters from noisy observations and, then, their quantitative relationships are established by using matrix computation tricks.

Extensive simulations, which are conducted on both linear and non-linear models under different sample size and noise level combinations, show that integral matching is superior to gradient matching, and, also the former is less sensitive to measurement error.

This paper explains why the Cusum operator is widely utilized in grey system models, thereby further solidifying the mathematical fundamentals of grey system models.

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.

In this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.

The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.

The study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

This chapter develops a set of two-step identification methods for social interactions models with unknown networks, and discusses how the proposed methods are connected to the identification methods for models with known networks. The first step uses linear regression to identify the reduced forms. The second step decomposes the reduced forms to identify the primitive parameters. The proposed methods use panel data to identify networks. Two cases are considered: the sample exogenous vectors span Rn (long panels), and the sample exogenous vectors span a proper subspace of Rⁿ (short panels). For the short panel case, in order to solve the sample covariance matrices’ non-invertibility problem, this chapter proposes to represent the sample vectors with respect to a basis of a lower-dimensional space so that we have fewer regression coefficients in the first step. This allows us to identify some reduced form submatrices, which provide equations for identifying the primitive parameters.

In the process of continuous casting and rolling of steel plate, due to the influence of rolling equipment and process, there are scratches, inclusions, patches, scabs and pitted surfaces on the surface of steel plate, which will not only affect the corrosion resistance, wear resistance and fatigue strength of steel plate but also may cause production accidents. Therefore, the detection of steel plate surface defect must be strengthened to ensure the production quality of steel plate and the smooth development of industrial construction.

(1) A steel plate surface defect detection technology based on small datasets is proposed, which can detect multiple surface defects and fill in the blank of scab defect detection. (2) A detection system based on intelligent recognition technology is built. The steel plate images are collected by the front-end monitoring device, then transmitted to the back-end monitoring center and processed by the embedded intelligent algorithms. (3) In order to reduce the impact of external light on the image, an improved Multi-Scale Retinex (MSR) enhancement algorithm based on adaptive weight calculation is proposed, which lays the foundation for subsequent object segmentation and feature extraction. (4) According to the different factors such as the cause and shape, the texture and shape features are combined to classify different defects on the steel plate surface. The defect classification model is constructed and the classification results are recorded and stored, which has certain application value in the field of steel plate surface defect detection. (5) The practicability and effectiveness of the proposed method are verified by comparison with other methods, and the field running tests are conducted based on the equipment commissioning field of China Heavy Machinery Institute.

When applied to small dataset, the precision of the proposed method is 94.5% and the time is 23.7 ms. In order to compare with deep learning technology, after expanding the image dataset, the precision and detection time of this paper are 0.948 and 24.2 ms, respectively. The proposed method is superior to other traditional image processing and deep learning methods. And the field recognition precision is 91.7%.

In brief, the steel plate surface defect detection technology based on computer vision is effective, but the previous attempts and methods are not comprehensive and the accuracy and detection speed need to be improved. Therefore, a more practical and comprehensive technology is developed in this paper. The main contributions are as follows: (1) A steel plate surface defect detection technology based on small datasets is proposed, which can detect multiple surface defects and fill in the blank of scab defect detection. (2) A detection system based on intelligent recognition technology is built. The steel plate images are collected by the front-end monitoring device, then transmitted to the back-end monitoring center and processed by the embedded intelligent algorithms. (3) In order to reduce the impact of external light on the image, an improved MSR enhancement algorithm based on adaptive weight calculation is proposed, which lays the foundation for subsequent object segmentation and feature extraction. (4) According to the different factors such as the cause and shape, the texture and shape features are combined to classify different defects on the steel plate surface. The defect classification model is constructed and the classification results are recorded and stored, which has certain application value in the field of steel plate surface defect detection. (5) The practicability and effectiveness of the proposed method are verified by comparison with other methods, and the field running tests are conducted based on the equipment commissioning field of China Heavy Machinery Institute.

The promotion of new energy vehicles (EVs) is an effective way to achieve low carbon emission reduction. This paper aims to investigate the optimal pricing of automotive supply chain members in the context of dual policy implementation while considering consumers' low-carbon preferences.

This article takes manufacturers, retailers and consumers in a main three-level supply chain as the research object. Stackelberg game theory is used as the theoretical guidance. A game model in which the manufacturer is the leader and the retailer is the follower is established. The author also considered the impact of carbon tax policies, subsidy policies and consumer preferences on the results. Furthermore, the author investigates the optimal decision-making problem under the profit maximization model.

Through model solving, it is found that the pricing of EVs is positively correlated with the unit price of carbon and the amount of subsidies. The following conclusions can be obtained by numerical analysis of each parameter. Changes in carbon prices have a greater impact on conventional gasoline vehicles. Based on the numerical analysis of parameter β, it is also found that when the government subsidizes consumers, supply chain members will increase their prices to obtain partial subsidies. Compared with retailers, low-carbon preferences have a greater impact on manufacturers.

The new energy automobile industry involves many policies, including tax cuts, tax exemptions and subsidies. The policy environment faced by the members of a supply chain is complex and diverse. Therefore, the analysis in this article is based only on partial policies.

The authors innovatively combine the three factors of subsidy policy, carbon tax policy and consumer low-carbon preference, with research on the pricing of EVs. The influence of policy factors and consumer preferences on the pricing of EVs is studied.