Linear Fitting Function Research Articles

Loading pattern optimization of VVER-1000 reactor core based on the discrete golden eagle optimization algorithm

The main features of the loading pattern optimization (LPO) problem, such as high-dimensionality, multi-modality, and non-linearity, make it difficult to achieve a truly optimal configuration. In recent years, metaheuristic methods have been successfully used to solve this problem. In this research, a discrete golden eagle optimization (DGEO) algorithm has been developed to solve the LPO problem in the first cycle of VVER-1000 reactor core. To evaluate the proposed algorithm, a linear multi-purpose fitness function has been used to improve the safety parameters of the reactor core by obtaining a flatter power distribution during the first cycle, and also to enhance the economic parameters by increasing the cycle length and reducing the cost of fuel recycling. For this purpose, a FORTRAN program has been written to map the DGEO algorithm for the LPO problem using the PMAX and PARCS core calculation code to compute the fitness function in each iteration. To speed up the calculations, parallel computing has been applied in the written program. The results demonstrated that the loading pattern, which is suggested by the DGEO algorithm, enhances all the safety and economic parameters in the fitness function. Thus, the DGEO algorithm is highly reliable for the LPO problems in the VVER 1000 reactor core.

Solving the Binary Puzzle with Genetic Algorithm

The increased internet usage after the pandemic led the UN Forum to improve cybersecurity measures, with zero-knowledge proofs (ZKP) being a viable solution for securing confidential information. ZKP protocols can be demonstrated through the binary puzzle, an NP-complete logic puzzle with four specific constraints. The key contribution of this paper is its successful implementation of the genetic algorithm as a new method to solve the binary puzzle. The optimized fitness function determined the solution at an average of 1.33-2.33 generations for populations ranging from 100 to 500. Its quadratic property calculated the solution faster than the ordinary linear fitness function.

Noise Source Diagnosis Method Based on Transfer Path Analysis and Neural Network

Clarifying the noise source and the contribution of each path is essential for the system’s noise control. The auxiliary converter cabinet, which is a crucial component of rail transportation, has numerous intricate noise sources. The contribution of each path point must be inverted-solved using known transfer functions and target point test values when identifying noise sources. This article suggests a method for diagnosing noise using transfer path analysis and neural networks (TPA-NN). Firstly, the principle and scheme for analyzing the transmission path of the converter cabinet are proposed. The transfer function of each path is obtained by selecting suitable path points, reference points, and target points for air and structure acoustic vibration experiments. The external target point data are then combined with the neural network’s linear fitting function, and the contribution of each path is used as an output for network training while some path point contributions are rebuilt. The results indicate that the method’s outcomes are most accurate when the converter cabinet’s path point is 13 and the target point is 6. This approach offers an innovative technique for locating noise sources in intricate systems.

Digital anatomical study and clinical application of the ideal S2 alar-lliac screw trajectory

BackgroundTo investigate the ideal trajectory for the S2AI screw and to clinically validate its safety feasibility.MethodsThe 3D model was reconstructed from CT data of the pelvis of 30 selected adults, and the 3D coordinate system was established with the first sacral superior endplate as the horizontal plane. A set of cutting planes was made at 3 mm intervals in the coronal plane, and the cross-sectional internal tangent circles were divided in the target area. Using the linear fitting function, the axis of 90 mm length was calculated by the least squares method for each inner tangent circle center. The diameter of the axis is gradually increased until the first contact with the cortex, and the cylindrical model is the ideal screw trajectory. The intersection of the axis and the dorsal cortex is the screw placement point, which is located by Horizon Distance (HD) and Vertical Distance (VD); the diameter of the screw trajectory (d) is the diameter of the cylindrical model; the direction of the screw trajectory is determined by Sagittal Angle (SA) and Transverse Angle (TA). The screw trajectory orientation is determined by Sagittal Angle (SA) and Transverse Angle (TA). Based on the ideal screw trajectory, the 3D printed surgical guide and freehand techniques were used to verify its safety feasibility, respectively.ResultsThe screw placement points [HD (4.7 ± 1.0) mm, VD (19.7 ± 1.9) mm], screw placement directions [SA (31.3°±2.3°), TA (42.4°±2.3°)], and screw dimensions for the ideal screw trajectory of the S2AI were combined for analysis. (L is 90 mm, d is 13.2 ± 1.4 mm). The S2AI screw superiority rate [96.6% (56/58)] and reasonable rate [100%] were higher in the guide group than in the freehand group [90.0% (63/70), 97.1% (68/70)], but the differences were not statistically significant (P > 0.05). Although screws invaded the cortex in both groups, there were no associated adverse events in either group.ConclusionThe S2AI screw-based ideal trajectory placement is a safe, feasible and accurate method of screw placement.

Bidirectional piecewise linear representation of time series with application to collective anomaly detection

Directly mining high-dimensional time series presents several challenges, such as time and space costs. This study proposes a new approach for representing time series data and evaluates its effectiveness in detecting collective anomalies. The proposed method, called bidirectional piecewise linear representation (BPLR), represents the original time series using a set of linear fitting functions, which allows for dimensionality reduction while maintaining its dynamic characteristics. Similarity measurement is then performed using the piecewise integration (PI) approach, which achieves good detection performance with low computational overhead. Experimental results on synthetic and real-world data sets confirm the effectiveness and advantages of the proposed approach. The ability of the proposed method to capture more dynamic details of time series leads to consistently superior performance compared to other existing methods.

1,2, 3

In this research paper, a swarm evolutionary modeling technique called the Updated Multi-Objective Ant-Lion Optimizer (UMO-ALO) is applied to the modeling of Open Circuit Voltage (OCV) state-of-charge (SOC) of Lithium-ion cells with cathode-anode composition (LiMnO2/Li4TiO). The model approximates the battery SOC by considering several battery cell internal physical parameters and a linear fitness function governed by two objectives involving the charge and discharge response of the battery cell. Bound limited coefficients of the physical parameters are used in the optimization process. The UMO-ALO uses a special update procedure to reduce the computational run-time of standard MO-ALO and hence speeds up the generic optimizer. Simulations were performed using a very small real laboratory data obtained from the relevant field studies and for different trial-run configurations of UMO-ALO. The results from these simulations show very good fitness responses close to zero margins for both trial-run configurations.

Determination of manufacturing process failures priority under type 2 fuzzy environment: Application of genetic algorithm and Variable neighborhood search

The aim of this research is to propose the two-stage model to select a set of failures that need to be eliminated or reduced which leads to improved reliability and effectiveness of the manufacturing process in the automotive industry. In the first stage, uncertainties under the relative importance of risk factors and costs of manufacturing process downtime due to failure are modeled by type 2 fuzzy sets. The weights vector of risk factors is obtained by analytical hierarchical Process which is extended with type 2 fuzzy sets. Evaluation of risk factors at the level of each identified failure is based on failure mode and effect analysis which is widely used in practice. Determining the set of failures to be eliminated is set as a knapsack problem. The linear fitness function is defined as the ratio of the overall risk priority index and total costs. Maintenance costs incurred due to the realization of failure are limited by the available budget and in this knapsack problem are presented by a linear inequality. The solution to this problem is found by using the Genetic Algorithm and Variable Neighborhood Search. The model is verified with real-life data originating from automotive companies that exist in Serbia. Authors have managed to obtain suitable results on different knapsack problem instances. It is shown that the enhancement of the manufacturing process can be based on the proposed model.

Maximizing Revenue With Adaptive Modulation and Multiple FECs in Flexible Optical Networks

Flexible optical networks (FONs) are being adopted to accommodate the increasingly heterogeneous traffic in today’s Internet. However, in presence of high traffic load, not all offered traffic can be satisfied at all time. As carried traffic load brings revenues to operators, traffic blocking due to limited spectrum resource leads to revenue losses. In this study, given a set of traffic requests to be provisioned, we consider the problem of maximizing operator’s revenue, subject to limited spectrum resource and physical layer impairments (PLIs), namely amplified spontaneous emission noise (ASE), self-channel interference (SCI), cross-channel interference (XCI), and node crosstalk. In FONs, adaptive modulation, multiple FEC, and the tuning of power spectrum density (PSD) can be effectively employed to mitigate the impact of PLIs. Hence, in our study, we propose a universal bandwidth-related impairment evaluation model based on channel bandwidth, which allows a performance analysis for different PSD, FEC and modulations. Leveraging this PLI model and a piecewise linear fitting function, we succeed to formulate the revenue maximization problem as a mixed integer linear program. Then, to solve the problem on larger network instances, a fast two-phase heuristic algorithm is also proposed, which is shown to be near-optimal for revenue maximization. Through simulations, we demonstrate that using adaptive modulation enables to significantly increase revenues in the scenario of high signal-to-noise ratio (SNR), where the revenue can even be doubled for high traffic load, while using multiple FECs is more profitable for scenarios with low SNR.

Flow characteristics of a centrifugal fan with optimized edge curvatures of an impeller front disk

In this study, the flow characteristics of different radiated impeller front disk fans were investigated by computational fluid dynamics to explore the effect of the radiated impeller front disk of the centrifugal fan on the three-dimensional flow of the volute-free centrifugal fan. Specifically, the flow-static pressure performance curve of the prototype fan was obtained to compare the numerical simulation results with the experimental results, so as to verify the accuracy of the numerical simulation. Besides, the linear fitting function of the radian edge of the front disk of the impeller was adjusted to acquire improved optimized fans. After numerical simulation analysis, the modification increases the outlet flow, static pressure at the outlet of the fan, static pressure efficiency, and total efficiency by 19 m³/h, 4.7 Pa, 5.6%, and 6.8%, respectively. The research reveals that the curvature of the front disk edge of the impeller can increase the flow channel volume between the blades and reduce the energy loss generated inside the impeller, thereby improving the static pressure and efficiency of the fan.

Reassessment of mobility parameters for Cantor High Entropy Alloys through an automated procedure

An automated assessment procedure is performed in order to establish a sophisticated kinetic data bank, introduced and modified by applying consequential iteration steps through the cross-validation method. The nonlinear curve-fitting of the end-member parameters is replaced by a simple linear fitting function via the logarithmic form of the Arrhenius equation. The applied modifications allow us to increase the precision of the method by decreasing the fitting errors. The input data employed here are the tracer diffusion coefficients in the well investigated high entropy alloy Co–Cr–Fe–Mn–Ni. The resulting parameters are in an acceptable agreement with the previously defined parameters in the literature while providing an efficient robust tool for kinetic data base development so that it enable an adequate prediction of diffusion transport.

Percolation threshold and excluded volume of overlapping spherotetrahedral particle systems: Shape evolution from tetrahedron to sphere

Understanding the excluded volume of particle is of great importance in the evaluation of continuum percolation and random packing behaviors of particle systems in disordered media. Particle shape plays a crucial role in determining its excluded volume and the percolation threshold of particle systems. Real particles in nature usually have rounded corners. In this work, the rounded corner effect on the excluded volumes of spherotetrahedral particles and the percolation thresholds of continuum percolation systems of randomly orientated congruent overlapping spherotetrahedral particles, is systematically investigated. We characterize the shape evolution of spherotetrahedron from an ideal tetrahedron (Trr = 0) to a perfect sphere (Trr = 1) via a rate of roundness Trr as its shape descriptor. The excluded volume of spherotetrahedron is theoretically formulated by the second virial coefficient and the geometrical properties of spherotetrahedron. In addition, the excluded volume is also simulated in order to verify the correctness of the theoretical model. On the other hand, the percolation threshold of congruent overlapping spherotetrahedron systems is analyzed by using a Monte Carlo finite-size scaling analysis. The critical volume fraction ϕc representing the percolation threshold as the particle shape evolution from Trr = 0 to Trr = 1 is determined with a high degree of accuracy. Moreover, a linear fitting function on Trr for the percolation threshold is proposed and shown to yield accurate predictions of ϕc. We find that ϕc is a universal monotonic increasing function of Trr, as well as the dimensionless excluded volume is a universal monotonic decreasing function of Trr. This work has practical applications in predicting effective transport and mechanical properties of disordered media.

Displacement Linearity Improving Method of Stepping Piezoelectric Platform Based on Leg Wagging Mechanism

It is difficult to obtain linear output displacements for stepping piezoelectric platform due to their discontinuous outputs. Inspired by the theory that the maximum static friction force is greater than the sliding friction force, in this letter, we propose a bipedal alternating inertial actuation mode (BAIAM) to improve the displacement linearity of the stepping platform. The output displacements are measured, the linear fitting is carried out by the least square method, the correlation coefficient and linear fitting function are used to evaluate the displacement linearity, and the correlation coefficients of the forward and backward motions are calculated as 0.9998 and 0.9999 in BAIAM, respectively, which verifies the effectiveness of the proposed method. The closed-loop experiments in BAIAM are also carried out, and the steady-state errors for the target position of ±40 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m within ±0.2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m in the point-to-point positioning control experiments are achieved. The experimental results confirm that the developed platform can be applied to precision fields requiring a large travel range, planar two-degree-of-freedom motion, and linear outputs.

FPGA Implementation for the Sigmoid with Piecewise Linear Fitting Method Based on Curvature Analysis

The sigmoid activation function is popular in neural networks, but its complexity limits the hardware implementation and speed. In this paper, we use curvature values to divide the sigmoid function into different segments and employ the least squares method to solve the expressions of the piecewise linear fitting function in each segment. We then adopt an optimization method with maximum absolute errors and average absolute errors to select an appropriate function expression with a specified number of segments. Finally, we implement the sigmoid function on the field-programmable gate array (FPGA) development platform and apply parallel operations of arithmetic (multiplying and adding) and range selection at the same time. The FPGA implementation results show that the clock frequency of our design is up to 208.3 MHz, while the end-to-end latency is just 9.6 ns. Our piecewise linear fitting method based on curvature analysis (PWLC) achieves recognition accuracy on the MNIST dataset of 97.51% with a deep neural network (DNN) and 98.65% with a convolutional neural network (CNN). Experimental results demonstrate that our FPGA design of sigmoid function can obtain the lowest latency, reduce absolute errors, and achieve high recognition accuracies, while the hardware cost is acceptable in practical applications.

Unique Ligand Exchange Dynamics of Metal–Organic Polyhedra for Vitrimer-like Gas Separation Membranes

Unique Ligand Exchange Dynamics of Metal–Organic Polyhedra for Vitrimer-like Gas Separation Membranes

Faraday wave instability characteristics of a single droplet in ultrasonic atomization and the sub-droplet generation mechanism

Compared with the traditional mechanical atomization technology, ultrasonic atomization technology has been widely used in industry in recent years because of its higher energy efficiency and environmental friendliness. However, the physical mechanism of ultrasonic atomization of the individual droplet has not been studied, especially the evolution of Faraday instability and the formation mechanism of sub-droplets, leading to a lack of scientific theoretical guidance for the application of this technology. Here, we observed different Faraday wave patterns and evolution processes on the surface of the individual droplet using high-speed camera technology. The wettability of the droplet is significantly enhanced by the vibration effect. Interestingly, the Faraday waves of highly viscous droplets show multiple concentric semicircular ripple shapes. Droplet atomization is the result of Faraday wave mode transition and instability evolution induced by inertial forces, and both viscosity and surface tension play a suppressive role in the development of Faraday instability. The vibration frequency of stable Faraday waves was traced, and the effects of amplitude, surface tension, viscosity, and liquid volume on the Faraday wave wavelength and number were investigated. The characteristic parameters of Faraday wave instability evolution such as atomization amplitude threshold and atomization time were investigated under different experimental conditions. It is found that for low-viscosity liquids, the atomization amplitude threshold depends mainly on the surface tension, while for high-viscosity liquids, the atomization amplitude threshold is influenced by both viscosity and liquid volume. The effects of surface tension, viscosity, and volume on the atomization time are similar to those on the atomization amplitude threshold. We investigated the kinetic process of sub-droplet generation and showed that differences in Rayleigh-Plateau instability and capillary pinch-off mechanisms lead to different patterns of sub-droplet generation, where the former depends on the capillary number threshold and the latter can be divided into the protrusion break mode and the ligament break mode. The proportion of these two modes was investigated under different experimental conditions to quantitatively evaluate the selectivity of the mother droplet atomization mode. For the first time, the dispersion distribution of the sub-droplets was explained by using the length and number characteristics of the ligaments. The correlation analysis of sub-droplet size on ligament length and ligament number was established, and a linear fitting function was obtained.

Comparing Central Aortic Pressures Obtained Using a SphygmoCor Device to Pressures Obtained Using a Pressure Catheter.

This study compared aortic pressures estimated using a SphygmoCor XCEL PWA device (ATCOR, Naperville, IL) noninvasively with aortic pressures obtained using pressure catheters during catheterization procedures and analyzed the impact of a linear-fit function on the estimated pressure values. One hundred and thirty-six patients scheduled for cardiac catheterization procedure were enrolled in IRB approved studies. Catheterization procedures were performed according to standard-of-care to acquire aortic pressure measurements. Immediately after the catheterization procedure with the pressure catheters removed, while the patients were still in the catheterization laboratory, central aortic pressures were estimated with the SphygmoCor device (using its inbuilt transfer function). The error between measured and estimated aortic pressures was evaluated using Bland-Altman analysis (n = 93). A linear-fit was performed between the measured and estimated pressures, and using the linear equation the error measurements were repeated. A bootstrap analysis was performed to test the generalizability of the linear-fit function. In a subset of cases (n = 13), central aortic pressure values were also obtained using solid-state high-fidelity catheters (Millar, Houston, TX), and the error measurements were repeated. The magnitude of errors between the measured and estimated aortic pressures (mean errors >6.4 mm Hg; mean errors >8.0 mm Hg in the subset) were reduced to less than 1 mm Hg after using the linear-fit function derived in this study. For the population examined in this study, the SphygmoCor data must be used with the linear-fit function to obtain aortic pressures that are comparable to the measurements obtained using pressure catheters. Trial Numbers NCT03243942 and NCT03245255.

Experimental Research on Evaluation of Soil Water Content Using Ground Penetrating Radar and Wavelet Packet-Based Energy Analysis

Soil water content is one of the most important factors affecting the safety and stability of buildings or structures, especially in roadbeds, slopes, earth dams and foundations. Accurate assessments of soil water content can ensure the quality of construction, reduce construction costs and prevent accidents, among other benefits. In this study, ground penetrating radar (GPR) was used to detect and evaluate changes in soil water content. The GPR signal is usually nonstationary and nonlinear; however, traditional Fourier theory is typically suitable for periodic stationary signals, and cannot reflect the law of the frequency and energy of the GPR signal changing with time. Wavelet transform has good time-frequency localization characteristics, and therefore represents a new method for analyzing and processing GPR signals. According to the time-frequency characteristics of GPR signals, in this paper, a new biorthogonal wavelet basis which was highly matched with the GPR waveform was constructed using the lifting framework of wavelet theory. Subsequently, an evaluation method, namely, the wavelet packet-based energy analysis (WPEA) method, was proposed. The method was utilized to calculate the wavelet packet-based energy indexes (WPEI) of the GPR single-channel signals for clay samples with water contents ranging from 10% to 24%. The research results showed that there was a highly correlated linear relationship between the WPEI and the soil water contents, and the relationship between the two was fitted with a linear fitting function. The feasibility of the method was verified by comparing our results with those obtained using classical wavelet bases to perform the wavelet packet transform. The large-area, continuous scanning measurement method of GPR was shown to be suitable for evaluations of soil water contents in roadbeds, slopes, earth dams, and foundations.

Abstract 9538: Comparison of Central Aortic Pressures Obtained Using an Invasive Pressure Catheter and the Noninvasive Sphygmocor Device

Introduction: The SphygmoCor (ATCOR, Naperville, IL) device utilizes a generalized transfer function based on patient’s age and gender to derive the aortic pressure pulse from the brachial-cuff based pressure measurements. This study compared aortic pressures obtained using SphygmoCor with aortic pressures obtained during cardiac catheterization. Hypothesis: Mean differences in aortic pressures obtained using SphygmoCor and pressure catheters will be less than 5 mmHg. Methods: After IRB approval, 136 patients were enrolled. During standard-of-care catheterization procedure, aortic pressure measurements were obtained using fluid-filled catheters. In a subset of patients (n = 13) the aortic pressure values were also obtained using solid-state high-fidelity Millar catheters. Immediately after the catheterization procedure, while the patients were still in the catheterization laboratory (on the procedure table), central aortic pressures were estimated with the SphygmoCor device. The measured and estimated aortic pressures were compared using linear regression and Bland-Altman analysis. A linear fit was performed to derive an additional transfer function to convert SphygmoCor pressure values to catheter-based aortic pressures, and the resulting differences in pressure values were compared. A bootstrap analysis was performed to test the generalizability of this transfer function. Results: Mean differences in systolic, diastolic and pulse aortic pressures obtained using the two techniques ranged from 6.5 to 18.0 mmHg (p &lt; 0.001). In the subset with high-fidelity catheters, the differences ranged from 8.0 to 18.9 mmHg. With the linear-fit transfer function, the differences in systolic, diastolic and pulse aortic pressures were low (&lt; 1 mmHg) corresponding to a reduction in bias noted with Bland-Altman analysis. The bootstrap analysis of the transfer function (100 iterations) achieved a coefficient of variation for the root mean square error &lt; 8.4% for systolic, diastolic and pulse aortic pressures. Conclusions: The magnitude of the differences between the SphygmoCor-estimated and catheter-based systolic, diastolic and pulse aortic pressures reduced considerably after using the linear-fit transfer function derived in this study.

Inclusive fitness and Hamilton’s rule in a stochastic environment

The evolution of cooperation in Prisoner’s Dilemmas with additive random cost and benefit for cooperation cannot be accounted for by Hamilton’s rule based on mean effects transferred from recipients to donors weighted by coefficients of relatedness, which defines inclusive fitness in a constant environment. Extensions that involve higher moments of stochastic effects are possible, however, and these are connected to a concept of random inclusive fitness that is frequency-dependent. This is shown in the setting of pairwise interactions in a haploid population with the same coefficient of relatedness between interacting players. In an infinite population, fixation of cooperation is stochastically stable if a mean geometric inclusive fitness of defection when rare is negative, while fixation of defection is stochastically unstable if a mean geometric inclusive fitness of cooperation when rare is positive, and these conditions are generally not equivalent. In a finite population, the probability for cooperation to ultimately fix when represented once exceeds the probability under neutrality or the corresponding probability for defection if the mean inclusive fitness of cooperation when its frequency is 1/3 or 1/2, respectively, exceeds 1. All these results rely on the simplifying assumption of a linear fitness function. It is argued that meaningful applications of random inclusive fitness in complex settings (multi-player game, diploidy, population structure) would generally require conditions of weak selection and additive gene action.

Adaptive parameter of standard deviation enhances the power of noninvasive prenatal screens

Purpose Traditional Z-test methods during noninvasive prenatal screens (NIPS) use the fixed parameter of standard deviation (SD), which ignores the influence of actual sequencing read counts of a sample on the results. The aim of this study is to eliminate the influence of the sequencing depth of individual samples on the results and enhance the power of NIPS. Methods In this study, we propose an improved NIPS method, which calculates the SD in the Z-score process adaptively according to the actual read count of the test sample. Our approach obtained the SD linear fitting function along with the read count with a large number of reference samples, in which SD and read count fit well. The effectiveness of our enhanced NIPS method was evaluated on three common trisomy syndromes and five recurrent CNV syndromes with 3219 and 6592 samples based on whole genome sequencing of maternal peripheral blood. Results A total of 3,219 pregnant samples have been used for validating the proposed method on detecting fetal trisomy syndromes (T13, T18, and T21), in which eight false negative (FN) samples have been corrected as true positive (TP) and eight false positive (FP) samples have been fixed as true negative (TN) with our proposed adaptive-SD method. Another 6592 samples were used to compare the two methods on detecting five recurrent fetal copy number variation (CNV) syndromes, in which the FP samples have decreased from 99 to 39. Conclusions Our adaptive-SD NIPS method shows more power on detecting both trisomy syndromes and five recurrent CNVs in the pregnant samples with diverse read counts. Besides, our proposed method contributes to lower FP and FN samples than the traditional Z-test method in NIPS. Our results show that our enhanced NIPS methods are effective in detecting both abnormal fetal trisomy syndromes and recurrent CNV syndromes in pregnant women.