Sentiment analysis is one of the fields of affective computing, which detects and evaluates people’s psychological states and sentiments through text analysis. It is an important application of text mining technology and is widely used to analyze comments. Bullet screen videos have become a popular way for people to interact and communicate while watching online videos. Existing studies have focused on the form, content, and function of bullet screen comments, but few have examined bullet screen comments using natural language processing. Bullet screen comments are short text messages of different lengths and ambiguous emotional information, which makes it extremely challenging in natural language processing. Hence, it is important to understand how we can use the characteristics of bullet screen comments and sentiment analysis to understand the sentiments expressed and trends in bullet screen comments. This study poses the following research question: how can one analyze the sentiments ex-pressed in bullet screen comments accurately and effectively? This study mainly proposes an ERNIE-BiLSTM approach for sentiment analysis on bullet screen comments, which provides effective and innovative thinking for the sentiment analysis of bullet screen comments. The experimental results show that the ERNIE-BiLSTM approach has a higher accuracy rate, precision rate, recall rate, and F1-score than other methods. In the Internet world, people have the right to publish information. Netizens not only post product reviews, but also express their opinions on everything. Social media has become a medium for people to share about their lives, obtain information, and communicate. Social media enables users to publish content on platforms to share information with other users and to communicate with each other . The conAt the same time, with the continuous development of online video platforms and the popularity of smartphones, users find it more convenient to watch videos, and the amount of video data and the number of video users are increasing year by year. Due to the increasing competition among major video websites and platforms, traditional video platforms have gradually transformed into a new type of social media. For example, bullet screen video is very popular among young people. Bullet screen comments move from right to left on the video screen and synchronize with the timeline of the video. When watching bullet screen videos, users can send real-time bullet screen comments and share and exchange ideas with other users . As a noHowever, because bullet screen video is a real-time comment system that has emerged in East Asian countries, such as China, South Korea, and Japan, in recent years, other countries have conducted less research on it . To our This study hopes to help governments and enterprises to monitor public sentiment in social media by studying the emotional content of bullet screen comments. Therefore, this study poses the following research question: how can one analyze the sentiments expressed in bullet screen comments accurately and effectively? To solve the research question, this study proposes an ERNIE-BiLSTM approach to analyze the sentiments expressed in bullet screen comments. This study adopts pre-trained models in natural language processing and deep learning methods to analyze short text messages and analyze the sentiments expressed in bullet screen comments.Sentiment analysis is one of the fields of affective computing, which detects and evaluates people’s psychological states and sentiments through text analysis . SentimeMost data are unstructured and can’t be predefined in specific ways, especially texts in articles, social media, documents, or emails. Traditionally, it is difficult for enterprises to analyze, classify and identify all kinds of texts because of time-consuming and high cost. Therefore, sentiment analysis can be regarded as a feasible way to investigate the opinions, emotions, or attitudes of texts for products, services, products, or online reviews . It is uBesides, sentiment analysis which can be also called opinion mining is to deeply analyze texts in documents, webs, or reviews in order to extract the key meanings and recognize the polarity classifications ,14. In oBullet screen videos have become a popular way for people to interact and communicate while watching online videos. Compared to comments in discussion forums or product reviews, bullet screen comments are short texts with a time order and focus. Sentiment analysis focuses on ways to analyze the emotional information contained in bullet screen comments. Liu et al.  defined To our knowledge, most of the above studies used traditional methods. There is still room for improvement in the efficiency and effectiveness of these methods. At the same time, bullet screen comments contain a large number of unknown words, and traditional methods have limited accuracy for sentiment analysis. Different from previous studies, this study mainly proposes an ERNIE-BiLSTM approach for sentiment analysis on bullet screen comments, which provides effective and innovative thinking for the sentiment analysis of bullet screen comments.This study collects appropriate bullet screen comments and conducts three experiments to verify the correctness and effectiveness of the proposed ERNIE-BiLSTM approach for sentiment analysis on bullet screen comments. This study mainly collects bullet screen comments on the Bilibili platform and uses a web crawler method to collect all the relevant bullet screen videos and comments from 6 February 2020 to 6 March 2020. The dataset contains over 20,000 bullet screen comments in all the videos of the one-star action for a Dingding event. Ripley  suggesteFurthermore, for all the collected bullet screen comments, this study first excludes noisy data (including nonsense text or emoticons) to avoid false sentiment analysis results. This study artificially labels the sentiments of all comments to facilitate model testing. In addition, because Chinese differs from English in terms of syntax, it is necessary to segment Chinese text and form a word sequence with complete and accurate semantic expression. Therefore, this study uses transformer-based pre-trained models for word embedding.n modules. If we use the transformer encoder modules as compute nodes, we find that the input of the node of each layer is the output of the previous layer. Bidirectional encoder representation from transformers (BERT) is a pre-trained language representation model proposed by Google in 2018. Google uses a large amount of text data and adopts an unsupervised learning method to train the model, which includes numerous transformer encoder modules. The overall structure of BERT is shown in mbedding . Token embedding .(1)Masked language modeling (MLM): BERT randomly masks 15% of the words from a sentence, and inputs the vector of the masked words in the hidden layer into the Softmax classification layer. Then, the model replaces 80% of the words with masked symbols, replaces 10% of the words with a random word, and leaves the other 10% of the words unchanged. The model aims to solve the problem of “label leakage” in the traditional bidirectional recurrent neural network model.(2)Sentence prediction: When BERT is applied to sentence prediction, it can calculate the relationship between two sentences, and uses the binary classifier to predict whether the input sentence is true and its label. In the model, 50% of the sentences are true sentences and are labeled as IsNext. The other 50% of sentences are obtained by negative sampling and are labeled as NotNext.As a pre-trained model, BERT mainly performs two tasks:Sun et al.  proposedT, unifies the text content T into the form of characters to obtain the sequence of characters c-th text, dd-th word in each text (see Equation (2)):The ERNIE model vectorizes the text dataset e-th word:We input each character of i-th word:The final output is a sequence Recurrent neural networks (RNNs) that employ recurrent links among hidden layers were applied in the artificial intelligence field. However, RNN encounters a problem of learning the long-term historical data . A Long i, f, o, and c are the input gate, forget gate, output gate, and cell activation vector, respectively. All these vectors have the same size as the hidden vector h. The W terms denote the weight matrices from the cell to gate vectors. Here, tan h denotes the output activation function .,35.34,35Artificial neural networks can handle simple binary classification problems with only one or two hidden layers. As the proposed sentiment classification is a positive and negative binary classification problem, this experiment tests the settings of the number of hidden layers  and comprehensively evaluates the processing efficiency. The number of neurons in the hidden layer can be calculated by Equation (12) :(12) means that the predicted sentiment and the actual sentiment are both positive. False positive (FP) means that the predicted sentiment is positive, but the actual sentiment is negative. False negative (FN) means that the predicted sentiment is negative, but the actual sentiment is positive. True negative (TN) means that the predicted sentiment and the actual sentiment are both negative.This study applies four evaluation metrics as the measurement standards of this experiment to evaluate the performance of the artificial neural network model, including accuracy rate, precision rate, recall rate, and F-score ,39,40. TThe accuracy rate is shown in Equation (13):The precision rate is shown in Equation (14):The accuracy rate is the ratio of the number of correctly predicted samples in the sentiment analysis to the total number of text comments. The precision rate is the ratio of the number of correctly predicted samples in the sentiment analysis to the number of samples predicted to be positive . The difference between the two is that the accuracy rate considers all the samples, while the precision rate only considers the samples that are predicted to be positive. Therefore, the accuracy rate can directly measure the proportion of correct predictions for all the samples in the sentiment analysis. The precision rate can be used to accurately measure the proportion of correct predictions for all positive samples in sentiment analysis.The recall rate is shown in Equation (15):The recall rate refers to the ratio of the number of text sentiments to the actual number of sentiment classifications, and it is used to measure the reliability of the model’s prediction.The F1-score is shown in Equation (16):The F1-score is the harmonic mean value of the precision rate and the recall rate. It is used to measure the two indicators’ performance.In this experiment, the output layer is divided into one layer and two layers, and the dropout rate is divided into six values of 0, 0.2, 0.4, 0.6, 0.8, and 1. Each model has 12 combinations and 12 output results, and we need to find the optimal parameter settings, as shown in This study proposes an ERNIE-BiLSTM approach that applies special pre-trained models to train the word vectors and then inputs the trained word vectors into a BiLSTM network model to extract text features for the sentiment analysis. This experiment mainly compares the proposed ERNIE-BiLSTM approach with other common methods (BERT-BiLSTM and Word2Vec-BiLSTM) to verify the short-text sentiment analysis’s performance. As the above method is based on pre-trained models and a BiLSTM network, we use the variable-controlling approach to conduct the experiments.We divide the experiment into two parts. First, we test the differences in the performance of the BiLSTM network model in the text sentiment analysis under different word vector models. Second, we test the differences in the performance of the three methods under different feature extraction models. This experiment uses BiLSTM to extract the features of the short text and uses three different models to train the word vectors. Isnain et al.  found thThis experiment compares the performance of a text sentiment analysis between the BERT approach and ERNIE approach and the proposed BERT-BiLSTM approach and ERNIE-BiLSTM approach.Word vector models use vectors to represent Chinese text. High-performance word vector models can effectively improve the accuracy of sentiment classification. We use BiLSTM to extract features from the word vectors obtained by three-word vector representation methods and then perform a binary classification using a sigmoid classifier. The previous experiment analyzes differences in the performance of different word vector methods under the same BiLSTM model. In this experiment, we compare the BiLSTM network model based on the BERT or ERNIE word vector model with the pre-trained BERT and ERNIE approach to obtain the performance of four complete training models in sentiment classification. The results of the experiment are summarized in After collecting the bullet screen comments on the Bilibili platform, this experiment uses the ERNIE-BiLSTM approach to analyze trends in text sentiment and uses the susceptible-infectious-recovered model (SIR) to further analyze the public opinion strength of the Bilibili platform and determine overall trends in online comments, which can be used for important management decisions.Kermack and McKendrick  proposedAfter 16 February, once Dingding had released its official public relations video, the number of susceptible people gradually exceeded the number of infectious people—susceptible people can be regarded as people whose stance was biased toward Dingding. The growth rate of negative comments gradually declined and became negative, and the growth rate of positive comments was higher than that of negative comments. At the same time, the number of communicators continued to show a large negative growth rate, and as the number of positive comments increased, the growth rate of recovered people became higher than that of communicators. This shows that the public opinion was full of comments that refuted the communicators’ opinions, indicating a gradual improvement in the public opinion of the one-star action for the Dingding event. Dingding’s official public relations video thus played a role in influencing the direction of public opinion.This study finds that communicators play a key role in influencing public opinion. When the growth in the number of communicators remains high, the strength of public opinion forces companies to face the pressure of negative comments. When the growth rate in the number of communicators is higher than 66%, it means that the trend of public opinion on the event is gradually deteriorating, and enterprise managers should pay attention to this to ensure a timely response to manage public opinion.In this study, the pre-trained models of ERNIE segment texts by word. These models differ from traditional methods that require Chinese word segmentation and do not need to refer to a frequently updated dictionary. At the same time, pre-trained models and retraining can use the text vectors derived from context to solve the problem of unknown words. This study also uses BiLSTM to divide the text vectors obtained from pre-trained models and uses forward LSTM and backward LSTM to extract features. Therefore, it can accurately determine the sentiment of texts with contrasting transition words. From the above-mentioned experiments, we find that the processing performance of the BiLSTM approach with pre-trained models is better than that of the Bi-LSTM approach without pre-trained models and the BiLSTM approach with traditional word representation. Therefore, the proposed sentiment analysis model is effective for the sentiment analysis of short text comments with a large number of contrast transition words and new words. In terms of performance evaluation indicators, such as accuracy rate, precision rate, recall rate, and F1-score, the proposed model performs better than other similar natural language processing models, and has certain advantages in public opinion analysis on social platforms.The sentiment of user comments is the most important factor for public opinion pre-warning. The negative sentiment of comments affects the strategy of a company, and the positive sentiment may indicate the degree of user satisfaction with the behavior of a company. The sentiment of user comments allows a company to better understand the current public opinion regarding it and accordingly adjust its strategies or behaviors, thereby reducing the probability of large-scale public opinion incidents and their impact on the company. This study finds that sentiment in user comments is affected by many factors, such as the intention of the videos, the trend in opinion leaders’ comments, and the sentiment of popular comments. These factors can increase the accuracy of public opinion analysis. The characteristics of changes in public opinions obtained from past public opinion incidents give enterprises sufficient time and data to respond to public opinion events .Traditional word vector representation methods and recurrent neural networks have a few shortcomings in natural language processing. Traditional word vector representation methods have difficulties in dealing with situations where the context has different meanings (such as Word2Vec) and recurrent neural networks have vanishing gradient and gradient explosion problems. Although LSTM addresses vanishing gradient problems, it can only process in one direction. This study adopts the BiLSTM method, combines forward LSTM and backward LSTM in the text sentiment analysis, solves the problem of semantic processing in one direction, and uses the pre-trained models of ERNIE to effectively improve the accuracy of sentiment analysis.This study proposes an ERNIE-BiLSTM approach for sentiment analysis on bullet screen comments. After collecting bullet screen comments from the Bilibili platform, this study preprocesses the data to discard meaningless data. First, this study uses ERNIE to encode word vectors to represent the semantics of short texts. It uses BiLSTM to extract text features, deeply analyze text semantics, and complete the sentiment analysis of bullet screen comments. The experimental results show that the ERNIE-BiLSTM approach has a higher accuracy rate, precision rate, recall rate, and F1-score than other methods.Last, this study conducts an integrated analysis of the one-star action for a Dingding event through the experiment on public opinion strength and uses the analysis and pre-warnings of public opinion to help enterprises understand development trends in public opinion about an event and responses to an event. In addition, all short texts in the datasets used in our experiments were within 128 characters. If the model needs to process long texts with more than 300 characters, the knowledge concepts and graphs contained in the text will be more complex. The overall performance of the ERNIE model is still significantly better than that of the BERT model with pre-trained data of the same size.We suggest several directions for further research. As the sentiment category of the dataset is not just positive and negative, it can include sentiments such as joy, anger, and sadness to improve the accuracy of the analysis. In addition, in the subsequent complex text sentiment analysis, if the aspect concept can be considered, the applicability of the sentiment analysis model will be effectively improved.


This study introduces and verifies a basic mechanism of surface topography evolution in electron beam additive manufacturing (E-PBF). A semi-analytical heat conduction model is used to examine the spatio-temporal evolution of the meltpool and segment the build surface according to the emerging persistent meltpool domains. Each persistent domain is directly compared with the corresponding melt surface, and exhibits a characteristic surface morphology and topography. The proposed underlying mechanism of topography evolution is based on different forms of material transport in each distinct persistent domain, driven by evaporation and thermocapillary convection along the temperature gradient of the emerging meltpool. This effect is shown to be responsible for the upper bound of the standard process window in E-PBF, where surface bulges form. Based on this mechanism, process strategies to prevent the formation of surface bulges for complex geometries are proposed. Surfi-Sculpt® process. The transition of the melt pool regime from a lens-shaped to a persistent line-shaped melt pool was observed for higher beam powers and velocities ,27T at tThe motion of the heat source is described by the coordinate system where Equation . TherefoThe surface temperature distributions for each process parameter set is calculated to evaluate the melt pool evolution over the course of the hatch. In order to obtain continuous information about the melt pool evolution, the time step size was chosen such that the beam motion within one time step is limited to the length of one beam diameter per time step. The melt pool envelope of each time step was determined using the liquidus temperature. Previous research showed that melt pool geometries in the stationary state of the hatch can be classified as trailing or persistent. A melt pool is identified as persistent when a line shaped melt pool emerges and the melt pool is still liquid when the beam returns to the same position of the adjacent hatch line . This pelifetime a is complifetime b at eachOver the course of the hatch, these areas expand further towards the center of the hatch until a stationary state is reached. In case of the parameter combination with higher energy input in The numerical calculation of the melt pool lifetime enables the prediction of persistent regions and their correlation with the final surface topographies for complex geometries. For this purpose, a single layer remelting experiment on CMSX-4 substrate was conducted using a cylindrical cross section with variable scan lengths a. In thiIn order to correlate the calculated persistent regions with the final surface topography of the E-PBF process, the scan rotation after each layer has to be considered. The application of a 90The spatio-temporal evolution of the melt pool over the course of a hatch can be divided into distinct local melt pool regimes. Initial temporary persistent domains form at the turning points. During the transient phase of the hatch, the superposition of temperature fields from subsequent hatch lines then leads to cumulative heating, and the melt pool lifetime increases gradually until a quasi-stationary state is reached. Hence, temporary persistent domains extend further towards the center of the hatch until a constant extension is reached, as can be observed in As detailed in Local changes of the surface topography are the consequence of local material transport. Material transport is driven by the effects of recoil pressure on the melt pool due to evaporation effects ,18,19,20In case of a trailing melt pool, a teardrop shaped melt pool follows the beam movement along the surface and the material transport phenomena are well studied ,35. WhilSince the melt pool volume and melt pool lifetime are small, material transport remains minor. By superimposing material displacement and beam movement for a single line, only material transport towards the tail and the sides of the melt pool remains, as all material displaced towards the front of the melt pool is reincorporated into the melt pool. The material transport towards the tail of the melt pool from one line, however, is counteracted by the subsequent line moving in the opposite direction, as detailed in In case of a permanent persistent melt pool, the same underlying principles governing material transport can be applied. In this case, however, the highest temperature gradient as well as surface tension gradient and therefore material transport, due to thermocapillary convection, arise in the direction opposite to the lateral melt pool propagation direction. As a result, material is transported towards the rear end of the melt pool. The superposition with the beam movement shows that material transport in this direction is not counteracted, and material is transferred from the liquid melt pool onto previously solidified material d, leavinPartial persistent melt pool regimes are defined by a combination of temporary and permanent persistent domains, as seen in in The final surface topography of additively manufactured samples results from the superposition of material transport for each scan direction over the build height. If material transport is homogeneous, which is the case for a trailing melt pool a,d and fThe transition from a trailing to a permanent persistent melt pool with increasing energy input and beam velocity may be responsible for the upper boundary of the classical process window, where fabricated samples show pronounced surface bulges . HoweverThe extent of the final material pile up for parameter combinations in the partial persistent melt pool regime, however, also depends on the actual melt pool geometry. While the necessary heat input for the formation of a permanent persistent melt pool decreases for higher lateral velocities, the melt pool volume also decreases. Additionally, the distance between the beam interaction area and the end of the melt pool increases, as the melt pool experiences a pronounced growth in lateral extension, which was already observed by Pistor et al.  and BreuFinally, based on the findings of this work, strategies to prevent surface bulges are based on establishing constant material transport conditions at each point of the hatch. This can be accomplished either by establishing a trailing or a permanent persistent regime, that covers the complete hatch area. In addition, leveraging lower beam return times in higher speed regions of the process window can also mitigate the risk of surface bulges and prevent subsequent process instabilities or even machine damage.With the help of numerical simulations, the spatio-temporal evolution of the melt pool was classified into three different regimes as a function of processing parameters. Experimentally, each of the corresponding melt surfaces exhibit a characteristic surface morphology and topography, which emerge from the combination of material transport and beam movement. Material transport is driven by recoil pressure due to evaporation and thermocapillary convection along surface tension gradients. While homogeneous material transport occurs over the complete hatch surface for a trailing and permanent persistent melt pool, resulting in an even surface, a partial permanent persistent melt pool shows heterogeneous material transport. In this case, material is transported from the temporary persistent regions towards the permanent persistent domain, resulting in material accumulation and the creation of a surface depression of the temporary persistent regions. The final surface topography of an additively-manufactured part emerges from the superposition of material transport from all hatch directions of previous layers. While this effect was determined to be responsible for the upper limit of the processing window, dense samples with even surface morphologies can be fabricated above this limit with the onset of a permanent persistent melt pool that covers the complete sample width. Based on these findings, strategies to prevent surface bulges focus on establishing homogeneous material transport conditions, especially for complex geometries.


The concentration of air pollutants is traditionally explained by complex physical and chemical processes of dispersion and advection. This is the reason why the prediction of air quality is usually addressed through deterministic models, such as Chemical Transport Models (CTMs).However, the CTMs show several limitations and constraints. Their performance depends on an updated emission inventory of the urban area, which is often compromised in developing countries. They also struggle to make an accurate air pollution forecast in complex terrain regions. Moreover, they require high computational power, in order to run time-consuming simulations.More recently, statistical models based on Machine Learning (ML) algorithms have appeared as a valuable alternative to tackle many disadvantages of the CTMs. They seem particularly relevant to provide a fine resolution at an urban scale, where the estimation of air contamination is of the most importance for health concerns. In that sense, ML could become the new paradigm for pollution forecasting.The main goal of this Research Topic is to understand if ML can become the new standard for air quality prediction. Among the several ML methods, we intend to identify the most suitable algorithms for atmospheric pollution forecasting. Such an investigation considers all the dimensions of the prediction performance, which includes both the accuracy and the interpretability of the models. For example, the non-linear models  tend to be more accurate but less interpretable than a linear regression.Saheer et al. explain that ML can take into account several heterogenous factors, such as urban traffic, aerial imagery of terrains and vegetation, and weather conditions, for a more reliable prediction of air quality. The authors propose a cost-effective framework composed of different machine learning methods, from statistical to deep learning algorithms.The first paper highlights the fact that a data-driven method such as ML can consider an infinite number of factors affecting air quality, which can improve drastically the prediction. Fan et al. compare the performance of a chemical transport model (AIRPACT) and two machine leaning (ML) models to forecast O3 in Kennewick . The first ML model (ML1) uses the random forest (RF) classifier and multiple linear regression (MLR) models, and the second model (ML2) uses a two-phase RF regression model. ML1 and ML2 are the best models to predict high and low O3 pollution events, respectively. On top of that, the ML models require much less computational resources than AIRPACT, which suggests that ML is a better solution than CTMs to forecast O3.The benefit of ML over the CTM approach is demonstrated in the second article. 3 but can be applied to predict any kind of pollutants. Mendes et al. use Classification and Regression Tree (CART) and multiple regression (MR) to forecast PM10, PM2.5, NO2, and O3 concentrations in Portugal (Lisbon and Madeira) and Macao. The proposed models are able to predict the concentration of the pollutants for the next day, with a good accuracy.The third study shows that ML is not only a suitable method to predict OChau et al. propose a new approach based on Weather Normalized Modeling to get a more reliable estimation of the concentration of pollutants under a business-as-usual assumption. Several Deep Learning (DL) algorithms and Gradient Boosted Machine (GBM) are tested to quantify the impact of the human mobility reduction on the concentration of the criteria pollutants  in Quito, Ecuador. The results show that Long-Short Term Memory (LSTM) and Bidirectional Recurrent Neural Network (BiRNN) outperform the other algorithms. All the pollutants have significantly reduced, except O3 that increased by titration effect. Besides revealing the better accuracy of DL over the other methods, this work identifies the most important factors to predict air pollution.Finally, the last manuscript addresses the question of the effect of the COVID-19 Lockdown on air quality change. Overall, the studies of this Research Topic tend to demonstrate that statistical or machine learning is a powerful alternative method to the traditional CTM approach, whatever the aspect of pollution forecasting considered. ML is a fast and affordable technique which requires less computational power for an accuracy that can be higher than CTM. Also, the recent progress in the ML algorithms allow a disclosure of the models, which were until now considered as a black box. Resolving the model interpretation issue can definitely rank the ML approach as the best method for predicting air quality.YR has written the article. RZ has revised and edited the text. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Traditional manufacturing system inspections are primarily conducted through microtools. Nowadays, the size of consciously manufactured parts that is getting smaller and smaller, wherein unwritten methods are subject to subjectivity, often resulting in reckless deviations. It is necessary to develop a highly efficient and correct discovery technique. Given the leaned flexibility of traditional manufacturability analysis methods based on cognitive notoriety and empire foundation, the reality that existing manufacturability analysis methods based on full scientific support cannot give a specific purpose for capability manufacturability. A deep cognition support framework grants the manufacturability analysis example. Manufacturing separative methods are presented as imitate. First, a large enumeration of 3D CAD plan with specific manufacturability are made by digital modeling technology, wherein the tier genealogy is realized to cause the data adjustments required for thorough academics. Then, concavity-oriented designs are established on the PointNet entangle form manufacturability. Dense learned grids were analyzed, and network parameter tuning and management were done; then comparisons with voxel-representation-enabled three-dimensional convolutional neural networks (3D-CNN) and existing methods revealed detailed literature for fabricating networks with better robustness and lower algorithm cycle complexity; finally, the actual completion of the network is verified through the example section, and the manufacturability of the cave shape is analyzed to identify the unmanufacturable overall form and explain its considerations. The experimental results have shown that the rule can determine the specific reasons for the unmanufacturable shape under the condition of ensuring the complete notification accuracy ratio, and has a great reproducibility value. Currently, in product design, product descriptions and manufacturing instructions are mostly included independently. Designers often only consider product structure and provinces while ignoring the possible problems of subsequent processing. Failure to fully consider them may lead to the inability to improve capabilities under the existing manufacturing resource environment. In a way to clarify this proposition, it is necessary to perform a manufacturability analysis of the parts in the project layer. Manufacturability analysis refers to thinking about alternatives in the manufacturing process within the product intent, allowing designers to plan the shape and structure of capabilities within the constraints of the manufacturing process and the manufacturing facilitation environment while supporting repetitive management of fixed process information in the manufacturing process analysis and saver constraints. In appendage, this is a prerequisite for able part advancement. A design average that has been analyzed and perfect for manufacturability can greatly reduce the manufacturing cost of the product and deprive the development time. Currently, manufacturability analysis systems are forcibly maintained within the limit of teaching disfavor and basin baseness –6. FactoIn view of this, scholars have expounded on the problem of product manufacturability analysis from the aspects of manufacturability analysis mode, system display, and erudition cost. For example, Hu Yanjuan proposed a characteristic-based evaluation method for the manufacturability of self-propelled gears, and introduced the nonbody characteristic modeling and optimization technology based on intelligent algorithms into the manufacturability evaluation system. Yao Chen  built knThree-dimensional dummies are relatively complex, and savvy literature on 3D sight cannot currently be done overnight. Therefore, scholars propose to use voxel, point blackening, and other methods to represent 3D patterns, and customize the sagacious letters method to learn its data. For specimens, Zhang et al.'s  Habit 3DThere are many factors that affect the machinability of holes. This paper only examines the machining laws of the concave structure and machinability. Reference  is conciSince it is difficult to obtain big data of 3D CAD floor plans, this wallpaper adopts a parametric formal modeling system, combined with crack manufacturability management, to generate a manufacturability analysis data set for training the network. The ram judgment is customary CATIA to randomly jointly mine the shape to one-third of the stable size while making sure it has only one hole. Specifically, first, get used to CATIA to create part patterns with cave features and export a design brief with key parameters. Then, supported by the manufacturability principle of the hole, the key parameters of the shape are randomly propagated and written into the design table. Based on the data in the index, secondary development using CATIA tells the interface to grow several response parts dummy. To categorize voids more clearly, each void in the product data is limited to a maximum of one nonmanufacturable component. Then, corresponding to the above rules, it is necessary for CATIA subordinates to develop relevant interfaces to trigger the 3D CAD trend and generate corresponding tickets. It shows the clearance features for different manufacturability categories and the corresponding one-hot codes for that category. This newspaper disseminated a total of 5,000 3D CAD models through the above methods, randomly selected 4,000 designs as training specifications for mystery learning, and finally put 1,000 models into an application as validation.A given tarnish is a given set of 3D tracks. This time, the nonsolid 3D CAD graphics are all generated by CATIA, and the virtual model is discretized through the significant interface in the CATIA secondary development tool CAA, and the same number of points is maintained in each part through the pattern. Two thousand forty-eight points are extracted per 3D CAD plan and each item contains only coordinate complaints. The affected feature data need to be re-normalized, that is, the coordinate values of all stages are compressed to be between 0 and 1. Due to the perturbation removal and rotation invariance of thorn cloud data, deep learning is not immediately accustomed. The carpel of the PointNet network proposed in Science  is to exK-dimensional royal vector z to another K-dimensional real vector σ(z) such that each chemical element in σ(z) is between 0 and 1. Ramble, the calculation of all elements is 1, where zj and σ(z)j represent the jth water of vector z and vector σ(z), respectively, relative. The data cooled by multiple sensors can be stored using big data warehousing technology, and the data can be mined through the wear-and-tear neural network algorithm program and crowd algorithm rules. Understanding the decision-making system can determine the operating attitude of the processing system if a storage failure state in the manufacturing process is determined. Adjustment; if it is necessary to adjust the entire process flow and product flow, the production direction can be temporarily closed, and the production will continue after the product and program are optimized to ensure the processing quality of the product.Downsampling the shape graph to reduce the size and thus the number of parameters; 2. Perform form lineage. Second, the PointNet network guarantees removal and rotation invariance by locating point contamination data. Alignment exercises are done by teaching a data transformer mesh (T-Net) to own the transformation spreadsheet and double the input data to achieve the transformation of the input data. Therefore, this paper takes the PointNet grid as the basic structure and transforms it to study the manufacturability considerations. The point cloud annoyance of hole feature manufacturability analysis is mainly stable T-Net and feature extraction network. The service of the two data transformation networks is to transform the input data and intermediate feature data to a height that is particularly suitable for network learning, while the responsibility of the formal descent network is to perform layer-by-layer shape extraction data on the specified cloud. It has several 2D convolutional bases and a large number of normalization layers worn in the ReLU excitation office (1). Then, add a SpatialDropout2D band  and compG = , the desired confidence weight vector is z = , the corresponding combination of subnets is Nn = , thus forming the fault matrix G and the confidence weight matrix z, append the dependency spreadsheet to each secondary spider web.In the process of geo-mechanical capabilities, in a system with a clear understanding of processing and manufacturing, the analog-digital mint can be combined with the physical factory. Modeling, process instructions, and bump instructions are extended from second-hand analog and digital manufacturing plants, and product advancement and manufacturing are carried out by the second-hand existing intelligent equipment and machine-controlled production lines. During the progress and manufacturing process, the information about the processing and manufacturing delay can also be fed back to the intelligent control terminal, and the process and protrusion instructions can be corrected by using the analog and digital bloomery to improve the processing quality. In a skilled manufacturing process of the mechanical capabilities of the globe, in a system with an increased degree of automation, the working process can be monitored by remote true repeat monitoring. When an unthought-out bankruptcy or procedural industry problem is discovered for a machine, propositional revelation is immediately fed back to understanding care and control systems to adjust protrusions or treatment plans to correct protrusion effects. In the aqiqiy-delay supervision process, the process of an artificial neural network can be used, and the parsing algorithm of the unreserved influence database can be used to distinguish the tokens that the bicycle may already exist or grow sorted. The basic principle is: suppose the intelligent neural network measures the weakness vector Or for any fusion rise gi greater than a certain threshold, a failure may occur. With this in mind, real-time oversight of the parts custodian's prosecution for fault is possible. When a breakdown occurs, the attitude of the times to automatically sue needs to be adjusted to correct for the particularity of handling. During processing, cognitive decision-making of the auditory ossicles is achieved using the cognitive diagnostic process of bicycle failure or processing quality. In the exchange processing of rural mechanical capabilities, the state parameters of the workpiece and the epigenetic type of the workpiece are collected and taught through sensors, and the tip is transmitted to the central processor for data analysis. The neural network defect diagnosis algorithm program is customized and determined. There are no weaknesses. If there is a fault, the rules are sent directly to the inspection system; if there is no shortage, regulation can continue. With the continuous development of electronic computer hardware and software systems, the emergence of tainted platform technologies, virtual compositions, moral narratives, and potentially camouflaged mechanical products become options. Using a cloud platform and enabling fake software, it is even possible to fake a running farm machine, as well as the training of a Georgia machine. Through the feedback of false data, more technical data allusions can be provided for the design of agricultural machinery, and the optimization of products can be realized before the production of fruit functions. In the intelligent manufacturing process of agricultural machinery parts, the corrosion platform can play an important role in simulation. Because in the process of 3D modeling development, enabling assembly and similarity calculation product capabilities require the comprehensive loading capacity and running speed of electronic computers, and the blackening platform adopts enabling shared storage and collaborative similarity calculation, which is very important. Largely dismissed. Computer behavior. Loading capacity and computing speed provide viable computer resources for understanding the manufacturing of rural mechanical components. Using the quick measure of the blackening scheme data processor, a practical fork of the 3D special-shaped tool can be established, and the confrontation between the tool and the workpiece can be concealed during the 3D machining of the George mechanic ability, and the machining process can be optimized. After completion, record the physical school shift for the procedure. The practicalness of potential steal behavior software UG can go beyond the moral machining of rural mechanical parts. In counterfeit software, it is the only requirement to devise a blank model with formability, then select the appropriate library to utility agreeing to the eminent processing parameters, and then accomplish the potential alikeness of the processing procedure and assimilate to the processing program. Border. Through practical feint, the correct doll passing for anapophysis can be mastered, the processing results can be optimized through backer-deed march data, and workpiece instances can also be gained.y = a + bx + cx2. A convolutional neural network (CNN) is a forward grid (9) whose fret structure is mainly decomposed into input, hidden, and output layers. Hidden layers include convolutional layers and full layers. The input layer is used for en features and can handle multidimensional data. The convolutional layer performs feature extraction on the input data and suppresses the manifold convolution kernel. The parameters of the volume layer include the dimensions of warp kernel, intersection, and padding, which together define the specifications of the product, forming a description of the convolution process. The entire floor is dominated by taste. The output layer produces per-pixel classification springs instantaneously.In general digital copy processing, you must preprocess your own data, including monochrome, smoothing, sharpening, and thresholding. In this paper, the detection of local sharpness is very important for the later GA-CNN algorithm rule failure classification, and edge discovery processing is required. The study is contained within a 3 × 5 area, assuming that the sharpening of the curve is delineated by Based on the cognitive manufacturing system, the combined production line of George Machinery products can produce machine-like performance, and in the unmanned workshop, George Machinery can manufacture the automatic assembly of the ability. In the perceptual production process of agricultural machinery, construction data can be applied to various aspects of the production result. The mining and processing of massive data is also a very important link. Reasonable processing of construction data can save more intense and important costs for the processing and manufacturing process of products and improve fruit efficiency.In addition to the robotic-like assembly capabilities of agricultural machinery, the combination of flax parts can also be used in more intelligent manufacturing systems. When processing tractor panels, some capabilities that cannot be shredded need to be accomplished through application technology. Manual waving is not only inefficient but also inefficient. And the precision is not as good as the robot automatic welding technology, the application of the intelligent manufacturing system makes the robot's ability to manipulate the tractor very simple. The intelligent automatic rifle processing technology can greatly improve the processing efficiency and ensure the processing quality and high-quality products before the ability description. Optimization also entails optimizing the procedural handling of the product and the resulting performance after narrative, moderately preparing for the uplift technology and process flow. If a compact shape tool is used for processing, the result in the optimization process will inevitably require repeated processing and labor, with a high-speed charging and durable motorcycle; if the simulation experience is used to simulate the processing process and inspect the product, it can effectively improve efficiency and cost reduction. The virtual manufacturing system can use the virtual clothes bowl to imitate the processing process of the parts, and can also observe the movement of the machine during the processing process, can avoid interference between the workpiece and the clothes, etc., and can provide a safe data reference. For solid bicycle tool processing.3D modeling software UG is a way to design agricultural machinery capabilities. The deduction usage and interface provided by UG is the habit of writing callback functions, and the parameterization scheme of agricultural machinery parts is supported by templates. The parametric design of precision mechanical parts is actually to modify the size parameters of the parts in the learned foundation and examples to coordinate with the design requirements so that the arrangement of the templates and the size can perceive the specified requirements of modern capabilities. Part parametric design process. When optimizing the capability parameters supported by data mining during pregnancy, the capability optimization subsystem is a way of proving the point, line, boundary, and other instructions of the capability model, and then the massive data mining subsystem is interested in training the parameters' ability. The software of the whole system is compiled into ∗.dll and ∗.dlg files, and the concrete realization saver is shown in the following. Taking the rural roadheader's capability sketch as an example, the reliability of the agricultural machinery digital planning system has been verified. Click “Bushing” in “Case Inference Model” on the tenzel donzel of the system, the system will automatically jump to the action inference design interface; then, the designer can start the “Bushing” specification according to the design requirements to get the “Bushing” ‘s display. Drawing. After the action inference model is sculpted, the integral parameters may not be of final quality. At this point, you can capture the “big data mining model” to polish the component parameters, and the system will automatically save the model and display the 3D fashion on the interface.To support the effectiveness of the reinforcement learning-based manufacturability analysis process for fracture shapes in this paper, quantitative and qualitative comparisons with learning methods –17 and bCompared with the usefulness of the fictional 3D-CNN in this article, the details netting supported on the detail cloud data has industry advantages: (1) the amount of point cloud data is much smaller than the amount of voxel data, which is 2.1% of the amount of voxel data; (2) 3D convolution is expensive. In this paper, we induce voxel data of 100 clocks, choose about 3000 s, and perform 210 training sessions on the point-colored data, which only takes 4500 s. The point cloud data genre can hold a lot of ages; (3) voxelize parts, which would leave the integrated count of the grid in a fruitless state (the interior of the section is indeed empty) and not suitable for convolving it into intrinsically useful information. The feature cloud data are all extracted from the epigenes of the parts, so this problem does not hold; (4) since the shape of the hollow feature utility in this paper is relatively simple, the 3D-CNN based on voxel data has a correction in the manufacturability analysis logo, verifying authenticity can deceive 94.5%. When the imagination of the part is complex, the voxel data will not be able to show some specific shapes. It works better only by voxelizing the parts with high disentanglement, but at this time, the volume of the voxel data grows cubically. The amount of point damage data is linearly related to the entanglement of the part. If there is a lack of progress in complex capabilities, the specified amount of cloud training data is much smaller than the amount of voxel data.In the design of the manufacturing system of agricultural machinery components, cloud platform technology and virtual simulation software are introduced to realize the intelligent decision-making of the manufacturing system. The virtual resource sharing and collaborative parallel computing of cloud platform technology are used to provide virtual processing and virtual assembly of complex parts. The computing resources are provided, and the machining of parts and the virtual assembly test are realized by using the simulation virtual software. Taking the virtual manufacturing of complex parts of agricultural chassis as an example, the cloud platform and virtual simulation software were used to successfully realize the virtual processing and virtual assembly of products, which provided an important reference for the research on new processing methods of agricultural machinery parts.


Rotating-coil measurement systems are widely used to measure the multipolar fields of particle accelerator magnets. This paper presents a rotating-coil measurement system that aims at providing a complete data set for the characterization of quadrupole magnets with small bore diameters (26 mm). The PCB magnetometer design represents a challenging goal for this type of transducer. It is characterized by an aspect ratio 30% higher than the state of the art, imposed by the reduced dimension of the external radius of the rotating shaft and the necessity of covering the entire magnet effective length (500 mm or higher). The system design required a novel design for the mechanical asset, also considering the innovation represented by the commercial carbon fiber tube, housing the PCB magnetometer. Moreover, the measurement system is based primarily on standard and commercially available components, with simplified control and post-processing software applications. The system and its components are cross-calibrated using a stretched-wire system and another rotating-coil system. The measurement precision is established in a measurement campaign performed on a quadrupole magnet characterized by an inner bore diameter of 45 mm. Magnets are one of the main components in particle accelerators, where they are used to steer and focus the particle beam along the nominal trajectory. Dipole magnets are used for steering/bending the particle beam, whereas quadrupole magnets focus and squeeze the beam. In this context, field quality plays an essential role . Field eThe field quality, expressed in terms of the strength and phase of the main field component, plus the unavoidable higher error harmonics see , is a rerotating-coil method [One of the most relevant techniques to test accelerator magnets is the l method ,6,7,8,9,l method ,11,12.In the context of an ongoing collaboration  between Driving plasma accelerator beams requires a particular beam manipulation and associated magnetic elements. The most critical components of this machine are the quadrupole magnets. The features of the quadrupole magnet prototype BTF7, which has been tested at CERN with the prototype rotating-coil system, are summarized in D and length L, simply supported at both ends, is given in the first approximation by the following expression [E its effective Young’s modulus, and the numerical coefficient The characterization of small-bore magnets is challenging. The sag of a cylindrical tube such as the measurement coil shaft, having diameter pression :(1)d=5αρarmonics . The imp2O3) has an exceptionally high An example of a small rotating-coil magnetometer is presented in , which dions. In , a ø8 mmSince the sag of a simply supported shaft grows with the fourth power of its length, coils significantly shorter than the magnet are commonly used to characterize magnets whose length exceeds one or two meters. For example, a rotating-coil system was developed at CERN for measuring the local magnetic flux density of quadrupoles for the HL-LHC Insertion Region (IR) , charactThe geometric requirements imposed by the EuPRAXIA quadrupole magnets exceed the performance of all these systems. This paper aims to present the design, calibration, and validation of a prototype ø26 mm diameter rotating-coil system to be used for the measurement of the EuPRAXIA quadrupole magnets. The smallest foreseen bore diameter is 30 mm, which applies to the final focus quadrupoles and drives the requirement for the rotating-coil shaft diameter. The corresponding shaft aspect ratio is n-th complex harmonic coefficient, and n corresponds to a specific flux distribution generated by an ideal m. Higher-order harmonics, arising from imperfections and manufacturing tolerances, are used as indications of the field quality. For an ideal quadrupole magnet (n = 2), the main field component is given byThe air gap of a magnet can be modeled as a region free of current sources. Considering a cylindrical volume, coaxial with the gap, sufficiently extended so that the field at both ends can be considered to vanish, the integral magnetic field density satisfies the e radius . For z_=The amplitude of the two components varies linearly with the distance from the origin. The coefficients The origin of the reference system is referred to as the magnetic center, and it represents where all multipolar field components of order This choice arises from the typical tolerance values of accelerator magnets, where the harmonics are in the order of  crucial ,22,23,24Rotating-coil magnetometers belong to the family of induction coil sensors, where the magnetic field is measured through the flux variation induced in a sensing coil . According to Faraday’s law of induction, the voltage at the terminal of a sensing coil is proportional to the rate of change of the magnetic flux:Rotating-coil magnetometers are composed of a certain number of induction coils, generally long rectangular loops of wire, constrained in width by the magnet aperture diameter. Considering a point-like winding case, the geometry of an ideal induction coil can be described by the complex points ertainty .N turns, a total area L, the linked magnetic flux can be calculated asGiven an induction coil with n. These coefficients are usually normalized to Equation  becomesThe complex field harmonic coefficients The EuPRAXIA project application represents a quite extreme case for the proposed typology of transducers, planned to be installed in a rotating shaft with an inner diameter of 26 mm and an overall length of 640 mm. The shaft dimensions allow coverage of the entire magnet length of 440 mm and its fringe field region.The aspect ratio of the proposed PCB coil shaft, defined as The realization of such a small-radius rotating-coil system significantly impacts the size of the coil array and, in particular, the geometric width of each coil and their area. A reduced area means reduced sensitivity to the field harmonic components. The proposed coil array design aims at counterbalancing this effect.The adopted technology for the sensing coils is based on the Printed Circuit Board (PCB) technology, a well-known alternative to the traditional wound coils ,18,19. T1% level .The proposed PCB coil array was produced at CERN. A PCB array of 5 identical coils, each in the shape of a rectangular and planar spiral, positioned in a radial configuration, was designed. The problem of the geometric constraints was addressed by designing the PCB array with the highest possible number of PCB layers in the available space to increase the turn density and the coil sensitivity. In the adopted design, the PCB layers are connected in series with metallic holes drilled in the compressed stack of layers. The PCB layers have the same nominal surface, and the connections of the pads are placed close together to minimize the spurious surface of wires between them. A picture of the produced PCB coil array and a schematic cross-section representation of the PCB array inside the rotating shaft are shown in The design parameters of the PCB array are reported in The PCB coil array is inserted in a cylindrical shaft that allows rotation around its longitudinal axis. The shaft was realized with a carbon fiber tube, produced by Refitech, readily available on the market at a very low cost, in a wide range of lengths and thicknesses. Besides being non-magnetic, the carbon fiber composite has an attractive armonics . With re® plastic, leading to fast and cost-effective design modifications and reproducibility. Connection head and spacer dimensions were easily modified to perfectly adapt to the PCB’s final thickness. Adjustable support platforms and vertical V-shaped stages were designed to suspend the whole rotating system in the magnet aperture, such that the shaft rotation axis is in the mechanical center of the quadrupole magnet. A 3D view of the PCB coil array, equipped with connection heads and spacers, and of the assembled carbon fiber shaft is shown in The PCB is installed at the center of the tube using semi-cylindrical centering spacers. Two connection heads are installed at the extremities of the tube. All connection and positioning pieces are 3D-printed in Accura 25in μrad) , provide® framework. Post-processing, including flux integration and harmonic analysis, was carried out with Matlab® instead.A data acquisition system, USB-6366  from NatWhile the coil rotates, the induced voltages in the five coils are recorded synchronously on separate channels of the ADC. In a quadrupole magnet, where the field harmonics of interest for beam control typically do not go above the order absolute voltage, used to evaluate the main field component, and a compensated voltage, used to evaluate the higher-order harmonics. The absolute voltage is the output of one of the two outermost coils in the array. The compensated voltage, which provides the highest signal level in any field multipole of order bucking, can be realized by inter-connection of the coil terminals  and acquiring their combination, or numerically, by the individual acquisition of the coil signals . For the proposed system, digital compensation has been adopted  algorithm. The complex field harmonic coefficients are then computed using Equation , where tEquation , plugginm when the reference system is translated. In an ideal quadrupole The feed-down phenomenon is the appearance of spurious field harmonic errors of order The measured harmonic coefficients can then be corrected using the expressionThe main field module is obtained from the normal and skew components of The phase of the harmonic coefficients is based on the position of the encoder index, which is, in principle, arbitrary due to mechanical tolerances. The absolute and compensated harmonic coefficients are rotated such that the measured main field corresponds to the known type of the magnet under test; in our case, this is defined as a normal quadrupole, hence The last step of the post-processing is the normalization of the harmonic coefficients with respect to the main field module:The accuracy of rotating-coil magnetometers depends on many factors. One significant contribution is given by sensitivity factors, mainly dependent on the knowledge of the coil area and rotation radius. These quantities are obtained by calibration against a reference field (area) and a field gradient (radius). Area calibration is typically performed prior to the assembly of the magnetometer to verify the quality of the coil production and identify defects such as inter-turn short circuits, which are difficult to detect through resistance measurements. Calibrating the rotating radius of each coil requires the final ball bearings to provide the final rotation axis for the best accuracy; therefore, it should performed on the fully assembled probe. In addition to the calibration, a basic mechanical characterization was carried out to evaluate the leading indicators of rotation quality and acquisition, such as loose contacts, misaligned mechanics, and vibrations.The surface calibration was performed at a field of 1 T in a reference dipole magnet available at CERN, having a relative spatial uniformity of the magnetic flux density of mA can be obtained fromAs The magnetic surface calibration was performed on two PCB arrays. The results are compared to design coil area g over the magnetic length The calibration of the coil radii was carried out in the BTF7 quadrupole magnet, used as a reference. The calibration of the coil radii requires knowledge of the field gradient. A measurement performed by a Single-Stretched Wire (SSW) system was used as a reference. The integrated gradient y is the coil’s vertical displacement from the PCB array plane. From Equation , which is the ratio between the field and excitation current, was measured in DC mode on current plateaus from 0 A up to 100 A and compared with the results obtained by a Single Stretched Wire (SSW) measurement system. The magnet Transfer Function is shown in bucking. In the adopted digital bucking configuration, The number of coils in the PCB array depends on the compensation scheme necessary for the magnet to be tested, and it is chosen during the design phase. Mechanical imperfections (due to assembly errors) and rotation errors (vibration and torsion) degrade the metrological performance, giving rise to spurious harmonic content . Since aA ø30 mm rotating-coil probe, previously in use at CERN, was used to test the same quadrupole magnet for the cross-checking of the ø26 mm rotating-coil system, in terms of measured harmonic field components. Measurements were performed adopting two pre-cycling conditions: (i) after degaussing, (ii) pre-cycling the magnet with three cycles between 0 and 100 A. The ø30 mm rotating-coil measurement system includes a fast digital integrator  for voltC, differ from the design value by around The PCB technology adopted for coil production allowed high control over track positioning, albeit with some issues. Both Coil A in PCB Array 1 and Coil D in PCB Array 2 are missing around Equation , combinepp. Higher rotation speed values would increase the amplitude of the induced voltages, but were observed to cause noticeable flexural vibrations and were therefore discarded. The higher-frequency torsional components observed in the speed spectrum in The mechanical characterization allowed us to choose the optimal rotation speed as a trade-off between the coil output voltage amplitude and vibration effects. Results show speed uniformity less than The field homogeneity of the BTF7 quadrupole was measured at the nominal current value of 93 A and the results are expressed in terms of magnetic multipoles in units of In this article, the design and development of a new small-diameter rotating-coil measurement system prototype, needed to test the field quality of small-diameter (30 mm or higher) bore quadrupoles for the European project EuPRAXIA, is presented. Accurate measurements of the field harmonics in accelerator magnets require the construction of a dedicated rotating-coil shaft of the largest possible diameter. The proposed magnetometer design is based on an array of identical coils realized in PCB technology and mounted in a cylindrical shaft with a diameter of ø26 mm.Some considerations about the manufacturing process were reported. Excluding from analysis two defective coils, the accuracy of track positioning on the PCB can be evaluated to be around ® used for the inserts, and the need to retouch them slightly on the lathe, the quality of the rotation is very good, with torsional vibrations peaking at the safely high frequency of The results obtained from the mechanical characterization essentially validate the innovative mechanical design, which is based on inserting the PCB coil array in a carbon fiber tube by means of 3D-printed plastic inserts. Despite the low rigidity of the Accura 25 Comparison with other measurement instruments proved that our prototype rotation coil system can achieve an absolute accuracy of the main integrated gradient of approximately Commissioning this prototype system has provided valuable experience to progress in the design of the production instrument. First of all, different 3D-printed materials and techniques will be tested for the inserts and the shaft end connections, with the goal of minimizing or avoiding completely the need for further mechanical retouches. The set of screws and pins that lock the PCB and the inserts in place inside the carbon fiber tube should also be redesigned, to facilitate the disassembly process, as this may be needed for maintenance. Finally, the shaft support system shall be augmented with the possibility of shifting horizontally the instrument within the magnet bore, so as to allow one to improve the accuracy of the in situ radius calibration procedure, as described in . The fin


The observation of magnetoresistance (MR) varying with the rotation of magnetization in the plane perpendicular to the electric current is an important discovery in spintronics in recent years. The famous conventional anisotropic MR (AMR) says that the resistance of a polycrystalline magnetic material must depend on magnetization component along the current direction only, thus cannot account for this newly observed unusual AMR (UAMR). This UAMR leads to the notion of the spin-Hall MR (SMR) in the famous SMR theory. However, the SMR theory may only explain UAMR observed in heavy-metal/magnetic-insulator bilayers, not other types of bilayers. Here, we present a two-vector theory that can explain not only all existing experiments on the unusual angular dependence of longitudinal and transverse resistivity when the magnetization rotates in three mutually perpendicular planes, but also how three amplitudes of MR angular oscillation are related to each other. The theory is very general and its correctness depends only on the assumption that the magnetization and interfacial field are the only vectors affecting electron transport besides of other scalar variables such as the temperatures and impurities. Experiments that can test this theory against the SMR theory are also proposed. The ubiquitous UAMR occurs in the non-magnetic polycrystalline metallic-film13, no matter whether it is a heavy metal with strong spin-orbit coupling or not as long as it is highly susceptible to magnetism, and no matter whether the magnetic layer is insulating or not. UAMR exists also in a magnetic polycrystalline metallic-film14 in contact with a non-magnetic insulating layer. In comparison with the well-known usual anisotropic magnetoresistance (AMR) that says resistance depends only on the magnetization component along the current, UAMR depends not only on two magnetization components perpendicular to the current, but also on them differently.A dramatic development during the debate of the transverse spin Seebeck effect14 in a compact form. Denote the interface of a bilayer heterostructure as the xy-plane and current along the R are constants whose physical meaning are clear. y-direction. In addition to the term of 15, 5 although it is mathematically the same as R and 13. R-term is normally known as the anomalous Hall effect. In terms of above terminology, the usual AMR corresponds to In order to appreciate the unusualness of UAMR, let us summarize its main experimental features16 provides the popular explanation of UAMR in a bilayer of one non-magnetic heavy metal film and one magnetic insulating film. Due to the spin-Hall effect, a charge current in the heavy metal generates a y-polarized spin current propagating toward heterostructure interface. This spin current, in turn, induces a charge current opposite to the original current in the heavy metal through the inverse spin-Hall effect such that the current is reduced and resistivity of the heavy metal increases by a factor of Spin-Hall magnetoresistance (SMR) theory14 for bilayers of one magnetic metal layer and one either magnetic or non-magnetic insulating layer. In summary, a successful theory that can fully account for observed UAMR in various types of bilayers is yet to be developed. This problem, as well as other subtle ones, motivates this study.Although the picture of spin polarized electron transmission and reflection at a heterostructure interface in the SMR theory is opposite to that of tunnelling-magnetoresistance theory, the justification is that polarized electrons exert no torque on a collinear magnetized insulator and cannot pass their spin angular momentum to the insulator such that spin current cannot but reflect back to the heavy metal. SMR theory may be able to explain the UAMR in bilayers of heavy metals with magnetic insulators, but it would be unnatural to explain similar results of bilayers of one heavy metal and one magnetic metal because the assumption of above reflection and transmission of spin current by a magnet is not consistent with physics picture of giant magnetoresistance and tunnelling magnetoresistance. According to giant and tunnelling magnetoresistance, it is easier (harder) for a polarized current to pass through a magnet when its magnetization is parallel  to the current polarization than that when the magnetization is perpendicular to the incoming electron spins. By the same argument of spin-current enhanced resistivity, SMR theory should predict, for example, In this paper, we show that UAMR of a bilayer is the natural outcome of polycrystalline metal(s) whose resistance depends on two vectors. One is the magnetization of the bilayer, and the other is an interfacial field perpendicular to the heterostructure interface.Following the convention in most studies of UAMR, unit axis vectors 18. Each of the three Cartesian tensors is not irreducible19, and can be decomposed into irreducible forms of a scalar, a vector, and a traceless symmetric tensor. Thus, from M is the magnitude of magnetization M and For the linear response, the electric field entclass1pt{minimaxy- and yz-, and zx-planes and define angle x-axis when xy-plane; or angle z-axis when yz-plane (zx-plane). We then have the usual anisotropic magnetoresistance xy-plane; newly discovered UAMR yz-plane; and zx-plane. Clearly, both phases and amplitudes of 14. Thus, UAMR does not need to involve the spin-Hall and the inverse spin-Hall effects. In some bilayers such as 9, an additional three-fold angular dependence of To further see that Eq.  has exac12 such that yz-plane (perpendicular to the current). This observation is difficult to understand within the SMR theory, but is a natural outcome of the case of 15. Whether xz-plane. This is the consequence of Real bilayer heterostructures show various possible relative values of 14. Thus the thickness-dependences of UAMR provides the information of interacting range of the interfacial potential or interfacial field. The optimal thickness, at which the UAMR is most pronounced, contains information of interface roughness. So far, UAMR are found in bilayers of non-magnetic film on a magnetic layer. From the theory presented in this paper, similar results should exist in bilayers of two different magnetic layers that could be both magnetic polycrystalline metals or one polycrystalline metal and one magnetic insulator. If one uses strong magnetic field to align the magnetisations of the two magnetic layers in the same direction in angular dependence measurement of MR, then the above analysis is applicable. Otherwise, one should generalize the theory into the case of three vectors. In a short summary, there are experimental ways to distinguish the current theory from the popular SMR theory. One important remark is to exclude the metallic single crystal that will introduce extra contributions to the angular dependences of magnetoresistance15.As shown above, UAMR can be perfectly understood from the combined actions of magnetism and interfacial field of a bilayer on electron transport. According to this mechanism, the UAMR should decrease with thickness of polycrystalline metal film when the film thickness is larger than interacting range of the interfacial field such that shunting effect dominates and resistance from interface region is less important. One should also expect that UAMR decreases when the film thickness is smaller than the interface-roughness in structure and physical properties such that interfacial field characterized by 5. In comparison, there are only four material parameter in this theory. These four parameters defined in Eq. . These five parameters cannot be directly extracted from transport measurements, and are obtainable by fitting thickness dependences of conductivity to certain theoretical models plus other independent experiments such as ferromagnetic resonance on the same bilayersd in Eq.  as \docu20. Of course, UAMR is not as fundamental as gravitation theory, and our results are a relationship between MR and magnetization, not a partial differential dynamical equation as the Einstein’s gravitation theory is.It should be emphasised that a complete theory is presented here with precise predictions of how MR should vary in three mutually perpendicular planes, and how their amplitudes should be related to each other. Several very feasible experiments are proposed to test this theory against the SMR theory. The theory is so general that any achiral system, no matter how complicate its microscopic Hamiltonian and interactions might be, must agree with the results presented here. The approach is similar to the derivation of Einstein’s gravitation theory that is about possible construction of a rank 2 tensor out of metric tensorIt should also be interesting to study chiral heterostructure when reciprocity condition does not hold. Follow exactly the analysis above, it is easy to see that UAMR of chiral system should be described as Onsager reciprocal relation breaks down for our bilayers involving magnetization since the magnetic materials do not respect reversibility. Of course, extra symmetries can impose further restriction on the possible structure of the resistivity tensor. It should also be pointed out that this manuscript and Ref. 15 consider different systems although they share the similar mathematical technique and ask similar question. Reference 15 study the angular dependence of resistance of homogeneous samples such as ferrimagnets or antiferromagnets described by at least two order parameters. On the other hand, this manuscript consider bilayers heterostructure with at least one magnetic layer. The objective is to provide a natural explanation for the universal angular dependences in three mutually orthogonal planes. Both layers could be metallic, or one metallic and one insulating. Both of them can be magnetic, or one magnetic and one non-magnetic.In conclusion, unusual angular dependence of magnetoresistance in bilayers consisting of one non-magnetic film and one magnetic film can be explained by a two-vector resistance theory if the metallic layer(s) is polycrystalline. It is predicted that similar behaviours should also hold for bilayers of two different magnetic films. The general UAMR can come from physics beyond the spin-Hall and inverse spin-Hall effects. Experiments that can test this theory are also proposed.


In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on a rapid parameter analysis. In this study, an analytic model of transient heat conduction for bi-layered FEHs is proposed, which is solved by a novel symplectic superposition method (SSM). In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. The Laplace inversion gives the eventual temperature solution in the time domain. Comprehensive time-dependent temperatures by the SSM are presented in tables and figures for benchmark use, which agree well with their counterparts by the finite element method. A parameter analysis on the influence of the thermal conductivity ratio is also studied. The exceptional merit of the SSM is on a direct rigorous derivation without any assumption/predetermination of solution forms, and thus, the method may be extended to more heat conduction problems of FEHs with more complex structures. Electric heating devices have attracted scholarly interest due to their important engineering and medical applications during the past few decades, including resistive micro heaters , electroThe FEHs developed in recent years can be divided into two major categories. One is on polymers with a variety of conductive compositions, including transparent copper fiber heaters , metal nGreat efforts have been made to achieve temperature uniformity in FEHs via periodic wire structures embedded into substrate layers. Various conductive wire heaters, which are composed of metallic nanowires , carbon In recent years, we have proposed a novel analytic symplectic superposition method (SSM) that has been successfully applied to bending , bucklinCompared with the conventional methods, the exceptional merit of SSM is the inherent rigorous derivation without any assumption and pre-determination of solution forms, which enables it to serve as a general method for new analytic solutions. Although the main applications of the SSM have been on the mechanical problems of structures, it may find access to some new issues that are physically different from the mechanical problems.In this study, we make an SSM-based successful attempt to achieve the transient heat conduction analysis for bi-layered FEHs. The governing equation in the Hamiltonian system is introduced in oy axis, with the entire dimensions along ox and oy axes being As is shown in itten as (1)1αi∂THere, the quantities with a subscript The BCs at the upper and lower surfaces yieldoy axis and the periodicity along the ox axis, respectively.In this study, it comes to either Dirichlet type, with The Laplace transform of a real function fined as (3)F(s)=s represents the Laplace transform parameter. Introduce the Lagrangian function [y. Based on the principle of the least action for the transient heat conduction process [The governing equation and BCs are converted into the Laplace transform domain:function :(5)Li=ki process , we acquIt is noted that for the transient heat conduction process, the entransy dissipation rate closely connects to the integral of the convolution of heat flux and negative temperature gradient over the time and space domain, whose convolution integral consists of the influence of the time evolution. In addition, the transient heat conduction process includes both the dissipating and non-dissipating processes, and thus, its variational function could include both the dissipating and non-dissipating terms ,28, as dDefiningThe Hamiltonian function is introduced according to Equations (7) and (8) asc matrix .x, and y, we haveSeparating the variables in the symplectic space as The general temperature solution in the Laplace transform domain is thereforeSince the main purpose of this study is to provide an SSM-based analytic model of transient heat conduction for bi-layered FEHs, a general problem with an arbitrarily positioned point heat source at structed a. In theIn Layer 1 b, the heThe eigenvalues are thusThe corresponding eigenvectors areIt is necessary to mention that thogonal . MoreoveSince all eigenvectors have been obtained for the Layer 1 problem, the state vector can be expanded according to the symplectic orthogonality and conjugacy, yieldingSubstituting Equation (21) into Equation (10) yieldsFrom the second of Equation (12), we havex over Multiplying both sides of Equation (25) by Substituting Equation (29) into Equation (27), we obtain Layer 1 b in the Following the same logic as described above, with the BCs at the top surface exposed to air and the interface between Layer 1 and Layer 2:  Layer 2 c in the Both the temperature and heat flux should be continuous at the interface at By Equation (35), the coefficients It should be pointed out that an explicit expression of the inverse Laplace transform is strikingly complicated, and thus, it is not presented here.a/100 to achieve the convergent numerical solutions.To provide comprehensive numerical and graphical results as benchmarks for further structural designs, the analytic transient heat conduction results of bi-layered FEHs are given by the SSM with verification by the FEM. The considered circumstances are given with the following parameters: As revealed by the temperature results marked in bold in The temperature results at typical locations within a broad time range are tabulated in a/2, a/2), are plotted in To give more intuitive results, To further study the influence of thermal properties on the heat conduction behavior, a parameter analysis for Case 1 is conducted by changing the thermal conductivity In this study, an analytic model of transient heat conduction by symplectic superposition is established for bi-layered FEHs and is well verified by the FEM modeling. By converting the problems in the Laplace transform domain into the Hamiltonian system, the mathematical techniques such as separation of variables and symplectic eigen expansion become available for deriving some new analytic solutions. The high accuracy and rapid convergence of the SSM are well confirmed by the numerical results as compared with the FEM results shown in tables and figures. The time-dependent temperature results, including the steady-state results, and the effect of thermal conductivity ratio on heat conduction have also been investigated. The developed analytic model provides a theoretical basis for transient heat conduction analysis of bi-layered FEHs, and it may be extended to more complicated problems, such as those of multi-layered FEHs and orthotropic FEHs. It is also worth mentioning that although the present solution does not involve Robin-type BCs, the SSM may be extended to heat conduction problems under such BCs as well.