Discrete Production Research Articles

Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator, we are interested in the corresponding eigenvalues, more exactly, in their asymptotic behavior. Thus, we can determine a limit value which links this asymptotic behavior and the uniform norm of the orthonormal polynomials in a logarithmic scale. This value appears in the theory of reproducing kernel Hilbert spaces. On the other hand, we tackle a more general case than the one considered in the literature previously.

Research on E-Commerce Product Quality Monitoring Sampling Method

This paper researches the features of quality monitoring sampling of E-commerce products, analyzes the current status of development of E-commerce industry, and proposes an E-commerce product quality monitoring sampling survey method on the basis of the research on the existing E-commerce product quality monitoring literatures and standards from the perspective of mastering the overall quality situation of the category of products sold through E-commerce channels, and the contents include the determination of quality monitoring object and quality characteristics as well as the determination of the monitoring total and the construction of the sampling frame and sampling method, etc. This method is applicable to the estimation of product quality level of the monitoring total as discrete individual products or quantitative packaged bulk materials and provides theoretical and technical supports for the work of quality monitoring sampling of E-commerce products in our country.

An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables

AbstractWe derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term‐by‐term balance in the kinetic, internal, and potential energy budgets, ensuring an energy‐consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit‐explicit time stepping algorithm.

Self-optimizing machining systems

In this paper the idea of Self-Optimizing Machining Systems (SOMS) is introduced and discussed. Against the background of Industry 4.0, here the focus is the technological level of discrete workpiece production by mechanical machining processes utilizing related machine tools and equipment. Enabling technologies, principles, and methods are described that allow for the implementation of machining systems which are capable of adapting their parameters and settings autonomously, in order to optimize for productivity, quality, and efficiency in manufacturing. Following a description of the meaning and a definition of SOMS as well as a historical retrospection, the required elements of SOMS are discussed and exemplary approaches are presented. Based on sophisticated process planning, monitoring, adaptive control, simulation, artificial intelligence, and machine learning, strategies, state-of-the-art solutions for self-optimization in machining applications are introduced. Several examples showcase how different types of enabling technologies can be integrated synergistically, to improve the manufacturing of parts by SOMS. Finally, the future potential of SOMS as well as challenges and needs are summarized. The paper especially considers the results of the CIRP Cross-STC Collaborative Working Group on SOMS.

Solving a Two-Stage Continuous-Discrete Problem of Optimal Partition–Allocation with a Given Position of the Centers of Subsets

A method and algorithm of solving a two-stage continuous-discrete problem of optimal partition–allocation are proposed. On the one hand, the problem is a generalization of the classical transportation problem in the case where production (storage and recycling) amounts at given points are unknown in advance, and are sought as a solution of the corresponding continuous problem of optimal partitioning of a set of continuously allocated consumers (suppliers) onto their service areas by these points. On the other hand, the problem generalizes discrete two-stage production–transportation problems to the case of a continuously allocated consumer. Operation of the proposed algorithm is demonstrated by solving a model problem.

A Referenced Cyber Physical System for Compressor Manufacturing

Compressor is a typical high-end discrete product，with the shortening of product life cycle and the enhancement of the degree of product customization, the traditional compressor manufacturing system architecture cannot meet the requirements of comprehensive digital management of compressor from body scheme design to parts production line, logistics management, operation and maintenance monitoring and evaluation. This paper presents a compressor manufacturing system architecture based on digital twinning, and establishes an Internet platform for compressor industry oriented to remote coordination from three aspects of compressor design, production, operation and maintenance. The platform includes industrial Internet infrastructure layer, physical space entity model layer, virtual space multidimensional model layer, physical space and virtual space multidimensional model correlation and mapping layer, big data intelligent analysis decision-making layer, and digital twin application layer. Through the establishment of the compressor product design and simulation model of digital twin, compressor production process digital twin model, compressor fault diagnosis and remote operations digital twin model, implementation is based on the number of compressor collaboration in manufacturing industrial Internet platform twin system, leading the transformation and upgrading of intelligent manufacturing industry, compressor industry sustainable development ability and international competitiveness.

Restart policies to maximize production quality in mixed continuous-discrete multi-stage systems

In sectors as semiconductor fabrication, pharma industry and food production, discrete production processes are intertwined with continuous production processes. Since continuous processes frequently produce large batches of material requiring fairly long processing times, restart policies aiming at scrap reduction especially due to work-in-progress perishability are commonly used to control the material flow in multi-stage production systems. A performance evaluation model integrating control mechanisms is proposed to assess the impact of local restart policies at system level. A real case study in the food production is presented, where the parameters of restart policies are optimized to maximize production quality.

Lévy's martingale characterization and reflection principle of G-Brownian motion

In this paper, by a new kind of discrete product space method for martingales, we obtain Lévy's martingale characterization of G-Brownian motion without the nondegenerate condition. Based on this characterization, we prove the reflection principle of G-Brownian motion. Furthermore, we use Krylov's estimate to get the reflection principle of the general G˜-Brownian motion.

A pragmatic approach for optimizing gas lift operations

The oil flow rate in a single vertical well undergoing gas lift operations is complicated by three factors: (1) The flow is driven by gas injection, in addition to the fluid flow potential gradient applied along the well, (2) the well is interfaced with a porous and permeable reservoir contributing with a fluid feed, and (3) the wellbore geometry may consist of concentric pipes of varying diameters and lengths, rather than a single-diameter pipe. Dimensional analysis is applied to this complex, highly nonlinear production problem, in order to develop empirical models for predicting the optimal gas injection rate and the maximum oil production rate that may be produced from continuous gas lift operations. Two pairs of coupled dimensionless groups are revealed. The first pair consists of a dimensionless pressure drop (π1) adjusted to the complex wellbore geometry, and a dimensionless ratio of kinetic to viscous forces (π2) which accounts for the porous medium feed. A constructed database for 388 vertical wells producing by continuous gas lift operations has been used to validate the dimensionless groups. A power-law relation is revealed between the dimensionless groups π1 and π2, allowing to construct an analytical model for predicting the maximum oil production rate that corresponds to the optimal gas injection rate. The second pair consists of two groups denoted χ1 and χ2. The group χ1 is a dimensionless pressure drop with adjustment being augmented to account for the temperature effects on gas flow. Similar to π2, the dimensionless group χ2 is a ratio of kinetic to viscous forces, adjusted to account for the porous medium feed. However, χ2 is a function of the injection rate, instead of the oil production rate. Likewise, a power-law relation is revealed between χ1 and χ2, allowing to construct an analytical model for predicting the optimal gas injection rate. All power-law relations yield high correlation coefficients when the validation data are segregated according to a discrete productivity index. The analytical models developed by applying dimensional analysis appear to capture the physical controls of gas lift operations. Intuitively, the optimal gas injection rate depends on the pressure gradient along the pipe, the wellbore geometry, the temperature conditions at the bottom of the well and in the stock-tank, the oil density, and on the productivity index. Similarly, the maximum oil production rate, corresponding to the optimal gas injection rate, depends on the pressure gradient along the pipe, the wellbore geometry, the oil density, the productivity index which is implicitly affected by the oil permeability, and viscosity. Unlike multivariate nonlinear regression analysis, the application of dimensional analysis for deriving the analytical models, presented in this study, does not require a presumed functional relationship. In retrospect, dimensional analysis evades the guessing process associated with nonlinear regression analysis.

Classical Sobolev Orthogonal Polynomials: Eigenvalue Problem

We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal polynomials with respect to this Sobolev inner product are eigenfunctions of a differential operator and obtaining the asymptotic behavior of the corresponding eigenvalues is the principal goal of this paper.

The possibility of applying calculation based on queuing theory with the aim of real-time control

Possibilities of using mathematical models of the theory of queues for the purpose of control of processes of discrete productions modeled by it in real time are investigated. As a model example, a system for managing the rearrangements of service items in queues was considered. For the analysis the methods of calculation of BMAP-controlled systems and the methods of the theory of recovery on periods of employment for queues with vacancies of requirements were used.As a result of research it is found out that mathematical modeling in the theory of queues can be used for simulation of discrete production for the purpose of design and the production analysis, but cannot be used for management of the modeled processes in real time.

A Quantum Calculus Analogue of Dynamic Leontief Production Model with Linear Objective Function

In this paper, we present a new formulation for the Leontief production model using quantum calculus analogue. This formulation unifies discrete and continuous Leontief production models. Also, the classical Leontief production model is obtained by choosing q = 1. In addition, briefly give an introduction to quantum calculus. We present the formulation for continuous Leontief production models as well as quantum calculus models. Moreover, we establish the weak duality theorem and the strong duality theorem for quantum calculus analogue. Furthermore, using the objective functions for the primal and the dual quantum calculus models, we can easily obtain upper and lower bounds for the value of production at any production plan. Finally, examples are provided in order to illustrate the given results.

How Valuable are Patent Blocking Strategies?

Firms use patents for blocking competitors’ innovation activities. Offensive blocking is a practice whereby firms patent alternatives of a focal invention preempting technological substitutes produced by competitors. Defensive blocking entails the creation of patent portfolios that block technologies in order to increase competitors’ willingness to trade patents. This paper examines the private value of both patent blocking strategies with the use of a novel measure of the offensive and defensive “blocking power” of patent portfolios. We show that both strategies increase firms’ market value. In discrete (complex) product industries, however, only offensive (defensive) patent blocking is associated with higher value.

Logarithmic Sobolev inequalities in discrete product spaces

AbstractThe aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: for a fixed probability measure q on , ( is a finite set), and any probability measure on , (*) $$D(p||q){\rm{\le}}C \cdot \sum\limits_{i = 1}^n {{\rm{\mathbb{E}}}_p D(p_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,...,{\rm{ }}Y_n )||q_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,{\rm{ }}...,{\rm{ }}Y_n )),} $$ where pi(· |y1, …, yi−1, yi+1, …, yn) and qi(· |x1, …, xi−1, xi+1, …, xn) denote the local specifications for p resp. q, that is, the conditional distributions of the ith coordinate, given the other coordinates. The constant C depends on (the local specifications of) q.The inequality (*) ismeaningful in product spaces, in both the discrete and the continuous case, and can be used to prove a logarithmic Sobolev inequality for q, provided uniform logarithmic Sobolev inequalities are available for qi(· |x1, …, xi−1, xi+1, …, xn), for all fixed i and fixed (x1, …, xi−1, xi+1, …, xn). Inequality (*) directly implies that the Gibbs sampler associated with q is a contraction for relative entropy.In this paper we derive inequality (*), and thereby a logarithmic Sobolev inequality, in discrete product spaces, by proving inequalities for an appropriate Wasserstein-like distance.

A differential equation for varying Krall-type orthogonal polynomials

In this contribution, we consider varying Krall-type polynomials which are orthogonal with respect to a varying discrete Krall-type inner product. Our main goal is to give ladder operators for this family of polynomials as well as to find a second-order differential-difference equation that these polynomials satisfy. We generalize some results that appeared recently in the literature.

The Sphere Packing Bound for DSPCs With Feedback à la Augustin

Establishing the sphere packing bound for block codes on the discrete stationary product channels with feedback ---which are commonly called the discrete memoryless channels with feedback--- was considered to be an open problem until recently, notwithstanding the proof sketch provided by Augustin in 1978. A complete proof following Augustin's proof sketch is presented, to demonstrate its adequacy and to draw attention to two novel ideas it employs. These novel ideas (i.e., the Augustin's averaging and the use of subblocks) are likely to be applicable in other communication problems for establishing impossibility results.

Machining Chatter Prediction Using a Data Learning Model

Machining processes, including turning, are a critical capability for discrete part production. One limitation to high material removal rates and reduced cost in these processes is chatter, or unstable spindle speed-chip width combinations that exhibit a self-excited vibration. In this paper, an artificial neural network (ANN)—a data learning model—is applied to model turning stability. The novel approach is to use a physics-based process model—the analytical stability limit—to generate a (synthetic) data set that trains the ANN. This enables the process physics to be combined with data learning in a hybrid approach. As anticipated, it is observed that the number and distribution of training points influences the ability of the ANN model to capture the smaller, more closely spaced lobes that occur at lower spindle speeds. Overall, the ANN is successful (>90% accuracy) at predicting the stability behavior after appropriate training.

Sequence learning is driven by improvements in motor planning.

The ability to perform complex sequences of movements quickly and accurately is critical for many motor skills. Although training improves performance in a large variety of motor sequence tasks, the precise mechanisms behind such improvements are poorly understood. Here we investigated the contribution of single-action selection, sequence preplanning, online planning, and motor execution to performance in a discrete sequence production task. Five visually presented numbers cued a sequence of five finger presses, which had to be executed as quickly and accurately as possible. To study how sequence planning influenced sequence production, we manipulated the amount of time that participants were given to prepare each sequence by using a forced-response paradigm. Over 4 days, participants were trained on 10 sequences and tested on 80 novel sequences. Our results revealed that participants became faster in selecting individual finger presses. They also preplanned three or four sequence items into the future, and the speed of preplanning improved for trained, but not for untrained, sequences. Because preplanning capacity remained limited, the remaining sequence elements had to be planned online during sequence execution, a process that also improved with sequence-specific training. Overall, our results support the view that motor sequence learning effects are best characterized by improvements in planning processes that occur both before and concurrently with motor execution. NEW & NOTEWORTHY Complex skills often require the production of sequential movements. Although practice improves performance, it remains unclear how these improvements are achieved. Our findings show that learning effects in a sequence production task can be attributed to an enhanced ability to plan upcoming movements. These results shed new light on planning processes in the context of movement sequences and have important implications for our understanding of the neural mechanisms that underlie skill acquisition.

WeldANA: Welding decision support tool for conceptual design

This paper describes a methodology and reference implementation created to aid design engineers in the early phases of design for a new discrete product. The decision support tool is used to understand design decisions and their relation to manufacturability considerations, in particular, the weldability of a design. As such, we have defined four metrics (partability, setup/orientation, accessibility, and preparation) that encapsulate good structural weldment design. Those metrics have been codified in a software tool that interacts directly with a commercial CAD package as part of a manufacturability analysis decision support tool suite that also includes machining and casting assessment capabilities. This paper focuses on weldment manufacturability analysis, WeldANA. Several common use cases are used to demonstrate the efficacy and efficiency of the approach for use in the early stages of the design process.

Dose of remote limb ischemic conditioning for enhancing learning in healthy young adults.

Remote limb ischemic conditioning (RLIC) is a technique in which tissues distant from the target organ are exposed to brief, sub-lethal bouts of ischemia. The effects of remotely applied ischemic conditioning are systemically transferred to the target organ, and typically manifested as protection from subsequent ischemic injury. Previous studies in our lab have found and confirmed that RLIC enhances learning and retention during motor training on a balance task. The current study tested the effect of RLIC dose (number of cycles) on learning enhancement in young, healthy adults. Forty healthy participants age 18-40years were randomized to receive 5 cycles of sham conditioning (n = 9), 3 cycles of RLIC (n = 11), 4 cycles of RLIC (n = 10), or 5 cycles of RLIC (n = 10) using a blood pressure cuff around the upper arm once a day for 7 consecutive weekdays (Days 1-7). Participants concurrently trained on a balance task, bimanual cup stacking task, and a discrete sequence production task on Days 3-7. Change in performance on each of the three tasks was compared across groups. Participants in all four groups improved their performance on each of the three tasks over time. However, RLIC at any dose did not enhance learning on any of the three tasks. While RLIC is safe, inexpensive, and clinically feasible, reproducibility may be challenged by unidentified factors, raising critical challenges to the straightforward translation of RLIC for improving rehabilitation outcomes in individuals recovering from neurological injury.