Optimization of Random Feature Method in the High-Precision Regime

Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in terms of both accuracy and efficiency.Potentially,the optimization problem in the RFM is more difficult to solve than those that arise in traditional methods.Unlike the broader machine-learning research,which frequently targets tasks within the low-precision regime,our study focuses on the high-precision regime crucial for solving PDEs.In this work,we study this problem from the following aspects:(i)we analyze the coeffcient matrix that arises in the RFM by studying the distribution of singular values;(ii)we investigate whether the continuous training causes the overfitting issue;(ii)we test direct and iterative methods as well as randomized methods for solving the optimization problem.Based on these results,we find that direct methods are superior to other methods if memory is not an issue,while iterative methods typically have low accuracy and can be improved by preconditioning to some extent.

Exploration of the Impact Mechanism of Government Credibility Based on Variable Screening Method

Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. In recent years, researchers’ research on government credibility has mostly focused on exploring theories and mechanisms, with little empirical research on this topic. This article intends to apply variable selection models in the field of social statistics to the issue of government credibility, in order to achieve empirical research on government credibility and explore its core influencing factors from a statistical perspective. Specifically, this article intends to use four regression-analysis-based methods and three random-forest-based methods to study the influencing factors of government credibility in various provinces in China, and compare the performance of these seven variable selection methods in different dimensions. The research results show that there are certain differences in simplicity, accuracy, and variable importance ranking among different variable selection methods, which present different importance in the study of government credibility issues. This study provides a methodological reference for variable selection models in the field of social science research, and also offers a multidimensional comparative perspective for analyzing the influencing factors of government credibility.

Modeling habitat suitability of range plant species using random forest method in arid mountainous rangelands

Mountainous rangelands play a pivotal role in providing forage resources for livestock, particularly in summer, and maintaining ecological balance. This study aimed to identify environmental variables affecting range plant species distribution, ecological analysis of the relationship between these variables and the distribution of plants, and to model and map the plant habitats suitability by the Random Forest Method(RFM) in rangelands of the Taftan Mountain, Sistan and Baluchestan Province, southeastern Iran. In order to determine the environmental variables and estimate the potential distribution of plant species, the presence points of plants were recorded by using systematic random sampling method(90 points of presence) and soils were sampled in 5 habitats by random method in 0–30 and 30–60 cm depths. The layers of environmental variables were prepared using the Kriging interpolation method and Geographic Information System facilities. The distribution of the plant habitats was finally modelled and mapped by the RFM. Continuous maps of the habitat suitability were converted to binary maps using Youden Index(?) in order to evaluate the accuracy of the RFM in estimation of the distribution of species potentialhabitat. Based on the values of the area under curve(AUC) statistics, accuracy of predictive models of all habitats was in good level. Investigating the agreement between the predicted map, generated by each model, and actual maps, generated from fieldmeasured data, of the plant habitats, was at a high level for all habitats, except for Amygdalus scoparia habitat. This study concluded that the RFM is a robust model to analyze the relationships between the distribution of plant species and environmental variables as well as to prepare potential distribution maps of plant habitats that are of higher priority for conservation on the local scale in arid mountainous rangelands.

Estimation of wear performance of AZ91 alloy under dry sliding conditions using machine learning methods

The wear behavior of AZ91 alloy was investigated by considering different parameters,such as load(10−50 N),sliding speed(160−220 mm/s)and sliding distance(250−1000 m).It was found that wear volume loss increased as load increased for all sliding distances and some sliding speeds.For sliding speed of 220 mm/s and sliding distance of 1000 m,the wear volume losses under loads of 10,20,30,40 and 50 N were calculated to be 15.0,19.0,24.3,33.9 and 37.4 mm3,respectively.Worn surfaces show that abrasion and oxidation were present at a load of 10 N,which changes into delamination at a load of 50 N.ANOVA results show that the contributions of load,sliding distance and sliding speed were 12.99%,83.04%and 3.97%,respectively.The artificial neural networks(ANN),support vector regressor(SVR)and random forest(RF)methods were applied for the prediction of wear volume loss of AZ91 alloy.The correlation coefficient(R2)values of SVR,RF and ANN for the test were 0.9245,0.9800 and 0.9845,respectively.Thus,the ANN model has promising results for the prediction of wear performance of AZ91 alloy.

Response of train-bridge system under intensive seismic excitation by random vibration method

Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation,the intensity of which is larger than 7,acts in train-bridge system.Firstly,the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established,where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom,while the single-span simple supported bridge subsystem is composed of 102D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support.Secondly,Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system.The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method,respectively solved by precise integral method and Newmark-βmethod through the inter-system iterative procedure.Finally,the results are compared with the case under the weak seismic excitation,and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution.In a high probability,the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.

DYNAMIC CHARACTERISTIC ANALYSIS OF FUZZY-STOCHASTIC TRUSS STRUCTURES BASED ON FUZZY FACTOR METHOD AND RANDOM FACTOR METHOD

A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh＇s quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable＇s moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.

Random failure mechanism method for assessment of working platform bearing capacity with a linear trend in undrained shear strength

A bearing capacity evaluation for the surface strip foundation on a working platform modelled on a twolayered substrate is considered in the study.The upper layer is assumed as man-made and wellcontrolled and thus non-variable.The lower layer modelling natural cohesive soil is subjected to spatial variability of undrained shear strength.The random failure mechanism method(RFMM)is used to evaluate the bearing capacity.This approach employs a kinematic assessment of the critical load and incorporates the averaging of three-dimensional(3 D)random field along dissipation surfaces that result from the failure mechanism geometry.A novel version of the approach considering an additional linear trend of undrained shear strength in the spatially variable layer is proposed.The high efficiency of the RFMM algorithm is preserved.The influences of foundation length,trend slope in the spatially variable layer,fluctuation scales,and thickness of the homogenous sand layer on the resulting bearing capacity evaluations are analysed.Moreover,for selected cases,verification of the RFMM based assessment obtained using random finite difference method(RFDM)based on 3 D analysis is provided.Two types of analyses are performed using RFDM based on associated and non-associated flow rules.For associated flow rule which corresponds to RFMM,the RFMM is conservative and efficient and thus it seems preferable.However,if RFDM employs non-associated flow rule(much lower dilation angle for sand layer),the efficient RFMM is no longer conservative.For this situation,a combined approach that improves the efficiency of the numerical method is suggested.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD AND ITS VERIFICATION FOR EFFECTIVE PROPERTIES OF COMPOSITE MATERIALS

The present study aims at developing a new method-RandomMicrostructure Finite Element Method (RMFEM) for the effectiveproperties of com- Posite materials. In this method, a randommicrostructure Model is used to simulate the microstructure of thereal composite materials. The physical fields in such a randomMicrosturucture model under specified boundary and initial Conditionsare analyzed by finite element method.

Randomized Kaczmarz algorithm for CT reconstruction

The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.

Analysis on Pseudo Excitation of Random Vibration for Structure of Time Flight Counter

Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method（PEM）is an effective method for calculation of random vibration.Due to complicated and coupling random vibration in rocket or shuttle launching,the new staging white noise mathematical model is deduced according to the practical launch environment.This deduced model is applied for PEM to calculate the specific structure of Time of Flight Counter（ToFC）.The responses of power spectral density and the relevant dynamic characteristic parameters of ToFC are obtained in terms of the flight acceptance test level.Considering stiffness of fixture structure,the random vibration experiments are conducted in three directions to compare with the revised PEM.The experimental results show the structure can bear the random vibration caused by launch without any damage and key dynamical parameters of ToFC are obtained.The revised PEM is similar with random vibration experiment in dynamical parameters and responses are proved by comparative results.The maximum error is within 9%.The reasons of errors are analyzed to improve reliability of calculation.This research provides an effective method for solutions of computing dynamical characteristic parameters of complicated structure in the process of rocket or shuttle launching.

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over ＂fast＂ variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the ease without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated.The analysis is based on a special Zhuravlev transformation,which reduces the system to the one without impacts or velocity jumps,and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses.The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset.A perturbation-based moment closure scheme is proposed for the case of nonzero offset.The effects of damping,detuning,and bandwidth and magnitudes of the random excitations are analyzed.The theoretical analyses are verified by the numerical results.The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD FOR EFFECTIVE NONLINEAR PROPERTIES OF COMPOSITE MATERIALS

Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of linear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an effective tool to investigate the nonlinear problems.

Shexian Bupleurum Alleviates Insomnia and Improves Symptoms of Anxiety and Depression:A Randomized Double-Blind Placebo-Controlled Clinical Trial

Objective:To observe the clinical efficacy of Shexian bupleurum on insomnia based on evaluation scales and polysomnogram(PSG).Methods:A total of 260 patients suffering from insomnia admitted to the outpatient department of Handan Central Hospital were included in a randomized,double blind,placebo-controlled trial.The patients were randomly divided into two groups:a control group(receiving placebo,n=150),and an intervention group(receiving Shexian bupleurum treatment,n=110).The clinical trial lasted for 4 weeks.The Pittsburgh Sleep Quality Index(PSQI),Insomnia Severity Index(ISI),Patient Health Questionnaire(PHQ)-9,Generalized Anxiety Disorder(GAD)-7,17 items of Hamilton Depression Scale(HAMD-17),and Hamilton Anxiety Scale(HAMA)were used to evaluate the patients at baseline as well as two weeks and four weeks after treatment;the Treatment Emergent Symptom Scale(TESS)was used to evaluate adverse reactions;polysomnography(PSG)was used to monitor and analyze their sleep characteristics at baseline and four weeks after treatment.Results:The PSQI,ISI,PHQ-9,HAMD-17,and HAMA scores of the intervention group significantly decreased compared to the control group,while the total sleep time,rapid eye movement sleep latency,stage 2 sleep,deep sleep,rapid eye movement sleep,and sleep efficiency of the intervention group significantly increased compared to the control group.The PHQ-9 score of the control group only decreased two weeks after treatment(p<0.05)compared to the intervention group.In addition,there were no obvious adverse events in both the intervention group and the control group.Conclusion:Shexian bupleurum not only improves sleep quality,but also relieves depression and anxiety in patients who suffer from insomnia.

Set Programming Method and Performance Improvement of Phase Change Random Access Memory Arrays

A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference （I1 - I2） of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.

EDGEWORTH EXPANSION FOR NEAREST NEIGHBOR- KERNEL ESTIMATE AND RANDOM WEIGHTING APPROXIMATION OF CONDITIONAL DENSITY

In this paper,Edgeworth expansion for the nearest neighbor\|kernel estimate and random weighting approximation of conditional density are given and the consistency and convergence rate are proved.

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.

Structural modal parameter identifi cation and damage diagnosis based on Hilbert-Huang transform

Traditional modal parameter identifi cation methods have many disadvantages,especially when used for processing nonlinear and non-stationary signals.In addition,they are usually not able to accurately identify the damping ratio and damage.In this study,methods based on the Hilbert-Huang transform(HHT) are investigated for structural modal parameter identifi cation and damage diagnosis.First,mirror extension and prediction via a radial basis function(RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition(EMD),which is a crucial part of HHT.Then,the approaches based on HHT combined with other techniques,such as the random decrement technique(RDT),natural excitation technique(NExT) and stochastic subspace identifi cation(SSI),are proposed to identify modal parameters of structures.Furthermore,a damage diagnosis method based on the HHT is also proposed.Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure.The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure.Finally,acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches.The results show that the proposed approaches based on HHT for modal parameter identifi cation and damage diagnosis are reliable and practical.

Influence of Reclamation Works on the Marine Environment in a Semi-Enclosed Bay

The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effect on the flow and material transport has been emphasized, and a thirty-year mean value of wind has been considered in the numerical simulation. As a whole, even after the reclaiming and dredging are conducted, the flow pattern looks similar to the original state. However, velocity variations up to 20% to 100% appear in the vicinity of the construction area. In the case of summcr wind forcing, the seawater exchange rate increases from 71.6% to 82.9% after the reclaiming and dredging, as indicated by a particle-tracking method. On the contrary, in the case of winter wind forcing, thc seawater cxchange rate appears to be 97.2% under natural conditions but decrcases slightly to 93.2% aftcr the rcclaiming and dredging. Thus, the wind forcing plays an important role in controlling the seawater exchangc rates. The seawater cxchange rate is further improved by 15% if the dredging is simultaneously carried out with the reclaiming. This suggests that the dredging can be an effective means to mitigate the variation of flow.

Stability and reliability of pit slopes in surface mining combined with underground mining in Tonglushan mine

Slope stability is of critical importance in the process of surface-underground mining combination. The influence of underground mining on pit slope stability was mainly discussed, and the self-stabilization of underground stopes was also studied. The random finite element method was used to analyze the probability of the rock mass stability degree of both pit slopes and underground stopes. Meanwhile, 3D elasto-plastic finite element method was used to research into the stress, strain and rock mass failure resulting from mining. The results of numerical simulation indicate that the mining of the underground test stope has certain influence on the stability of the pit slope, but the influence is not great. The safety factor of pit slope is decreased by 0.06, and the failure probability of the pit slope is increased by 1.84%. In addition, the strata yielding zone exists around the underground test stope. The results basically conform to the information coming from the field monitoring.