Multipoint Method Research Articles

A Multi-Point Iterative Analysis Method for Vibration Control of a Steering Wheel at Idle Speed

Steering wheel vibration control is of great significance to improve the ride comfort of vehicles. However, the coupling effect of the multi-source vibration transfer path makes it difficult to screen out the abnormal vibration transfer intervals. Therefore, a multi-point iterative analysis method (MIAM) is presented in this paper. In addition, this paper researches the characteristics of the main vibration transmission path of a truck and proposes a new vibration isolation structure. Considering the structural characteristics of the modal deformation of the car body, the installation orientation of the measuring point is further adjusted according to the area formed by modal deformation nodes, and a simplified vibration transfer path is presented. After weighing the vibration data of the sensor and considering the vibration transfer rate as the analysis index, the abnormal interval of vibration transmission on the main path was detected. The effectiveness of the improved structure is verified with the modal verification analysis of an extracted steering system model. In addition, the experimental results show that the improved measures reduce the total vibration of the steering wheel by 34% and offsets the peak corresponding frequency by 4.8%, showing the effectiveness of the proposed method and proving its advantages for other vibration control problems.

The output of a shock wave on the inner surface of a cylindrical liner

The results of the experimental investigations of the dynamics of the axisymmetric compression of a metallic liner are presented in this work. The studies were carried out using a high-speed camera with nanosecond resolution. It is shown that the detonation wave formed by the multipoint initiation method has a complex three-dimensional cellular structure, where first-order node lines and second-order nodes are present. The hydrodynamic instabilities formed upon the exit of the shock wave onto the inner surface of a metallic liner do not smooth out as they contract, but increase.

Applying multi-point statistical methods to build the facies model for Oligocene formation, X oil field, Cuu Long basin

Multi-point statistic method (MPS) can overcome the inherent disadvantages of traditional method based on variogram and object modeling, simultaneously allow the modeling progress, and become more flexible and rational. The algorithms based on variogram and gridding geological model are able to control the final result under the collection of samples’ data (well data) and another corresponding data (seismic). Though, these methods have trouble in modeling the shape of geological features. Then, object-modeling method can generate digitized geological features with responsible shapes; conversely, a final result in accordance with an input data is difficult to achieve. Combining the advantages of two mentioned methods, MPS describes the relationship of data in space based on the group of adjacent points or has a certain relationship, it allows the generation of digitized geological features corresponding with responsible shapes, and moreover, it is able to control the final result under a collection of input data (whose nature is still the pixel-based). The Oligocene reservoir, X field, was formed in fluvial/lacustrine and sedimentary mainly deposited in Northwest–Southeast, which is primarily affected by latitude—sub-latitude faults’ system. An Oligocene facies model of X field is built based on MPS, and it will show the geological features more clearly than the existing one. It also shows the remarkable ability on controlling the final result. MPS allows to combine a lot of different data (geology, seismic, outcrop, etc.) with the geological viewpoints which are shown by training image and itself proves the superiority over traditional methods. Duration of each model simulation is approximately 3000 s and huge size (over 15 million cells), and it is better while compared with 1717.8750 s in case of sequential simulation by SISIM method and default properties.

Estimation of radon release rate for an underground uranium mine ventilation shaft in China and radon distribution characteristics

Radon, known to be a human carcinogen, is one of the most concerned radionuclides in uranium mining which need to be monitored and controlled. A large amount of radon is discharged to the atmosphere mainly through underground ventilation shafts for underground uranium mining. There are many studies on radon release of uranium mine, but the differences of the measured radon results are very big. In this paper, a typical underground uranium mine in China is chosen as a case study. This study finds that distribution of radon concentration and airflow speed inside the ventilation shaft are extremely uneven, but the distributions are respectively stable and regular for a fixed cross-section at the wellhead depth of 0–1 m. There is also a stable numerical relationship between the radon release rate and the product of radon concentration and airflow speed at the center for any cross-section in the shaft. Based on this regulation, a multipoint interpolation-integration method and a one-point method for calculating radon release from underground ventilation shaft are proposed in this paper. The results show that the difference between these two methods is 2–10%, the one-point method is more suitable and convenient to be applied for the long-term monitoring radon release rate from uranium mine ventilation. The research results in this paper can be applied in the estimation of radon release rate for other underground uranium ventilation shafts.

Surface enriched nanofiber mats for efficient adsorption of Cr(VI) inspired by nature

Adsorption is a surface process. By evolution, nature has created design principles such as scaffolds that allow to carrying surface bound agents at high density. We used a nanofibrous pullulan/poly(vinyl alcohol)/poly(acrylic acid) (Pul/PVA/PAA) support to carry surface active PAMAM dendrimer similar to spores attached to mushroom gills. A monolayer of ceria (CeO2) nanoparticles served as the linker between PAMAM and the nanofiber. The nanocomposite was a highly effective Cr(VI) adsorbent and the maximum adsorption capacity qmax = 847 mg g−1 is the highest reported value for the same kind of materials so far. The materials was characterized by scanning electron microscopy (SEM), thermogravimetric analysis (TGA), Fourier transform-infrared spectroscopy (FTIR), zeta potential and multipoint BET method to measure the specific surface area. Removal of Cr(VI) from aqueous media was tested under different batch and fixed bed column operation conditions such as pH, temperature and competing ions. Thermodynamic properties were determined based on a modified Langmuir adsorption isotherm and the adsorption kinetic was investigated. Positive entropy of adsorption and an endothermic adsorption process was found, while the rate-limiting step was pseudo second order which is associated with a chemisorption process. The nanocomposite was reusable and up to 95% of the adsorbed Cr(IV) ions were recovered by alkyne washing.

General efficient class of Steffensen type methods with memory for solving systems of nonlinear equations

There are a very small number of high quality derivative free methods with memory for solving a system of nonlinear equations numerically. Motivated and inspired by the fact, we propose a more efficient general class of Steffensen type multipoint methods with memory. This proposed class requires one divided difference and inverse of only one matrix per full iteration. We also demonstrate their applicability and illustrate that these methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations numerically. For quantitative comparison, we have also computed total number of convergent points and convergent percentage along with basins of attractions on a number of test problems to recommend the best quality algorithm.

POWER COEFFICIENT IN ONE POINT LIQUID LIMIT TEST FOR SOILS OF NORTHERN TURKEY AT VARIOUS TEMPERATURES

In this study, the power coefficient of one-point liquid limit equation given by ASTM 4318-17 is evaluated for weathered volcanic deposits of Northern Turkey. Total of 35 soil samples taken from depths ranging from 0.2 m to 4 m from 8 different sites in the city of Rize and one site in Trabzon, Turkey are used, and a total of 77 Atterberg limit tests are conducted. Three different sample preparation methods are used: (1) starting from in-situ moisture content without any drying, (2) drying at 60°C oven, (3) drying at 110°C oven. For liquid limit determination by one-point method, the best fitting power coefficient is evaluated for different sample preparation conditions separately, and are compared with the power coefficient suggested by ASTM D4318-17. Soils used in this study are in ML-OL to MH-OH zones in plasticity chart and the liquid limit values vary in the range of 35% to 103% (moist preparation). Liquid limits obtained by multi-point method and the ones obtained by one-point method are found to be similar to each other. It is concluded that although the power coefficient changes (in the range of 0.106 to 0.133 with an average value of 0.120) due to sample preparation technique, they are close to ASTM-suggested power value of 0.121, and the differences in resulting liquid limits are negligibly small (0-2%).

An efficient and optimal higher-order scheme in general way for simple zeros

The inspiration behind of this paper is to suggest an iteration function of sixteenth-order in a general way which is applicable to every earlier optimal multi-point eighth-order formula provided whose first substep should be the classical Newton’s method. The presented technique meet the expectation of classical Kung-Traub conjecture regarding the optimality of multi-point methods without memory. Further, we fully investigated the theoretical and computational properties of the proposed scheme through the main theorem which demonstrates the convergence order and the term of asymptotic error. Computational consequences that the proposed methods are superior than the earlier studies of sixteenth-order in terms of approximated roots, terms of asymptotic error, residual errors in the considered functions, variation in two consecutive iterations, etc.

Performance evaluation of a recently developed soil water content, dielectric permittivity, and bulk electrical conductivity electromagnetic sensor

CS655 Water Content Reflectometer (WCR) (Campbell Scientific, Inc., Logan, UT, USA) is a recently developed multiparameter electromagnetic sensor measuring volumetric soil water content (θ), bulk soil electrical conductivity (σb), and temperature. In this study, CS655 sensor’s performance was investigated through laboratory experiments using a set of liquids with known dielectric and salinity properties and soils featuring a wide range of conditions (including physico-chemical properties, water regimes and salinity of the water solution). The sensor’s performance was analyzed in comparison with WET and ML2 theta probe (Delta-T Device Ltd, Cambridge, UK) dielectric sensors. It was found that CS655 apparent dielectric permittivity (εa) readings were higher than that of Topp’s permittivity-water content relationship, especially at higher soil water content values, as much as 12 dimensionless permittivity units. The results suggested that the relationship between experimentally measured soil water content (θm) and εa was strongly linear (0.911<R2<0.997). The most accurate results were provided by the multi-point calibration method. Moreover, for the case of non-conductive soils, Kelleners’s method provides similar εa values with CS655 sensor readings for a maximum σb value of about 0.8 dS m−1. Concerning the use of empirical calibration equations, which include the effect of bulk electrical conductivity in εa, the obtained results suggest that the equation θ=aεa+b+cσb has a strong physical basis and adequate performance (RMSE<0.03 m3 m-3). Finally, the investigation of the εa-σb relationship revealed that it is strongly linear and that slope mainly depends on the pore water electrical conductivity (σp), which is closely related to the soil solution salinity in contact with plant roots that influences plants growth. The Malliki-Walzcak model provide more reliable σp predictions as compared to the Hilhorst model.

Static and Dynamic Responses of Reinforced Concrete Structures under Sudden Column Removal Scenario Subjected to Distributed Loading

In this paper, static and dynamic experiments on reinforced concrete beam-column frames under single-column-removal scenario applying a multipoint loading method were conducted. One of the objectives was to investigate structural behavior compared with the single-point loading method, which has been popularly used in previous studies. By equally applying point loads at four locations of the double-span beam structure, the test setup successfully simulated the uniformly distributed loading condition, which is generally applicable for gravity loads in practice. Compared with the previously conducted static tests based on concentrated loading method, structural response from the static tests under multipoint loading condition differed not only on load-bearing capacity but also on failure sequence and displacement profile. On the basis of the test results, the analytical relationship between behaviors of the two loading methods was developed and verified. Compared with the static tests, the dynamic tests highlighted dynamic effects created by the column loss event and confirmed the structural behavior and failure modes observed in the static environment. The dynamic tests also verified the correctness and conservatism of the dynamic assessment framework using a previously proposed energy-based approach. Most important, both the static and the dynamic tests of structures under distributed loads showed less development of catenary action against progressive collapse compared with concentrated loading tests.

Construction and efficiency of multipoint root-ratio methods for finding multiple zeros

Several root-ratio multipoint methods for finding multiple zeros of univariate functions were recently presented. The characteristic of these methods is that they deal with mth root of ratio of two functions (hence the name root-ratio methods), where m is the multiplicity of the sought zero, known in advance. Some of these methods were presented without any derivation and motivation, it could be said, out of the blue. In this paper we present an easy and entirely natural way for constructing root-ratio multipoint iterative methods starting from multipoint methods for finding simple zeros. In this way, a vast number of root-ratio multipoint methods for multiple zeros, existing as well new ones, can be constructed. For demonstration, we derive four root-ratio methods for multiple zeros. Besides, we study computational cost of the considered methods and give a comparative analysis that involves CPU time needed for the extraction of the mth root. This analysis shows that root-ratio methods are pretty inefficient from the computational point of view and, thus, not suitable in practice. A general discussion on a practical need for multipoint methods of very high order is also considered.

Calculation of the numerical benchmark NURISP based on the complex MRNK + KEDR-D

The Kurchatov Institute developed the MRNK software package that provides the solution of the nonstationary neutron transfer equation based on the multipoint kinetics method. Currently, work is underway to improve the MRNK software package - connecting feedback on the thermophysical properties of reactor materials. To determine the thermophysical parameters, the KEDR-D program is used - a modified version of the stationary three-dimensional KEDR program for calculating non-stationary processes. The task was set to verify the MRNK + KEDR-D complex based on published data for the international numerical benchmark NURISP. The report presents the stages of achieving the goal (calculation of the stationary state of the core and comparison with the reference data; investigation of fast transient process and comparison with reference data.) In this paper, the data obtained for the MRNK + KEDR-D complex are compared with the data obtained for the Tripoli4-SubChanFlow and DYN3D-FLICA, DYN3D-SubChanFlow complexes. When calculating the steady state of the active zone, the results are in excellent agreement with the results obtained on foreign complexes. Discrepancies in temperature of the fuel and coolant, density of the coolant and distribution of energy release over the height of the assembly are minimal.When calculating the fast transient process (removal of control rods in the central fuel assembly in 0.1 s), the results are consistent with the reference data satisfactorily. There are discrepancies in the area of the greatest impacts of feedback. A comparison was made of the dependence of the temperature of the fuel and the coolant, the power change over time.

A method for generating multiple solutions for multipoint five-axis tool positioning

Multipoint machining (MPM) strategies are a class of methods that use the flexibility of a five-axis machine to position a tool in close proximity of the desired surface so that the tool touches the surface on at least two points of contact. However, existing multipoint methods cannot control the spacing between the two points of contact. This paper presents a new technique, called the Drop, Spin, and Tilt (DST) method that can generate multiple contact points at varying distances around the first point of contact. The multiple DST second points of contact were used to manually generate a toolpath with uniform spacing between the two points of contact. While a uniform space could be attained at most tool positions, problem cases were encountered demonstrating that more work is required for an algorithmic version of this process. The proposed method was implemented in a symbolic algebra system and verified on a variety of surfaces.

Verification of iterative matrix solutions for multipoint kinetics equations

Multipoint kinetic equation systems have been solved numerically using matrix algebra software and 1st to 4th order implicit schemes based on single-step matrix propagators. These matrix schemes have been validated successfully on demanding point kinetics benchmarks with various prescribed reactivity insertions. Verification tests have also been performed on a simple 3-region fast reactor core model with asymmetric step or ramp reactivity insertions and cross-checked with the multipoint kinetics SACRE code developed at INL and based on existing and validated stiff ODE solver packages. Accurate results can be obtained at a limited time expense. The reason for intriguing results obtained in some transients has been elucidated and linked to the multipoint matrix coefficient interpolation method during the transient.

A multipoint voltage-monitoring method for fuel cell inconsistency analysis

Traditionally, only one set voltage monitor was used for fuel cell diagnosis and bipolar plate was regarded as the equipotential body. This study presents a novel analysis about this classic method, and proves that only one-set voltage monitor cannot obtain the real health status of every cell. Experimental results point out that the voltage of each cell along the cell gas channel is variable. The current and voltage redistribution phenomenon, caused by the cell interaction, was observed in the fuel cell stack with graphite bipolar plate. Thus, a one-dimensional model has been proposed to explain the mechanism of the current and voltage redistribution with cell interaction. Simulation result shows that, as long as the abnormal cell exists, the current and voltage distribution of the whole stack is significantly affected. Finally, a multipoint voltage-monitoring method has been developed for fuel cell consistency analysis. New method was applied in a specially designed four-cell stack to validate the model analysis. Additionally, the proposed method was used to diagnose anode starvation, which cannot be easily detected using only the one-set voltage monitor for the anode inlet. All experiments and modeling works prove that the multipoint voltage-monitoring method is effective for fuel cell consistency analysis.

Synchrotron X-ray diffraction based method for stress intensity factor evaluation in the bulk of materials

A generalised approach for determining the stress intensity factor in the bulk of non-transparent materials is presented. The new approach combines experimental elastic strain data, measured with powerful synchrotron X-ray diffraction, with an elastic model based on Williams’ series development. The stress intensity factor is calculated using a multi-point over-deterministic method where the number of experimental data points is higher than the number of unknowns describing the elastic field surrounding the crack-tip. The tool is tested on X-ray strain measurements collected on a bainitic steel. In contrast to surface techniques the approach provides insights into the crack tip mechanics deep within the sample and makes full use of the plastic zone data. Satisfactory results are obtained with 1 term in the series development and a smaller region of interest. By increasing the number of terms, it is possible to improve the accuracy in the SIF predictions but this requires a larger region of interest.

A Combined Experimental-Numerical Method to Evaluate Powder Thermal Properties in Laser Powder Bed Fusion.

Powder bed metal additive manufacturing (AM) utilizes a high-energy heat source scanning at the surface of a powder layer in a predefined area to be melted and solidified to fabricate parts layer by layer. It is known that powder bed metal AM is primarily a thermal process, and further, heat conduction is the dominant heat transfer mode in the process. Hence, understanding the powder bed thermal conductivity is crucial to process temperature predictions, because powder thermal conductivity could be substantially different from its solid counterpart. On the other hand, measuring the powder thermal conductivity is a challenging task. The objective of this study is to investigate the powder thermal conductivity using a method that combines a thermal diffusivity measurement technique and a numerical heat transfer model. In the experimental aspect, disk-shaped samples, with powder inside, made by a laser powder bed fusion (LPBF) system, are measured using a laser flash system to obtain the thermal diffusivity and the normalized temperature history during testing. In parallel, a finite element (FE) model is developed to simulate the transient heat transfer of the laser flash process. The numerical model was first validated using reference material testing. Then, the model is extended to incorporate powder enclosed in an LPBF sample with thermal properties to be determined using an inverse method to approximate the simulation results to the thermal data from the experiments. In order to include the powder particles' contribution in the measurement, an improved model geometry, which improves the contact condition between powder particles and the sample solid shell, has been tested. A multipoint optimization inverse heat transfer method is used to calculate the powder thermal conductivity. From this study, the thermal conductivity of a nickel alloy 625 powder in powder bed conditions is estimated to be 1.01 W/m K at 500°C. [DOI: 10.1115/1.4040877].

A cell interaction phenomenon in a multi-cell stack under one cell suffering fuel starvation

Cell interaction is the main factor resulting in a shorter lifespan for multi-cell stacks than for a single fuel cell stack. To explain this mechanism, we propose a cell interaction phenomenon in which one cell experiences fuel starvation. A specific voltage distribution along the straight channel direction has been observed with an innovative multipoint monitoring method. This phenomenon also can be used for fuel starvation diagnosis. This study proposes an ingenious simplified two-chamber model to analyze the current and voltage redistribution mechanism under fuel starvation. The reliability of this model has been validated in this paper. The model shows that current convergence resulted by fuel starvation in one cell can lead to a concomitant local current convergence in nearby normal cells. Based on our calculation, >85% of reaction current concentrates in the anode inlet region of the fuel-starved cell, resulting in a 70% current convergence in the two adjacent normal cells. A serious corrosion of the fuel-starved cell is observed in the post-mortem study. The faulty cell presents a 5° contact angle decrease and a 28% ECSA loss. Scanning electron microscopy and Transmission electron microscopy results show that the decline of anode outlet regions’ cathode catalyst layers are more serious. Some optimal strategies have been proposed to solve this problem.

New Measurement Method for Spline Shaft Rolling Performance Evaluation using Laser Displacement Sensor

In order to control the quality of spline shaft in rolling process, an efficient measurement method for rolling performance evaluation is essential. Here, a newly developed on-machine non-contact measurement prototype based on laser displacement sensor and rotary encoder is proposed. The prototype is intended for the automated evaluation of the spline shaft rolling performance by measuring the dimensional change of tooth root, which is correlated with the surface residual stress and micro-hardness. Laser displacement sensor and rotary encoder are used to record the polar radius and polar angle of each point on measuring section. Data are displayed in a polar coordinate system and fitted in a gear. Through multipoint curvature method, the roots of spline shaft are recognized automatically. Then, the dimensional change can be calculated by fitting the radius of the tooth root circle before and after rolling. Systematic error covering offset error is also analyzed and calibrated. At last, measurement test results show that the system has advantages of simple structure, high measurement precision (radius error < 0.6 μm), high measurement efficiency (measuring time < 2 s) and automatic control ability, providing a new opportunity for the efficient evaluation of various spline shafts in high-precision mechanical processing.

Accelerating multi-point statistics reconstruction method for porous media via deep learning

Reconstruction of three-dimensional (3D) porous media from a single two-dimensional (2D) image or limited morphological information has been an outstanding problem. Specifically, multi-point statistics (MPS)-based methods have been proved to be effective and promising to address this problem. Besides, recently sampling-based MPS methods that reconstruct 3D microstructure layer by layer have attracted increasing attention, for its relatively lower computational cost and memory demand. However, due to the nature that one has to search and match multi-point information in a data structure like binary tree or list for each simulation, it is very time-consuming, especially for large template used to reconstruct geometrically complex media. In this paper, to overcome this challenge, for the first time to the best of our knowledge, an accelerating reconstruction method based on deep learning is proposed. Specially, conditional generative adversarial networks (CGAN) is leveraged to model and characterize the relation between the sampling image which contains conditioning data and the target void-solid image. Unlike conventional MPS-based method generally performing simulation point by point, our method is able to directly translate the sampling image to the target one instantaneously, thus leading to a significant speedup factor (∼760 for 2D reconstruction and ∼25 for 3D reconstruction on CPU). Meanwhile, to assess the performance of our method, we test it on sandstone samples, and two-point correlation function, lineal-path function and two-point cluster function, as well as local porosity distribution are quantitatively compared with those of the target microstructure. The comparison indicates that our method is of high efficiency while preserving good agreement of statistical functions with that of the target system. We remark that our approach opens the door to a new methodology that incorporating machine learning/deep learning techniques into conventional methods to address CPU- or memory-demanding issues in a wide range of related fields.