Set Function Research Articles

Mechanism and Method of Auxiliary Decision-Making for Dispatching Real-time Operation in Electric Spot Market

Starting from the market rules of the pilot provinces of the domestic spot market, this paper analyzes the mechanism of market intervention and suspension, the mechanism of the power supply period, and the mechanism of market clearing anomaly. At the same time, combined with the real-time operation of the Inner Mongolia power grid, the traditional dispatching mode and the power spot market operation dispatching mode are compared. Given the abnormal frequency, section overload, and insufficient spinning reserve in real-time operation, an auxiliary decision mechanism of manual intervention in the power spot market is proposed. The mechanism includes load bias setting, section limit bias setting, deviation monitoring, and other auxiliary functions, which provide a method of quick intervention under the electric spot market to ensure the safe and stable operation of the power grid.

A systematical framework for process operational safety index design and synthesis

With the demand for improving production efficiency and the application of advanced process control, modern chemical production has increasingly attached importance to process operational safety. A systematical framework for process operational safety index (POSI) design and synthesis is proposed in this work. The notion of general operational safety is defined firstly, and safety critical variables are introduced for quantification. With the consideration of dynamics and robustness, the relationships between safety critical variables and POSI are discussed sufficiently. Based on these relationships and the frameworks of reachable set, flexibility index and control barrier function, the formula forms of POSI are further determined and summarized. Finally, the feed-forward neuron network is utilized as an approximator and classier to improve the continuity and usability of POSI.

Semi-supervised dual-task cross-consistency constraint network for 3D cardiac MRI segmentation

目的 针对人体组织器官及病灶区域的3维图像分割是计算机辅助医疗诊断的重要前提，是医学影像3维可视化的重要技术基础。深度学习方法在医学图像分割任务中的成功通常取决于大量有标注数据。半监督学习利用未标注数据容易获取的优点，在模型训练过程中使用少量标注数据和大量未标注数据进行学习，缓解了数据标注昂贵耗时的问题，在医学图像分割中受到了广泛关注。为更好地利用无标注数据，提升医学图像分割效果，提出一种新的一致性正则方法用于半监督3维医学图像分割。方法 模型以V-Net为基础架构，通过扩展网络结构，在均带有分割任务及回归任务属性的双任务主副解码器之间添加了用于正则化约束的交叉损失，构建了具有形状感知的基于双任务的交叉一致性正则网络SACC-Net （shape-aware cross-consistency regular network based on dual tasks），实现将数据层面和模型层面的扰动融合进多任务机制的一致性正则方法，使模型能够更好地利用未标注数据的有效先验信息，并且具有更好的泛化性能。结果 在MICCAI 2018（Medical Image Computing and Computer Assisted Intervention Society）心房分割挑战赛公布的数据集中的3维左心房核磁共振成像上验证本文算法，在仅使用训练集中10%的有标注数据的实验组中，Dice系数、Jaccard指数、HD（Hausdorff distance）距离和平均对称表面距离分别为88.01%、78.89%、8.19和2.09。在另一组仅使用20%的有标注数据的实验中Dice系数、Jaccard指数、HD距离和平均对称表面距离分别达到90.11%、82.11%、6.57和1.78。结论 本文提出的半监督分割模型性能显著，综合了数据、模型和任务层面的一致性正则约束，与其他半监督方法相比分割效果更好且具有更佳的泛化性能。;Objective Three-dimensional（3D）image segmentation of human tissues，organs and lesion areas is projected for computer-aided diagnosis and medical images-related 3D visualization. Thanks to the emerging deep learning technique，fully-supervised network models have been developing intensively in relevant to medical image segmentation tasks. However，it is challenged for a large amount of annotated data and 3D image segmentation data-labeled is costly and inefficient. Semi-supervised learning is focused on a small size of data-labeled and sufficient data-unlabeled in terms of easy acquisition of unlabeled data，which can alleviate the cost and time-consuming problem of data labeling. Our research is focused on new consistency regular method for semi-supervised 3D medical image segmentation model. To improve the medical image segmentation effect，our model can use unlabeled data through the fusion of different consistency methods. Method The network model is demonstrated on the V-Net，which can remove the residual structure of encoding and decoding. To get efficient features of unlabeled data，the proposed shape-aware cross-consistency regular network is introduced via the V-Net network structure extension on the basis of an encoder and two independent decoders-involved dual tasks （shape-aware cross-consistency regular network based on dual tasks（SACC-Net）），which are divided into a main decoder a and an auxiliary decoder b. The output of encoder-shared is transmitted to the two decoders after noise disturbance. At the same time，the two decoders can output the prediction results after each iteration. To increase the generalization and anti-noise ability of the model，it can minimize the difference between the two parts of the results during the training process. Additionally，the proportion of labeled samples in the training samples is extremely small because the feature distributions between the pre-processed medical image samples are relatively similar. To improve the learning ability of the model to segmented samples further，geometric prior information constraints are melted into the segmentation target. A shape-aware regression layer is added at the end of each decoder as well. During the training phase，each decoder can output two parts of the prediction results at the same time. That is，the total output of each iteration-after network consists of four parts. It can be used to decode the segmentation map SA and the signed distance map output by the decoder A，and the segmentation map SB and the signed distance map output by the decoder B through the dual-task consistency of each decoding part. To enhance the model’s ability and learn the effective features of segmentation targets to a greater extent， constraints and cross constraints can be used to realize a consistent regular method that combines data-level and modellevel disturbances with multi-task mechanisms，and make better use of unlabeled data. Result Our algorithm is validated on the MRI data set published in Atrium Segmentation Challenge held by MICCAI（Medical Image Computing and Computer Assisted Intervention Society）in 2018. The experiment is divided into two test groups based on the amounts proportion of labeled data. In the training set，10% annotated data is used only in the experimental group，the Dice coefficient， Jaccard index，HD （Hausdorff distance） distance，and average symmetric surface distance is reached to 88. 01%， 78. 89%，8. 19，and 2. 09 of each. In the other group，20% annotated data of the experiments are used only. The median Dice coefficient，Jaccard index，HD distance and average symmetric surface distance can be reached to 90. 14%， 82. 11%，6. 57，and 1. 78 each as well. Furthermore，In respect of the shape perception method using the level set function for regression tasks，the Dice evaluation index can be improved by 0. 69 and 0. 60 in comparison with shape-aware semi-supervised net（SASS Net）in 10% and 20% of the marked training results. Each improvement is reached to 1. 44% and 0. 72% in terms of comparative results of dual-task consistency（DTC）trained with 10% and 20% labeled data. Conclusion The semi-supervised segmentation model（SACC-Net）is illustrated for the criteria optimization for both of the region and boundary-based segmentation，which can incorporate the level-consistency of its data，model and task. The constrained method has its potential segmentation effect and generalization performance for semi-supervised methods.

Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

In this paper, we consider solving the topology optimization for steady-state incompressible Navier-Stokes problems via a new topology optimization method called parameterized level set method, which can maintain a relatively smooth level set function with a local optimality condition. The objective of topology optimization is to find an optimal configuration of the fluid and solid materials that minimizes power dissipation under a prescribed fluid volume fraction constraint. An artificial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition. Although a great deal of work has been carried out for topology optimization of fluid flow in recent years, there are few researches on the topology optimization of fluid flow with physical body forces. To simulate the fluid flow in reality, the constant body force (e.g., gravity) is considered in this paper. Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design, and demonstrate the feasibility and superiority of the proposed method in dealing with unstructured mesh problems. Three 3D numerical examples demonstrate the proposed method is feasible in three-dimensional.

“Too Soon on Earth”: A Biophilosophical Model of Schizophrenia. Some Implications for Humanoid Robots

This paper presents a new explanatory model for schizophrenia based upon philosophical, molecular and neurobiological hypotheses as well as on years of experience in observing and treating these patients. To start with, a novel interpretation of the Hegelian concept of mediation is presented. Mediation is defined as the rejection of non-realizable programs, such as thoughts and ideas, at a certain point in time in the evolution of a living system. Whenever a system treats non-realizable programs as if they were realizable, its ability to “test the reality” is lost, and consequently a loss of ego-boundaries may occur. On the molecular level, I will try to show how “non-splicing” of introns during the mRNA splicing process is equivalent to a loss of the rejection function corresponding to mediation. At the cellular level in the brain, mediation can be explained in terms of glial-neuronal interactions. Glia exert a spatio-temporal boundary setting function determining the grouping of neurons into functional units. Mutations in genes that result in non-splicing of introns can produce truncated (“chimeric”) neurotransmitter receptors. I propose that such dysfunctional receptors are generated in glial cells and that they cannot interact properly with their cognate neurotransmitters. The glia will then lose their inhibitory-rejecting function with respect to the information processing within neuronal networks. This loss of glial boundary setting could be an explanation for the loss of ego or body boundaries in schizophrenia. Pertinent examples of case studies are given attempting to deduce the main symptoms of schizophrenia from the proposed hypothesis. Some implications for the design of delusional robots are also discussed. Finally, the evolutionary potency of non-coding introns is philosophically interpreted that schizophrenics may be “too soon on earth”.

An Active Contour Model Based on Local Pre-Piecewise Fitting Bias Corrections for Fast and Accurate Segmentation

The lack of grasp of the image information and the unstable fluctuation of the model energy may cause segmentation failure of the active contour model (ACM). Minimizing the impact of these two factors is critical. A local pre-piecewise fitting (LPPF) bias correction model for fast and accurate segmentation is proposed in this paper. It defines a pre-fitting function of local regions and an energy function. The grayscale information of small areas in the image is fully extracted, so that the contour accurately locates the target. Then, the optimal solution to the estimated value of the bias field is obtained. The real image information is described by the bias field, and the energy function of the model is constructed. The optimized distance regularized term and neighborhood average filtering method are utilized to achieve level set function regularization and contour smoothing. This optimization process reduces the amount of calculation and improves the robustness of LPPF model. Experiments are performed to verify that LPPF model has strong robustness to initial contours and has ability to segment blurry images while satisfactory segmentation efficiency and accuracy are obtained.

The interference between new media and traditional media. Assessing the impact of new tools on conventional media content

"The media industry has been disrupted by technological developments. In journalism, competition has emerged between traditional media such as television or radio and new media. It’s natural that people spend more time on these new platforms and journalists have to adapt to secure their profession. The theoretical objective is to assess how the basic function of agenda setting by journalists has changed in the new information ecosystem. Empirically, the paper aims to show how the content of news magazines in the media in Romania has changed over time with the expansion of new media. The paper examines the content of TV news bulletins according to the source of the images used. A content analysis to explain the current situation compared to 10 years ago, when the new media did not know such an amplitude. By analysing a series of 77 news programmes, 862 news items, the article assesses the audience’s participation in the production of news, but also the public institutions that use technology to impose their own messages. The results suggest that in 2021 the share of news with downloaded content (not the work of journalists) has increased 12-fold compared to the same period analysed ten years ago. This raises questions about who sets the agenda and what the identity of the traditional journalist is in the face of technological advances. Keywords: Mass-communication, New Media, Agenda Setting Theory, Mediatization"

Game of Life-like Opinion Dynamics: Generalizing the Underpopulation Rule

Graph dynamics for a node-labeled graph is a set of updating rules describing how the labels of each node in the graph change in time as a function of the global set of labels. The underpopulation rule is graph dynamics derived by simplifying the set of rules constituting the Game of Life. It is known that the number of label configurations met by a graph during the dynamic process defined by such rule is bounded by a polynomial in the size of the graph if the graph is undirected. As a consequence, predicting the labels evolution is an easy problem (i.e., a problem in P) in such a case. In this paper, the generalization of the underpopulation rule to signed and directed graphs is studied. It is here proved that the number of label configurations met by a graph during the dynamic process defined by any so generalized underpopulation rule is still bounded by a polynomial in the size of the graph if the graph is undirected and structurally balanced, while it is not bounded by any polynomial in the size of the graph if the graph is directed although unsigned unless P = PSpace.

Testing the Difference of Means of Populations With Respect to Intuitionistic Fuzzy Sets

In this study, the tests of statistical hypotheses with crisp data using small samples are extended to with the membership function and the non-membership function of the intuitionistic fuzzy set. The test procedure of statistical hypotheses for means of two normally distributed populations with respect to any intuitionistic fuzzy set is proposed.

Advances in additive number theory

We obtain sufficient conditions to know if given a positive even integer number and a set of positive integer numbers being all even or all odd, such a number can be expressed as sum of two elements of this set. As consequence we obtain a result which, when applied to the prime numbers set, would prove Goldbach's Conjecture provided that certain conditions are satisfied. These hypothesis include Prime Consecutive Conjecture, which is a generalized form of Twin Prime Conjecture. In addition, we extend these results to sets of positive real numbers, even for two different sets. We also obtain a recurrent approximation of \pi(x) for enough large real x, being \pi the distribution function of the prime number set, which uses whichever expression of x as product of enough large factors. We also state this approximation in a more general context, give upper and lower bounds for the error, and show that this approximation is asymptotically equivalent to \pi(x).

An Enhanced Tree Routing Based on Reinforcement Learning in Wireless Sensor Networks

In wireless sensor networks, tree-based routing can achieve a low control overhead and high responsiveness by eliminating the path search and avoiding the use of extensive broadcast messages. However, existing approaches face difficulty in finding an optimal parent node, owing to conflicting performance metrics such as reliability, latency, and energy efficiency. To strike a balance between these multiple objectives, in this paper, we revisit a classic problem of finding an optimal parent node in a tree topology. Our key idea is to find the best parent node by utilizing empirical data about the network obtained through Q-learning. Specifically, we define a state space, action set, and reward function using multiple cognitive metrics, and then find the best parent node through trial and error. Simulation results demonstrate that the proposed solution can achieve better performance regarding end-to-end delay, packet delivery ratio, and energy consumption compared with existing approaches.

Detoxification Cytochrome P450s (CYPs) in Families 1-3 Produce Functional Oxylipins from Polyunsaturated Fatty Acids.

This manuscript reviews the CYP-mediated production of oxylipins and the current known function of these diverse set of oxylipins with emphasis on the detoxification CYPs in families 1-3. Our knowledge of oxylipin function has greatly increased over the past 3-7 years with new theories on stability and function. This includes a significant amount of new information on oxylipins produced from linoleic acid (LA) and the omega-3 PUFA-derived oxylipins such as α-linolenic acid (ALA), docosahexaenoic acid (DHA), and eicosapentaenoic acid (EPA). However, there is still a lack of knowledge regarding the primary CYP responsible for producing specific oxylipins, and a lack of mechanistic insight for some clinical associations between outcomes and oxylipin levels. In addition, the role of CYPs in the production of oxylipins as signaling molecules for obesity, energy utilization, and development have increased greatly with potential interactions between diet, endocrinology, and pharmacology/toxicology due to nuclear receptor mediated CYP induction, CYP inhibition, and receptor interactions/crosstalk. The potential for diet-diet and diet-drug/chemical interactions is high given that these promiscuous CYPs metabolize a plethora of different endogenous and exogenous chemicals.

Lens structure segmentation from AS-OCT images via shape-based learning

Background and objectivesThe lens is one of the important refractive media in the eyeball. Abnormality of the nucleus or cortex in the lens can lead to ocular disorders such as cataracts and presbyopia. To achieve an accurate diagnosis, segmentation of these ocular structures from anterior segment optical coherence tomography (AS-OCT) is essential. However, weak-contrast boundaries of the object in the images present a challenge for accurate segmentation. The state-of-the-art (SOTA) methods, such as U-Net, treat segmentation as a binary classification of pixels, which cannot handle pixels on weak-contrast boundaries well. MethodsIn this paper, we propose to incorporate shape prior into a deep learning framework for accurate nucleus and cortex segmentation. Specifically, we propose to learn a level set function, whose zero-level set represents the object boundary, through a convolutional neural network. Moreover, we design a novel shape-based loss function, where the shape prior knowledge can be naturally embedded into the learning procedure, leading to improvement in performance. We collect a high-quality AS-OCT image dataset with precise annotations to train our model. ResultsAbundant experiments are conducted to verify the effectiveness of the proposed framework and the novel shape-based loss. The mean Intersection over Unions (MIoUs) of the proposed method for lens nucleus and cortex segmentation are 0.946 and 0.957, and the mean Euclidean Distance (MED) measure, which can reflect the accuracy of the segmentation boundary, are 6.746 and 2.045 pixels. In addition, the proposed shape-based loss improves the SOTA models on the nucleus and cortex segmentation tasks by an average of 0.0156 and 0.0078 in the MIoU metric and 1.394 and 0.134 pixels in the MED metric. ConclusionWe transform the segmentation from a classification task to a regression task by making the model learn the level set function, and embed shape information in deep learning by designing loss functions. This allows the proposed method to be more efficient in the segmentation of the object with weak-contrast boundaries. Concise abstractWe propose to incorporate shape priors into a deep learning framework for accurate nucleus and cortex segmentation from AS-OCT images. Specifically, we propose to learn a level set function, where the zero-level set represents the boundary of the target. Meanwhile, we design a novel shape-based loss function in which additional convex shape prior can be embedded in the learning process, leading to an improvement in performance. The IOUs for nucleus and cortex segmentation are 0.946 and 0.957, while the MED that reflects the accuracy of the boundary are 6.746 and 2.045 pixels. The proposed shape-based loss improves the SOTA model for nucleus and cortex segmentation by an average of 0.0156 and 0.0078 in IOU, and 1.394 and 0.134 pixels in MED. We transform segmentation from classification to regression by making the model learn a level set function, resulting in improved performance at the boundary with weak contrast.

Supermodularity and valid inequalities for quadratic optimization with indicators

AbstractWe study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult, the specific set function for the rank-one quadratic can be minimized in linear time. We show that the convex hull of the epigraph of the quadratic can be obtained from inequalities for the underlying supermodular set function by lifting them into nonlinear inequalities in the original space of variables. Explicit forms of the convex-hull description are given, both in the original space of variables and in an extended formulation via conic quadratic-representable inequalities, along with a polynomial separation algorithm. Computational experiments indicate that the lifted supermodular inequalities in conic quadratic form are quite effective in reducing the integrality gap for quadratic optimization with indicators.

Marine sedimentary uranium to barium ratios as a potential quantitative proxy for Pleistocene bottom water oxygen concentrations

Oxygen is essential for marine ecosystems, and it is linked by respiration to carbon storage in the deep ocean. Reconstructing oxygen concentrations in the past has been limited by the absence of quantitative, rather than qualitative, proxies, but several new (semi-) quantitative oxygen proxies have recently been developed. In this study we explore the possibility of adding bulk sedimentary uranium (U) to this list by normalizing it to barium (Ba). First, U/Ba and bottom water oxygen concentrations are compared on a global scale, using a core top database, in pelagic environments greater than 200 m water depth. Then, the relationships between U/Ba and bottom water oxygen are examined on smaller spatial scales: within each ocean basin and regionally within the Eastern Equatorial Pacific, the Arabian Sea, and Western Equatorial Atlantic. At this regional scale, where secondary influences on the behavior of both U and Ba may be more spatially uniform, empirical piecewise linear calibrations are developed and subsequently tested on downcore records. U/Ba-based oxygen reconstructions generally agree with those derived from previously published alkenone preservation and benthic foraminiferal surface porosity records. Several limitations to the utility of U/Ba as a proxy for oxygen have also been identified. The proxy should only be applied in the uppermost sedimentary intervals that contain porewater sulfate to minimize barite diagenesis, and phosphorus contents should be monitored for the potential influence of apatite on uranium content. U/Ba is more successful at recording oxygen concentrations during mean glacial and interglacial periods than during climate transitions, when the timing and amplitude may be more sensitive to burndown and smoothing. Conservative errors on the calibrations result in the greatest utility of U/Ba in regions with relatively high oxygen concentrations (e.g., >50 μmol/kg) and large oxygen variability (±10 s of μmol/kg). Even with these caveats, U/Ba is only one of two quantitative oxygen proxies potentially capable of recording variability above 50 μmol/kg, and further investigation into its functionality in different environmental settings is worthwhile in the endeavor to reconstruct the full marine range of oxygen concentrations in the past.

Semi-supervised learning from coarse histopathology labels

ABSTRACT Ultrasound imaging is commonly used to guide sampling the prostate tissue in transrectal biopsies, followed by detection of cancer through histopathological analysis and coarse labelling of sampled tissue. Ideally, the procedure should be improved by developing machine learning solutions that can identify the presence of cancer in ultrasound images to guide the biopsy procedure. Training a fully supervised learning model using coarse histopathology labels suffers from weakly annotated data which introduce label noise for each image pixel. To address this challenge, we propose a semi-supervised framework for learning with noisy labels. We leverage a two-component mixture model to cluster the training data into clean and noisy label samples based on their loss values. Then, during the semi-supervised training phase, we utilise the well-known MixMatch algorithm which incorporates consistency regularisation, entropy minimisation, and the Mixup regularisation as well as the cross-entropy loss function for noisy and clean sets, respectively. We evaluate the proposed framework with prostate ultrasound data obtained from 71 subjects, while sampling 264 biopsy cores. We achieve balanced accuracy, sensitivity, and specificity of 78.6%, 80.0%, and 77.1%, respectively. In a detailed comparison study, we demonstrate that our proposed framework outperforms the fully supervised method with state-of-the-art robust loss functions.

An Application Method for the use of Neutrosophic Soft Mappings in Decision-Making the Diagnosis of Covid-19 and Other Lung Diseases

Covid-19 is an epidemic that has spread rapidly around the world and be direct damages the lung in recent years. Many researchers struggled for months trying to find a diagnosis and therapy for this epidemic. As a result of these studies, they have identified common of many symptoms of the epidemic disease with some lung diseases like flu, colds and even allergies. It can say that it is difficult to determine the exact disease type as lung diseases show similar symptoms. Because the elements of indeterminacy and falsehood are commonly ignored in practical assessments, it’s difficult to identify precision can’t anticipate the period of therapy and in the patient’s progress history. In order to after eliminate this uncertainty decide on the definitive diagnosis, a mathematical model was put forward by using neutrosophic soft set theory and function properties of this theory. These concepts are necessary and sufficient to accurately diagnose diseases by connecting with mathematical modeling. This study makes easier to establish a link between patients’ symptoms and therapy patterns. A table is created in fuzzy interval [0, 1] for put in order the type of disease among various lung diseases. Diagnosing the disease and finding the best therapy depends on the neutrosophic soft mapping. Finally the generalized neutrosophic soft mapping are utilized map to help predict the duration of therapy until the disease is cured.

Some New Results for the Kampé de Fériet Function with an Application

The generalized hypergeometric functions in one and several variables and their natural generalizations appear in many mathematical problems and their applications. The theory of generalized hypergeometric functions in several variables comes from the fact that the solutions of the partial differential equations appearing in a large number of applied problems of mathematical physics have been expressed in terms of such generalized hypergeometric functions. In particular, the Kampé de Fériet function (in two variables) has proved its practical utility in representing solutions to a wide range of problems in pure and applied mathematics, statistics, and mathematical physics. In this context, in a very recent paper, Progri successfully calculated the 2F2 generalized hypergeometric function for a particular set of parameters and expressed the result in terms of the difference between two Kampé de Fériet functions. Inspired by his work, in the present paper, we obtain three results for a terminating 3F2 series of arguments 1 and 2, together with a transformation formula of a 3F2(z) generalized hypergeometric function in terms of the difference between two Kampé de Fériet functions. One application of this result is also provided. The paper concludes with six reduction formulas for the Kampé de Fériet function. Of note, symmetry occurs naturally in the generalized hypergeometric functions pFq and the Kampé de Fériet function involving two variables, which are the two most important functions discussed in this paper.

Improved Dempster–Shafer Evidence Theory for Tunnel Water Inrush Risk Analysis Based on Fuzzy Identification Factors of Multi-Source Geophysical Data

Water inrush is one of the most important risk factors in tunnel construction because of its abruptness and timeliness. Various geophysical data used in actual construction contain useful information related to groundwater development. However, the existing approaches with such data from multiple sources and sensors are generally independent and cannot integrate this information, leading to inaccurate projections. In addition, existing tunnel advanced geological forecast reports for risk projections interpreted by human operators generally contain no quantitative observations or measurements, but only consist of ambiguous and uncertain qualitative descriptions. To surmount the problems above, this paper proposes a tunnel water inrush risk analysis method by fusing multi-source geophysical observations with fuzzy identification factors. Specifically, the membership function of the fuzzy set is used to solve the difficulty in determining the basic probability assignment function in the improved Dempster–Shafer evidence theory. The prediction model of effluent conditions fuses seismic wave reflection data, ground penetrating radar data, and transient electromagnetic data. Therefore, quantitative evaluations of the effluent conditions are achieved, including the strand water, linear water, seepage and dripping water, and anhydrous. Experimental evaluations with a typical tunnel section were conducted, in which the state of the groundwater from a series of geological sketch reports in this sectionpaper were used as ground truth for verification. The experimental results revealed that the proposed method not only has high accuracy and robustness but also aligns well with different evidence effectively that generally contradicts manual interpretation reports. The results from 12 randomly selected tunnel sections also demonstrate the generalization abilities of the proposed method.

A Level Set Based Density Method for Optimizing Structures with Curved Grid Stiffeners

A level set based density method is proposed for the optimization of structures with curved grid stiffeners. It combines the ideas of both the level set method and the three-field approach of the SIMP method to explicitly describe the fully-resolved details of stiffeners. The iso-contours of two basic level set functions are used to describe the curvilinear paths of two groups of stiffeners, and a cosine-transformation is respectively applied to the two basic level set functions so that the stiffeners are endowed with the information of width. Radial basis functions are used to parameterize the two basic level set functions. Thereafter, the two cosine-transformed level set functions are combined together by using a differentiable maximum function, and one obtains a pseudo density function. Finally, a threshold projection is applied to the pseudo density function, and one arrives at a physical density with a black-white pattern where the black stripes represent the stiffeners. The physical density is directly used for the finite element analysis. Several numerical examples prove that the proposed design optimization method is effective. • A novel description model of curved grid-stiffener is developed. • Cosine-transformation is applied to basic level set function. • Cosine-transformed level set functions are combined to describe density. • RBF is used to parameterize the basic level set function.