Quadratic Fitting Function Research Articles

Axial stress measurement for tightened bolt based on the effect of stress on ultrasonic wave attenuation

ABSTRACT Accurate assessment and monitoring of axial stress during the service life of the bolt connection is of great significance in ensuring the stability and reliability of the aerospace structure. The current acoustoelastic method requires both transverse and longitudinal mode waves and is less sensitive to small-size bolts, resulting in relatively larger errors in the evaluation of axial stress. In this paper, an axial stress measurement method with only a single longitudinal/transverse transducer for tightened bolts based on a novel attenuation-based model is introduced. The ultrasonic responses under axial preload in different frequency bands are comprehensively reflected through the energy attenuation coefficient matrix. In addition, an experimental method for selecting the optimal frequency band is given. Furthermore, the semi-permanent coupling method is proposed to provide a stable coupling condition to verify the feasibility of the attenuation-based model. Loading tests and ultrasonic tests were conducted on two kinds of strength-grade materials to obtain the calibration curves of both the longitudinal and transverse attenuation models. The experimental results show that the energy attenuation coefficient is positively correlated with the axial stress in a specific frequency range and the calibrated curve has a high fitting rate with a quadratic fitting function. The average relative error of the prediction results is less than 7.5%, which is better than the conventional acoustoelastic effect model.

Influence of stabilizing ions and sintering process on the thermal conductivity of α‐SiAlON ceramics

Abstractα‐SiAlON ceramics with different stabilizing ions of Yb, Dy, Nd, Y, Ca, and binary stabilizing ions of (Yb + Ca) and (Yb + Nd) were prepared by spark plasma sintering at 1600°C and gas pressure sintering at 1800 and 1900°C, and their thermal conductivity was investigated. It was found that α‐SiAlON ceramics with larger and heavier stabilizing ions had lower thermal conductivity and the thermal conductivity could be further reduced by using binary stabilizing ions, which can be explained by phonon scattering from point defects. At the same time, the samples prepared at lower sintering temperatures showed smaller grain sizes and lower thermal conductivity. The relationship between the thermal diffusivity of samples and temperature was studied, where the dependence of inverse thermal diffusivity on temperature was better fitted by a quadratic fitting function than the usual linear one over a wide temperature range from 25 to 800°C.

Clinical applications of machine learning in the survival prediction and classification of sepsis: coagulation and heparin usage matter

BackgroundSepsis is a life-threatening syndrome eliciting highly heterogeneous host responses. Current prognostic evaluation methods used in clinical practice are characterized by an inadequate effectiveness in predicting sepsis mortality. Rapid identification of patients with high mortality risk is urgently needed. The phenotyping of patients will assistant invaluably in tailoring treatments.MethodsMachine learning and deep learning technology are used to characterize the patients’ phenotype and determine the sepsis severity. The database used in this study is MIMIC-III and MIMIC-IV (‘Medical information Mart for intensive care’) which is a large, public, and freely available database. The K-means clustering is used to classify the sepsis phenotype. Convolutional neural network (CNN) was used to predict the 28-day survival rate based on 35 blood test variables of the sepsis patients, whereas a double coefficient quadratic multivariate fitting function (DCQMFF) is utilized to predict the 28-day survival rate with only 11 features of sepsis patients.ResultsThe patients were grouped into four clusters with a clear survival nomogram. The first cluster (C_1) was characterized by low white blood cell count, low neutrophil, and the highest lymphocyte proportion. C_2 obtained the lowest Sequential Organ Failure Assessment (SOFA) score and the highest survival rate. C_3 was characterized by significantly prolonged PTT, high SIC, and a higher proportion of patients using heparin than the patients in other clusters. The early mortality rate of patients in C_3 was high but with a better long-term survival rate than that in C_4. C_4 contained septic coagulation patients with the worst prognosis, characterized by slightly prolonged partial thromboplastin time (PTT), significantly prolonged prothrombin time (PT), and high septic coagulation disease score (SIC). The survival rate prediction accuracy of CNN and DCQMFF models reached 92% and 82%, respectively. The models were tested on an external dataset (MIMIC-IV) and achieved good performance. A DCQMFF-based application platform was established for fast prediction of the 28-day survival rate.ConclusionCNN and DCQMFF accurately predicted the sepsis patients’ survival, while K-means successfully identified the phenotype groups. The distinct phenotypes associated with survival, and significant features correlated with mortality were identified. The findings suggest that sepsis patients with abnormal coagulation had poor outcomes, abnormal coagulation increase mortality during sepsis. The anticoagulation effects of appropriate heparin sodium treatment may improve extensive micro thrombosis-caused organ failure.

Research on UAV Large Scale Mapping and its elevation fitting

Due to the influence of the external environment and the limitation of data processing methods, the accuracy of the unmanned aerial vehicle (UAV) aerial photogrammetry needs further studies in the aspect of mapping large-scale topographic maps. In order to verify whether the measurement accuracy of the UAV aerial photography system meets the requirements of large-scale topographic maps, this paper conducts an accuracy test on a topographic map, using the surface fitting model, the plane fitting model, quadratic surface fitting and polyhedral function method fitting based on field measured data. The fitting of four models to the elevation points by the combined polyhedral function method. The elevation difference between the flat area and the mountain area was corrected, and the elevation accuracy of the four methods was compared. This paper shows that in flat areas the elevation accuracy of the surface fitting model is better than the plane fitting model, quadratic surface fitting, and polyhedral function method fitting. In the mountainous region, the elevation accuracy of the quadratic surface fitting model is better than that of the plane fitting model, surface fitting model, and polyhedral function method.

Comparative Study of Unconstrained Mechanical Optimization Methods Based on Two-variable Rosenbrock Function

The unconstrained optimization method (UOM) plays an important role in the field of physics, mathematics, statistics, etc. Rosenbrock function is a 4-degree function with a curved canyon. It is most suitable for testing UOM. However, the test hasn't done. We have written 14 UOM computer programs, 12 of which contain our new algorithm. From the optimal result, the 2-order approximation direction is the best, followed by the conjugate direction, followed by the negative gradient direction. For quadratic fitting function method, linear fitting gradient method and unbounded polyhedron deformation method, a new algorithm for moving points was proposed. When the new point is better than all of the other points, the other points should close up to it. And when the new point is worse than all of the other points, it should close up to the best point or center point. The improvement of moving points makes these optimization directions be effective for complex objective functions.

Development of MIMO–OFDM system and forward error correction techniques since 2000s

The multi-input multi-output–orthogonal frequency division multiplexing (MIMO–OFDM) system serves as one of the most promising techniques that support high data rate and high performance in diverse fading channel conditions. The paper presents an overview of MIMO–OFDM wireless technology, covering advances in physical-layer design, various space–time codes, space–frequency codes and efficient concatenated forward error correction techniques, along with interleaving to yield reduced bit error rate performance (BER). Further, the paper presents the evolution of various performance metrics that are reported since the 2000s in the literature. The evolution outcome is examined using a quadratic nonlinear fitting function to assess the interesting performance metrics. Since BER versus SNR analysis is found as the interesting performance study of the MIMO–OFDM system, the current status of the achieved BER under varying SNR is reviewed and presented.

Optimization of the diffuser in a centrifugal pump by combining response surface method with multi-island genetic algorithm

The diffuser plays a significant role in the performance of a centrifugal pump, especially for a high-power centrifugal pump. Therefore, to improve the efficiency of a centrifugal pump, optimization of a vaned diffuser is proposed in this work. The steady simulations were carried out by solving the three-dimensional Reynolds-averaged Navier–Stokes equations with a shear stress transport turbulence model. The numerical head and efficiency were validated by the experimental results of the original pump, and the results show that the predicted performance of the numerical simulation is in good agreement with the experimental results. Four design variables of the diffuser including the diffuser inlet diameter D3, diffuser inlet width b3, diffuser inlet angle α3, and diffuser wrap angle ϕ2 were selected to design by the CFturbo 9.0. The diffusers under test were selected using the orthogonal experiment method using the orthogonal array L16(44). The effect of the four variables on the pump’s efficiency was investigated by the predicted efficiency of 16 diffusers. A quadratic polynomial fitting function for the variables and efficiency was constructed using the response surface method. The optimal values were obtained by solving the response function with the multi-island genetic algorithm. Through the analysis of the range and quadratic regression, it was found that the diffuser wrap angle has the most significant influence on efficiency. The efficiency of the optimal pump increased by 8.65% compared with the original scheme. The velocity distributions in the diffuser inlet and volute were improved and became more uniform. The total pressure in the diffuser and volute of the optimal pump was higher than that of the original pump.

Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots.

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot’s pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area.

Development of unfolding method to obtain pin-wise source strength distribution from PWR spent fuel assembly measurement

An unfolding method has been developed to obtain a pin-wise source strength distribution of a 14 × 14 pressurized water reactor (PWR) spent fuel assembly. Sixteen measured gamma dose rates at 16 control rod guide tubes of an assembly are unfolded to 179 pin-wise source strengths of the assembly. The method calculates and optimizes five coefficients of the quadratic fitting function for X–Y source strength distribution, iteratively. The pin-wise source strengths are obtained at the sixth iteration, with a maximum difference between two sequential iterations of about 0.2%. The relative distribution of pin-wise source strength from the unfolding is checked using a comparison with the design code (Westinghouse APA code). The result shows that the relative distribution from the unfolding and design code is consistent within a 5% difference. The absolute value of the pin-wise source strength is also checked by reproducing the dose rates at the measurement points. The result shows that the pin-wise source strengths from the unfolding reproduce the dose rates within a 2% difference.

Solution of the Crow-Kimura and Eigen Models for Alphabets of Arbitrary Size by Schwinger Spin Coherent States

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an $h$-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary $h$ and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler's theorem for homogeneous functions is used to derive this `thermodynamic' formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine $h=2$ alphabet and the nucleic acid $h=4$ alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the $h=4$ and $h=20$ cases. We derive the maximum principle for the Eigen model for general $h$. The general result for the Eigen model reduces to a known result for $h=2$. Examples are presented for the nucleic acid $h=4$ and the amino acid $h=20$ alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.

Error Thresholds in a Mutation–selection Model with Hopfield-type Fitness

The deterministic limit of a Hopfield-type mutation-selection model in the sequence space approach is investigated. Genotypes are identified with two-letter sequences. Mutation is modelled as a Markov process, fitness functions are of Hopfield type, where the fitness of a sequence is determined by the Hamming distances to a number of predefined patterns. Using a maximum principle for the population mean fitness in equilibrium, the error threshold phenomenon is studied for quadratic Hopfield-type fitness functions with small numbers of patterns. Different from previous investigations of the Hopfield model, the system shows error threshold behaviour not for all fitness functions, but only for certain parameter values.

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

The replicator equation model for the evolution of individual behaviors in a single species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional continuously stable strategy (CSS) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger neighborhood invader strategy (NIS) concept is needed if the supports are arbitrary.

A rank-one fitting algorithm for unconstrained optimization problems

This paper proposes a rank-one modified fitting algorithm. The main feature of the approach is that the update formula for the deflection matrix in an iteration is deduced from a quadratic fitting function, not from the traditional quasi-Newton equation. Under some mild assumptions, the algorithm is globally and linearly convergent.

Mutation-selection models solved exactly with methods of statistical mechanics.

We reconsider deterministic models of mutation and selection acting on populations of sequences, or, equivalently, multilocus systems with complete linkage. Exact analytical results concerning such systems are few, and we present recent and new ones obtained with the help of methods from quantum statistical mechanics. We consider a continuous-time model for an infinite population of haploids (or diploids without dominance), with N sites each, two states per site, symmetric mutation and arbitrary fitness function. We show that this model is exactly equivalent to a so-called Ising quantum chain. In this picture, fitness corresponds to the interaction energy of spins, and mutation to a temperature-like parameter. The highly elaborate methods of statistical mechanics allow one to find exact solutions for non-trivial examples. These include quadratic fitness functions, as well as 'Onsager's landscape'. The latter is a fitness function which captures some essential features of molecular evolution, such as neutrality, compensatory mutations and flat ridges. We investigate the mean number of mutations, the mutation load, and the variance in fitness under mutation-selection balance. This also yields some insight into the 'error threshold' phenomenon, which occurs in some, but not all, examples.

Revision of a dosage‐effect relationship for the prevalence of noise‐related annoyance

More than a decade has passed since Schultz (1978) derived a relationship between noise exposure and the prevalence of annoyance from the findings of various social surveys of community response to general transportation noise sources. Numerous measurements of the prevalence of noise‐related annoyance have been published in subsequent years. A least‐squares quadratic fitting function to a set of 427 data points (developed by addition of 266 new data points to the original set of 161 data points) differs little from the third‐order polynomial fit to the original data set. [Work supported by U.S. Air Force Noise and Sonic Boom Impact Technology Program under Contract F33615‐86‐C‐0530.]