Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that facilitates such a process.Both multilayer perceptron(MLP)-based NN and convolutional neural network(CNN)models are trained to map the q-profile to the plasma current density J-profile,and vice versa,while satisfying the Grad–Shafranov radial force balance constraint.When the initial target models are trained,using a database of semianalytically constructed numerical equilibria,an initial CNN with one convolutional layer is found to perform better than an initial MLP model.In particular,a trained initial CNN model can also predict the q-or J-profile for experimental tokamak equilibria.The performance of both initial target models is further improved by fine-tuning the training database,i.e.by adding realistic experimental equilibria with Gaussian noise.The fine-tuned target models,referred to as fine-tuned MLP and fine-tuned CNN,well reproduce the target q-or J-profile across multiple tokamak devices.As an important application,these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers,where the desired input quantity is the safety factor instead of the plasma current density.

Optimizing slope safety factor prediction via stacking using sparrow search algorithm for multi-layer machine learning regression models

The safety factor is a crucial quantitative index for evaluating slope stability.However,the traditional calculation methods suffer from unreasonable assumptions,complex soil composition,and inadequate consideration of the influencing factors,leading to large errors in their calculations.Therefore,a stacking ensemble learning model(stacking-SSAOP)based on multi-layer regression algorithm fusion and optimized by the sparrow search algorithm is proposed for predicting the slope safety factor.In this method,the density,cohesion,friction angle,slope angle,slope height,and pore pressure ratio are selected as characteristic parameters from the 210 sets of established slope sample data.Random Forest,Extra Trees,AdaBoost,Bagging,and Support Vector regression are used as the base model(inner loop)to construct the first-level regression algorithm layer,and XGBoost is used as the meta-model(outer loop)to construct the second-level regression algorithm layer and complete the construction of the stacked learning model for improving the model prediction accuracy.The sparrow search algorithm is used to optimize the hyperparameters of the above six regression models and correct the over-and underfitting problems of the single regression model to further improve the prediction accuracy.The mean square error(MSE)of the predicted and true values and the fitting of the data are compared and analyzed.The MSE of the stacking-SSAOP model was found to be smaller than that of the single regression model(MSE=0.03917).Therefore,the former has a higher prediction accuracy and better data fitting.This study innovatively applies the sparrow search algorithm to predict the slope safety factor,showcasing its advantages over traditional methods.Additionally,our proposed stacking-SSAOP model integrates multiple regression algorithms to enhance prediction accuracy.This model not only refines the prediction accuracy of the slope safety factor but also offers a fresh approach to handling the intricate soil composition and other influencing factors,making it a precise and reliable method for slope stability evaluation.This research holds importance for the modernization and digitalization of slope safety assessments.

Comprehensive safety factor of roof in goaf underdeep high stress

The safety factor of roof under deep high stress is a quantitative index for evaluating roof stability.Based on the failure mode of surrounding rock of stope roof,the mechanics model of goaf roof is constructed,and the internal force of roof is deduced by the theory of hingeless arch.The calculation method of roof safety factor(K)under the environment of deep mining is proposed in view of compression failure and shear failure of roof.The calculation formulas of shear safety factor(K1),compression safety factor(K2)and comprehensive safety factor(K)of roof are given.The influence of stope span and roof thickness on roof stability is considered in this paper.The results show that when the roof thickness remains constant,the roof safety factor decreases with the increasing of the stope span;when the stope span remains constant,the roof safety factor increases with the increasing of the roof thickness.The deep mining example shows that when the stope span is 30 m and the roof thickness is 10 m,the roof comprehensive safety factor is 1.12,which indicates the roof is in a stable state.

Three-dimensional stability of landslides based on local safety factor

Unlike the limit equilibrium method(LEM), with which only the global safety factor of the landslide can be calculated, a local safety factor(LSF) method is proposed to evaluate the stability of different sections of a landslide in this paper. Based on three-dimensional(3D) numerical simulation results, the local safety factor is defined as the ratio of the shear strength of the soil at an element on the slip zone to the shear stress parallel to the sliding direction at that element. The global safety factor of the landslide is defined as the weighted average of all local safety factors based on the area of the slip surface. Some example analyses show that the results computed by the LSF method agree well with those calculated by the General Limit Equilibrium(GLE) method in two-dimensional(2D) models and the distribution of the LSF in the 3D slip zone is consistent with that indicated by the observed deformation pattern of an actual landslide in China.

Hysteresis of Dam Slope Safety Factor under Water Level Fluctuations Based on the LEM Coupled with FEM Method

Water level variations have caused numerous dam slope collapse disasters around the world,illustrating the large influence of water level fluctuations on dam slopes.The required indoor tests were conducted and a numerical model of an actual earth-filled dam was constructed to investigate the influences of the water level fluctuation rate and the hysteresis of the soil-water characteristic curve(SWCC)on the stability of the upstream dam slope.The results revealed that the free surface in the dam body for the desorption SWCC during water level fluctuations was higher than that for the adsorption SWCC,which would be more evident at higher water levels.The safety factor of the upstream dam slope initially decreased and then increased for the most dangerous water level as the water level rose and fell.The water level fluctuation rate mainly influenced the initial section of the safety factor variation curve,while the SWCC hysteresis mainly affected the minimum safety factor of the water level fluctuations.The desorption SWCC is suggested for engineering design.Furthermore,a quick prediction method is proposed to estimate the safety factor of upstream dam slopes with identical structures.

Toroidicity Dependence of Tokamak Edge Safety Factor and Shear

Using a simple analytical model equilibrium, the dependence of tokamak edge safety factor qedge which can be understood as qa for a limiter device or 595 for a divertor device, and the shear value are calculated and compared with the ITRE-recommended formula. This dependence relation is useful in designing the medium and small aspect ratio tokamaks and reactors.

Method of Calculating the Safety Factor Profile on the HT-7 Tokamak

A method of calculating the safety profile on the HT-7 tokamak has been described in this paper. It is derived from Maxwell's equations, among which we-mainly use .two of them: one is the magnetic field diffusion equation, and the other is Ampere's Law. This method can be also used to evaluate the safety factor on other devices with a circular cross sections. It is helpful to the study of the plasma MHD behavior on the HT-7 tokamak.

Proposed Simplified Procedure for Safety Factor Scaling for Various Life Cycles

It is common to assume that structures are designed in view of 50 year life cycle as per Euro-Code 2 and other codes. In special cases, structures are designed in view of longer life cycle, such as bridges, important infrastructure facilities, important religious structures or in case of extended returning period of seismic event or floods. Beside issues of durability and maintenance aspects, this involves also the need to cover the probability of exceeding characteristic design live loads during the extended period, while keeping the same levels of the accepted risk that were assumed by the various codes, as good enough for the standard 50 year life cycle. Bearing in mind that design procedures, formulations, materials characteristic strengths and partial safety factors are used for these structures as per the existing codes, scaling of partial safety factors, or alternatively an additional ＂compensating＂ factor is required. A simplified approach and procedure to arrive at a reasonable calibration of the code safety factors based on 50 years to compensate for an extended life cycle, based upon structural reliability considerations, is proposed.

Calculation of the Safety Factor of the Ohmic HL-2A Single Null Divertor Discharge

The safety most important factor profile is one of the the plasma discharge. For limiter configuration, people usually use the following cylindrical approximation formula to calculate it q（r）=5r^2BT/RIp where r is the minor radius of the plasma toms, R is the major radius （in m） , BT is the toroidal magnetic field （in T）, Ip is the total toroidal current（in MA）.

Safety factors for anterior pedicle screw fixation tunnel in axis

Objective To investigate feasibility and safety of anterior pedicle screw fixation tunnel in the axis so as to provide theoretic evidence for further clinical application.Methods Thirty-two dry axis specimens were used foranterior

LSSVM-based approach for refining soil failure criteria and calculating safety factor of slopes

The failure criteria of practical soil mass are very complex,and have significant influence on the safety factor of slope stability.The Coulomb strength criterion and the power-law failure criterion are classically simplified.Each one has limited applicability owing to the noticeable difference between calculated predictions and actual results in some cases.In the work reported here,an analysis method based on the least square support vector machine(LSSVM),a machine learning model,is purposefully provided to establish a complex nonlinear failure criterion via iteration computation based on strength test data of the soil,which is of more extensive applicability to many problems of slope stability.In particular,three evaluation indexes including coefficient of determination,mean absolute percentage error,and mean square error indicate that fitting precision of the machine learning-based failure criterion is better than those of the linear Coulomb criterion and nonlinear power-law criterion.Based on the proposed LSSVM approach to determine the failure criterion,the limit equilibrium method can be used to calculate the safety factor of three-dimensional slope stability.Analysis of results of the safety factor of two three-dimensional homogeneous slopes shows that the maximum relative errors between the proposed approach and the linear failure criterion-based method and the power-law failure criterion-based method are about 12%and 7%,respectively.

Factor of safety of strain-softening slopes

Stability analysis of strain-softening slopes is carried out using the shear strength reduction method and Mohr-Coulomb model with degrading cohesion and friction angle.The e ffect of strain-softening behavior on the slope factor of safety is investigated by performing a series of analyses for various slope geometries and strength properties.Stability charts and equations are developed to estimate the factor of safety of strain-softe ning slopes from the results of traditional stability analysis based on perfectly-plastic behavior.Two example applications including an open pit mine in weak rock and clay shale slope with daylighting bedding planes are presented.The results of limit equilibrium analysis and shear strength reduction method with perfectly-plastic models were in close agreement.Using perfectly-plastic models with peak strength properties led to overly optimistic results while adopting residual strength properties gave excessively conservative outcomes.The shear strength reduction method with a strain-softening model gave realistic factors of safety while accounting for the process of strength degradation.

Relationship between critical seismic acceleration coefficient and static factor of safety of 3D slopes

Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers,e.g.static safety of factor(static FoS)or the critical seismic acceleration coefficient,while little attention has been given to the relationship between the slope stability numbers and the critical seismic acceleration coefficient.This study aims to investigate the relationship between the static FoS and the critical seismic acceleration coefficient of soil slopes in the framework of the upper-bound limit analysis.Based on the 3D rotational failure mechanism,the critical seismic acceleration coefficient using the pseudo-static method and the static FoS using the strength reduction technique are first determined.Then,the relationship between the static FoS and the critical seismic acceleration coefficient is presented under considering the slope angleβ,the frictional angleφ,and the dimensionless coefficients B/H and c/γH.Finally,a fitting formula between the static FoS and the critical seismic acceleration coefficient is proposed and validated by analytical and numerical results.

Probability evaluation method for cable safety of long-span cable-stayed bridges

A method of cable safety analysis is proposed for safety evaluation of long-span cable-stayed bridges. The Daniels＇ effect and the probability of broken wires in the cable are introduced to develop the cable strength model and the reliability assessment technique for long-span cable-stayed bridges based on the safety factors analysis of stay cables in service. As an application of the proposed model, the cable safety reliability of the cable No. 25 of Zhaobaoshan cable-stayed bridge in China is calculated. The effects of various parameters on the estimated cable safety reliability are investigated. The results indicate that the proposed method can be used to assess the safety level of stay cables in cable-stayed bridges effectively. The Daniels＇ effect should be taken into account for assessment, and the probability of broken wires can be used to simulate the deterioration of stay cables in service.

Behavior of transporting pipeline sections without and with hydrogen exposure based on full-scale tests

Pipeline transport of hydrogen is one of today’s economic and environmental challenges.In order to find safe and reliable application of both existing gas and build new pipelines,it is essential to carry out tests on full-scale pipeline section,including the potentially more dangerous places than the main pipe,the girth welds.For the investigations,pipeline sections of P355NH steel with girth welds were prepared and exposed to pure hydrogen at twice the maximum allowable operating pressure for 41 days.Subsequently,full-scale burst tests were carried out and specimens were cut and prepared from the typical locations of the failed pipeline sections for mechanical,and macro-and microstructural investigations.The results obtained were evaluated and compared with data from previous full-scale tests on pipeline sections without hydrogen exposure.The results showed differences in the behavior of pipeline sections loaded in different ways,with different characteristics of the materials and the welded joints,both in the cases without hydrogen exposure and in the cases exposed to hydrogen.

Comparative Study on Structural Redundancy of Cable-Stayed and Extradosed Bridges Through Safety Assessment of Their Stay Cables

This study provides new insights into the comparison of cable-stayed and extradosed bridges based on the safety assessment of their stay cables.These bridges are often regarded as identical structures owing to the use of inclined cables;however,the international standards for bridge design stipulate different safety factors for stay cables of both types of bridges.To address this misconception,a comparative study was carried out on the safety factors of stay cables under fatigue and ultimate limit states by considering the effects of various untoward and damaging factors,such as overloading,cable loss,and corrosion.The primary goal of this study is to describe the structural disparities between both types of bridges and evaluate their structural redundancies by employing deterministic and nondeterministic methods.To achieve this goal,three-dimensional finite-element models of both bridges were developed based on the current design guidelines for stay cables in Japan.After the balanced states of the bridge models were achieved,static analyses were performed for different safety factors of stay cables in a parametric manner.Finally,the first-order reliability method and Monte Carlo method were applied to determine the reliability index of stay cables.The analysis results show that cable-stayed and extradosed bridges exhibit different structural redundancies for different safety factors under the same loading conditions.Moreover,a significant increase in structural redundancy occurs with an incremental increase in the safety factors of stay cables.

Finite element model with imposed slip surfaces for earth mass safety evaluation

The study of earth masses requires numerical methods that provide the quantification of the safety factor without requiring detrimental assumptions. For that, equilibrium analysis can perform fast computations but require assumptions that limit its potentiality. Limit analysis does not require detrimental assumptions but are numerically demanding. This work provides a new approach that combines the advantage of both the equilibrium method and the limit analysis. The defined hybrid model allows probabilistic analysis and optimization approaches without the assumption of interslice forces. It is compared with a published case and used to perform probabilistic studies in both a homogeneous and a layered foundation. Analyses show that the shape of the density probability functions is highly relevant when computing the probability of failure, and soil elasticity hardly affects the safety of factor of the earth mass.

A Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Safety Level and Reliability Index for Bank Slope Stability

Based on statistics and analysis of the safety factor of unstable bank slopes, the relation between safety level and reliability index of stability is studied and discussed, and then the elementary calibrating calculation is carried out to the levels of safety and reliability for bank slope stability in the range of safety factors stipulated in existing China Technical Specifications for Port Engineering - Foundation Part (1987) and to those reached by some stable bank slopes already built. The results show that the reliability index beta in the effective stress method is able to reach a high value of 2.4 similar to 4.1 (mid-value 3.25), while the value of beta in other three kinds of total stress method can just reach a lower value of 0.5 similar to 2.8 (mid-value 1.65), which are in conformity with the engineering experience in China, and thus acceptable. Some suggestions are also given in this paper to the adoption of the value of beta(0)-objective reliability index for bank slope stability.