Chile was severely hit by the COVID-19 pandemic. The implementation of social distancing measures strongly affected the Chilean economy: the unemployment rate grew rapidly as well as the proportion of population temporarily excluded from the labour force. This article analyses the strategies deployed by Chilean households to cope with the impact of the pandemic at the intersection with household structure and its socio-economics characteristics. Secondary data analysis from the Encuesta Social COVID-19 , carried out by the Chilean Ministry for Social Development and Families, were used to analyse the income-generating and expenditure-minimising strategies adopted by households during the early months (March to July of 2020) of the pandemic. The results show that 60.3% of households experienced a drop in family income, 70.3% indicated that they had to use at least one income-generating strategy, and 76.6% at least one expenditure-minimising strategy during the early months of the pandemic. Indebtedness and decapitalisation characterised most of the coping strategies adopted by households. While living in multigenerational households does not protect family members from declining economic well-being, older people living in one- and two-generation households were found to be least affected economically during the crisis. They were also less likely to resort to these coping strategies, insofar as their income was mainly secured from pensions. Although female-headed households did not show a greater reduction in income than male-headed households, they were more likely to adopt income-generating strategies. This article draws attention to the possible effects of decapitalisation and indebtedness on the long-term economic well-being of households with different structures, and the resulting inequalities in their capacity to recover from the effects of the pandemic. The findings suggest that having a source of family income that is not dependent on labour market flows is crucial in times of crises. In countries with limited welfare provision, such as Chile, families play a central role in protecting individuals from critical situations. Flows of support among extended family members take place on a daily basis, even if they maintain an independent residence. The implementation of social distancing measures to face the COVID-19 pandemic in Chile, which included localised lockdowns and mandatory mobility restrictions, applied earlier and more stringently for older people , straineWith a first confirmed case on 3 March 2020, Chile was severely hit by the COVID-19 pandemic, reaching the highest rate of infections per capita globally by mid-June 2020 . The peaAll these measures had a significant economic impact on the Chilean population. Official figures from the Central Bank of Chile show a contraction of GDP in 2020 of 5.8% . AccordiCOVID-19 measures, such as the closure of nurseries and schools, and the introduction of remote working in a large number of occupations, generated a significant increase in the unpaid care workload, especially for women. According to a longitudinal survey conducted in July 2020, both men and women increased the average number of hours spent in housework and childcare compared to the situation before the pandemic . While tThree main social protection measures were introduced during the early months of the pandemic . The firIn addition, it is important to note that the Chilean welfare care regime is not universal. Most monetary and non-monetary transfers focus on the most vulnerable groups of the population, guaranteeing them a minimum income and an “ethical” family income. Due to the strong targeting and low amounts provided by these programmes, their scope was very limited and left an important part of the population unprotected during the economic crisis induced by the pandemic.In this context, two population groups were found to be particularly vulnerable to the impacts of the COVID-19 pandemic: older people, due to their higher morbidity and mortality from the virus, as well as the effects of lockdowns and specific restrictions on their mobility; and women, due to job loss and the increase in unpaid care workloads resulting from confinement and the closure of nurseries and schools.The aim of this article is to analyse household coping strategies during the COVID-19 pandemic in Chile, and to determine how they were related to household structure and socio-economics characteristics. Secondary analysis of data from the Encuesta Social COVID-19, carried out by the Ministry for Social Development and Families in Chile, was used to examine the income-generating and expenditure-minimising strategies deployed by households during the early months (March to July) of the COVID-19 pandemic. To take account of the uneven impact of the pandemic on different population groups, the household typology adopted considers the generational composition of households, distinguishing between older people aged 65 and above, adults aged 18–64 and children under the age of 18, and between female and male household heads using self-reporting criteria.Previous research on the subject in Latin America has shown that some households are better equipped than others to cope with the negative effects of different kinds of shocks , 1998. TOne of the main criticisms levelled against the concept of family or household strategies and their use in economic decision-making within households is the failure of analysts to question the notion that the family (or household) group has intentionality, interests and rationality, independent of the individuals that compose it . FeminisAn important body of Latin American research has analysed the survival strategies deployed by poor urban households during the debt crisis and the subsequent process of structural adjustment in the 1980s. In this context, household extension – based primarily on multigenerational coresidence – has long been a widespread strategy adopted by families to cope with crises, enabling them to save on housing costs and bring able-bodied members into the household to contribute to salaried and domestic work . As exteMore recently, Latin American research has highlighted the importance of intergenerational solidarity in coping with the effects of economic deprivation, and with flows of financial and non-financial support both within and between households . In ChilResearch on the debt crisis and fiscal austerity in southern Europe since 2008 highlighted the “cushioning” role of the extended family on the impact of unemployment, low wages and the reduction of welfare for the economic well-being of individuals . In thisStudies analysing the domestic impact of the COVID-19 pandemic show that family coping strategies rely heavily on intergenerational solidarity. Comparing the cases of England and South Africa, Intergenerational coresidence has been found to facilitate flows of support among family members during the current crisis in many other countries. In the United States, for example, the coresidence of young adults with their older parents increased as a result of the pandemic owing to the sharing of resources as a means of reducing expenditure . In SpaiLatin American research conducted during the debt crisis in the 1980s and the subsequent process of structural adjustment stressed the relationship between female-headed households and poverty . HoweverAn earlier study noted that the position that women occupy within the household matters in understanding how female-headed households cope with poverty . Older fMuch of the previous research on the coping strategies of female-headed households focused on developing countries. In Indonesia, the livelihood strategies of female-headed households were based on the reduction of household food consumption, and indebtedness to neighbours or relatives providing childcare . A studyResearch on coping and survival strategies carried out by female-headed households during the COVID-19 pandemic received much less attention than the impact on their household income. For example, a qualitative study conducted in the United States emphasised the ability of single mothers to generate active strategies to earn a living and care for their children, while managing the tension between production and reproduction . To a laA broad consensus exists around the notion that the economic impact of measures of social distancing, confinement and large-scale closures of workplaces and schools during the COVID-19 pandemic affected women to a greater extent than men, especially in female-headed households . The redThe data source for this article is the Encuesta Social COVID-19, a panel survey carried out by the Ministry of Social Development in Chile to identify the social consequences of the COVID-19 pandemic on the living conditions of families. The survey is based on a random sample of nationally representative households: the first wave took place in July 2020  and the second in November 2020 . This article analyses data from the first wave collected at the peak of the first outbreak of the pandemic in Latin America.The analysis is based on a sub-sample of 4,044 households headed by individuals aged 20 and older. The sub-sample excluded 329 cases for which no income information was available, 31 cases with no information about the level of education of the household head, and 9 cases of households composed of elderly people and children.The analysis contained two dependent variables: the number of income-generating strategies and the number of expenditure-minimising strategies carried out by households in Chile during the first months of the COVID-19 pandemic, as summarised in The analysis also includes two main predictors: household type (based on the number of generations coresiding) and sex of the household head. The dummy variable for the sex of household head identifies whether or not the household head is a woman. The Encuesta Social COVID-19 uses a measure of household headship based on a self- or proxy-reporting criterion, which has some limitations. Feminist research has highlighted, for example, the risk of under-estimating the real magnitude of female headship, by making those women who are the main income contributors to their household invisible. Despite this limitation, previous analyses carried out by the authors showed that this measure of household headship is strongly related to owner-occupancy and economic measures of household headship . It has Because multigenerational (mostly three-generation) households are better equipped to cope with economic shocks, they might be expected to require fewer adaptive strategies to maintain their living standards during the pandemic.Since the income of the older adults is less dependent on fluctuations in the labour market, households composed of older adults  might be expected to require fewer adaptive strategies to maintain their living standards during the pandemic.As female-headed households have suffered more than other types of households during the crisis and are especially active in delivering survival strategies, they might be expected to require more adaptive strategies to maintain their living standards during the pandemic than male-headed households.The finding reported here evaluate the role played by household structure and socio-economic characteristics in explaining income-generating and expenditure-minimising strategies during the early months of the COVID-19 pandemic.The descriptive analyses showed that the economic crisis generated by the pandemic had a significant impact on the economic well-being of households in Chile. As illustrated in When the decrease in household income is analysed by household headship, no significant differences are observed according to whether the household is male headed or female headed. This finding contrasts with the available evidence showing that women were most likely to be affected by job loss during the crisis. One possible explanation for this finding is that female-headed compared to male-headed households implemented more – and more effective – income-generating strategies to compensate for decreasing household income.In the context of decreasing household income, a significant proportion of households in Chile adopted various coping strategies, either to generate additional income or to reduce current expenditure. Of all households in Chile, 70.3% indicate that they had to use at least one income-generating strategy during the early months of the pandemic. As shown in The analyses show that three-quarters of households in Chile adopted at least one expenditure-minimising strategy during the first months of the pandemic. As shown in Since households were known to have suffered an unequal economic impact according to their composition and headship, it is important to examine whether the strategies adopted also differed according to these characteristics. Households that experienced a decrease in their income were more likely to have carried out income-generating strategies than households that had not suffered a loss of income, irrespective of their composition or headship. Among the former, higher proportions were reported in one-generation households composed only of adults, two-generation households composed of adults and children and three-generational households. These results provide initial support for Hypothesis 2, which expected that households composed of older people would be less likely to adopt active strategies to increase income and reduce household expenses. When analysing the differences by household headship, households headed by women reported carrying out more income-generating strategies than households headed by men, whether or not they had suffered a decrease in their income, as anticipated in Hypothesis 3.Importantly, a high proportion of households that had not experienced a decrease in their income also reported having implemented income-generating strategies during the pandemic. Given the cross-sectional nature of the data, it is not possible to know whether they were preventive-type strategies in a context of economic uncertainty, or whether these households did not suffer a loss of income because of the strategies implemented.A binary logistic regression analysis was used to predict the performance of income-generation and expenditure-minimising strategies in a nationally representative sample of households . Households that reported not having carried out these strategies during the first months of the pandemic were used as a reference category, in comparison to households having carried out at least one such strategy. An odds ratio of more than 1 means that the odds of an event occurring are higher for this category than in the reference category.When compared to one-generation households composed only of adults (without children or older adults), one-generation households composed only of older people and two-generation households composed of adults and older people were less likely to have carried out income-generation strategies, net of other factors. These results provide some support for Hypothesis 2, which expected households composed of older people to be less likely to adopt active strategies to increase income and reduce household expenses. Contrary to what was expected in Hypothesis 1, three-generation households were found to be as likely as one-generation households composed of adults to carry out income-generating strategies.As suggested by other research on the subject, female-headed households were more often found to be carrying out income-generating strategies than male-headed households. The odds of performing income-generating strategies in female-headed households were 30% higher than those registered in male-headed households. This finding supports Hypothesis 3, by showing that female-headed households, who were severely affected by the pandemic, were especially prone to adopt income-generating and expenditure-minimising strategies.Household size had a significant positive effect on the odds of carrying out income-generating strategies. Larger households were more likely to carry out income-generating strategies, whereas the family status of the household head had no significant effect on the implementation of these strategies.A strong association was observed between household income level and the odds of carrying out income-generating strategies. Households with higher income levels were more likely to perform this kind of strategy. The number of employed persons within the household had a negative effect on the implementation of income-generating strategies in households with three or more employed members, and they were less likely to carry out these strategies. Household heads with incomplete high school education were also less likely to carry out income-generating strategies.The receipt of state financial support did not have a significant effect on the likelihood of carrying out income-generating strategies. The implementation of a lockdown lasting less than 2 months increased the odds of carrying out income-generating strategies.Columns 5–7 of Female headship did not have a strong significant effect (sig.= 0.083) on the odds of carrying out expenditure-minimising strategies once income level and other household characteristics have been taken into account. Interactions between female headship and household income quintile (not included in this article) also show no significant effect, except in the case of female-headed households of quintile IV, which are more likely to deploy expenditure-minimising strategies than male-headed households of the wealthiest (V) income quintile.This finding would seem to contradict what is expected by Hypothesis 3 by suggesting that female-headed households are not particularly active in adopting strategies that seek to minimise expenditure, despite having been more severely affected by the crisis. This contradiction could be explained by the fact that these households were more often associated with the presence of children, which limited their options for reducing expenses. It is also possible to interpret this finding as a result of receiving child support from children’s fathers. However, it should be noted that family law in Chile does not guarantee that women and children receive economic support from their former husbands or fathers, as illustrated by the considerable number of claims for alimony that the courts receive each year, and the fact that the non-payment of alimony is the main cause of imprisonment in Chile . More reAs with income-generating strategies, a strong association was observed between household income level and expenditure-minimising strategies. Households with lower incomes were less likely to adopt these strategies than households with higher incomes. Having three or more employed members in the household reduced the odds, whereas the level of education of the head of the household did not have a significant effect. By contrast, receiving state financial support was found to have a significant negative effect on the likelihood of carrying out expenditure-minimising strategies. Although limited in scope and at a low level, households receiving state financial support were less likely to perform these types of strategies, whereas the implementation of localised lockdowns for two or more months increased the odds of carrying out expenditure-minimising strategies.In the context of the Global South, Chile was one of the first countries to be affected by the retreat of the state from the provision of welfare. The reduction in social assistance and the privatisation of public services took effect during the dictatorship of Augusto Pinochet (1973–1990). The burden of welfare provision was transferred from the state to families and individuals, with dramatic consequences for the middle- and low-income groups. During the debt crisis and subsequent structural adjustment of the 1980s in Latin America, the lack of state support meant that almost half the population fell into poverty . The comThe findings reported in this article provide new insights into the strategies adopted by households in Chile to cope with the economic effects of the COVID-19 pandemic. Previous literature on the subject, both in Latin America and in other countries, identified intra- and inter-household strategies involving support flows between extended family members. It highlighted the entry into the labour market of household members who were not employed prior to the crisis; the adjustments made in the consumption patterns of basic goods and services; reconfigurations in living arrangements, either to support vulnerable family members, or to incorporate members who contributed income or domestic work to the household, by increasing flows of financial support and the provision of care for grandchildren. The findings presented in this article confirm the value of these different strategies during the pandemic. They also identify other actions carried out by households, thereby contributing a more complete picture of the way in which households confront critical situations.The use of household savings and the sale of household goods emerged as a widely used income-generating strategy among Chilean households. This finding suggests that a process of decapitalisation of households was taking place, resulting from the liquidation of assets to generate additional income to cope with the crisis. By depleting the assets accumulated by households during years of effort, the decapitalisation process raises questions about how households will survive over time.A second significant finding concerns the generation of debt as a coping strategy, either to produce income or to reduce expenses. The results from the study show that indebtedness takes place both in the framework of informal networks − borrowing money from family, friends, neighbours or acquaintances − or, to a lesser extent, through the financial system. The analysis shows that a substantial proportion of households defaulted on servicing debts during the pandemic to reduce their expenditure.Two aspects of the Chilean context contribute to an understanding of these findings. Firstly, the significant number of social services privatised during the Pinochet dictatorship (1973–1990), as a consequence of the neoliberal turn of the State, had increased the financial burden on households and their vulnerability to the present crisis. Secondly, the Chilean economy has been characterised in recent decades by a systematic process of household financialisation, largely affecting poor households . This prAnother finding from the research highlights the key role that older people played in developing household responses to the crisis. Except for the case of three-generation households, those composed of older people were found to be the least affected by the loss of economic well-being during the crisis. They were also less likely to resort to coping strategies, either to generate income or reduce expenditure. This finding is largely attributable to the fact that the income of older people was derived primarily from pensions, which protected them from labour market fluctuations. In view of the negative impact of some of the strategies identified in the article on the long-term economic well-being of households , these households would seem to be better equipped to recover from the impact of the pandemic.This finding does not mean that older people in Chile enjoy more favourable economic conditions than the rest of the population. On the contrary, the low level of pensions resulting from a system based on individual capitalisation mean that they live in conditions of extreme economic precariousness. Data obtained from the Superintendent for Pensions  show that 50% of retired people in Chile received a pension below US $205 in 2020, an amount that represents half the legal minimum wage for that year (US $410). Although low, pensions provide a stable income stream for their households, which prevented their level of economic well-being from deteriorating further during the pandemic.The findings from the study suggest that having a source of family income not dependent on labour market flows is crucial in times of crisis. Furthermore, this observation lends support to the literature on intergenerational relationships that highlights the role of older people in contributing to the well-being of younger generations, whether through financial support, assistance with childcare or housing. Despite being more exposed to the risk of contracting and dying from COVID-19, older people were found to be less at risk economically, unless they had depleted their pension funds by drawing down their reserves as authorised by the government in July 2020. This finding could usefully be taken into account in discussions by the Chilean Congress about the future reform of the pension system and the introduction of a universal minimum income.In line with research in other countries on the social impacts of the COVID-19 pandemic, the findings reported here show the significant impact that the crisis had on women as household heads. They were more likely to carry out income-generating strategies, with adverse consequences for decapitalisation and indebtedness, although they were not more likely to implement expenditure-minimising strategies. A possible explanation for these somewhat unexpected finding is that the options for reducing expenses on basic goods and services, such as food, health, heating, water, gas and electricity, education and housing, were limited for the many female-headed households composed of lone mothers with children. Another explanation could be that female-headed households were used to getting by on a very low income, and to being in debt, as suggested by research on poor families in wealthy societies .Public health measures implemented early in the pandemic − localised lockdowns – were found to increase the likelihood of households adopting coping strategies. Lockdowns lasting less than two months made households more likely to implement strategies to generate additional income. Similarly, localised lockdowns lasting more than two months increased the likelihood of households adopting expenditure-minimising strategies. These findings provide evidence on the negative effect of measures that restrict people’s mobility on the domestic economy of households. By contrast, targeted financial aid in the early months of the pandemic, no matter how limited, made households less likely to adopt coping strategies aimed at reducing their consumption of basic goods and services and to generate debt when paying bills. These findings suggest that measures restricting mobility need to be accompanied by more generous universal financial assistance to compensate for the loss of household income.The question that remains following this analysis of household strategies during the early months of the pandemic concerns the longer-term effectiveness of these strategies. The data for this article were collected in July 2020 when the duration of the pandemic was uncertain. Future research on the subject using longitudinal survey analysis will allow us to identify whether the implementation of income-generating and expenditure-minimising strategies was able to cushion the impact of the crisis on the economic well-being of households in the longer term, and to identify in what type of households these strategies were most effective. Future research will also reveal the medium and long-term effects of the process of household decapitalisation and indebtedness on their coping strategies in helping or hindering the post-pandemic recovery process.


The paper structure of historical prints is sort of a unique fingerprint. Paper with the same origin shows similar chain line distances. As the manual measurement of chain line distances is time consuming, the automatic detection of chain lines is beneficial. We propose an end-to-end trainable deep learning method for segmentation and parameterization of chain lines in transmitted light images of German prints from the 16th Century. We trained a conditional generative adversarial network with a multitask loss for line segmentation and line parameterization. We formulated a fully differentiable pipeline for line coordinates’ estimation that consists of line segmentation, horizontal line alignment, and 2D Fourier filtering of line segments, line region proposals, and differentiable line fitting. We created a dataset of high-resolution transmitted light images of historical prints with manual line coordinate annotations. Our method shows superior qualitative and quantitative chain line detection results with high accuracy and reliability on our historical dataset in comparison to competing methods. Further, we demonstrated that our method achieves a low error of less than 0.7 mm in comparison to manually measured chain line distances. Since ancient times, paper has played a prominent role as a carrier for information. In the 16th Century, the only available paper was laid paper, which was manually produced in paper mills. Wood, old rags, and other ingredients were stamped and macerated in water into a pulp of fibers. Then, the paper was scooped by hand using a mold with a wire sieve made of closely spaced “laid” wires and perpendicular more widely spaced “chain” wires. After scooping the fibers from the vat, the remaining fibrous web on the wire sieve forms the paper . For eveIn this paper, we propose an end-to-end trainable method for segmentation and parameterization of chain lines in transmitted light images of German prints from the 16th Century. Our method exploits the power of deep neural networks in combination with prior knowledge from image and signal processing. We trained a conditional generative adversarial network by using a multitask loss for line segmentation and line parameterization. For the estimation of line coordinates, we designed a fully differentiable pipeline that comprises the steps of line segmentation, horizontal alignment and 2D Fourier filtering of line segments, line region proposals, and differentiable line fitting. For training and evaluation, we created a dataset of high-resolution transmitted light images of historical prints for which we manually annotated line coordinates. Our ChainLineNet learns to detect the chain lines with high reliability even if there are interferences caused by watermarks or if the lines are partly occluded by the ink of the artwork; cf. To digitize the paper structure of historical prints, several imaging techniques, e.g., beta-radiography, transmitted light photography, transmitted infrared, or thermography, can be applied. Transmitted light photography is a very fast application, inexpensive, and very easy to handle. Hence, additional image processing might be necessary due to interferences such as ink that remain visible. These interferences disappear in the images using the other modalities, but especially beta-radiography is only applicable for large institutions due to the necessary technical and financial input.There are a few approaches for the automated segmentation of chain lines of paper. Van der Lubbe et al.  assumed In our previous work , we traiLooking more generally at the task of line detection in the fields of wireframe detection and semantic and horizon line detection, deep learning has been extensively applied.Wireframe detection is the detection of line segments and junctions in a scene to describe all kinds of geometric objects or architectures . Huang eFor the application of semantic lines or horizon detection in natural scenes, Lee et al.  proposedAnother related group to our chain line segmentation method consists of contour detection methods using generative adversarial networks (GANs), as the chain lines and contours have a similar shape, and hence, both are sparse segmentation tasks. Contour detection datasets usually contain multiple ground truth annotations per image by different annotators, since the amount of annotated lines differs between the annotators depending on the subjective decision of the individual annotator whether a contour is important enough to be drawn. ContourGAN  uses a cOur proposed method for the segmentation and detection of chain lines in transmitted light images of historical prints is illustrated in Our chain line segmentation network is a conditional generative adversarial network (cGAN)  consistiWe jointly trained the generator network for the tasks of line segmentation and line parameterization in an end-to-end fashion by only using differentiable modules and functions inspired by known operator learning , while tG is fed with a random noise vector z to generate the output image y, while the discriminator D is trained to distinguish real images from fake images. In the case of conditional GANs, the output of the generator y is additionally conditioned to an input, e.g., an image x. Thus, the generator is trained to generate realistic-looking images that are directly related to the input images. The objective function of cGAN is formulated as:In generative adversarial networks (GANs), the generator network and the discriminator network are alternately optimized. The generator G learns to produce precise line segmentation masks D, which learns to detect those fake ones. The cGAN loss is generally combined with a task loss. We extended this approach by also including the line coordinates’ estimation process for the generator task loss:The cGAN principle can be directly applied to the line segmentation task. The generator SAC loss  and the The prediction of the line parameters is subdivided into the parts of line segmentation, prediction of the main line orientation to horizontally align the lines, 2D Fourier filtering, line region proposals, and line fitting with differentiable sample consensus (DSAC) , as illuAs can be seen in the centered 2D Fourier magnitude image in ing DSAC . Then, wNext, we rotated the predicted segmentation masks, the ground truth segmentation masks, and the ground truth line coordinates; see As convolution with a filter kernel in the time domain is elementwise matrix multiplication in the Fourier domain, we can simply multiply the 2D Fourier image with a matrix that has only zero elements except for a vertical band of width x-direction ) consists of the following steps:z, m line hypotheses a and intercept b of the line equation Line hypothesis sampling: Based on the predicted point coordinates Hypothesis selection: A scoring function x- and y-direction, for which we used the soft inlier scores as the weights.Hypothesis refinement: The hypothesis is refined by using the weighted Deming regression for line fitting , which iNext, we extracted for each bounding box the maximal AC. DSAC  formulatThe DSAC loss function, which we incorporated into our task loss function, is defined as:Since we applied DSAC to each bounding box region separately and the bounding box positions are determined automatically based on the segmentation output of the network, we needed to assign one ground truth line to each bounding box. We distinguish three cases: (1) If there is only one ground truth line inside the bounding box region, this one is selected. (2) If the region contains multiple ground truth lines, we chose the longest line. (3) Lastly, if there is no ground truth line inside the region, we selected the line with the minimal distance of its start and end points to the borders of the region.The DSAC loss minimizes the distance of the predicted lines to the closest ground truth lines; however, if too few bounding boxes are predicted, some ground truth lines will not be included. To account for these false negatives, we defined a second line loss term, the MLE loss, that picks for each ground truth line the closest predicted line of the best hypothesis Since the network architecture is fully convolutional, the complete images are fed to the GAN and are processed in the same manner as for training, resulting in the line predictions of the rotated image. Hence, to obtain the final line coordinate predictions of the original image, the inverse rotation is applied to the predicted lines.In this section, we describe our dataset for chain line detection in historical prints, we evaluate the performance of our method for line segmentation and line parameterization, and compare it to the state-of-the-art methods and to manual line measurements.The dataset consists of high-resolution grayscale transmitted light images of prints from the 16th Century, including portraits of Martin Luther and contemporaries. For our dataset, we selected in total 95 images in which the chain lines were recognizable by the human eye. All images contain chain lines that are either horizontally or vertically distributed at approximately the same distances.x and y coordinates of the start and end points, as well as the corresponding mask images  and the discriminator network were trained from scratch for 100 epochs with early stopping by using the Adam optimizer, a learning rate of  λ0=1000 , λBCE=0.Prior to training, we augmented our training and validation set in an offline manner with rotated images, i.e., rotations by 90 degrees were applied to produce the same number of vertical and horizontal lines. During training, we applied online data augmentation  of our previous work [ of our pn output  for our The quantitative results for line detection and parameterization for the test set consisting of 48 images and in total 342 correct lines are summarized in The comparison for the pixel mean line error of true positive lines, depicted in Next, we compare the chain line distance intervals to the reference measurements in ison see b. PatchUThe qualitative results are shown in Overall, our method achieves excellent performance, but there are some limitations. In the case of bent wires, our method cannot determine the exact chain line, but only an approximation, because we assumed straight lines for our model. Difficult images, where the chain lines are densely covered with ink, the paper is in an abraded condition, or when lines in the border area of the image are only partly depicted, can lead to false positives or false negatives. Under very difficult image conditions, the application of DSAC can lead to inaccurate line predictions, e.g., if a too large bounding box size is determined by our method or the estimated rotation angle is not accurate enough. In these cases, the bounding box might contain line segments or noise that do not belong to the actual line. Difficult cases need to be reviewed by art technologists, but our method achieves a high success rate such that it can greatly support the art technologists in their analysis of the artworks.We presented an end-to-end trainable deep learning method for chain line segmentation and parameterization in historical prints. In the experiments, we showed that our ChainLineNet achieves the best visual and quantitative chain line detection results for our historical print dataset. Moreover, the comparison of the automatically computed chain line distance intervals with the manually measured distance intervals by an art technologist shows a low error of less than 0.7 mm. The high accuracy and reliability of our method give the opportunity to automatically compare the chain line distances of a larger number of historical prints in order to draw conclusions about the origin of the papers. Thus, our automatic deep-learning-based method can be very beneficial to support the art historical and technological research of museums and libraries. Future work could build on the automatic chain line detection and distance computation to extract chain line distance patterns and perform a similarity search to identify moldmates.


The use of neural networks and reinforcement learning has become increasingly popular in autonomous vehicle control. However, the opaqueness of the resulting control policies presents a significant barrier to deploying neural network-based control in autonomous vehicles. In this paper, we present a reinforcement learning based approach to autonomous vehicle longitudinal control, where the rule-based safety cages provide enhanced safety for the vehicle as well as weak supervision to the reinforcement learning agent. By guiding the agent to meaningful states and actions, this weak supervision improves the convergence during training and enhances the safety of the final trained policy. This rule-based supervisory controller has the further advantage of being fully interpretable, thereby enabling traditional validation and verification approaches to ensure the safety of the vehicle. We compare models with and without safety cages, as well as models with optimal and constrained model parameters, and show that the weak supervision consistently improves the safety of exploration, speed of convergence, and model performance. Additionally, we show that when the model parameters are constrained or sub-optimal, the safety cages can enable a model to learn a safe driving policy even when the model could not be trained to drive through reinforcement learning alone. Autonomous driving has gained significant attention within the automotive research community in recent years ,2,3. TheEnd-to-end approaches have recently risen in popularity, due to the ease of implementation and better leverage of the function approximation of Deep Neural Networks (DNNs). However, the high level of opaqueness in DNNs is one of the main limiting factors in the use of neural network-based control techniques in safety-critical applications, such as autonomous vehicles ,9,10,11.We combine the safety cages with reinforcement learning by intervening on unsafe control actions, as well as providing an additional learning signal for the agent to enable safe and efficient exploration.We compare the effect of the safety cages during training for both models with optimised hyperparameters, as well as less optimised models which may require additional safety considerations.We test all trained agents without safety cages enabled, in both naturalistic and adversarial driving scenarios, showing that even if the safety cages are only used during training, the models exhibit safer driving behaviour.We demonstrate that by using the weak supervision from the safety cages during training, the shallow model which otherwise could not learn to drive can be enabled to learn to drive without collisions.This work extends our previously developed Reinforcement Learning (RL) based vehicle following model  and virtThe remainder of this paper is structured as follows. A brief overview of relevant works in this field is given in this Section. For a more in-depth view of deep learning based autonomous driving techniques, we refer the interested readers to the review in . One of Since then, these works have inspired a number of deep learning techniques, with imitation learning often being the preferred learning technique. For instance, Zhang et al.  and Pan However, RL-based techniques have shown promising results for autonomous vehicle applications ,37,38. TVirtual safety cages have been used in several cyber-physical systems to provide safety guarantees when the controller is not interpretable. The most straightforward application of such safety cages is to limit the possible actions of the controller to ensure the system is bounded to a safe operational envelope. If the controller issues commands that breach the safety cages, the safety cages step in and attempt to recover the system back to a safe state. This type of approach has been used to guarantee the safety of complex controllers in different domains such as robotics ,45,46,47In our previous work , we deveHere, we extend on this approach by utilising the safety cages to improve the safety of a RL based vehicle motion controller, and using the interventions of the safety cages as weak supervision which enables the system to learn to drive more safely in an online manner. Weak supervision has been shown to improve the efficiency of exploration in RL  by guidit, the agent takes an action Reinforcement learning can be formally described as a Markov Decision Process (MDP). The MDP is denoted by a tuple {function . As showE the Q-function is denoted by:Deep Deterministic Policy Gradient (DDPG)  extends The Q-function can be estimated by the Bellman equation for deterministic policies as:As the expectations depend only on the environment, the critic network can be trained off-policy, using transitions from a different stochastic policy with the state visitation distribution J with respect to the actor parameters The actor network parameters gradient  from theFor updating the networks, mini-batches are drawn from a replay memory networks , which cTo encourage the agent to explore the possible actions for continuous action spaces, noise is added to the actions of the deterministic policy Here, the chosen noise process  process , which gv is the velocity of the host vehicle in m/s, and Virtual safety cages provide interpretable rule-based safety for complex cyber-physical systems. The purpose of these safety cages is to limit the actions of the system to a safe operational envelope. The simple way to achieve this, would be to limit the upper or lower limits of the system’s action space. However, by using run-time monitoring to observe the state of the environment, the safety cages can dynamically select the control limits based on the current states. Therefore, the system can be limited in its possible courses of action when faced with a safety-critical scenario, such as a near-accident situation on a highway. We utilise our previously presented safety cages , which lThe TTC and TH metrics were chosen as the states monitored by the safety cages as they represent the risk of potential collision with the vehicle in front, thereby providing effective safety measurements for our vehicle following use-case. We utilise two metrics as the TTC and TH provide complimentary information; the TTC measures time to a forward collision assuming both vehicles continue at their current speeds, whilst TH measures distance to the vehicle in front in time and makes no assumptions about the lead vehicle’s actions. For example, when the host vehicle is driving significantly faster than the vehicle in front, as the distance between the vehicles gets closer the TTC approaches zero and correctly captures the risk of a forward collision. However, in a scenario where both vehicles are driving close to each other but at the same speed, the TTC will not signal a high risk of collision even though in this scenario if the lead vehicle begins to break, the two vehicles would be in a likely collision. In such a scenario, the two vehicles will have a low headway, therefore monitoring the TH will correctly inform the safety monitors of a collision risk.b, is then chosen as the largest braking value between the two safety cages and the RL agent as given by bTH2, except for emergency braking manoeuvrers, which occurred on average once an hour, which used an acceleration in the range 2. The output from the RL agent is the gas and brake pedal values, which are continuous action values used to control the vehicle. As in  m/s2. At the start of the episode, the coefficient of friction is randomly chosen in the range For the naturalistic driving, similar lead vehicle behaviours were used to those during training, with velocities in the range  m/s and acceleration  m/sr Critic  based veThe results from the naturalistic driving scenarios are summarised in Utilising machine learning to expose weaknesses in safety-critical cyber-physical systems has been shown to be an effective method for finding failure cases effectively ,67. We uThis reward function encourages the adversarial agent to minimise the headway and make collisions happen, while capping the reward at 100 ensures that the reward does not tend to infinity as the headway reaches zero.As this lead vehicle used in the adversarial testing can behave very differently to those seen during training, this testing focuses on investigating the models’ generalisation capability as well as their response to hazardous scenarios. Each DDPG model is tested under two different velocity ranges; the first limits the lead vehicle’s velocity to the same as the training scenarios with In this paper, a reinforcement learning technique combining rule-based safety cages was presented. The safety cages provide a safety mechanism for the autonomous vehicle in case the neural network-based controller makes unsafe decisions, thereby enhancing the safety of the vehicle and providing interpretability in the vehicle motion control system. In addition, the safety cages are used as weak supervision during training, by guiding the agent towards useful actions and avoiding dangerous states.We compared the model with safety cages to a model without them, and show improvements in safety of exploration, speed of convergence, and the safety of the final control policy. In addition to improved training efficiency, simulated testing scenarios demonstrated that even with the safety cages disabled, the model which used them during training has learned a safer control policy by maintaining a minimum headway of 1.69 s in a safety-critical scenario, compared to 1.53 s without safety cage training. We additionally tested the proposed approach on shallow models with constrained parameters, and showed that the shallow model with safety cage training was able to drive without collisions, whilst the shallow model without safety cage training collided in every test scenario. These results demonstrate that the safety cages enabled the shallow models to learn a safe control policy while otherwise the shallow models were not able to learn a feasible driving policy. This showed that the safety cages add beneficial supervision during training, enabling the model to learn from the environment more effectively.Therefore, this work provides an effective way to combine reinforcement learning based control with rule-based safety mechanisms not only to improve the safety of the vehicle, but also incorporating weak supervision in the training process for improved convergence and performance.This work opens up multiple potential avenues for future work. The use-case in this study was a simplified vehicle following scenario. However, extending the safety cages to consider both longitudinal and lateral control actions, as well as potential objects on other lanes, would allow the technique to be applied to more complex use-cases such as urban driving. Moreover, comparing the use of the weak supervision for different use-cases or learning algorithms  would help with understanding the most efficient use of weak supervision in reinforcement learning. Furthermore, extending the reinforcement learning agent to use more high dimensional inputs, such as images, would allow investigation into how the increased speed of convergence helps in cases where the sample inefficient reinforcement learning algorithms struggle. Finally, using the safety cages presented here in real-world training could better demonstrate the benefit in both safety and efficiency of exploration, compared to the simulated scenario presented in this work.


Human mobility data are indispensable in modeling large-scale epidemics, especially in predicting the spatial spread of diseases and in evaluating spatial heterogeneity intervention strategies. However, statistical data that can accurately describe large-scale population migration are often difficult to obtain. We propose an algorithm model based on the network science approach, which estimates the travel flow data in mainland China by transforming location big data and airline operation data into network structure information. In addition, we established a simplified deterministic SEIR (Susceptible-Exposed-Infectious-Recovered)-metapopulation model to verify the effectiveness of the estimated travel flow data in the study of predicting epidemic spread. The results show that individual travel distance in mainland China is mainly within 100 km. There is far more travel between prefectures within the same province than across provinces. The epidemic spatial spread model incorporating estimated travel data accurately predicts the spread of COVID-19 in mainland China. The results suggest that there are far more travelers than usual during the Spring Festival in mainland China, and the number of travelers from Wuhan mainly determines the number of confirmed cases of COVID-19 in each prefecture. Human mobility has become a hot research topic in the scientific community in recent years because of its application value in many fields ,3,4,5,6.To cope with the lack of human mobility data, researchers have established spatial interaction models to estimate travel flow by using local statistical survey data. The main spatial interaction models are gravity models and radiation models ,15, whicRecently, some large-size Internet companies have integrated mobile device location big data obtained from users and released a human mobility data product, opening up a new situation for estimating travel flow data ,22,23. AIn this study, we propose an algorithm model that combines mobile device location big data with real airline operation data to estimate the dynamic travel flows because it is difficult to collect the number of inter-prefecture travelers. In addition, we established a simplified deterministic SEIR-metapopulation model based on the early spread of COVID-19 in mainland China to demonstrate the use of estimated travel flows.The original data used in the study were obtained from the migration big data platform developed by Baidu and Tencent. Baidu and Tencent are the two largest Internet companies in China and have more than 500 million active users, covering almost all mobile phone users in the country. They provide location services in their applications, and the collected location big data can fully and truly reflect the status of human mobility. The Baidu Map Migration Big Data Platform calculates and processes hundreds of billions of positioning data collected every day and releases the migration proportion data from the provincial and prefecture levels in mainland China . A detaiThe daily airline operation data of all civil airports in mainland China were obtained from VariFlight Company , includiIn order to reconstruct the spread of COVID-19 in mainland China using a mathematical model, we obtained COVID-19-related data from the National Health Commission of China , includiAll the data mentioned above are anonymous aggregated data and do not involve personal information.In order to estimate the human mobility patterns in mainland China and build a human mobility network (directed network) between all prefectures, we propose a data fusion algorithm model based on the network science approach, which can estimate travel flow data in mainland China. Here, we use the network adjacency matrix The modeling is mainly carried out in three steps. First, the relationship between the daily total departure/arrival population of different prefectures is obtained from the migration proportion data and converted into a bipartite network. Here, the total departure population of a prefecture indicates the number of all individuals leaving this prefecture on one day, and the total arrival population of a prefecture indicates the number of all individuals entering this prefecture on one day. This bipartite network is undirected and weighted and we can estimate the total departure/arrival population of all prefectures by using it if the total departure/arrival population of an arbitrary prefecture is known. Second, the total departure/arrival population of an arbitrary prefecture  is estimated using the ratio estimation method combined with airline operation data and the proportions of transportation modes. Lastly, using the breadth-first traversal algorithm, the total departure/arrival population of all prefectures is estimated. Furthermore, the travel flows between any two prefectures are estimated. More details about the model algorithm are described in Step 1: Generate star structure network. All prefectures are coded and sorted, and the migration proportion data of each prefecture are sequentially converted into a star network of arrival type and a star network of departure type. Specifically, the migration proportion data of a prefecture list 100 sources, 100 destinations, and the proportion of people on each route out of the total people entering (or leaving) the prefecture. A detailed description of the migration proportion data is available in Here, the star network of arrival type can be expressed as Step 2: Generate a bipartite network. For any two prefectures Under the premise that there are data on the migration proportions In the model, we implemented this iterative estimation process by traversing the bipartite network. First, in order to build a bipartite network, we generated a node of arrival type and a node of departure type in the bipartite network that correspond to each prefecture. For example, corresponding to prefecture Step 3: Estimate the total departure/arrival population of all prefectures. To estimate the total departure/arrival population of all prefectures, we need to input the state value of an arbitrary node of the bipartite network According to the estimation method introduced above, the number of travelers on multiple departure routes of prefecture Furthermore, the ratio estimation method is used for estimating the total departure population of prefecture After estimating the total departure population of prefecture Step 4: Build the human mobility network. In this study, we describe the human mobility pattern in mainland China in the form of a weighted directed network. The nodes of the human mobility network are all prefectures in mainland China. Edges in the network characterize the state of travel between the prefectures. Specifically, the matrix element Here, we estimate the travel flows between prefectures using the estimation results of the total departure/arrival population of all prefectures and the migration proportion data. First, we use the estimation results of the total departure population of all prefectures. For example, the estimated total departure population of prefecture The outbreak of COVID-19 in Wuhan coincided with the Spring Festival travel season in China, and a large number of returnees left or passed through Wuhan. After clarifying the infectiousness of COVID-19, the Chinese government adopted strict intervention strategies, including locking down Wuhan and restricting travel across mainland China. In order to verify the effectiveness of the travel flows estimated by our model in predicting epidemics, understanding the early propagation dynamics of COVID-19, and evaluating the effectiveness of intervention strategies, we established a simplified spatial mechanism model of COVID-19 to simulate its spread in mainland China.Based on the traditional SEIR compartment model we established a deterministic SEIR-metapopulation model that incorporates human mobility factors and considers intervention strategies such as quarantine and travel restrictions . In detaIn the metapopulation model, travel flows on different dates are considered to be independent of each other, that is, in each time step, the movement of the individuals in the previous time step is not considered. The quantity of state of each compartment in each subpopulation is updated according to the human mobility network adjacency matrix Considering that some infected persons with obvious symptoms cannot participate in travel normally, the proportion of symptomatic infected individuals that can travel normally is assumed to be After updating the individual movements of all subpopulations, the transfer of individuals between different compartments in each subpopulation based on the epidemiological natural history of COVID-19 and the implementation of intervention strategies is modeled by the following:Medical researches show that individuals with no symptoms (during the incubation period) infect others just like the symptomatic ,40,41. Tof China , for indWe simulated the spread of COVID-19 from 1 January 2020 and the simulation was divided into two periods. The first period was from 1 January to 23 January (Wuhan was in lockdown from 23 January), in which period, the estimated travel flow data were used for modeling the spatial propagation of COVID-19 in mainland China. In order to simplify the model, we set some parameters to be constants in the two periods. The average number of daily effective contacts of individuals was set to According to related research on social contact patterns, the average number of social contacts in China has decreased significantly after the Chinese government clarifying the infectiousness of COVID-19 ,43. ThusSome parameters in the model were unknown, and the set of unknown parameters was denoted as m (CNLP) . Thus, tIn order to accurately understand the human mobility patterns in mainland China, we designed an inter-prefecture travel flow estimation model based on mobile device location big data and airline operation data. In order to verify the effectiveness of the travel flow data estimated by our model in predicting epidemics, first, we conducted a correlation analysis on the cumulative number of confirmed cases of COVID-19 and the number of travelers from Wuhan. fmincon function in MATLAB. A set of possible values of the parameters were obtained, which are shown in the Furthermore, we established a deterministic SEIR-metapopulation model that reproduces the spread of COVID-19 in mainland China to demonstrate the significance of the estimated travel flow data for the spatial spread mechanism model of epidemics. In the early stage of the epidemic, the health department had insufficient knowledge of the new virus and a lack of diagnostic programs, which resulted in a large difference between the number of reported confirmed cases and the actual number of infections in Wuhan. On the other hand, infection cases of other prefectures appeared late, so the reported case data are more accurate. Based on the above considerations, we used the cumulative number of confirmed cases in mainland China (excluding Hubei Province) from January 24 to February 17 for model parameter fitting. We solved this nonlinear optimization using the In this study, considering the availability and accuracy of airline operation data and the large sample size of the mobile device location big data, we designed an algorithm model to estimate the inter-prefecture human travel flow in mainland China. The data required for the model are mainly the proportion of migration and the proportion of transportation modes. In other areas where such data are available, the human mobility pattern can also be estimated by this model. Our estimated human mobility pattern in mainland China shows that individuals’ travel distances are subject to long-tailed distribution, which is consistent with the general conclusions of human mobility in other studies. In addition, individuals in China are more inclined to travel between prefectures of the same province. Compared to traditional statistical survey data, mobile device location big data can provide detailed and dynamic personnel location changes in real time, and the large-scale human mobility patterns estimated using mobile device location big data can better reveal the characteristics of human social activities.The use value of travel flow data estimated by our model is demonstrated in the work reproducing the spread of COVID-19. The cumulative number of confirmed cases in each prefecture is highly correlated with the estimated number of travelers from Wuhan. Moreover, in the established spatial spread mechanism model, the predicted curve fits the real confirmed case data well. However, there are several limitations in epidemic simulation modeling. First, it should be pointed out that we did not consider the stochasticity factor in the simulation and we simply established a deterministic epidemic model. Second, we fitted the epidemic parameters via using just one time series data. When solving nonlinear programming problems, what we want to do most is to calculate a global minimizer. However, this is very difficult, and finding a local minimizer through numerical algorithms is the best attempt we can do. Thus, it is difficult to guarantee that a unique set of values of parameters that gives the best fit can be obtained. Therefore, the uncertainty of the solution will cause that we cannot guarantee that the obtained parameters fit reality because the values of the parameters have certain realistic epidemiological significance. Our simulated epidemiological transmission may only guarantee that the number of confirmed cases fit reality, while the dynamics of other compartments may be different from the real scenario. We hope that the public health department will release more anonymized cases data, and that researchers with these data will carry out more in-depth studies on the epidemiological parameters.In addition, considering the complexity of establishing a stochastic SEIR model on 337 prefectures, we simply divided mainland China into three subpopulations in this study. Follow-up work can establish metapopulation models for all prefectures to obtain higher resolution simulation results. Furthermore, researchers can obtain the proportional data of transportation modes among all prefectures in mainland China, based on which number of inter-prefecture travelers with different transportation modes can be calculated. Therefore, researchers can model and study the spread of infectious diseases with different means of transportation.


We present here linear and nonlinear finite element analyses of a newly designed deployable rapid assembly shelter (DRASH J) manufactured by DHS Systems. The structural analysis is carried out in three stages. Firstly, single composite tubes (struts) under three-point bending are modeled with five layers of orthotropic materials in three different orientations and the simulation results are compared with the actual test data for validation. Secondly, a comprehensive structural model for the entire shelter is constructed with the consideration of two types of strut scissor points, namely natural and forced scissor (crossing) points, as well as partial-fixed hub joints, which allow rotations along individual hub slots (grooves). Finally, a simplified structural model is created by introducing fixed joints for the scissor points as well as rigid links for the hubs. With sufficient verifications with experiments and different modeling methods, linear and nonlinear finite element analyses are then carried out for both the comprehensive and simplified shelter models. Based on the simulation results, we are able to identify a few critical issues pertaining to proper design and modifications of such shelter systems, such as various end wall supports pertaining to the overall structural stability. The deployment of deployable rapid assembly shelters (DRASH) in a field emergency can be accomplished minutes after arrival at the crisis areas for both military and civilian missions. DHS Systems provides state-of-the-art technology in such portable sheltering. The key frame of the shelter comprises of composite tubing structures with pre-attached interior and exterior covers. So far, limited study has been performed for the entire structure stability of the J shelter with respect to snow load. The research presented in this work is particularly important because it provides the first linear and nonlinear structural analysis for the entire J shelter as well as necessary verification comparisons with both experiments and different modeling methods.The structural analysis is carried out with three levels of modeling. Firstly, single composite tubes (struts) under three-point bending are modeled with five layers of orthotropic materials in three different orientations and the simulation results are compared with the test data for validation. Secondly, a comprehensive structural model for the entire shelter is created with two different types of scissor (crossing) points, namely natural and forced scissor points, as well as a realistic hub model which allows one rotational degree of freedom within the hub slot (groove). Finally, a simplified structure is introduced, in which all scissor points are replaced with fixed joints, whereas hubs are substituted by a set of translational rigid links. For the entire structure analysis, all struts are modeled as isotropic and homogeneous three-dimensional beam elements of which the effective Young’s modulus and the bending rigidity are derived in the first stage based on both simulation and experimental data. In the following section, we illustrate the mathematical model and the key physical assumptions corresponding to the initial assemblage process, the mechanical behavior of the composite beams, and various strut connections within the shelter structure. The key findings and assumptions will be reiterated in P and l is the span of the beam.In general, each strut consists of five layers of fiber-reinforced composite materials wrapped around in three different orientations to produce high strength with minimum weight. Since the J shelter is composed of over a hundred struts interconnected with pins and hubs to form the main shelter arch, it could be an insurmountable task to model the entire shelter structure with such composite shell models. Thus, for simplicity, the composite struts are modeled as three-dimensional isotropic and homogeneous beam elements in the global models. The effective Young’s modulus is derived from the three-point bending test and can be expressed asm, h, and z represent the meridional , hoop , and radial directions of the composite tube, respectively. The orientation of an orthotropic layer refers to the angle between the meridional direction and the major orthotropic material principal direction. Of course, Poisson’s ratios must satisfy the usual compatibility condition In For the structural analysis, we start with linear analyses of both comprehensive and simplified models. Then, we employ the linearized buckling, collapse, and nonlinear analyses, which take into account the geometrical nonlinearities, in order to calculate the maximum snow load that the entire shelter structure can sustain prior to structural instability. Furthermore, the reaction forces at the shelter supports are also calculated with respect to the collapse load.The basic concept of nonlinear structural analyses can be best illustrated in the following iteration proceduret and It is obvious that in the linear analysis, the tangent stiffness matrix By substituting the first equation in Equation  into EquConsequently, implementing the second equation in Equation , we obtaIn fact, Equation  can alsoTo obtain the collapse point as well as the load-displacement curve beyond the initial buckling point, i.e., to derive the post-buckling curve, we can use a displacement-controlled (LC) or load-displacement-constraint method (LDC) loading sequence. The basic concept of the LDC method is to derive the load scaling factor Equation ,(7)t+ΔtSince we introduce an additional unknown, ferences ,5,6,7,8.The computer simulations presented in this study are performed with the ADINA program, which consists of the program on heat transfer in solids ADINA-T, the program on displacements and stresses ADINA, the program on fluid flows and heat transfer ADINA-F, the pre-processor ADINA-IN, and the post-processor ADINA-PLOT. Both the geometry and the corresponding mesh can be generated in ADINA-IN. A detailed description of the recent development of the ADINA program is available in references ,10,11.In this section, we discuss some in-depth modeling procedures, namely, the three-point bending of a single composite strut, the natural and forced scissor points of two crossing struts, and the hubs.P). The cross-sectional properties of the composite tubes are listed in l), and the center point loading (P) are As shown in The three-point bending experiment of the J shelter has produced a deflection of Case 1Four lines share a common node at the intersection point, which represents a completely fixed joint.Case 2Four lines rigidly linked through four end points occupying the same geometrical point, which represents the same physical model as Case 1, however, its finite element procedure is different.Case 3Four lines share a common point, at which only the translational degrees of freedom are constrained.Case 4Rigid links are separately employed along the two crossing struts, which means, within the crossing struts, only the translation degrees of freedom are constrained.Case 5A truss element is introduced to physically connect two points at the vicinity of the intersection point.In the J shelter, there are numerous scissor points between struts which can be divided into two basic groups. One of them is the so-called natural scissor point group which does not introduce significant initial stress within the composite strut, and the other one is called the forced scissor point group, which does introduce significant initial bending, i.e., initial stress, during the structural assemblage. Notice, however, although the struts in such scissor points are connected with a pin, if we model the composite tube as a beam, the rotational degrees of freedom along the struts are continuous just as all the translational degrees of freedom. To verify our assumptions, we introduce two sets of mathematical models as shown in The center point deflection results are used as measures of the accuracy of various constraints and boundary conditions. It is obvious from With respect to the hubs, as illustrated in The entire structure models, as shown in According to To properly account for the snow load, we use the following conventional mass lumping procedure in finite element methods to redistribute the equivalent snow load to beam joints,The distributed snow loads are illustrated in In finite element analyses, the collapse load of a structure can be obtained with linearized buckling, collapse, and nonlinear analyses. In general, linearized buckling analysis is not as accurate as the other two approaches and depends very much on the starting point. However, to obtain an accurate estimation of the collapse load, in this work, we employ all three procedures. As shown in Since the entire shelter is supported by two rows of joints on each side, it is also understood from the physically intuition that the interior and exterior rows of pin points can be subjected to both compression and tension. Such distributions of reaction forces are confirmed in The main contribution of this work is to establish a finite element analysis protocol for a series of DRASH shelters. In particular, an in-depth study of the J shelter is carried out using the ADINA finite element package. The key contributions of this study are two-fold: firstly, from a composite shell modeling of a typical strut, we derive the equivalent Young’s modulus and bending rigidity of the shelter strut; and secondly, we establish two structural models, one with fairly realistic finite element models for the scissor points and hubs, and the other with simplified boundary and constraint conditions. The final conclusion based on both structural models is that the maximum snow load that the J shelter can withstand is near (1)The static load-displacement curve suggests that the structure is strong and the self-weight of the shelter can be ignored. In addition, the shelter roof displacement is relatively small under prescribed snow loads.(2)The entire structure will collapse if subjected to (3)The designs of scissor points and hubs are detrimental to the entire structural stability. In particular, hubs at certain locations are prone to rotation, and preventive measures, such as to align the hub against the rotational direction or make the hub as symmetric as possible, should be considered.(4)The stability of risers and the rigidity of center joints are also important design factors with respect to the entire structural safety. In particular, unsymmetric collapse modes must be avoided by improving the resistance of rotations at the center joints. In particular, by introducing end walls, the resultant collapse load is increased to In summary, through the finite element analysis and some comparison with the existing experimental data, we derive the following design information:The mathematical models and finite element solutions presented in this paper clearly demonstrate the potential of using similar simulation procedures to achieve better and more optimal designs of various portable shelters with composites.


This paper proposes a method for detecting non-line-of-sight (NLOS) multipath, which causes large positioning errors in a global navigation satellite system (GNSS). We use GNSS signal correlation output, which is the most primitive GNSS signal processing output, to detect NLOS multipath based on machine learning. The shape of the multi-correlator outputs is distorted due to the NLOS multipath. The features of the shape of the multi-correlator are used to discriminate the NLOS multipath. We implement two supervised learning methods, a support vector machine (SVM) and a neural network (NN), and compare their performance. In addition, we also propose an automated method of collecting training data for LOS and NLOS signals of machine learning. The evaluation of the proposed NLOS detection method in an urban environment confirmed that NN was better than SVM, and 97.7% of NLOS signals were correctly discriminated. The global navigation satellite system (GNSS) is currently used in various location-based services. As of 2020, various countries have launched and are operating their own positioning satellites, and there are approximate 30 satellites available for positioning on average, and thus the availability of satellite positioning is expected to significantly increase. One of the most sought-after location-based services is stable positioning in urban environments with many buildings. However, despite the increase in the number of positioning satellites, large positioning errors occur suddenly in urban environments. This positioning error is caused by multipath signals, where GNSS signals are reflected or diffracted by buildings and other objects . There aOn the other hand, in an urban environment with many buildings, GNSS signals emitted from out-of-sight satellites hidden behind buildings are often received by the antennas through reflection and diffraction. In this case, a larger-than-normal error occurs in GNSS positioning . This isBecause the pseudorange observed by the NLOS signal is heavily biased against the true distance, the positioning results are usually significantly deteriorated when the pseudorange of the NLOS signal is used for positioning calculations . This psA method of NLOS discrimination using GNSS receiver output is proposed for NLOS discrimination using signal-to-noise ratio (SNR) ,8,9. ThiIn this study, we proposed a novel NLOS multipath detection method that can employ machine learning techniques to enhance the GNSS positioning performance in urban environments, where NLOS multipath signals lead to major positioning errors. The basic idea of the proposed method is to integrate a discriminator in the GNSS signal processing that discriminates NLOS from the results of the GNSS signal correlation outputs instead of discriminating NLOS from GNSS observations such as SNR. The GNSS signal correlation result is the primary GNSS output and contains information on NLOS signals. The proposed method learns the “features of the shape of the correlation function”, which is the output of GNSS signal correlation processing. We propose two supervised learning methods, one with a support vector machine (SVM) and the other with a neural network (NN), and compare their levels of performance.NLOS multipath errors have long been studied as a serious problem in GNSS positioning. The countermeasures against NLOS multipath errors can be classified into four categories: (1) the rejection of GNSS positioning results that contain such errors, (2) the identification of NLOS signals from GNSS observations and their exclusion from the positioning calculations, (3) the estimation and correction of NLOS multipath errors, and (4) the suppression of NLOS reception in the RF section. The latter method is a more fundamental countermeasure for NLOS multipath errors.(1) The rejection of GNSS positioning results containing NLOS multipath errors is a countermeasure against such errors. Several methods have been proposed to detect jumps in GNSS positioning, such as methods using a Chi-square test  in posit(2) NLOS signals are identified from GNSS observations and excluded from the positioning calculation, which is the most studied NLOS multipath reduction method. Receiver autonomous integrity monitoring (RAIM)-related techniques are used to detect large GNSS ranging errors in the observed GNSS pseudorange . However(3) An estimation and correction is an ideal countermeasure to deal with NLOS multipath errors. If an NLOS signal is rejected in an urban environment, problems such as an insufficient number of satellites and a deterioration of the satellite geometry will occur. A few methods for correcting NLOS multipath errors using 3D maps have been proposed ,22. Howe(4) Suppression of the NLOS reception in the RF section is a more fundamental countermeasure for NLOS multipath errors. For example, the use of a choke ring antenna  and a duBy contrast, recent developments in machine learning techniques have led to significant research into improving the GNSS positioning accuracy through machine learning ,29,30,31The contributions of this paper are as follows.The idea of direct machine learning of a GNSS signal correlation output, which is the most primitive GNSS signal processing output, is an innovative approach.In this study, multiple machine learning methods  are applied to compare the performance of an NLOS signal detection. There have been few examples of applying an NN to GNSS signal processing, and NLOS discrimination using an NN has been a significant achievement.We devised a data acquisition device that automatically collects labeled NLOS signals to collect training data, which is a problem in supervised machine learning.We applied the proposed machine learning method to GNSS signals acquired in a real urban environment.The remainder of this paper is organized as follows: First, in In this study, an NLOS multipath discriminator using a GNSS signal correlation output is implemented in a software GNSS receiver. Various classification methods using machine learning have been proposed. In this study, supervised machine learning methods, SVM and NN, are applied to the NLOS classification problem. An SVM uses a kernel trick technique to transform the input data to find the optimal bounds of the target classes. The designers of a discriminator need to extract the NLOS features from the input signal themselves, and the SVM classifies the signal based on the extracted features. For this reason, it is important for an SVM to determine features that can fully explain the NLOS signal correctly. By contrast, an NN is frequently used in classification problems. An NN is a computational model inspired by the manner in which biological neural networks in the human brain process information. Unlike an SVM, in an NN, features for classification are automatically acquired during the learning process. Therefore, the performance does not depend on the features extracted by the designer, as in an SVM. However, an NN generally requires a large number of training data. The method for obtaining a labeled NLOS signal for training is described in A feature of the proposed method is that it discriminates the NLOS signal by directly learning the correlation output of the NLOS multipath signal; the correlation function of the NLOS multipath signal is significantly distorted compared to an LOS multipath signal with a direct signal. First, the shape of the correlation function for the LOS and NLOS multipath signals is clarified. We denote The case in which the direct signal In In the case of an NLOS correlation function, there is no direct signal, and the first reflected signal is distorted by the second reflected signal. The NLOS signal correlation function is a combination of the reflected or diffracted signal correlations. The multipath amplitude ratio of the NLOS signals From Therefore, the NLOS correlation function is more susceptible to the second signal than the LOS correlation function, resulting in a large distortion of the correlation function. For this reason, the NLOS correlation function does not have an ideal clean triangular shape.We also consider the effect of the relative phase on the correlation function. From Equations  and 4),,4), the We use these phenomena to detect NLOS signals. We created an NLOS classifier based on the machine learning of the features of the NLOS correlation shape. To realize machine learning from the features of the correlation shape, we extract the features of the NLOS correlation function using an actual dataset and use it to construct the NLOS classifier. However, a typical GNSS receiver only outputs a PVT solution. Therefore, we use a software GNSS receiver to obtain the signal correlation outputs in GNSS signal processing.The next question is how to extract and discriminate the features of the NLOS from the distorted NLOS correlation output. In this study, we first extract the geometric features of the NLOS correlation output and attempt to classify it using an SVM. In addition, NLOS features are automatically extracted using an NN to identify the NLOS.As mentioned in the previous section, the direct and reflected signal correlation functions are combined in the LOS multipath signals. Consequently, the reflected signals distort the code correlation function of the direct signal, and the resulting code-tracking error causes an LOS multipath error. NLOS signal does not contain direct signals; the combined correlation function is more distorted than that in the case of LOS multipath signals.jth in-phase correlator output at time k is represented as follows:k is as follows:We use multiple correlator outputs to extract NLOS features for SVM. GNSS incoming signal is multiplied by the in-phase (I) and quadrature (Q) locally generated carriers, and then the signals are correlated with a slightly shifted PRN code generated in the GNSS receiver. We use the multi-correlator structures; thus, Signal strength versus elevation angleNumber of local maxima of the correlation outputsDistribution of the delay of the maximum correlationIn developing a successful SVM classifier, appropriate feature extraction is very important. We extract the features of the NLOS signals from multi-correlator outputs for SVM to construct the NLOS classifier. In this study, we extract the following features:The magnitude of the correlation peak is related to the GNSS signal strength. In general, the signal strength of the reflected or diffracted signals is weaker than that of the directly received signals. As a result, the signal strength can be used to detect NLOS signals. Even in ordinary GNSS positioning calculations, the SNR, which represents the GNSS signal strength, is widely used to exclude NLOS multipaths and select satellites for the positioning calculations ,8. BecauThe coefficients t is calculated as follows:M is the total number of correlations that are non-coherently integrated. The value of The NLOS feature M times. It is expected that the number of local maxima is almost 1 in the case of LOS signals. By contrast, the number of local maxima will increase in the case of NLOS signals.According to M times. It can be concluded that the variance of delay of the NLOS correlation output is greater than that of the LOS signal.In the LOS correlation function from In constructing the NLOS signal classifier, we use an SVM, one of the supervised machine learning algorithms . SVM usey output from a neuron is represented by an input element b.We employ neural networks to construct NLOS signal classifiers. A neural network is a computational model inspired by the manner in which biological neural networks in the human brain process information. A signal b are adjusted using the backpropagation method in the neural networks. For the backpropagation method, a loss function for calculating the difference between the output and correct value is defined, and the gradient is optimized to be minimized between the output and input layers.The neuron fires when the sum of the weighted inputs exceeds a threshold. A function that determines how to fire an input signal is called an activation function A neural network can be decomposed into an input layer, a hidden layer, and an output layer. In the classification case, the number of output layer units is the number of classification classes. Because this research classifies LOS and NLOS signals, there are two output layers. First, as a preprocessing of the input data, we normalize the output of the GNSS signal correlation values using the relationship between the satellite elevation angle and the signal strength. To remove the variation in amplitude owing to the satellite elevation angle, similar to with an SVM, Equation  is used.In this study, we create an NLOS detection classifier using an SVM and an NN. We use the shape of the GNSS correlation outputs to detect the NLOS signals. There are many types of signal correlators, such as early late correlators, narrow correlators, and double delta correlators. The correlation shape, which is the output of the correlators, depends on the number of correlation points and the sampling frequency of the front-end. The receiver bandwidth also affects the correlation shape. In the consumer’s GNSS receiver, these correlator models are a total black box, and we cannot obtain the correlation output. Thus, we use a software GNSS receiver to address this problem. Software receivers are widely recognized and used in GNSS research because of their configurational flexibility and ease of use. We use a self-designed GNSS signal correlator by applying a software GNSS receiver and use a front-end  GNSS-SDRLIB, which is an open-source software GNSS receiver . The samTo obtain the LOS and NLOS reference data, we use fish-eye images and verify the NLOS signals from the images. A large number of training data are required for machine learning, which are not easy to collect through a manual check of the fish-eye images. Furthermore, to obtain accurate LOS and NLOS references, accurate azimuth angle information of a fish-eye camera is required to project the satellite position onto the fish-eye image. Therefore, in this study, we created a device that automatically collects the NLOS reference signals for training.(i)First, the device captures a sky image using a fish-eye camera. Two GNSS receivers record GNSS raw observations .(ii)Second, the sky image is binarized to recognize buildings that constitute obstacles to a direct signal. A binarized sky image can be used as a mask to determine the NLOS signal.(iii)Next, the elevation and azimuth angle of the satellites are computed through GNSS positioning. The azimuth angle of the fish-eye camera can then be computed by the moving-base positioning using two GNSS antennas/receivers. Note that the estimated azimuth angle may contain errors owing to the effect of the NLOS multipath signals.(iv)We project the satellite position onto a binarized fish-eye image using the estimated azimuth angle of the fish-eye camera.(v)The satellite visibility is automatically determined based on whether the buildings and satellite are overlapped. The temporal NLOS satellites can be determined.(vi)We then exclude the NLOS satellites and again estimate the azimuth angle of the fish-eye camera using the moving-base positioning. By excluding the NLOS satellite, the correct camera azimuth can be expected to be estimated.(vii)We repeat the process of (iii) through (vi) until the estimated azimuth angle of the fish-eye camera converges.The flow of the NLOS detection using a fish-eye image is as follows:Finally, we can obtain a reference for the correct satellite visibility. We collected the actual LOS and NLOS GNSS correlation outputs using this device to create an NLOS signal classifier.We evaluated the NLOS classification performance of the proposed method. The experiments were conducted in actual urban environments . We employed MATLAB to construct the NLOS signal classifier using an SVM and an NN. The parameters set for machine learning are listed in The actual correlation output was obtained and visualized to investigate the extraction of NLOS features from the correlation output of NLOS signals. We computed the GPS LOS and NLOS correlation outputs. Here, the sampling frequency and bandwidth of the RF front end are 20 and 4.2 MHz, respectively. We compute the proposed NLOS features for SVM from the actual correlation outputs. We compared a general satellite selection method using the GNSS SNR threshold with the two proposed methods. The SNRs of the reflected and diffracted NLOS signals are typically lower than those of the direct signals. The SNR threshold was set to −5 dB from the SNR–elevation curve shown in Equation . When thTP, correct detection), true negative , false negative , and false positive  in each classification test. We then calculated the average classification rate (A), average recall (R), average precision (P), and average F-Measure (F) using the following equations [We used typical evaluation statistics used in binary classification. We calculated true positive (quations .(14)A=TThe NLOS detection methods using machine learning for the GNSS signal correlation values could discriminate the NLOS with much higher accuracy than a method using the GNSS SNR threshold. We believe that this was because we had extracted the appropriate features of the NLOS correlation outputs by SVM and NN. In the cross-validation results from Comparing the results of NN and SVM, the performance of NN was slightly higher. This result suggests that the NLOS features extracted by NN using the signal correlation values directly were more effective than the NLOS features designed by humans.The data presented in this paper were obtained in the same city, and it has not been verified whether the same model can be applied to different cities. In the future, we plan to check whether the model learned across different cities has sufficient generalizability. If the model is to be applied to cities with completely different shapes and distributions of buildings, it is thought that it may be necessary to add training data obtained in those cities.In terms of the computational cost, an NN has a higher computational cost than an SVM. During the training stage of the NNs, the computation time depends on various hyperparameters, although it is 5 to 10 times longer than training with SVM. During the test stage, the average processing time required for 100 samples in the current model using MATLAB was 0.66 ms for the SVM and 1.27 ms for the NN. Both methods can be executed in real-time; however, because an SVM is less computationally expensive, in cases in which the computational resources are limited, an SVM is considered more effective than an NN.We proposed NLOS multipath detection methods that can employ machine learning techniques and software-based GNSS receiver to enhance the GNSS positioning performance in urban environments, where NLOS multipath signals lead to major positioning errors. We employed SVM and NN to construct the NLOS signal classifier in this study. In the SVM, we extracted the three features of the shape of the multi-correlator output. In the NN, we directly input the multi-correlator output to construct the NLOS classifier. The NLOS classification experiments in actual urban environments show that the NN has slightly better classification performance than SVM, and 97.7% of the NLOS multipath signals were correctly discriminated. In future studies, we plan to collect more training data for the NLOS classifier to improve the NLOS classification ratio and create classifiers for satellites other than those used by GPS.In this study, we evaluated the discrimination performance using a cross-validation method. However, the data are all taken within the same city (Tokyo). To further evaluate the generality of the proposed method, it is necessary to evaluate the NLOS discrimination method using data obtained from different cities and to evaluate the NLOS discrimination of mobile vehicles in the future.