Test Problems Research Articles

Determining the factors influencing the reproducibility of measurements in the asymmetric cycle «coercive return—magnetization»

The induction of coercive return and induction of coercive force inversion can be used for magnetic structure analysis. On the example of the problem of heat treatment testing of 20H2M steel, the influence of the remagnetization rate and the resolving power of the current source on the magnitude and character of the obtained dependences is shown. It is established that a high rate of remagnetization and a large step of current setting are interfering factors complicating the reproduction of measurement results and obtaining reliable dependences.

Research on FPC coils with limited turns in planar electromagnetic tomography

Electromagnetic tomography (EMT) is a non-destructive testing method that reconstructs electrical parameter distribution based on boundary electromagnetic measurement data along electromagnetic rotation projection. The coil is a critical component of the EMT system, used to excite and detect changing magnetic fields. The performance of excitation-detection with specific coils directly affects the quality of the reconstructed image. The traditional EMT coils are wound coils. The excitation-detection performance of the coils is enhanced by increasing the number of turns to obtain better imaging quality. A larger coil volume has better sensitivity, but it cannot meet the space constraints of many applications. To solve this problem, this paper proposes a method using extremely thin FPC coil arrays as EMT sensors. To verify the feasibility of FPC coil imaging with a limited number of turns, firstly, this article analyses the excitation-detection capabilities of FPC coil with 1 to 12 turns through a combination of simulation and experiment. Secondly, the impact of excitation-detection capability on the EMT sensitivity matrix was studied. Finally, a 4×4 8-Turns FPC coil sensor was designed for image reconstruction experiments. The experimental results show that FPC coils with limited turns can be used for image reconstruction and to solve the problem of planar nondestructive testing in a small space.

Design, development and multi-scenario application of portable multifunctional test master based on μM-PMU: The case study of Lingang new City Grid, Shanghai

With the large-scale access of new energy generation and electric vehicle charging piles to the grids, power generation and loads are characterized by random fluctuations and intermittency, which affect the stable operation of the distribution network. μM-PMU is capable of realizing the dynamic process monitoring of the grids. In order to solve the function and performance testing problems of multiple application scenarios of μM-PMU, this thesis develops a portable master station based on synchronous phasor measurement system to realize zero drift, voltage amplitude measurement accuracy, voltage phase angle accuracy, current amplitude measurement accuracy, current phase angle measurement accuracy, frequency measurement accuracy, voltage amplitude change with frequency accuracy, and voltage phase angle change with frequency accuracy, Accuracy of current amplitude with frequency change, accuracy of current phase angle with frequency change, active power accuracy, reactive power accuracy, amplitude step response, phase angle step response, frequency step response, a total of 15 test items. It can automatically calculate test results and generate test reports according to different equipment models, reducing the mistakes and calculation errors that may be caused by manually recording test data and improving the accuracy of test results and calculation precision.

Encoding innate ability through a genomic bottleneck

Animals are born with extensive innate behavioral capabilities, which arise from neural circuits encoded in the genome. However, the information capacity of the genome is orders of magnitude smaller than that needed to specify the connectivity of an arbitrary brain circuit, indicating that the rules encoding circuit formation must fit through a "genomic bottleneck" as they pass from one generation to the next. Here, we formulate the problem of innate behavioral capacity in the context of artificial neural networks in terms of lossy compression of the weight matrix. We find that several standard network architectures can be compressed by several orders of magnitude, yielding pretraining performance that can approach that of the fully trained network. Interestingly, for complex but not for simple test problems, the genomic bottleneck algorithm also captures essential features of the circuit, leading to enhanced transfer learning to novel tasks and datasets. Our results suggest that compressing a neural circuit through the genomic bottleneck serves as a regularizer, enabling evolution to select simple circuits that can be readily adapted to important real-world tasks. The genomic bottleneck also suggests how innate priors can complement conventional approaches to learning in designing algorithms for AI.

Turret-index optimisation with mathematical programming and metaheuristic approaches

This paper addresses the turret-index optimisation problem by proposing two mathematical programming approaches based on quadratic programming (QP) and constraint programming (CP). In addition, a metaheuristic algorithm based on weighted superposition attraction (WSA) is developed due to the combinatorial complexity of the problem. Despite attempting to linearise the QP formulation for problem resolution, both the QP and Linearized QP models prove ineffective for medium and larger-sized instances, providing solutions only for small-sized problems. In the second mathematical programming approach, a novel CP model is introduced in the literature. While CP can rapidly offer optimal solutions for small-sized problems, it only provides satisfactory solutions for medium and larger-sized problems within the predetermined computational time limits and does not guarantee optimal results. On the other hand, through computational analysis and relevant statistical tests, the proposed WSA algorithm provides the best solutions for all test problems within a reasonable computational time.

On the Dai–Liao conjugate gradient method for vector optimization

Several conjugate gradient (CG) parameters have led to promising methods for optimization problems. However, some parameters, such as the Dai-Liao (DL+) and modified Polak-Ribière-Polyak (EPRP) methods, have not yet been explored in the vector optimization setting. This paper addresses this gap by proposing the DL+ and EPRP+ methods to vector optimization. We start by developing a self-adjusting DL+ algorithm to find critical points of vector-valued functions within a closed, convex, pointed cone with a nonempty interior. The algorithm is designed to satisfy the sufficient descent condition (SDC) with a Wolfe line search; if this condition is not satisfied, the algorithm adjusts by redefining the DL+ to meet the SDC. We establish the global convergence of this algorithm under the assumption of SDC without requiring regular restarts or convexity assumption on the objective functions. Similarly, we developed the EPRP+ algorithm using the same approach as the DL+ algorithm. Furthermore, under exact line search, the DL+ and EPRP+ methods reduce to Hestenes-Stiefel (HS) and Polak-Ribière-Polyak (PRP) methods, respectively. We present numerical experiments on some selected test problems sourced from the multiobjective optimization literature that demonstrate the effectiveness and practical implementation of the proposed algorithms, highlighting their promising potential.

Bounding the family-wise error rate in local causal discovery using Rademacher averages

Many algorithms have been proposed to learn local graphical structures around target variables of interest from observational data, focusing on two sets of variables. The first one, called Parent–Children (PC) set, contains all the variables that are direct causes or consequences of the target while the second one, known as Markov boundary (MB), is the minimal set of variables with optimal prediction performances of the target. In this paper we introduce two novel algorithms for the PC and MB discovery tasks with rigorous guarantees on the Family-Wise Error Rate (FWER), that is, the probability of reporting any false positive in output. Our algorithms use Rademacher averages, a key concept from statistical learning theory, to properly account for the multiple-hypothesis testing problem arising in such tasks. Our evaluation on simulated data shows that our algorithms properly control for the FWER, while widely used algorithms do not provide guarantees on false discoveries even when correcting for multiple-hypothesis testing. Our experiments also show that our algorithms identify meaningful relations in real-world data.

A Novel Resource-Aware Distributed Cooperative Decision-Making Mechanism for Connected Automated Vehicles

<div>This article proposes a new model for a cooperative and distributed decision-making mechanism for an ad hoc network of automated vehicles (AVs). The goal of the model is to ensure safety and reduce energy consumption. The use of centralized computation resource is not suitable for scalable cooperative applications, so the proposed solution takes advantage of the onboard computing resources of the vehicle in an intelligent transportation system (ITS). This leads to the introduction of a distributed decision-making mechanism for connected AVs. The proposed mechanism utilizes a novel implementation of the resource-aware and distributed–vector evaluated genetic algorithm (RAD-VEGA) in the vehicular ad hoc network of connected AVs as a solver to collaborative decision-making problems. In the first step, a collaborative decision-making problem is formulated for connected AVs as a multi-objective optimization problem (MOOP), with a focus on energy consumption and collision risk reduction as example objectives. RAD-VEGA then cooperatively solves this MOOP, taking into account the availability of AV’s onboard resources and the application layer characteristics of today’s ITS communication tools. The performance of the proposed mechanism is evaluated by solving the ZDT1 test problem and studying pareto-frontier solutions to the true front over time. The scalability of the proposed solution is estimated to be 305 CAVs, considering a communication bandwidth of 6 MB/s. Additionally, cooperative AV planning scenario examples are simulated, and the effectiveness of the proposed mechanism is demonstrated by comparing final and initial solutions after solving the MOOP using RAD-VEGA.</div>

An unconditionally stable numerical scheme for solving nonlinear Fisher equation

Abstract In this study, novel numerical methods are presented for solving nonlinear Fisher equations. These equations have a wide range of applications in various scientific and engineering fields, particularly in the biomedical sciences for determining the size of brain tumors. The challenges posed by the nonlinearity of the equations are effectively addressed through the development of numerical techniques. The nonlinearity is tackled using a combination of the method of lines and backward differentiation formulas of varied orders. This method is unconditionally stable, and its accuracy is evaluated using error norms. The methods are successfully validated against test problems with known solutions, demonstrating their superiority through comparative analyses with existing methodologies in the literature.

EFFECTS IN DISCRETE AND CONTINUOUS STRENGTHENING OF MACHINES ELEMENTS

The work describes approaches to problem solving of operational and effective improvement of the technical and tactical characteristics of military and civilian machines: tanks, armored vehicles, diesel locomotives, turbo-expander power plants, autonomous power plants of strategic objects, etc. For this purpose, fundamentally new methods of strengthening of contacting machines elements are being developed. These methods combine the advantages of discrete and continuous strengthening methods, which have largely exhausted their capabilities by now. Qualitative features and advantages of proposed discrete-continuous strengthening methods require effective implementation. We are talking about the justification of progressive technical solutions based on the criteria of strength and durability. For this purpose, the methodology of multi-criteria synthesis in the expanded space of design and technological parameters will be improved. In addition, as a basis for substantiating advanced technological solutions, a set of related problems of analysis of the stress-strain state, friction and wear is formed. Therefore, based on the improved system approach, a much higher level of strength and durability of the reinforced structural parts is achieved than with traditional methods. The results of test problems solving are illustrated. In the result, micro-macromodels are generalized to determine the joint influence of structural and technological factors, microstructure, physical and mechanical properties of materials of reinforced layers on the contact interaction and stress-strain state of representative fragments of the system of discrete-continuous reinforced bodies. The results of analysis of combined influence of structural and technological factors, microstructure, physical and mechanical properties of materials reinforced layers have been established on the contact interaction and stress-strain state of test representative fragments of the system of discrete-continuously reinforced bodies. At the same time, a significant influence of reinforced layers properties was established on strength of contacting bodies.

Vector synthesis of fault testing map for logic

Vector synthesis of fault testing (simulation) map for logic is proposed, which without simulation allows to determine of all faults detected on test sets, as well as determining test sets to detect specified faults. For synthesis, a superposition of smart data structures is used, containing: a deductive matrix D, as a derivative of the logical vector L, test truth table T, and fault truth table F. The deductive matrix is seen as the gene of functionality and base of fault simulation mechanism to solve all the problems of testing and verification. In the matrix synthesis, an axiom is used: all the mentioned tables are identical in shape to each other and always interact with each other convolutionally T⊕L⊕F=0. A universal deductive reversing converter “test-faults” and “faults-test” for logical functionalities of any dimension is proposed. Converter functions: fault simulation on test sets T→F and synthesis of test sets F→T to detect the specified faults. The converter can be used as a test generation and fault simulation service for IP-core system-on-chip (SoC) under the IEEE 1500 SECT standard. Based on the deductive matrix, a fault testing map for logic is built, where each test set is matched with the logic-detected faults of the input lines.

ThunderBoltz: an open-source direct simulation Monte Carlo Boltzmann solver for plasma transport, chemical kinetics, and 0D modeling

Abstract Plasma-neutral interactions, including reactive kinetics, are often either studied in 0D using ODE-based descriptions, or in multi-dimensional fluid or particle-based plasma codes. The latter case involves a complex assembly of procedures that are not always necessary to test effects of underlying physical models and mechanisms for particle-based descriptions. Here we present ThunderBoltz, a lightweight, publicly available 0D direct simulation Monte Carlo code designed to accommodate a generalized combination of species and arbitrary cross sections without the overhead of expensive field solves. It can produce electron, ion, and neutral velocity distributions in applied AC/DC E-field and/or static B-field scenarios. The code is built in the C++ standard library and includes a convenient Python interface that allows for input file generation (including compatibility with cross section data from the LXCat database), electron transport and reaction rate constant post-processing, input parameter constraint satisfaction, calculation scheduling, and diagnostic plotting. These codes can be accessed at the repository: https://github.com/lanl/ThunderBoltz. In this work we compare ThunderBoltz transport calculations against Bolsig+ calculations, benchmark test problems, and swarm experiment data, finding good agreement with all three in the appropriate field regimes. In addition, we present example use cases where the electron, ion, and background neutral particle species are self-consistently evolved to model the background kinetics, a feature that is absent in fixed-background Monte Carlo and n-term Boltzmann solvers. The latter functionality allows for the possibility of particle-based chemical kinetics simulations of the plasma and neutral species as a new alternative to ODE-based approaches.

ĐÁNH GIÁ THEO CHƯƠNG TRÌNH GIÁO DỤC PHỔ THÔNG 2018 - MỘT SỐ VẤN ĐỀ LÝ LUẬN VÀ THỰC TIỄN

In Vietnam, many legal documents have been issued to set out requirements for general education innovation, emphasizing innovation in testing and evaluating educational outcomes. However, theoretical issues related to the design of measurement tools, especially standardized tools, have not been fully and systematically studied for implementation in practice. In addition, although innovation in teaching methods and assessment is focused on, teachers still face many difficulties in designing and using assessment tools. The purpose of this paper is, through systematizing research and implementation practices, to provide some theoretical and practical issues on assessment according to the 2018 General Education Program, from which some test problems and ways to solve them are proposed. Keywords: Assessment; measurement; 2018 General Education Program; requirements to be achieved; technology.

Adaptive least-squares methods for convection-dominated diffusion-reaction problems

This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of imposing outflow boundary conditions. The coercivity of the homogeneous least-squares functionals are established, and the a priori error estimates of the least-squares methods are obtained in a norm that incorporates the streamline derivative. All methods have the same convergence rate provided that meshes in the layer regions are fine enough. To increase computational accuracy and reduce computational cost, adaptive least-squares methods are implemented and numerical results are presented for some test problems.

Multi-guided population co-evolutionary algorithm based on multiple similarity decomposition for large-scale flexible job shop scheduling problem

As manufacturing shifts towards large-scale production, the size of the workshop increases, and its search space exponentially expands. It is difficult for existing algorithms to obtain an ideal scheduling solution in an acceptable time. For the large-scale flexible job shop scheduling problem (LSFJSP), a multi-guided population co-evolutionary algorithm based on multiple similarity decomposition (MPCSD) is designed. Faced with the problem of high dimensionality and complex solution space, a multiple similarity decomposition strategy is proposed. It proceeds to group based on similarity information at the dimension and population level. To obtain convergence-preferred and diversity-preferred dimension groupings, a training-set solution selection method is proposed. Inspired by the idea of divide-and-conquer, a multi-guided co-evolutionary strategy is proposed. It improves the exploration efficiency of the algorithm in the search space. To test effectiveness on more complex LSFJSP, a set of large-scale test problems including LS1-12 are designed. On LS1-12, MPCSD is compared with seven other algorithms to demonstrate its superiority. MPCSD performed best on 11, 7, and 10 of the 12 test problems on Inverted Generational Distance (IGD), Hypervolume (HV) and Schott’s Spacing Metric (SP), respectively. Meanwhile, the Relative Deviation (RD) results showed that MPCSD obtained the best fitness performance.

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios χ∥/χ⊥⋙1 (with χ∥, χ⊥ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. The implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ∼(NΔt)1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios (χ∥/χ⊥=1010).

Optimization test function synthesis with generative adversarial networks and adaptive neuro-fuzzy systems

This paper presents an approach to synthesizing optimization test functions that couples generative adversarial networks and adaptive neuro-fuzzy systems. A generative adversarial network produces optimization landscapes from a database of known optimization test functions, and an adaptive neuro-fuzzy system performs regression on the generated landscapes to provide closed-form expressions. These expressions can be implemented as fuzzy basis function expansions. Eight databases of two-dimensional optimization landscapes reported in the literature are used to train the generative network. Exploratory landscape analysis over the generated samples reveals that the network can lead to new optimization landscapes with features of interest. In addition, fuzzy basis function expansions provide the best approximation results when compared against two symbolic regression frameworks over several selected landscapes. Examples are used to illustrate the ability of these functions to model complex surface artifacts such as plateaus. The proposed approach can be used as a mathematical collaboration tool that couples generative artificial and computational intelligence techniques to formulate high-dimensional optimization test problems from two-dimensional synthesized functions.

An IDFPM-based algorithm without Lipschitz continuity to constrained nonlinear equations for sparse signal and blurred image restoration problems

The derivative-free projection method (DFPM) is widely used to solve constrained nonlinear equations. To guarantee the convergence of the derivative-free projection method, the mapping should be Lipschitz continuous, which is a strict requirement in theory. Hence, it is interesting to design the new DFPM that possesses nice convergence under weaker theoretical hypothesis. In this paper, we propose an inertial DFPM-based algorithm (named IDFPM), in which the inertial extrapolation step is embedded in the design for the search direction. The global convergence of the proposed algorithm is obtained without the Lipschitz continuity of the mapping. Numerical experiments are carried out for two kinds of problems. The one consists of eight test problems from classical literature and the compressed sensing model. The numerical results show that the proposed algorithm is promising.

Shifted Legendre Gauss‐Lobatto collocation scheme for solving nonlinear coupled space‐time fractional reaction‐advection diffusion equations

AbstractThis work aims to develop and apply an algorithm for solving space‐time fractional reaction‐advection diffusion (STFRAD) nonlinear coupled equations with specified initial and boundary conditions by employing a Shifted Legendre Gauss‐Lobatto collocation (SLGLC) scheme. The fractional derivatives of time and space are defined in Caputo sense. The approximate solutions have been constructed with the help of shifted Legendre polynomials. The proposed numerical scheme reduces the coupled fractional order differential equations into a system of algebraic equations which can then be easily solved. The error analysis through the two test problems is carried out to validate the efficiency and efficacy of the method. The effect of advection and reaction terms, and various space‐time fractional order derivatives on the solution profiles have been studied and are shown graphically for different particular cases. It has been observed that the species whose transport is simulated using STFRADE shows higher concentration at a specific distance in porous media in case of integer order differential equations as compared to fractional order equations demonstrating overestimation of its impact in case of integer order differential equation. This is extremely important observation with respect to applications in the field of groundwater pollution management. The salient feature of the article is the stability and convergence analyses of the proposed scheme on the concerned model, which demonstrates the effectiveness and capabilities of the developed method.

An Efficient Algorithm for Sorting and Duplicate Elimination by Using Logarithmic Prime Numbers

Data structures such as sets, lists, and arrays are fundamental in mathematics and computer science, playing a crucial role in numerous real-life applications. These structures represent a variety of entities, including solutions, conditions, and objectives. In scenarios involving large datasets, eliminating duplicate elements is essential to reduce complexity and enhance performance. This paper introduces a novel algorithm that uses logarithmic prime numbers to efficiently sort data structures and remove duplicates. The algorithm is mathematically rigorous, ensuring correctness and providing a thorough analysis of its time complexity. To demonstrate its practicality and effectiveness, we compare our method with existing algorithms, highlighting its superior speed and accuracy. An extensive experimental analysis across one thousand random test problems shows that our approach significantly outperforms two alternative techniques from the literature. By discussing the potential applications of the proposed algorithm in various domains, including computer science, engineering, and data management, we illustrate its adaptability through two practical examples in which our algorithm solves the problem more than 3×104 and 7×104 times faster than the existing algorithms in the literature. The results of these examples demonstrate that the superiority of our algorithm becomes increasingly pronounced with larger problem sizes.