In February 2021, in response to emergence of more transmissible SARS-CoV-2 virus variants, the Canton Grisons launched a unique RNA mass testing program targeting the labour force in local businesses. Employees were offered weekly tests free of charge and on a voluntary basis. If tested positive, they were required to self-isolate for ten days and their contacts were subjected to daily testing at work. Thereby, the quarantine of contact persons could be waved.Here, we evaluate the effects of the testing program on the tested cohorts. We examined 121,364 test results from 27,514 participants during February–March 2021. By distinguishing different cohorts of employees, we observe a noticeable decrease in the test positivity rate and a statistically significant reduction in the associated incidence rate over the considered period. The reduction in the latter ranges between 18 and 50%. The variability is partly explained by different exposures to exogenous infection sources . Our analysis provides the first empirical evidence that applying repetitive mass testing to a real population over an extended period of time can prevent spread of COVID-19 pandemic. However, to overcome logistic, uptake, and adherence challenges it is important that the program is carefully designed and that disease incursion from the population outside of the program is considered and controlled. They suggest that this strategy can contribute to control the local epidemics and might even provide an alternative to extreme interventions with higher social, psychological, or economic costs, such as blanket lockdowns. However, due to logistic challenges and high costs, skepticism still remains against repetitive testing as its benefits haven’t been proven broadly yet6.Repetitive testing of people without noticeable symptoms has been proposed as a public health measure in response to COVID-19 pandemic. The concept relies on reducing the effective infectiousness period by isolating the positively tested individuals when they are presymptomatic or asymptomatic. Theoretical studies have demonstrated that repetitive mass testing helps contain the virus spread7. For repetitive population screening, however, specificity, test-to-notice time, and sensitivity to asymptomatic virus carriers are crucial, as they may hinder the effectivity of mass testing programs, if not chosen properly5. In addition, the behavior of the population may jeopardize the positive effects of testing if, for instance, participants do not correctly comply with instructions (i.e. not consistently isolating if tested positive)6. Finally, the success of mass testing depends on the possibility to cover a sufficiently large fraction of the population and their contacts. More empirical evidence is needed to evaluate the benefits of mass testing when applied to a real population over an extended period of time. There is still lack of field studies of sufficient coverage demonstrating that logistic, uptake and adherence challenges can be overcome.In the current pandemic, several types of SARS-CoV-2 tests with acceptable sensitivity for symptomatic cases have proven successful as diagnostic tools14. In Slovakia, a few rounds of population-wide mass testing were estimated to yield a 70% decline of infection prevalence11. Pilot mass testing based on Lateral Flow Devices (LFDs) has been conducted in Liverpool, where lower uptake compared to Slovakia’s was found (only 25% of the population was tested in a 4-week period)13. Here we report new evidence from a program in the Canton Grisons (Switzerland) suggesting that repetitive virus RNA mass testing is effective in reducing SARS-CoV-2 incidence. Our observational study gives further insight into effectivity of mass testing in presence of a significant number of exogenous contacts resulting from tourists and commuting labor force.To date, population-based mass testing has been carried out and documented in countries such as the UK, Denmark, China, South Korea, Austria, Luxembourg, and Slovakia, that have mostly used rapid antigen testsThe Canton of the Grisons, the largest in surface and easternmost Canton of Switzerland, shares borders with Italy, Austria and Liechtenstein, and has approximately 200,000 inhabitants. A large share of its economy is dedicated to tourism, e.g. in the past winter season, the Canton Grisons received around 200,000 tourists with 20% from abroad. Due to a high proportion of daily to weekly border crossing employees from the neighbouring countries, border disease control measures are less restrictive than in other parts of the world . The high incidence and death rates of COVID-19 both in Switzerland and in the neighbouring countries during October-November 2020 and the spread of the new variants , urged the Canton Grisons to launch a population-based mass testing campaign in order to intensify their mitigation strategy while maintaining cross-border socio-economical relationships.Based on the experience acquired from a few rounds of pilot mass testing conducted in selected municipalities, a repetitive testing strategy for employees was developed for the entire Canton. In the first week of February 2021, 174 companies were recruited, with approximately 100 businesses being added every week since then. The decision to focus on the working force was taken to maximize the benefits by targeting individuals with high mobility and large network of contacts (such as hotel employees), and to enable business continuity by preventing outbreaks in professional networks.The mass testing campaign relies on voluntary repetitive testing of unvaccinated employees, who are mostly tested once per week (twice per week in a few cases). If the test turns positive, employees are asked to self-isolate, while their work contacts are identified and offered daily testing for ten consecutive days. As long as they remain negative, they are allowed to continue to work on company’s premises with few restrictions (e.g. wearing mask and minimizing contacts when possible): they are asked to self-isolate only if their own test result is positive. This “test-and-release” protocol minimizes the number of people in quarantine and thereby limits possible burdens on the participating businesses. In addition, external contacts  of the infected employee are informed to take precautionary measures and test according to the associated contact tracing program. Even though they are not included in the mass testing program, their risk of infection will be reduced by having a part of their contact network (the employees enrolled in the mass testing program) regularly tested and a beneficial secondary effect is expected for the general canton’s population.15. Test processing is expedited by mixing the pools of 5 samples (5 to 1) by the automated platform in the laboratory. The results are communicated within 24 hours, resulting in a test-to-notice time of around 1 day .The collected saliva samples are analyzed by the Reverse Transcription Polymerase Chain Reaction (RT-PCR) methods. The use of saliva samples ensures convenience of participants during the testing process. By quantifying the operative characteristics of the tests, a high specificity of 0.999873  and sensitivity close to nasopharyngeal swab RT-PCR were foundSupplementary materials, Data pre-processing).In total, 1022 businesses, operating on 1358 sites, joined the program from the beginning of February until the end of March, 2021. A total of 121,364 tests were conducted among 27,514 employees without symptoms. Positive test results were found in 215 cases (0.78%)  are present at varying proportions over time. This might significantly influence the effectiveness of the program, since companies with a higher number of customer contacts or cross-border employees are prone to a higher disease incursion.Supplemenraty materials, Cohort definition ). Here, we analyze the first two months of this program until the Easter break period, for which the data is already consolidated.For these reasons, instead of focusing on population-based epidemiological quantities in the Canton, here we limit ourselves to a finer-grain analysis: we evaluate the impact of testing on the evolution of the epidemics among participants. Therefore, we consider two groups of employees: the first group consists of the newly enrolled ones, the second group of the ones who have been enrolled in the program for a longer time and have therefore been tested repeatedly. The testing results of the newly enrolled participants are used as a proxy for the spread of infection among the population outside of the program (control group without testing). To account for the influence of different epidemiological conditions at the time of enrollment, which change over time, we divided the repeatedly tested employees into different cohorts according to the week during which they joined the program  . We observe an increase in TPR among newly enrolled employees during the month of February, which is consistent with the increase in frequency of outbreaks in schools registered in this region, as well as with a concurrent expansion of the pandemic in several Swiss regions. The increase of TPR among the newly enrolled population results in quite different upstream epidemiological conditions for the different tested cohorts. Especially, the initial TPR value of the week 3 cohort is twice as high as the one corresponding to the week 1 cohort. Even though TPR was lower during enrollment of the week 1 cohort, this cohort shows a remarkably smaller and more uncertain reduction in TPR than the other two cohorts joining in later weeks.To infer the epidemiological changes among tested employees, we compute two complementary quantities: test positivity rate (TPR) and incidence rate ratio. The seven-day average TPR is calculated as the proportion of new positive cases to the total number of RT-PCR tests per seven days. Figure The reduction of TPR over the period in which the cohort is repeatedly tested varies from 73% (over 7 weeks) to 56% (over 6 weeks), for week 2 and week 3 cohorts, respectively. The week 1 cohort shows a 44% increase over the entire eight-week period. Notice that during the same eight-week period, TPR of the newly enrolled population almost doubles (reaching a peak of 0.28% in the fourth week of the program). In general, all three repeatedly tested cohorts of employees exhibit evident reductions in TPR when compared to the newly enrolled population. Yet given the relatively important uncertainty resulting from our small sample size, the critical question is if the reductions in TPR translate into a statistically significant drop in the incidence rate of the tested cohorts.Supplementary materials, Overview of statistical methods). The ratio between the incidence rate of each cohort with respect to the newly enrolled population is provided in Table As an integral measure of the reduction in the number of infections over the entire period, we calculate the incidence rate associated with the seven-day average TPR by normalizing the number of new positive cases by the person-time tested .The milder reduction in TPR and incidence rate of the week 1 cohort can partly be explained by a higher exposure to exogenous disease incursion due to the higher representation of the tourism sector and cross-border employees in week 1 cohort in comparison to week 2 and week 3 cohorts , around 200,000 tourists resulted in an additional exogenous infection source in the Canton. Around a quarter (26%) of all tests were carried out among people employed in the tourism sector. Remarkably, this business sector accounted for almost half (48%) of all positive tests, which results in a frequency of positive cases that is close to two times larger than in other business sectors.Supplementary materials, Cohort definition).Figure The number of tourists peaked around December and February, and started declining towards the middle of March. This variation in the number of tourists could explain the increase of TPR among the newly enrolled individuals (control group without testing) during the month of February (peaking around the fourth week) and the decline observed afterwards. The tourists and the large proportion of foreign workforce employed in the tourism industry are a potential source of exogenous disease incursion and can noticeably contribute to the incidence of COVID-19 in the Canton Grisons. The fluctuation in the proportion of businesses from the tourism sector in the three cohorts is a potential source of confounding effect in our analysis.Supplementary material, Effect of tourism and cross border commuters for the details).In particular, the week 1 cohort bears the highest proportion of the tourism work force and shows the least reduction in TPR. This might be explained by two effects. First, the employees who were mostly in contact with visiting tourists were subject to a higher disease transmissibility, resulting from a larger number of contacts with untested individuals (as tourists are not part of the program) and possibly coming from regions with higher prevalence. Second, many employees in this sector were crossing borders on a daily or weekly basis, hence their risk of exposure to infected individuals might differ from that of employees in non-tourism sectors, which mostly remained within the Canton during the time of our study. These hypotheses are supported by an analysis performed on a reduced data set from which a few touristic and near-border municipalities have been excluded. The reevaluated reduction in the incidence rate almost doubles from 18% to 34% for week 1 cohort, and increases from 48% to 51% for week 2 cohort, and from 43% to 61% for week 3 cohort . This is encouraging as it shows that intensifying repetitive testing can be a viable complement to the existing non-pharmaceutical intervention strategies to reach epidemic control.Several features contributed to the success of our testing program. The use of saliva based RT-PCR tests, with no nasal swab required, has certainly fostered a high participation rate and consistent repetitive testing: the program uptake among employees was 74% during February-March 2021, with an estimated drop-out by the second month lower than 10%. Furthermore, the high specificity of the employed RT-PCR tests assures that only a few false positive cases can be expected; this is important to keep testing and self-isolation effective also when the prevalence of the tested population is relatively low. Finally, the efficiency of the test analysis was improved by automated pooling of the samples in the laboratory, which allowed us to scale up the size of the tested population for a given testing capacity and to keep the test-to-notice time short.To define the objectives and plan a successful repetitive testing concept, it is important to carefully consider the interaction within and between the tested and untested sub-populations, as their dynamic is far from being homogeneous. On the one hand, the repeatedly tested individuals actively contribute to curb the virus spread: as the tested cohort itself benefits from a reduced incidence, their untested contacts are also exposed to a lower risk of infection. On the other hand, interactions of tested cohort with individuals outside of the program expose the former to the transmission risk originated from the latter, reducing the effectiveness of testing.The presented study is prone to certain limitations. Most importantly, our results rest on the assumption that there was no significant variation of confounding factors  among the different cohorts that have been considered. As the time window of the analysis predated the general public vaccination campaign, the analyzed data concerned people who were not vaccinated. Moreover, due to the lack of detailed data on the participants, we considered the business sector as a proxy for both age-distribution and socio-economic status of the tested work forces. Our results hint that the impact of the testing program in cohorts with similar mix of business sectors tend to be alike, which supports the choice of the business sector as the relevant proxy.Supplementary materials, Overview of statistical methods). Also, a higher number of tourists or cross-border employees from regions not covered by the testing program represented a potential source of disease incursion and were associated with a lower reduction of the incidence rate. In order to more efficiently control the epidemic, therefore it is important to adapt the testing program according to the varying level of exposure to the exogenous sources of infection. This can be achieved, for instance, by a larger uptake and a more frequent testing among individuals with an extended network of contacts outside of the program.Our analysis supports that a higher number of active participants per company site tended to correlate with smaller incidence rates, hence confirming the requirement of achieving a sufficiently large uptake among employees . This requires a coordinated engagement of policy makers, communities, and the public to adopt carefully designed testing programs that could be sustained over an extended period of time.Supplementary Information.


Strain localization is a significant issue that poses interesting research challenges in viscoelastic materials because it is difficult to accurately predict the damage evolution behavior. Over time, the damage mechanism in the amorphous structure of viscoelastic materials leads to subsequent localization into a shear band, gradually jeopardizing the materials’ elastic sustainability. The primary goal of this study is to further understand the morphological effects and the role of shear bands in viscoelastic materials precipitated by strain localization. The current study aims to consolidate the various failure mechanisms of a sample and its geometry (surface-to-volume ratio) used in torsional testing, as well as to understand their effects on stress relaxation durability performance. A torsional shear load stress relaxation durability test was performed within the elastic region on an isotropic viscoelastic sample made of silicon rubber and a 70% weight fraction of micron-sized carbonyl iron particles. Degradation was caused by a shear band of localized plasticity that developed microscopically due to stress relaxation durability. The failure pattern deteriorated as the surface-to-volume ratio decreased. A field-emission scanning electron microscope (FESEM) and a tapping-mode atomic force microscope (AFM) were used for further observation and investigation of the sample. After at least 7500 cycles of continuous shearing, the elastic sustainability of the viscoelastic materials microstructurally degraded, as indicated by a decline in stress performance over time. Factors influencing the formation of shear bands were observed in postmortem, which was affected by simple micromanipulation of the sample geometry, making it applicable for practical implementation to accommodate any desired performance and micromechanical design applications. In practice, an elastic product or part can withstand the distorting influence and deformation of a force and immediately return to its original state after the force is removed. When viscoelastic materials are introduced, they retain their original ability but exhibit viscous and elastic characteristics when deformed. The elastic ability, however, is dependent on and limited to a single designated maximum force. This limitation causes the material to deteriorate over time as the force becomes dynamic and localized. The material itself loses its ability to sustain elasticity due to microstructural degradation, requiring regular part replacement and maintenance. To address this issue, a viscoelastic material known as magnetorheological elastomer (MRE) with long-lasting elastic properties that change in response to external stimuli has been introduced ,2,3. ThiHowever, MRE degradation at the molecular level because of localized deformation poses a threat, especially over long periods of time. This has prompted many studies, as reported in the literature , to condSeveral studies ,15,16,17The primary goal of this study is to further understand the morphological effects and the role of shear bands in viscoelastic materials precipitated by strain localization. This study also aims to consolidate the various failure mechanisms of the sample and its geometry (surface-to-volume ratio) used in torsional testing, as well as to understand their effects on stress relaxation durability performance. Although the general form of the test does not show a significant change, the changes in the specimen size (surface-to-volume ratio) cannot be ignored. To date, the effect of these variables has not been well-understood. For morphological aspects, data accuracy and consistency are critical. Understanding the variability in the failure mechanism is essential for evaluating durability performance. This study investigates the effects of test geometry, specifically the surface-to-volume ratio, on the reported reduction stresses, assuming that the material’s failure process of stress relaxation remains consistent. The effect of different surface-to-volume ratios is evaluated morphologically for various mechanisms. Consequently, this study encourages innovation and significantly increases the number of scientific studies and technological capabilities in accordance with the 9.5 sustainable development (SDG) agenda.Process parameters that are varied or altered during the fabrication process can easily manipulate or affect the material properties of MRE. As a result, special consideration must be given to the fabrication process when producing MRE samples so that the full potential of MRE can be realized. Previous researchers have reported on related studies regarding the effect of particle fraction and MRE arrangement ,25,26,27The elastic performance of the MRE under dynamic shear stress relaxation was investigated using an oscillation parallel plate rheometer operating in the oscillatory shear mode . The temperature was set to 25 °C, which was maintained and controlled by the rheometer’s Viscotherm VT2, Anton Paar. The strain created by the oscillation of the rotating disc parallel plate was then set to a constant 0.01%, with a frequency of 1 Hz. The strain value was chosen within the elastic region known as the linear viscoelastic region (LVE). The strain level of 0.01% was determined in this study based on our initial rheological study of the sample and with the intention of understanding the structure at equilibrium, which is a good indication of how the material may respond; however, the material slightly shifts away from equilibrium at low deformation. Following durability testing, samples were prepared for microstructure analyses by cutting the sample  into segments with an approximate surface proportion of 1 mm × 10 mm. The surfaces of the cut samples were sputtered-coated before being examined with a field-emission scanning electron microscope  set to 1 kV accelerating voltage. The morphological studies on the MRE sample were further studied utilizing a tapping-mode AFM analysis on a NanoWizard 3, NanoOptics AFM  with a nanosensor tapping-mode monolithic-silicon AFM probe-type single-beam cantilever supplied by BudgetSensors, Sofia, Bulgaria.The micrographs of the MRE sample morphology taken with an FESEM revealed a considerable variation associated with the distinctive CIP arrangement and distribution. There was no discernible defective surface characteristic identified in relation to the effect of the curing process. , can be written as follows:h, as follows:In the case illustrated in dz2 < dz1, of the sample, in which the top oscillates relative to the stationary bottom due to an increase in the angle, Because the geometry of the deformation corresponds exactly to the earlier description of shear strain in Equation (2), the following can be written:r = 10 mm, and the decrease in the thickness dz2 < dz1 of the sample resulted in a decrease in relative tangential displacement, δ. Therefore, this geometrical deformation consideration demonstrates the volumetric diminution in the affected area during the durability test in comparison to the thicker sample, limiting the stress distribution. Continuous shear stress applied rapidly at a fixed deformation causes structure degradation, such as molecular relaxation, cross-link disentanglement, and structural rearrangement [In the stress relaxation durability test, the strain was fixed at 0.01%, the distance from the sample’s center was fixed at angement . Since sThe extensive studies on the use of AFM in investigating these stress relaxation and strain localization phenomena in MRE constitute the technical contribution of this work. This study’s findings will be useful for comprehending the microplasticity behavior in the formation of the shear band within a material’s elastic region. The declining performance when stress was applied during the continuous shearing process revealed the effect of microstructural degradation. Understanding the stress pattern using evaluations enables the detection of strain localization onset behavior, which refers to the start or initiation of microstructural deterioration. The sample that reacted to minor changes in its original condition was studied at this early stage. Based on this finding, it can be concluded that a slow degradation process occurred in this material during the initiation of the resilience condition, and the degradation changed as the test duration increased. Specifically, the molecular chain structure of this material is capable of sustaining the elastic performance, and improved sustainability can be achieved through the response to magnetic stimulation, which effectively alters the elastic performance. MRE conceptualization consists of a molecular chain structure and the cross-linkages of cured MRE, as shown in As shown, prior to the durability test, the matrix’s amorphous molecular structures were un-stretched with the initial cross-linkage position (red color) generated after the curing process. The CIPs were embedded in the matrix amorphous molecular structure with rigid spheres in the crystalline molecular structure at random. During shear, the velocity gradient that developed across the sample was greater at the most outer section and decreased toward the center. The shear band development and its mechanism significantly impacted the shear profile generated across the sample in this study. The illustrated figure depicts the mechanism of shear deformation in the sample’s center following durability testing. The stretched region was just below the localized elastic limits among the entangled amorphous molecular chains during the initial stress relaxation process, and the cross-linkages were then reversibly aligned. At this point, no permanent deformation occurred during the stretching. As a result, no visible marks could be seen. However, the constant shear load repeatedly softened the chains, eventually pushing them over the localized elastic limit. As a result, the plastic flow occurred in the inner portion of the molecular chain, just beyond the localized limit. The fluctuating stress that developed in the amorphous molecular chain was then attributed to chain deformation and rupture, as well as cross-linking at the soft dominated domain. Shear band deformation (yellow line) corresponded to molecular chain disentanglement, cross-linkage breaking, and the sequence of molecular slip events that contributed to shear band homogeneity.The purpose of this study was to determine the morphological effects of stress relaxation and the surface-to-volume ratio on MRE durability. According to the analysis results, the degradation pattern of the MRE samples varied toward stress relaxation within their elastic region and was influenced by the surface-to-volume ratio. This forensic investigation provided a critical morphological evaluation of the material quality and elastic performance. A complex and critical microstructural evaluation was established to determine the shear band constituted by strain localization during stress relaxation. The current study on the morphological effects of strain localization in the elastic region of MRE resulted in a more comprehensive understanding of the failure that occurs during stress relaxation durability performance. According to the current findings, the geometry effect (surface-to-volume ratio) of the sample plays a critical role in MRE elastically sustaining during stress relaxation. The morphological shreds of evidence established a correlation between the effect of the surface-to-volume ratio and stress relaxation durability performance. The use of AFM in the morphological analysis and the localized strain deformation zone contributes significantly to the current literature. The shear band was responsible for the MRE’s declining elastic performance, which could be a precursor to rupture. These findings could be used by design engineers and material scientists to select the appropriate material performance for various applications, thereby improving device capabilities and lifetimes. Material sustainability is critical to ensuring long-term durability and service life applications. This research could be used to optimize physical design parameters that are susceptible to durability performance under fixed small strain or deformation modes over long periods of time. In terms of industrial relevance, this research, for example, aids in understanding the effect of the geometrical design of the isolators and dampers used in adaptive vibration control in civil engineering. On a larger scale, estimating the life and degradation behavior of MRE products under all conditions is extremely useful, and the current study contributes to future industrial applications and technological advances in MRE durability evaluation. Even though the results achieved in this work are not immediately applicable to practical applications, they will be very useful in analyzing the failure or stress concentration of MRE applications, such as vibration isolators. In addition, to identify the effect of geometry (surface-to-volume ratio) on MRE durability, specifically under stress relation, an experimental test of MRE samples with different concentrations of curing agent needs to be explored.


Modern aircrafts require the assembly of thousands of components with high accuracy and reliability. The normality of drilled holes is a critical geometrical tolerance that is required to be achieved in order to realize an efficient assembly process. Failure to achieve the required tolerance leads to structures prone to fatigue problems and assembly errors. Elastomer-based tactile sensors have been used to support robots in acquiring useful physical interaction information with the environments. However, current tactile sensors have not yet been developed to support robotic machining in achieving the tight tolerances of aerospace structures. In this paper, a novel elastomer-based tactile sensor was developed for cobot machining. Three commercial silicon-based elastomer materials were characterised using mechanical testing in order to select a material with the best deformability. A Finite element model was developed to simulate the deformation of the tactile sensor upon interacting with surfaces with different normalities. Additive manufacturing was employed to fabricate the tactile sensor mould, which was chemically etched to improve the surface quality. The tactile sensor was obtained by directly casting and curing the optimum elastomer material onto the additively manufactured mould. A machine learning approach was used to train the simulated and experimental data obtained from the sensor. The capability of the developed vision tactile sensor was evaluated using real-world experiments with various inclination angles, and achieved a mean perpendicularity tolerance of 0.34°. The developed sensor opens a new perspective on low-cost precision cobot machining. Robotics, one of the key pillars of industry 4.0, has been increasingly used in aerospace manufacturing for grasping, painting, and precision machining operations such as drilling, deburring, fastening, and inspection . CompareDrilling high-strength aluminium and titanium alloys typically results in trapped heat in holes that are difficult to dissipate due to the generated friction and chip formation between the drill tool and the aerospace structure. In addition, most drilled holes form burrs on both sides of the structure, which promote cracks’ formation and propagation and reduce fatigue life ,6,7,8,9.Vision-based tactile sensing (VBTS) is an advanced perception technology that uses vision systems to monitor the deformation of an elastomer upon contact with different surfaces, which allows it to sense the topographic information of these surfaces. VBTS offers multiple advantages over conventional tactile sensors, including high spatial resolution, design simplicity, and low instrumentation requirements . These aTo date, no study in the literature has considered the design nor simulation of VBTS 94 systems to address the perpendicularity  challenges of robotics in the aerospace manufacturing industry. This paper demonstrates in detail the step-by-step process to develop a novel vision-based tactile sensor that provides the required perpendicularity measurements for drilling, deburring, and machining processes. Additionally, this paper outlines the Finite Element Analysis (FEA) and simulation of this novel sensor that can be used for design optimisation and Sim2Real learning. Finally, this paper evaluates the capabilities of the presented FEA simulations to accurately depict the sensor’s response in experimental settings, and introduces a Sim2Real deep learning model that leverages data from simulations to estimate perpendicularity within the specified tolerances of 2°. The remainder of this paper is organised as follows: The development of the vision-based tactile sensor started with a characterization process of three different elastomers’ materials aiming to select the most flexible one to achieve a high-sensitivity material to the applied deformation. After choosing the material, a CAD mould was designed with a cavity representing the geometry of the tactile sensor. The CAD model was 3D printed and used to prepare the elastomer tactile sensor by casting and curing the elastomer prepolymer. To create the markers, spherical plastic beads were used and placed on cavities created on the inner surface of the sensor. A schematic diagram of the process is shown in Silicone-based elastomers are semi-inorganic polymers with a silicon-oxygen chain and two hydrocarbon groups. Polydimethylsiloxane (PDMS) is a popular silicon-based elastomer that is not only used for micro/nanofabrication ,36,37 buThe characterisation of the elastomers was carried out using tensile testing experiments according to ASTM D-412C standard using a Birmingham universal mechanical testing machine . The 3D-printed mould representing the geometry of the tensile specimens was carried out using Zortax M200 3D printer, as in The fabrication of the vision-based tactile sensor starts with creating a CAD model, which represents the sensor’s hemispherical geometry. A mould design representing the cavity and core of the sensor model was also designed with a parting plan at the planar surface of the hemisphere. In addition, guidance pins were included in the core part to ensure easy assembly, The proposed vision-based tactile sensor consists of a housing structure made by 3D printing, the camera and the tactile surface, as illustrated in Z.The sensor was mounted on a UR10 robot manipulator that was programmed to press the surface up against the calibrated flat surface in different relative poses. For each pose, an image is sampled along with the pose measurements after achieving contact with the surface. A Finite element model was created using ABAQUS CAE  to characterise the sensor deformation when in contact with a wall at various inclination angles, as shown in The sensor model was assumed to have a uniform thickness, neglecting the variation due to markers’ fabrication and the plastic beads. The shell surface that carries the markers was assigned to the inner surface, considering the shell element thickness starts from the shell surface outward. The shell has been partitioned into a number of cells that make a group of nodes at the corners (intersections). The majority of the cells correspond to sensor markers, where the movement of the nodes represents the movement of the centre of the markers. −3) and a Poisson’s ratio of E is Young’s modulus, G is the shear modulus and v is Poisson’s ratio.™00-30 stress–strain data were employed to determine constants, see ensity ρ=050 kgm−3Mesh sensitivity analysis was carried out to optimise the element size at which a stable and accurate solution can be realised at a reasonable computational time. The results of the mesh sensitivity have been presented in The markers are hemispherical in shape, where they are stacked and stuck to the inner surface of the hemispherical sensor. This configuration makes the outer circular patterns affected by the side projection, where most of the markers are not perfectly projected to the camera plane, which makes a shift between the centers of the markers in the simulation and the experiment. The finite element model was first checked against the material properties to ensure that the developed stresses and strain due to the sensor deformation is within the implemented material model. X and Y directions, which can be captured and processed by the camera images and a deep-learning model.The finite element model was validated by comparing the simulated and experimental results of the tactile sensor markers, which were captured using the camera fitted to the cobot manipulator. X and Y directions. Over time, the error was calculated as the square difference between their locations, as shown in Equations ..X and Y U and V directions when the elastomer sensor is deformed by 10 mm stroke are shown in The last criteria by which we assess the FEA simulations is in terms of sim2real transferability to train deep learning (DL) models for the prediction of contact angle. The application of deep learning using neural networks has been established in many applications including recognizing complex patterns and images . To thatX is the pixel coordinates of the markers on the tactile sensor’s elastomer, and the output The objective of our DL model is to find the mapping n effect . Each fun effect . The dron effect . The finU and V for each of the 37 markers, resulting in an input vector of size 74. The initial simulation dataset consists of 143 different samples. To enhance the generalization and Sim2Real performance of the DL model, we augment the initial dataset to generate additional data. We perform augmentation by randomly perturbing the pixel coordinates of the elastomer’s markers. From the analysis in U and V directions by N pixels, where N is a uniformly sampled number in the range The DL model is trained purely on simulation data. Training data includes the contact angles in the range The DL model was trained using the ADAM optimization algorithm , with thThe performance of the developed DL model for estimating the contact angle was evaluated on an unseen subset of the simulation data, in addition to unseen experimental data.  devices  which maIn this paper, we presented a detailed procedure to design, simulate, validate, and fabricate a low-cost elastomer for a vision-based tactile sensor to support cobots for the machining of aerospace structures. The tactile sensor can measure the normality information of surfaces using a sensitive elastomer object, with internal markers relying on the deformation of the markers captured using a camera and processed using a deep learning approach. First, the mechanical characteristics of Dragon Skin, Ecoflex™00-50, and Ecoflex™00-30 elastomer materials were evaluated. Ecoflex™00-30 elastomer showed a lower elastic modulus and higher ductility, which made it a suitable elastomer for the proposed tactile sensor. A hemispherical finite element model of the tactile sensor with internal markers was developed using shell elements in contact with a rigid wall with different normalities. The tactile sensor was fabricated by the direct casting of the elastomer polymer onto an additively manufactured mould. The fabricated sensor demonstrated a good agreement with the simulation model. In addition, the deep learning model was trained using the simulation and experimental results of the sensor deformation. The deep learning model prediction of the contact angle shows exceptional sim2real transferability. The performance of the sensor shows a mean normality tolerance of 0.13°, which satisfies the requirements of aircraft manufacturing.


Three-dimensional light detection and ranging (LiDAR) sensors have received much attention in the field of autonomous navigation owing to their accurate, robust, and rich geometric information. Autonomous vehicles are typically equipped with multiple 3D LiDARs because there are many commercially available low-cost 3D LiDARs. Extrinsic calibration of multiple LiDAR sensors is essential in order to obtain consistent geometric information. This paper presents a systematic procedure for the extrinsic calibration of multiple 3D LiDAR sensors using plane objects. At least three independent planes are required within the common field of view of the LiDAR sensors. The planes satisfying the condition can easily be found on objects such as the ground, walls, or columns in indoor and outdoor environments. Therefore, the proposed method does not require environmental modifications such as using artificial calibration objects. Multiple LiDARs typically have different viewpoints to reduce blind spots. This situation increases the difficulty of the extrinsic calibration using conventional registration algorithms. We suggest a plane registration method for cases in which correspondences are not known. The entire calibration process can easily be automated using the proposed registration technique. The presented experimental results clearly show that the proposed method generates more accurate extrinsic parameters than conventional point cloud registration methods. Autonomous navigation technology has been applied to robots and vehicles. Furthermore, commercialization of autonomous navigation systems operating in urban environments has been accelerating in recent years. Consequently, the perception of environment in autonomous systems is becoming increasingly crucial for system and user safety. Therefore, many navigation systems are equipped with a sensor system consisting of multiple sensors of the same type or sensors with different modalities.Three-dimensional light detection and ranging (LiDAR) sensors provide accurate range measurements and abundant geometric information. A wide range of products for 3D LiDAR sensors has been developed in recent years, placing 3D LiDAR sensors among the most preferred in the field of autonomous navigation. Although the 3D LiDAR sensors that have high vertical resolution and a wide vertical field of view  provide a dense point cloud, it is not easy to apply them to commercial autonomous navigation systems because of their exorbitant prices. In this case, the 3D LiDAR sensors that have low vertical resolution  can act as substitutes because the prices of the vertically low-resolution LiDAR sensors are relatively lower than those of the high vertical resolution 3D LiDAR sensors, such as HDL-64. However, they have a narrow vertical field of view. It is essential for an autonomous navigation system to measure a wider range of the environment while lowering the cost of the entire system. Furthermore, there is a need for a sensor system that reduces blind spots. Consequently, multiple 3D LiDAR sensors are often applied to autonomous navigation systems. Because the LiDAR sensors are typically mounted on a robotic or vehicular platform at different locations and directions, the transformation between the sensors should be well defined. From this point of view, extrinsic calibration to estimate the relative position and rotation between the sensors should precede the operation of the autonomous navigation system.The importance of extrinsic calibration is evident for the following reasons: First, when commercializing autonomous navigation systems equipped with multiple sensors, large numbers of systems need to be calibrated in batches. Second, for research platforms, the poses of the sensors are often adjusted to find a suitable configuration. Furthermore, sensors are often attached and detached while inspecting the platform or reconfiguring the sensor systems. Therefore, the extrinsic calibration is not a one-off operation for the systems. Consequently, an easily applicable and accurate extrinsic calibration method is required.Regarding environmental perception, it is efficient for autonomous navigation systems to cover a wide ranging area with few sensors where possible, especially when using multiple sensors with the same modality. Therefore, multiple LiDAR sensors are forced to install the viewpoints of the sensors quite differently so that the sensor systems have a wide field of view. Consequently, the overlapping regions between the sensors are reduced. However, for extrinsic calibration, the reduced overlapping regions make it difficult to determine the extrinsic parameters between sensors. For this reason, point cloud registration algorithms ,2,3,4,5 Calibration methods using artificial calibration objects require processes for making the objects and for placing them in the target environments ,7,8. To There are several studies on motion-based extrinsic calibration. These methods are based on hand-eye calibration using structure from motion. The extrinsic parameter is calibrated using the motions obtained by each sensor. Because detection of mutual information is not required, it is usually used for the sensors with different modalities, such as LiDAR-Camera-IMU  or LiDARIn this study, we propose a method for extrinsic calibration of multiple 3D LiDAR sensors. The contributions of this paper are threefold. First, the proposed method uses plane objects in surrounding environments as calibration objects. Specifically, at least three planes whose normal vectors span Several studies have addressed the extrinsic calibration of one or more LiDAR sensors. One possible approach is matching geometrically distinctive features. Choi et al.  proposedAn alternative to extrinsic calibration of LiDAR sensors is the use of artificial objects such as reflective tape, poles, or boxes. Underwood et al.  proposedAttempts have also been made to determine the extrinsic parameters using the quality of a 3D point cloud. Levinson and Thrun  proposedPoint cloud registration algorithms, such as iterative closest point (ICP) variants ,2,3,4 anThis paper describes a calibration method for extrinsic parameters of multiple LiDAR sensors mounted on a robotic or vehicular platform at different locations and directions. The extrinsic parameters refer to the relative position and the relative angle from the reference LiDAR sensors to the other sensors. The purpose of this study is to define the transformation between LiDAR sensors by accurately estimating the six degrees of freedom (DOF) extrinsic parameters There are two assumptions for the proposed method. The first one is that at least three non-parallel planes are required within the common field of view of the LiDAR sensors. It is necessary that the normal vector of the plane should span The initial poses of each LiDAR sensor can be defined by a human operator. We define the initial poses as modeling poses. The modeling pose refers to the user-defined extrinsic parameters between LiDAR sensors, which are mounted on a robot or a vehicle platform in different positions and orientations. It can be obtained via a drawing of the sensor mount or by measuring the relative distance and angles between sensors with a ruler and protractor. However, it is difficult to determine the modeling pose because not all detailed drawings of sensor mounts installed in a robotic or vehicular system are publicly available. Even if a detailed drawing is provided, installation errors or mechanical distortion of sensor mounts lead to inaccuracy in the modeling poses. Because the errors between the modeling poses and the actual poses are inevitable, this study aims to reduce these errors.In this study, we set one of the sensors as a reference frame The proposed method is one approach to pairwise calibration ,21. HoweIn this section, we briefly describe the method of plane detection. First, segmentation of the point clouds is performed. There are some segmentation methods suitable for detecting plane features. A 3D LiDAR provides a dense point cloud in small-scale environments because the LiDAR is not far from the surrounding structures. In this case, we use region growing segmentation , which iA planarity filter is applied to the segmented point clouds to detect plane features. The filter tests three attributes concerned with the distribution of scan points on a segment. Let n). The segment to be considered as a plane feature should satisfy The point cloud of a planar structure has eigenvalues fined in ,25. The The initial extrinsic parameters between 3D LiDAR sensors can be estimated by matching plane correspondences. The correspondence between two consecutive scans can easily be detected using the similarity of the plane parameters. However, if there are no given sensor poses or if the modeling pose errors are large, it is difficult to find plane correspondences at once. Furthermore, if the sensors have considerably different points of view, it is difficult to obtain a corresponding plane between the point clouds captured by each sensor. Because LiDAR sensors are mounted on a robot or a vehicle platform in different positions and orientations, even if the same wall is measured, other parts of the wall can be measured by each sensor. Moreover, the distance between each sensor and the plane object is also different. Therefore, the plane objects captured by each sensor can have different shapes, sizes, and poses. This situation is evident in a LiDAR sensor with low vertical resolution and a low vertical field of view. In essence, it is unknown which plane of the reference sensor corresponds to which plane of the source LiDAR sensor. The plane registration corresponds to lines 2–17 of Algorithm 1.d from the origin of each sensor, and centroid The proposed method iterates the process of finding correspondences and matching the correspondences to determine the extrinsic parameters from unknown correspondences. Several test measures are calculated using the plane parameters to find the correspondences. Let w represents a weight for each test measure. Subsequently, the pair of planes with the smallest weighted sum is detected as plane correspondence (line 12). i-th target plane. If the similarity distance is above specific threshold value To detect corresponding planes, similarity distance To calculate the relative transformation between LiDAR sensors, the initial estimation of the extrinsic parameters is performed using the plane parameters of a set of plane correspondences. Let us define the correspondence planes of the reference sensor and the source sensor as Equation  is used lgorithm . Let us We can obtain a linear system by stacking  for the The closed form solution of the least-squares problem in  is givenk-th iteration satisfies In , the ranors N in  should bC is the number of plane correspondences, and i-th plane correspondence.In line 16 of Algorithm 1, the relative transformation between sensors is optimized using the scan points on the planes. A set of parameters The weight of the correspondence is computed as the inverse of the variance along the normal direction: lgorithm  to solveThe length of Jacobian matrix J is To validate our calibration approach, we conducted experiments using a robotic and a vehicular system. The systems were equipped with multiple low-resolution 3D LiDAR sensors (Velodyne VLP-16). Two LiDAR sensors were mounted on the robotic platform as shown in For the first step of the extrinsic calibration, we detected the plane features in the target environment and found the correspondences. The planarity filter stated in Because we did not know the correspondences between the planes detected by each sensor, the iterative process of finding correspondences and matching them was performed to detect the plane correspondence and to simultaneously compute the initial transform Optimized transform z-axis for the rear sensor. The point clouds before calibration are shown in The modeling poses of the LiDAR sensors were not set except for a 180-degree rotation on the Extrinsic calibration of the vehicular system was also performed using the proposed method. The entire process was the same as the calibration process for the robotic system. For the process of detecting plane features, the parameters applied to the segmentation methods and planarity filter were the same as those for the robotic system. The point clouds transformed by the determined extrinsic parameters are shown in To evaluate our calibration approach, we compared the proposed method with ICP  and its k-th corresponding plane pair is calculated as follows.i-th measurement point belonging to the k-th corresponding plane pair, and N is the total number of measurement points of a pair of correspondence planes.The RMSE for the For all methods, the RMSE was calculated for three cases: the ground plane, off-ground planes, and all planes. The lower value of the RMSE represents a more accurate extrinsic calibration result.The evaluation result on the robotic system is shown in the row referred to as (a) in The evaluation results on the vehicular system are shown in the rows referred to as (b) and (c) in x-axis of the reference coordinate system. Although the initial translation was given, the RMSE values for the ground planes were found to be more than 0.2 m.NICP and NDT failed to match the two sets of point clouds from the vehicular system when the initial translation was not given. We additionally set up the initial translation of the source LiDAR sensors. The initial translation was set to 2 m for The conventional registration methods shared a lower accuracy for the ground plane matching. The reason for this result is that the methods require a large number of corresponding points in overlapping regions. In the experiments, VLP-16 provides a sparse point cloud in a single scan. Furthermore, there were only small overlapping regions on the ground surfaces because the points of view of the LiDAR sensors were quite different. Therefore, the number of point correspondences on the ground was smaller than those not on the ground. Consequently, ICP variants and NDT did not achieve convergence on the ground planes. However, the proposed method was robust enough for the sensor configuration, where the points of view of the sensors were quite different because it utilized the plane models and variances of the plane correspondences.In this paper, we have presented a method for extrinsic calibration of multiple 3D LiDAR sensors using planar features. The only requirement is more than three independent planes that can easily be found in surrounding environments. Therefore, the proposed method does not require any environmental modifications. A plane registration method is presented to deal with cases in which the viewpoints of the LiDARs are significantly different. The proposed method iterates the process of assigning correspondences and aligning the correspondences to estimate the initial transformation. The uncertainties of the plane are also considered in the optimization process to lower the effect of the noisy plane.We conducted several experiments on a robotic and a vehicular system to validate our calibration algorithm. For evaluation, we compared the proposed method with ICP variants and 3D NDT. The proposed method showed better performance than the conventional registration methods in terms of accuracy. Therefore, we have demonstrated that the proposed method achieves robust performance using sensors with different points of view.


A phase error correction method is proposed to compensate for the phase error in super-resolution correlated imaging based on metamaterial antennas. The varying carrier frequencies of a metamaterial antenna can generate the random radiation field for super-resolution correlation imaging, but the variation of the signal carrier frequency leads to large phase errors in the imaging results. In this proposed method, the sampling matrix in the super-resolution correlated imaging algorithm is used to compensate for the phase errors. Each element of the matrix is multiplied by a compensation phase corresponding to the phase error, and the error is subtly removed from the algorithm. In the experiment, the antenna pattern at each frequency of the metamaterial antenna is measured and recorded. In addition, an external field experiment is also carried out, and the collected data are imaged with the improved algorithm. Experimental results show that this technology can effectively solve the effect of phase errors on imaging results caused by signal carrier frequency changes. Synthetic aperture radar (SAR) obtains high-resolution images by the relative motion in the distance direction between the radar carrier and the target. However, since there is no relative motion in forward-looking imaging, SAR cannot be used to image the target. In this case, the forward-looking imaging of targets requires radar correlation imaging techniques. The most important step in a correlation imaging technique is the generation of the random radiation field. The random radiation field can be generated by a phased antenna array with modulated random phase shift. In the array, each antenna transmits the random phase signal to achieve high-resolution forward-looking imaging. However, it is complicated and costly to produce phased array antennas. Metamaterial antennas can obtain a fixed and constant random radiation field at a specified carrier frequency, so metamaterial antennas can replace phased array antennas to obtain high-quality forward-looking imaging results ,2. HowevThe super-resolution correlation imaging algorithm on compressed sensing can be used to process the echo signals of the phased array antenna to perform fast imaging with high resolution. However, when a phased array antenna is replaced by a metamaterial antenna, the algorithm cannot achieve imaging normally due to the phase error introduced into the echo signals . For thiThe study of microwave metamaterials begins with the verification of various special phenomena at various phases using a variety of different metamaterial units and then attempts to explain their properties using existing theories. In the area of metamaterial aperture imaging, the focus is on the tunable and broadband properties of metamaterial units .The reconstruction of target images can be achieved rapidly with metamaterial antennas. The incoherent radiation pattern at each frequency of the metamaterial antenna can be used to quickly obtain incoherent detection data of the target through only a single detection. Then the target data are processed immediately by fast imaging algorithms to complete the reconstruction of the target image ,6. ThereThe metamaterial antenna in super-resolution imaging usually refers to a two-dimensional modulation array of metamaterials formed by a combination of metamaterial units. Compared with conventional antennas, a metamaterial modulation array can be flexibly designed to achieve electromagnetic wave spatial modulation ,9,10,11.Metamaterials possess some special electromagnetic properties when compared to conventional materials.(1)Negative refractionWhen a beam of light enters conventional materials, the light is refracted; the refracted light and the incident light are on either side of the normal line. Unlike conventional materials, in metamaterials, both the refracted light and the incident light are on the same side, which means metamaterials have negative refraction.(2)Inverse Doppler effectIn conventional materials, when the transmitter and receiver start to become closer, the frequency of the electromagnetic wave received increases. However, in metamaterials, when the transmitter and receiver start to become closer, the frequency of the electromagnetic wave received increases.(3)Inverse Cherenkov effectIn conventional materials, the index of refraction is positive, so the electromagnetic waves radiated after the radiation is generated propagate forward. In metamaterials, however, the index of refraction is negative, so the electromagnetic waves radiated from radiation are propagated backwards.(1).The patterns are random. The random radiation patterns at individual frequency points are not correlated within the desired range of detection angles;(2).The patterns have certain directionality. Random radiation patterns have high gain within the bound angle and small gain or zero at the unwanted angle.To ensure the performance of metamaterial antenna coded imaging, it is usually required that the broadband metamaterial antenna has certain directionality with randomness, statistically independent characteristics at each frequency within the broadband and consistency in the integrated direction ,17,18,19According to the design goals, three models of random phase distribution, random amplitude distribution and tunable hologram are usually used to carry out the randomly encoded metamaterial antenna design. The design of metamaterial antennas requires comprehensive consideration of performance index factors, such as antenna directionality, incoherent detection sample capacity and antenna integrated gain. Considering the need for antenna gain maximization, the spatial synthesis of electromagnetic waves using phase modulation has higher energy conversion efficiency and lower energy consumption than other models. Therefore, the design of random radiation metamaterial antenna based on random phase modulation is mainly discussed.The random phase tuning broadband metamaterial antenna design method is summarized as follows: firstly, the broadband metamaterial unit is designed. Through the structure design of the metamaterial unit, the equivalent radiation phase of the metamaterial unit can traverse the design phase range in the broadband range. Secondly, the combination of metamaterial units with different equivalent radiation phases is randomly deployed in blocks to achieve random encoding of the metamaterial antenna aperture and complete the design of the broadband metamaterial random encoding antenna.Since the metamaterial structure is etched on the microstrip lines, microstrip antennas with beam stacking effect are preferred. It is difficult to achieve the beam stacking effect with a single microstrip antenna, so an array of microstrip antennas is considered in the design ,22,23,24Random radiation metamaterial antennas are realized by etching metamaterial structural units on the surface of a PCB board as a substrate. Metamaterial units with different resonance frequencies are randomly distributed on the surface of the PCB board. The energy of the guided wave structure is coupled by the different metamaterial resonant units and radiated to free space, resulting in a two-dimensional antenna aperture that can operate at several different resonant frequencies. Due to the mutual coupling effect existing between the units, the resonant characteristics at different frequencies become irregularly varied. According to the above idea and design model, a set of Ka-band metamaterial antennas were processed and implemented, as shown in A comparison of the measured radiation pattern of the metamaterial antenna at different frequencies is shown in the Since the carrier frequency of the signal used by a metamaterial antenna needs to be constantly changed, the echo signals received by different signal modes are different. The difference between the received echo signal of a single-frequency signal with constant carrier frequency and a single-frequency signal with carrier frequency stepping was analyzed.The fundamental frequency echo of a single frequency signal with constant carrier frequency can be expressed as:The fundamental frequency echo of a stepped single-carrier frequency signal can be expressed as:It is obvious that Equation (2) has an extra In the work of radar, the transmitting field needs to be modulated by the transmitting antenna, the modulated transmitting field interacts with the target scattering field and the radar antenna receives the echoes after the interaction. The scene is discretized into multiple rectangular imaging grids. Assuming that the azimuthal equal-angle interval is It can be simply expressed as:The phase To satisfy the non-correlation of the radiation field in time, the number of samples If the unit size of the matrix imaging grid is smaller than the Rayleigh aperture resolution limit, the above equation can be solved to obtain the super-resolution imaging results.The radar parameters of the field experiment are shown in The experiments were carried out in eleven different scenes. Three different sizes of corner reflector were used in the experiment, which were large, medium and small. It should be noted that in order to enable the center of the scene to be displayed in the center of the figure, the distance 17 m from the radar was moved to the “0” scale during data processing. In other words, the “0” scale position of the ordinate indicates the distance 17 m from the radar. The negative direction means closer to the radar relative to this position, and the positive direction means further away from the radar relative to this position. Similarly, the abscissa indicates the azimuth, the position of the “0” scale indicates the center position of the radar line of sight, the direction to the negative number indicates to the left relative to the position and the direction to the positive number indicates to the right relative to the position.The detail of each experimental scene and the imaging results in the experimental scenes were as follows.As shown in As shown in As shown in As shown in As shown in As shown in As shown in As shown in As shown in As shown in As shown in According to the simulation parameters in From the comparison of In general, the results of this experiment were relatively good. This experiment proved that the improved algorithm can not only realize super-resolution imaging but also has the ability to compensate phase errors. The result graphs of each group of experiments are relatively noisy in a comprehensive view, but the highlights are relatively clear.


With the growing security demands in the public, civil and military fields, unmanned aerial vehicle (UAV) intrusion detection has attracted increasing attention. In view of the shortcomings of the current UAV intrusion detection model using Wi-Fi data traffic in terms of detection accuracy, sample size reduction, and model interpretability, this paper proposes a new detection algorithm for UAV intrusion. This paper presents an interpretable intrusion detection model for UAVs based on the belief rule base (BRB). BRB can effectively use various types of information to establish any nonlinear relationship between the model input and output. It can model and simulate any nonlinear model and optimize the model parameters. However, the rule combination explosion problem is encountered in BRB if there are too many attributes. Therefore, an evidential reasoning (ER) algorithm is proposed for solving this problem. By combining the capabilities of the ER and the BRB methodologies, a new evaluation model, named the EBRB-based model, is proposed here for predicting UAV intrusion detection, even in the case of a massive number of attributes. The global optimization of the model is ensured. A new interpretable and globally optimized UAV intrusion detection model is proposed, which is the main contribution of this paper. An experimental case is used to demonstrate the implementation and application of the proposed UAV intrusion detection method. UAV intrusion detection; Interpretable model; Evidential reasoning; Belief rule base; Global optimization Birnbach et al. Researchers have made significant progress in UAV intrusion detection. However, the following problems remain. First, the evaluation accuracy of the above model is often unsatisfactory. The reason for the low accuracy is the large parameter setting error and the lack of a suitable optimization mechanism. Second, in typical data-driven models, each model has multiple nodes with multiple layers. Thus, many parameters must be estimated. This requires a lot of data. Third, machine learning could be fundamentally uninterpretable Based on Dempster-Shafer's evidence theory Our main contributions are summarized as follows:(1) This paper provides a method for solving the problem of BRB combination explosion in UAV intrusion detection. By introducing the ER algorithm, the combination explosion problem of the belief rule base is solved by ensuring the reasonable fusion of multiattribute indices.(2) An interpretable global optimization detection model is constructed. A modeling process based on the EBRB model is constructed to provide an efficient and explicable reasoning process.(3) To reduce the influence of the uncertainty of the initial parameters on the model detection accuracy, this paper uses the P-CMA-ES optimization algorithm to optimize the model parameters.The remainder of this paper is organized as follows. In Section 2Aiming at overcoming the problems that are encountered in the existing UAV intrusion detection systems, a new UAV intrusion detection model is proposed based on EBRB in this paper.2.1Aiming at actual systems, the UAV intrusion detection model proposed in this paper will solve the following three problems:(1) Combinatorial explosion of BRBJ attributes; and Q is the parameter set of the ER algorithm for data fusion.UAV intrusion detection and evaluation systems face many problems, such as many evaluation indices and complex systems. When using an ordinary BRB to build a model, the Cartesian product operation is required between indicators when building the initial BRB. Therefore, too many indicators will lead to the explosion of the BRB rule combination and affect the performance evaluation results (2) Construction of an interpretable global optimization detection modelV represents the set of parameters required by the EBRB reasoning process; and Due to the limitations of various application fields, such as military and other high-risk areas, traditional data-driven UAV intrusion detection models cannot be used. When making high-risk decisions according to an algorithm's results, it is important to know which functions have and have not been considered by the model. Artificial intelligence algorithms have always been “black boxes”, unable to provide a way to understand their internal processes. Therefore, these algorithms cannot be applied to some special fields. In addition, the relevant interpretable model is a local optimization process. This will lead to local optimization of the model. The construction of an interpretable global optimization model for UAV intrusion detection is the second problem to be solved. To solve this problem, a new model is proposed based on EBRB in this paper. Equation (3) Reduction of the influence of the uncertainty in the initial parameter values on the evaluation accuracy of the initial modelIn the UAV intrusion detection model, the values of various parameters are difficult to accurately determine due to the complex mechanism of the UAV intrusion detection system. Therefore, the parameters need to be slightly adjusted to optimize the output results using an optimization algorithm. The basic strategy of optimization is to minimize the difference between the output of the prediction model and the output of the actual system. Therefore, optimization of the model parameters to reduce the impact of the uncertainty in the initial parameter values on the evaluation accuracy of the initial model is the third problem to be solved. To solve this problem, an optimization model based on P-CMA-ES is constructed. The optimization model is constructed using Equation 2.2To solve the above three problems in engineering practice, a new UAV intrusion detection model based on EBRB is constructed in this subsection.kth rule of the EBRB; L is defined as the number of rules in the EBRB; kth rule, reflecting the relative importance of the kth rule; ith antecedent attribute; kth rule is complete, and otherwise, it is incomplete; and Based on EBRB, the structure of UAV intrusion detection model is as Equation For the developed UAV intrusion detection model, the modeling process considering both interpretability and global optimization is illustrated in 3In this part, a new UAV intrusion detection model based on EBRB is developed. This model considers that BRBs have the disadvantage of rule combination explosion in the case of multiple attributes. The general method has the problem of local optimization. Therefore, a model structure based on EBRB is proposed. The structure of the intrusion detection model is adaptively adjusted based on the belief rules and weights, while maximizing its estimation accuracy is the optimization objective.In Subsection 3.1kth rule; ith antecedent attribute value in the input data, namely, the fusion results of the ER algorithm; ith antecedent attribute; and ith indicator in the EBRB.When different indicator data are used as the input of the intrusion detection model, they can be transformed into a unified attribute reference value matching degree through a reference value set by each indicator. The matching degree of the indicator input relative to the indicator reference value can be obtained by the following formula:Having too many input indicators , a multidimensional ellipsoid population  is generated through a normal distribution.Step 2: Projection operation. The solution is projected onto a hyperplane. The parameters are constrained.Step 3: Selection and reorganization operations. The population that satisfies the constraints and approaches the optimal solution is selected as the subpopulation.Step 4: Updating the covariance matrix. When all solutions in the population meet the constraints, the covariance matrix of the population is updated.Step 5: Repeating the above operations. Until the accuracy requirements are met, the final optimal parameter The execution process of UAV intrusion detection based on the EBRB model is illustrated in 3.3As illustrated in Step 1: Construction of the UAV intrusion detection evaluation model. The weight is obtained by the coefficient of variation method. The belief distribution of evidence is obtained by a rule-based method. Initial belief rules are constructed.Step 2: Construction of the intrusion detection optimization model based on EBRB. The P-CMA-ES optimization algorithm is used to optimize the model parameters.Step 3: Obtaining the optimized model parameters. Based on the optimized model, the test data are input into the model.Step 4: Testing of the optimized UAV intrusion detection model on the testing data. Finally, the intrusion detection evaluation results are obtained.4In this section, a UAV intrusion detection dataset This case includes three parts. The UAV intrusion detection evaluation model is constructed in Subsection 4.1Based on the UAV intrusion detection evaluation method developed in Section The dataset has the two key attributes: packet size and packet arrival interval. From these two key attributes, 9 relevant characteristics are obtained through statistical analysis. According to the statistical collection process of the dataset, the indicator of the dataset is divided into a packet size  Mean squared error (MSE)(ii) Root mean square error (RMSE)MAE can well reflect the actual situation of the predicted value error and is the first choice for model prediction performance evaluation. The smaller the value is, the better the prediction performance is.(iii) Mean absolute error (MAE)−4, 1.7937×10−2 and 2.5019×10−3, respectively. To evaluate the performance of the intrusion detection model constructed in this paper, a backpropagation neural network (BP) and SVM are used for comparative experiments. The average results of 50 repeated experiments are presented in To prove the excellent robustness of the optimization model, the experiment is repeated 50 times. After 50 experimental repetitions, the average MSE, RMSE and MAE values are 4.3075×10To further prove the robustness of the model, the accuracy and precision of the model are further evaluated when the number of training data is gradually reduced. Moreover, our model is compared with KNN, logistic regression (LR), NB, SVM, decision tree (DT) and random forest (RF). The model experiment is implemented in Python and MATLAB. The experiment is repeated 50 times for each model. The average accuracy, precision and F1_score results are presented in With the gradual reduction of the size of the training set, the indicator values of the proposed method remain above 99%, as presented in 5UAV intrusion detection has attracted increasing attention in various fields. Aiming to solve the security and accuracy problems in the process of UAV intrusion detection, an EBRB model was proposed in this paper.A new interpretable global optimization method was proposed for UAV intrusion detection in this paper. The feasibility of the method was verified by experiments, which has potential engineering application value. In future work, we will continue to study the security deduction of UAV intrusion detection. Security deduction determines the cause of intrusion and detects the intrusion of UAVs through reverse security reasoning.Through research on the causes of intrusion, the UAV intrusion detection model will be further strengthened. Through continuous development, a spiral principal UAV intrusion detection system will be formed, and the detection ability of the system will be continuously improved.Yawen Xie: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Wei He, Hailong Zhu, Ruohan Yang, Quanqi Mu: Conceived and designed the experiments; Analyzed and interpreted the data.Postdoctoral Science Foundation of China [2020M683736], the 10.13039/501100005046Natural Science Foundation of Heilongjiang Province of China [LH2021F038], the innovation practice project of college students in Heilongjiang Province , the graduate quality training and improvement project of 10.13039/501100013772Harbin Normal University [1504120015], the graduate academic innovation project of 10.13039/501100013772Harbin Normal University .Dr Wei He was supported by the http://mason.gmu.edu/~lzhao9/materials/data/UAV/Data associated with this study has been deposited at The authors declare no conflict of interest.No additional information is available for this paper.


A turnout switch machine is key equipment in a railway, and its fault condition has an enormous impact on the safety of train operation. Electrohydraulic switch machines are increasingly used in high-speed railways, and how to extract effective fault features from their working condition monitoring signal is a difficult problem. This paper focuses on the sectionalized feature extraction method of the oil pressure signal of the electrohydraulic switch machine and realizes the fault detection of the switch machine based on this method. First, the oil pressure signal is divided into three stages according to the working principle and action process of the switch machine, and multiple features of each stage are extracted. Then the max-relevance and min-redundancy (mRMR) algorithm is applied to select the effective features. Finally, the mini batch k-means method is used to achieve unsupervised fault diagnosis. Through experimental verification, this method can not only derive the best sectionalization mode and feature types of the oil pressure signal, but also achieve the fault diagnosis and the prediction of the status of the electrohydraulic switch machine. In a railway, a switch machine is track switch equipment that makes train transfer from one track to another, and it is an important signal device to ensure the train operation safety. A switch machine is often eroded under a poor working environment with high intensity and heavy load, which leads to fault occurrence. The fault of switch machines may cause serious accidents, such as train derailment and capsizing, resulting in heavy casualties and property losses. Fault detection of switch machines is very important for railway transportation safety. However, for a long time, the fault detection of switch machines mainly depends on the expert knowledge and experience of railway workers, or adopts a simple threshold setting method, which not only are inefficient but also bring a heavy workload to railway workers, which often leads to misjudgment.Recently, many fault diagnosis methods combining a support vector machine (SVM), fuzzy logic system, artificial neural network (ANN), and others have been constantly appearing. Asada  proposedThe intelligent fault diagnosis methods were also applied to some special electric switch machines, such as ZD6 and S700K. The similarity function was defined by the Fréchet distance, action current template curves were built, and the fault diagnosis method according to the greatest curve similarity was constructed for a ZD6 switch machine in . In 15]15], the However, there are other types of switch machine, which are applied in different railway passenger stations, freight stations, and marshalling stations. An electrohydraulic switch machine is a new type of switch machine that has appeared in China since the 1980s, which is suitable for the development trend of a high-speed railway. An electrohydraulic switch machine uses hydraulic transmission, and hydraulic oil is generally utilized as a working medium. Additionally, the oil pressure signal contains a lot of useful information about operation and the fault status of an electrohydraulic switch machine. Zhou  applied For the above reasons, a novel fault detection method for an electrohydraulic switch machine based on the sectionalized feature extraction according to the best time ratio from the oil pressure signal is proposed in this paper. The rest of the paper is organized as follows: In order to extract the features of the different action states in the switching process, the original oil pressure time series is divided into multiple intervals, and the feature parameters of each interval are calculated. In contrast to the method of directly extracting the statistical parameters of the entire oil pressure curve, this method of sectionalized feature extraction allows for the preservation of both the detailed feature information for each interval and the entire signal. According to the working principle of the electrohydraulic switch machine, the whole switching process is mainly divided into three stages: unlocking, conversion, and locking. Each stage is completed by a different working principle, so it makes sense to study the time ratio of the oil pressure signal sectionalization. Based on the working principle and practical experience, this paper proposes the “three-stage method” for the sectionalization of the oil pressure signal, with a sectionalized time ratio of 30%–60%–10%, which divides the entire oil pressure signal into three stages according to this time ratio, as shown in The process of feature extraction in each interval is to map the original oil pressure signals into the fault feature space. The time domain features can reflect the energy distribution and various effects of the signal and effectively represent the action states of the switch machine. In order to describe the state of the oil pressure signal for each interval, the following statistical features are used in this paper, and their calculation formulas are shown in We suppose that the original oil pressure signal is The oil pressure feature set inevitably contains a lot of noise and the random fluctuation caused by the non-stationarity of the oil pump, internal equipment, and environment. In addition, some of the extracted feature values change drastically, while others vary with small numerical fluctuations, which leads to the features with large fluctuations playing a more critical role than the others. Locally weighted regression (LWR) smoothing is a regression method used to smoothen a volatile time series. It is a nonparametric method where least squares regression is performed in localized subsets, which makes it a suitable candidate for smoothing any fluctuating numerical vector. LWR is superior to ordinary smoothing methods in filtering random changes and revealing feature trends .The process of LWR smoothing is simply defined as follows: First, the feature data are divided into small intervals with a sliding window, linear fitting is performed through weighted least squares within the interval, and the fitted value of the focal point in each interval is obtained. Then, this process is repeated continuously with the window sliding for all the feature data. Finally, the centers of these regression curves are connected to form a complete regression curve. LWR can remove error points polluted by noise and random fluctuation. LWR adds weight to the ordinary least squares, and the points near the fitting point should have a greater impact on the fitting value. Let us assume that we use LWR to smoothly fit a curve of  or cubic function (C function). The C function is commonly used in the first iteration, and the B function in the second iteration . The calLWR is employed to remove drastic changes, noise, and spike information and to improve the accuracy of fault classification.There are different unit dimension features that cannot make an evaluation in such a multidimension system. Therefore, in order to ensure the reliability of the results, it is necessary to normalize the oil pressure feature set. The normalization processing scales the data to a specific interval within a certain range. The purpose is to remove the unit limit of data and transform all the features into a nondimensional data. Here, we use min–max normalization to map the smoothed oil pressure feature set to domain (0–1). Min–max normalization can be calculated as:To reduce the computational complexity, traditional methods are to directly reduce the dimensions of the feature. Related methods include local linear embedding (LLE), local preserving projection (LPP), principal component analysis (PCA), and so on. These methods reduce the feature’s dimensions through space mapping . In 30,,30,31, tIf two features are completely related, they are mutually redundant features. We brought the idea of the max-relevance and min-redundancy (mRMR) algorithm in ; that isThe features selected by maximum relevance are likely to have some redundant features, the removal of which will have no effect on the classification result but will significantly reduce the computational effort of the classification algorithm. The selection and removal of mutually exclusive features using minimum redundancy is expressed as:Step 1: Collecting the oil pressure signals from the left and right sides of the oil cylinder of an electrohydraulic switch machine;Step 2: Sectionalizing the oil pressure signal according to the time ratio (30%–60%–10%) for three stages;Step 3: Calculating five types of time domain features of each segment for the oil pressure signal;Step 4: Smoothing the features by locally weighted regression (LWR) and normalizing the smoothed features by min–max normalization;Step 5: The max-relevance and min-redundancy (mRMR) algorithm is employed to eliminate redundant features and obtain the optimal fault feature set;Step 6: The mini batch k-means clustering method is used to achieve the fault detection of the electrohydraulic switch machine.The process of fault detection of an electrohydraulic switch machine based on the oil-pressure-signal-sectionalized feature extraction method is illustrated in The faults of the electrohydraulic switch machine being studied in this paper are mainly mechanical faults. Common mechanical faults include mechanical resistance, oil cylinder action not in place, oil cylinder in place with contact point not closed or rebound broken indication, and so on. Several common fault types and cause analysis are shown in A measuring device was used to collect oil pressure signals from an electrohydraulic switch machine. The measuring device consisted of an acquisition instrument, oil pressure sensors, and a computer. The signals were collected by deploying an oil pressure sensor on the left and right sides of the oil cylinder of the switch machine. The collected data of the sensors were transmitted to the acquisition instrument, which then was sent to the computer. The sensors collected approximately 1000 sets of oil pressure signals during the action process of the electrohydraulic switch machine with a sampling frequency of 50 Hz, an acquisition time of 12 s, and a measurement range of 0 to 14.8 MPa. In the experiments, five types of faults are made: fault-free , fault-free , turnout not locking , turnout not locking , abnormal resistance in the locking stages , as shown in The purpose of this fault clustering experiment was to evaluate the fault identification results of different sectionalized modes of feature extraction. The scheme not only extracted the most important feature types, but also identified the classes of fault clustering. At first, in order to be able to extract more valid information, the sectionalized mode of three stages with the time ratio (30%–60%–10%) and the five feature parameters proposed in Mini batch k-means clustering was used for clustering analysis in the experiments. The traditional k-means algorithm is used to calculate the distance from all sample points to all centers of mass. If the feature dimension of the sample is too large, the k-means algorithm will be very time-consuming. The mini batch k-means algorithm is an optimized variant of the k-means algorithm in which a small subset of data is randomly selected for each training to reduce computation time while optimizing the aim function.In order to better display data characteristics, PCA was used to reduce the dimension of feature sets to 2. The batch size was set to 100, and the other parameters were fixed in the experiments. The green cluster ) and the purple cluster ) were always close to each other in Additionally, the external metrics for the accuracy of the results were evaluated. To improve the experiment analysis, we reran mini batch k-means with 10 different initial random seeds, mean shift with 10 different eps, and density-based spatial clustering of applications with noise (DBSCAN) with 10 different bandwidths. Mean shift and DBSCAN were applied to compare the validity of different clustering methods. The average of accuracy and root-mean-square error (RMSE) for different datasets after clustering are shown in To verify whether the features obtained after eliminating redundant features with mRMR would have better performance on the clustering effect, the remaining features except for the selected features (Dataset I) with mRMR composed Dataset V. The experiment results were obtained by the average of 10 trials based on mini batch k-means. The validity of the proposed method was compared with different clustering methods. The diagnosis results for different datasets after clustering are shown in There is little research on fault detection methods for electrohydraulic switch machines now. This paper compared the proposed diagnosis method with the existing techniques for a fuzzy clustering algorithm  and greyThe experimental comparisons showed that the sectionalized feature extraction method according to the three action stages (30%–60%–10%) of a switch machine is more robust and effective for fault clustering than other methods. On the basis of the above sectionalization mode, it is necessary to choose the optimal features, and the most effective features can be singled out by mRMR method. Finally, the proposed diagnosis method of electrohydraulic switch machines based on mini batch k-means had the lowest misdiagnosis rate compared with other existing methods.Therefore, it can be found that the proposed intelligent fault detection method can not only get the optimal features and identify different action states, but also detect faults at a higher accuracy rate. The effectiveness of the proposed sectionalized feature extraction method is verified successfully by experiments.The fault detection of the electrohydraulic switch machine based on sectionalized feature extraction from the oil pressure signal during the working process was proposed in this paper. The fault detection framework for the electrohydraulic switch machine was established. First, the whole oil pressure signal was divided into three stages with the sectionalization time ratio (30%–60%–10%) according to the switching process. Five features of each stage of the oil pressure signal were computed, and the features were smoothed and normalized. Then, the mRMR algorithm was used to eliminate redundant features and derive the optimal feature set. The mini batch k-means clustering method was applied to achieve the fault detection of the electrohydraulic switch machine. The contrastive experiments verified the effectiveness and accuracy of the proposed method.We came to the conclusion that (1) the mean, peak-to-average ratio (PAR), and impulse (IM) of the oil pressure signal interval stage were superior to other types of features for the fault identification of an electrohydraulic switch machine, whereas kurtosis (Ku) and variance (Var) did not perform as well in terms of fault clustering. (2) Moreover, the features extracted from the unlocking and locking stages outnumbered those of the conversion stage, which meant the different fault information in each stage. (3) The fault detection method proposed in this paper, which was based on the unsupervised algorithm, can realize free-label fault detection in high recognition. The proposed method can provide support for railway staff without the cost of massive sample data. The experiments verified that the proposed diagnosis method could accurately identify faults of electrohydraulic switch machines and reduce economic costs. Due to the limited fault sample data collected in this paper, we will acquire more comprehensive fault sample data as much as possible in the next step to further increase the accuracy of the method. In the future, we will improve the method to fully meet the needs of practical engineering application.