Multiproduct manufacturer-retailer coordinated supply chain with adjustable rate for common parts, delayed differentiation, and multi-shipment

Operating in today’s turbulent and competitive world marketplaces, manufacturers must find the best production scheme and delivery policy to meet timely client’s multiproduct requirements and minimize the total manufacturing-shipment expenses. This study proposes a two-stage delayed differentiation model for a multiproduct manufacturer-retailer coordinated supply chain featuring the adjustable-rate for making common parts and a multi-shipment policy for transporting finished goods. The aim is to help present-day manufacturers achieve their operational goals mentioned above. The mathematical techniques help us build a specific model to explicitly represent the problem and derive its overall operating expense. Then, the convexity of the total expense is verified by Hessian matrix equations. The differential calculus helps derive the cost-minimized fabrication-shipment decision. This study offers an example to demonstrate the applicability and capabilities of our proposed model numerically. The following crucial information has been made available to the managers to facilitate their operating decision makings: (1) the problem’s best fabrication-shipment policy; (2) the collective influence of various common part’s completion rates and values on the problem’s total expenses and optimal fabrication-shipment policy; (3) the impact of various adjustable-rates in stage one on utilization and stage one’s uptime; (4) the details of cost contributors to the problem; and (5) the collective impacts of critical features on the problem’s performance.

Dynamics of moving-object grasped by a hybrid hand

When a heavy object is cooperatively grasped to move by several fingers of the robot hybrid hand, the inertial properties and the mass distribution of the object must influence largely on the operation precision, grasping stability, and the safety of both the hybrid hand and the object. Hence, it is an important and significant issue to establish and analyze the dynamics model of the moving-object cooperatively grasped by the hybrid hand in order to ensure the safety and grasping stability of the hybrid hand and the object. However, this research has not been conducted. In this paper, a dynamics model of the moving-object grasped by the hybrid hand is established, and its dynamics is studied and analyzed. First, a three-dimensional model of a hybrid hand formed by a novel parallel manipulator and three fingers is designed for cooperatively grasping object. Second, the kinematic formulas for solving the Jacobian matrices, the Hessian matrices, the general velocity/acceleration of the moving platform, and four active limbs of the parallel manipulator are derived. Third, the composite Jacobian matrix and the composite Hessian matrix of the hybrid hand are derived, and the general velocity/acceleration of the moving-object grasped by the hybrid hand is derived. Fourth, dynamics model of the hybrid hand is established, the formulas for solving the dynamic actuation forces of the three fingers and the dynamic actuation forces/torque and constrained forces of the parallel manipulator are derived. Finally, the theoretical solutions of the dynamics model of the moving-object grasped by the hybrid hand are verified by its simulation mechanism.

A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration

In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient.

Lane Line Extraction in Raining Weather Images by Ridge Edge Detection with Improved MSR and Hessian Matrix

To accurately detect lane lines in road traffic images at raining weather, a edge detection based method is studied, which mainly includes four algorithms. (1) Firstly an image is enhanced by an improved Retinex algorithm; (2) Then, an algorithm based on the Hessian matrix is applied to strengthen lane lines; (3) To extract the feature points of a lane line, a ridge edge detection algorithm based on five line detection in four directions is proposed, in which, in light on the possible positions of lane lines in the image, it detects the maximum gray level points in the local area of the detecting point within the pre-set valid detection region; and (4) After the noise removal based on the minimum circumscribed rectangles, the candidate points of lane lines are connected as segments, and for the gap filling between segments, in order to make connection correctly, the algorithm makes the filling in two steps, short gap and long gap fillings, and the long gap filling is made on the combination of segment angle difference and gap distance and gap angle. By testing hundreds of images of the lane lines at raining weather and by comparing several traditional image enhancement and segmentation algorithms, the new method of the lane line detection can produce the satisfactory results.

DETERMINATION OF GALAXY DISTRIBUTION WITH STATISTICAL MOMENTS

In this report we discuss topological studies of large scale structure of the Universe (LSS) from XMM-Newton, Sloan Digital Sky Survey and simulated data of galaxy distribution. Early works in this mentioned field were based on genus statistics, which is averaged curvature of isosurface of smoothed density field. Later, significant number of other methods was developed. This comprise Euler characteristics, Minkowski functionals, Voronoi clustering, alpha shapes, Delanuay tesselation, Morse theory, Hessian matrix and Soneira-Peebles models. In practice, modern topology methods are reducedto calculation of the three Betti numbers which shall be interpreted as a number of galaxy clusters, filaments and voids. Such an approach was applied by different authors both for simulated and observed LSS data. Topology methods are generally verified using LSS simulations. Observational data normally includes SDSS, CFHTLS and other surveys. These data have many systematical and statistical errors and gaps. Furthermore, there is also a problem of underlying dark matter distribution. The situation is not better in relation to calculations of the power spectrum and its power law index which does not provide a clear picture as well. In this work we propose some tools to solve above problems. First, we performed topology description of simple LSS models such as cubic, graphite-like and random Gaussian distribution of matter. Our next idea is to set a task for LSS topology assessment using X-ray observations of the galaxies. Although, here could be a major complication due to current lack of detected high energy emitting galaxies. Nevertheless, we are expecting to get sufficient results in the future encouraging comprehensive X-ray data. Here we present analysis of statistical moments for four galaxy samples and compare them with the behavior of Betti numbers. Finally, we consider the options of applying artificial neural networks to observed galaxies and fill the data deficiency. This shall enable to define topology at least for superimposed superclusters and other LSS elements.

Least-Squares Reverse Time Migration Using the Gradient Preconditioning Based on Transmitted Wave Energy

A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of “approximate transmission wavefield,” which is calculated based on the non-reflecting acoustic equation. The proposed method can effectively avoid a huge amount of calculation and storage required by the Hessian matrix or approximated Hessian matrix and can overcome the influence of reflected waves, multiples, and other wavefields on the gradient in gradient preconditioning based on seismic wave energy (GPSWE). The numerical experiments, compared with that using GPSWE, show that LSRTM using the gradient preconditioning based on transmitted wave energy (GPTWE) can significantly improve the imaging accuracy of deep target and accelerate the convergence rate without trivial increased calculation.

Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations

The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable cases induced by the coupling effect of mass and stiffness to be circumvented and may not be optimal for structures experiencing damages in both mass and stiffness. In this paper, the new BMUA tailored to estimating both mass and stiffness is presented by using two measurement states (original and modified systems). A new eigenequation with a stiffness-modified system is formulated to address the coupling effect of mass and stiffness. The posterior function is treated using an asymptotic approximation method, giving the new objective functions with stiffness modification. Analytical formulations of modal parameters and structural parameters are then derived by a linear optimization method. In addition, the covariance matrix of uncertain parameters is determined by the inverse of the Hessian matrix of the objective function. The performance of the proposed BMUA is evaluated through two numerical examples in this study; a probabilistic damage estimation is also implemented. The results show the proposed BMUA is superior to the traditional one in mass and stiffness updating.