Injection moulding is currently the most widely employed production method for polymer gears. Current standardised gear metrology methods, which are based on metal gear inspection procedures, do not provide the key information regarding the geometric stability of injection moulded gears and are insufficient for a thorough gear inspection. The study developed novel areal quality parameters, along with a so-called moulding runout quality parameter, with a focus on the injection moulding method. The developed parameters were validated on twenty-nine gear samples, produced in the same moulding tool using various processing parameters. The gears were measured using a high-precision structured-light 3D scanner. The influence of injection moulding process parameters on the introduced novel quality parameters was investigated. The developed moulding runout quality parameter proved to be effective in evaluating the shrinkage that can occur in the injection moulding process. The novel moulding runout parameter returned an average value of −21.8 μm in comparison to 29.4 μm exhibited by the standard parameter on all the gears, where the negative value points directly to mould shrinkages. The rate of cooling was determined to be the most influential factor for the shrinkage of the gear. The developed areal parameters demonstrated to be advantageous in characterising the deviations on the teeth more comprehensively. High-performance polymer gears are a modern technology that is increasingly replacing metal gears due to their many advantages. Mass production is cheaper if the gears are produced with injection moulding. They can operate without additional lubrication, which makes them interesting for applications where a lubricant is not desired . Polymer gears dampen vibrations better and have significantly lower operating noise . PolymerPolymer gears have a number of drawbacks, the most notable of which are reduced load-bearing capacity, poorer thermal conductivity, lower temperature stability, and poor manufacturing precision. While the load-bearing capacity is extremely important, several studies can be found on improving this property, either with improved gear design ,3 or impPolymer gears can be produced by classical cutting processes or, for large series production, by injection moulding . InjectiThe gears’ geometry is typically characterised by standard geometrical parameters defined in the standard ISO 1328-1:2013 . The codCurrently, gear measurement is predominantly done by tactile methods. A typical gear measurement procedure measures one profile on both flanks of three or four out of all the teeth, measuring one pitch point on each flank, and evaluating the deviations according to the standards ,18. ReceThis study aims to develop and introduce novel parameters, which would facilitate an enhanced gear inspection and better describe the deviations that occur during the injection moulding process.The basics for the 3D evaluation according to the surface model of the gear was firstly introduced by Werner Lotze . StöbeneDevelopment and evaluation of novel injection quality parameters and areal surface quality parameters.Investigation of the influence of injection moulding process parameters on the introduced novel quality parameters.Enhancement of the gear quality assessment using the developed analysis procedure.A method for rapid refinement of the injection moulding process parameters in order to achieve the required precision of the produced gears.The paper introduces new geometrical parameters and applies them to manufactured gears using the injection moulded process. In summary, the main goals of this paper are:The study aims to develop novel geometrical parameters for enhanced optical gear inspection. To validate the parameters, multiple gears were manufactured with the injection moulding process. The production of twenty-nine gears fabricated in the same moulding tool using various processing parameters is described in All the gears used in this study were produced using the POM-H thermoplastic Delrin 100 NC010 , which is widely used for polymer power transmission applications due to very favourable wear resistance and fatigue strength. The material’s most relevant thermomechanical and processing parameters are listed in The parameters of the manufactured gears (per VDI2736) are presented in As with other manufacturing methods, where many process parameters influence the geometric quality of products ,30,31,32In general, the key issue related to injection moulding gear production is the material shrinkage that occurs during processing. The thermoplastic POM is especially susceptible to geometric instability and requires special attention to the entire injection moulding process to achieve suitable accuracy of the produced gears. In our study, the gears were produced on a Krauss-Maffei CX80-160 machine using a single-cavity mould produced from 1.2343/X37CrMoV5-1 (DIN EN ISO 4957) steel, heat-treated to 49 ± 1 HRC. The gearing region and centre hole in the cavity were produced with an accuracy range of 0.01 mm. A triple-pin gate was implemented, with the pins positioned symmetrically above the centre-hole radius. To account for the polymer shrinkage after moulding, the cavity was expanded in the radial direction by an average rate of 2.2%.The process parameters of manufactured gears are shown in The optical measurements of the manufactured gears were performed using a structured light scanner. The ATOS Compact SCAN 5M  scanner was employed, which has a reported laboratory accuracy of about 2 µm. A standard calibration panel CP40 was used to calibrate the scanner before each test at room conditions. Ahead of measurement, the gears were coated with an anti-reflecting powder. The gears were placed on a turntable to capture the geometry from multiple angles. Markers were placed on the gears to help stitch the data from different views together. The scan is saved as an STL file. The process and setup are more accurately described in . The surThe gears were carefully aligned to the CAD model to ensure the proper determination of the workpiece deviations . The refThe scanned data was then processed with the software developed in our previous research . The detus study .The standard parameters, however, do not describe the total deviations that can occur on the gear. Furthermore, they do not take into account the possible shrinkage, which can occur during the injection moulding process. For this reason, a parameter Given that the developed inspection method enables a holistic acquisition of points, the parameters could be determined on the whole gear. Therefore, novel areal parameters to facilitate the available information are suggested and introduced in The first parameter, aiming to enhance the runout parameter Equation :(1)Fmr= that can occur during the injection moulding process. If the ideal displacement value is in the middle of the minimum and maximum value, the parameter d is calculated according to the standard, and the values of the parameter The limit values of the grades for 8-1:1995  as it al8-1:1995 . The limThe novel areal parameters for determining the flank surface deviations are determined in a manner similar to the standard flank parameters. However, as opposed to standard quality parameters, where only linear 2D profile measurements on four teeth are used, in this case, the surface data of all the teeth is taken along with the total deviation relative to the CAD reference geometry. Similarly to the process in the standard, the evaluation length is determined along the profile length and the width of the gear. Along the gear width, 90% of the data is considered for evaluation. Along the teeth profiles, 92% of data is considered for evaluation, starting from the base radius The roll length can be equated to the arc length of points T on the base circle that are formed by connecting a tangent from the measured points (index m) to the base circle. The coordinates quations  and 4)..yT, and Equation .(3)yT=rThe roll length can be calculated as the arc length using Equation . The parThis enables the calculation of new parameters flank surface deviation The flank surface deviation x (roll length) and z (gear width) be the independent variables and y (deviation) the dependent variable. The transformation we want to estimate is y direction. The coefficients To calculate the surface profile slope deviation Likewise, the surface lead profile slope deviation can be calculated as:x, y, and z of the maximal and minimal value are known, therefore, the coefficient To calculate the surface form deviation Equation :(10)ff,SThe parameter b, and reference diameter d are calculated according to the standard, and the values of the parameters are rounded accordingly to specified rules. The left and right flanks of the teeth are evaluated separately.The largest value of the parameters on all the teeth is taken, and the quality grade is determined according to the limit values defined by the equations below. These equations define the limit values for quality grade 5. The allowed deviations for the other quality grades are determined using the geometric series with a step of In determining the new areal parameters, instead of one least squared distance plane, two planes could be fitted with a slope in only one direction each. Furthermore, the parameter After the quality parameters were determined, an open-source data visualisation, machine learning, and data mining toolkit was used to perform the linear regression and to calculate the dependency of the quality parameters to each of the process parameters . The empThe results for the novel parameters are presented in The standard quality parameters are displayed in The quality grade limit values for the areal parameters seem to be set appropriately, however, the parameter The correlation of the different input parameters to the target parameter was evaluated using the Spearman correlation. The correlation is presented in The parameter e et al.  and Kuo e et al.  which ste et al. .The coefficients of the linear regression for parameter Equation :(15)Fmr=The results for the areal parameters are only shown for the left flank of the teeth because of space constraints. The correlations, shown in The flank surface deviation The surface form deviation The temperature of the water (mould) was determined to have the greatest influence on the surface profile slope deviation The surface lead profile slope deviation The general Equation  to calcuThe average value of the surface profile slope deviation  samples , denotesThe developed parameter The influence of the moulding process parameters on the new quality parameters was investigated. The rate of cooling was determined to be the most influential factor for the shrinkage of the gears, which we were able to determine through the parameter The developed analysis will contribute to an enhanced quality assessment of gears and a refinement of the injection moulding process parameters.The introduced quality parameters and evaluation methods are useful for both gear manufacturers and developers in R&D departments. With this method, we can quickly characterise the geometrical quality using commercially available scanners while considering surface deviations and shrinkages typical of injection moulded gears. The method also offers many possibilities for automating measuring procedures, which could allow measurements to be performed not only on a pair of samples from a batch but on a much larger number by means of automated in-process control.Injection moulding is a specific gear production process that results in distinct types of gear geometry deviations. This study presents an upgraded and enhanced geometric characterisation of injection moulded thermoplastic gears. New geometric parameters were proposed and evaluated on 3D-scan based measurement data of manufactured polymer gears. The main conclusions from the work in this study are as follows:Future work will include research on different gear geometries with the goal of confirming the general applicability of the developed methods on spur as well as helical polymer gears. Additionally, using the described metrological approach, the classical injection moulding method will be compared to the more recently developed Variotherm method, which, if properly implemented, can yield more precise plastic parts, as well as superior crystallisation homogeneity of the injection moulded polymer structure. The goal will be to perform a comprehensive analysis to assess which moulding method is more suitable in terms of achievable gear precision and general quality, as well as repeatability of the produced gears. Additionally, 3D-scanning-based areal measurement methods offer a unique possibility to automate the gear measurement and quality evaluation process, and such an approach is aimed to be studied in the future. Here, challenges like precise positioning and adjustment of the measurement point cloud as well as repeatability are crucial to obtain useful gear quality information while substantially speeding up the measurement process.


The measures taken to cope with the COVID-19 pandemic by governments worldwide have vast consequences on all areas of life. To assess the impact of the COVID-19 pandemic on long-term career development, we evaluated the work-family balance of medical doctors at nine German university clinics. The results indicate a severely disturbed work-family balance, which was mostly due to insufficient childcare, based on restrictions in school operations and childcare. Despite the newly created emergency childcare options, aiming to ensure the functioning of the “systematically important” professional groups, medical doctors feel that they are not sufficiently supported by the measures taken by local governments. Women, in particular, see their professional development at risk. Our results underline that proper and flexible childcare is essential for the career advancement of female medical doctors and is particularly important in times of crises such as the current COVID-19 pandemic. At university medicine clinics, increased work time flexibility and optimized schooling and childcare are needed to promote the career development of female as well as male medical doctors in the early stage of their careers.  The COVID-19 pandemic has resulted in severe restrictions in many areas of life. Initially, the focus was on the immediate health threat and the containment of the pandemic. In Germany, the central efforts of the state and society were meant to counteract an overload of the health system caused by the pandemic . These aWomen and children are considered to be the group that has been most severely socially affected by the consequences of the pandemic . More thThe gender care gap, which is the different time expenditure for unpaid care work for men and women, is aggravated by the pandemic. The gap in terms of equality between men and women is widening . The comThe gender gap is a scientifically proven fact in the medical sector, regardless of the COVID-19 pandemic. Although there are more female than male medical students, the number of women in leading academic medical positions is still by far comparably low. This fact is accompanied by a gender pay gap, further illustrating the gender inequalities in academic medicine . This apUniversity hospitals are considered one of the most important and indispensable pillars of healthcare in the current situation. For the first time in Germany, in this study we intended to depict the status of the work-family balance among doctors in German university hospitals in the context of the COVID-19 pandemic. This was achieved using a newly developed structured questionnaire, designed to characterize the areas of tension in a profession that has been structurally relevant since the first hour of the pandemic, in which attendance is predominantly mandatory and at the same time in which family obligations cannot be neglected. By focusing on the assessment of the perceived stress and the perception of the political measures implemented to secure a systemically important workforce, essential aspects of the work-family conflict have been brought into the light by the COVID-19 pandemic. Their analysis from the perspective of gender equality enables the deduction of suggestions for improving the work-family balance, as well as measures to promote gender equality during the COVID-19 pandemic and beyond.A structured 18-point questionnaire was designed to depict the areas of the professional and family life of medical doctors. It was organized in such a way as to collect data about gender, the number of children and qualifications, as well as the initial professional and family situation. In addition, there was a differentiation between workload and the combination of family obligations and workload. Furthermore options and suggestions for optimization were recorded and the effects of the current overall situation on each respondent’s own professional career were assessed. The questions were all closed questions with given possibilities of answer, with some questions having several possibilities for responses. Finally, the participants were able to voluntarily name their specialist area and add other aspects of importance in free text. However, this last part did not undergo analysis but served as a source of additional information to avoid missing central aspects not addressed in the questionnaire.The survey and the evaluation were carried out via the Evasys survey portal, anonymously and in accordance with data protection regulations. The results were analyzed automatically through the survey portal as all questions were closed. A statistical analysis of central aspects was carried out, using one-sided exact tests according to the Fisher test function in the statistical programming environment R .The survey was explicitly aimed at parents with children requiring care in the medical service at university hospitals. The invitation was sent via e-mail to all medical doctors at the University Medical Center Göttingen (UMG) and to eight other university hospitals nationwide: Bochum, Dresden, Duesseldorf, Freiburg, Greifswald, Kiel, Lübeck and Mainz. Contact was made via Equal Opportunities Representatives, who are connected via the Federal Conference of Equal Opportunities Representatives at Universities (Bundeskonferenz der Frauen- und Gleichstellungsbeauftragten an Hochschulen e.V (Bukof)), as well as through the German Medical Women’s Association. In the following, we will refer to the participating university clinics nationwide as Bukof clinics. The survey started on 14 May 2020, a reminder was sent by email on 2 June 2020 and the survey was closed on 5 June 2020.A total of 656 medical doctors from the nine university clinics (UMG and eight Bukof clinics) took part in the survey. Due to the high participation rate and the balanced gender ratio, the UMG collective was analyzed separately and compared with the nationwide collective of the Bukof clinics.At the UMG, the survey was sent to the entire “doctors distribution list”, comprising 1270 doctors. The survey was explicitly aimed at parents with children requiring care. At the UMG there were 447 medical employees with children under the age of 18 (48.7% women). One hundred eighty-nine colleagues took part, which corresponds to a participation (response rate) of 42.2%. The balanced participation of both genders (48.7% women and 51.3% men) was particularly noticeable, whereas women (82.5%) clearly comprised most of the 467 participants nationwide . Around The focus of activities of the doctors at the UMG and the Bukof clinics was predominantly conservative. Both collectives included employees from the “COVID-19 team” (colleagues who were primarily involved in the treatment of patients infected with SARS-CoV-2). Seventy percent of the doctors participating in the UMG and 72% of the doctors nationwide stated that they had at least two children .Most of the doctors  did not make use of private childcare before the start of the COVID-19 pandemic. They were therefore largely dependent on public childcare facilities to be able to carry out their professional activities. After the start of the pandemic, only a small proportion of the doctors were able to top up their existing private childcare or to initiate new ones in order to cover parts of the care or off-peak times . Emergency childcare (including public care facilities and company emergency childcare) was offered to 75.4% (UMG) and 72.2% (Bukof clinics) of the doctors; however, this only covered 22.6% (UMG) and 28.6% (Bukof clinics) of the working hours (proportions about the same for both sexes). We found that 66.7% of the doctors at the UMG and 69% nationwide felt that they were not adequately supported by the childcare modalities created.The majority of the doctors in both groups (>78%) rated the combination of work and family stress during the COVID-19 pandemic as higher or significantly higher than before. This again primarily applied to the women in both groups, with 85.2% (UMG) and 83.4% (Bukof clinics) . This reThe proportion of doctors in both groups with difficult or no options for working-time adjustments was similarly high (>60%). Only a small proportion (<10%) stated that working-time adjustments were not necessary due to their having sufficient childcare. Compensation by the partner was more likely for male doctors  than for female doctors (UMG: 9.3% Bukof clinics 11%) . FurtherOrganizational aspects were also in the foreground for both collectives, such as improving childcare and support from schools, as well as flexibility in terms of working hours and long-term planning. The focus was not on the possibility of reducing working hours; more freedom and flexibility was desired regarding working hours. Support through a stronger commitment from partners tended to be in the background, but here mostly female doctors from both collectives wished for better support .Thirty-three percent of those surveyed at the UMG stated that their careers were suffering under the current conditions; nationwide this was 37%. If one stratifies the data according to the gender of the UMG participants, it is noticeable that 36.3% of the female doctors stated that their careers were suffering from the changed conditions, compared with only 29.5% of the male doctors . LookingRegardless of their profession, a high level of stress has been reported for many parents during the pandemic ,17. ThisOverall, it is becoming clear that the political requirements for creating emergency care and its practical implementation are insufficient. Their effectiveness should be reconsidered promptly and corrective measures should be taken. This is of particular importance in order to not further undermine the already insufficient measures to promote equality and a work-family balance for female doctors.For most doctors, emergency care does not adequately reflect working hours, even if they work part-time. Even the somewhat extensive, newly-created emergency childcare offered within the companies, which were often highlighted very positively in the free text comments in this study, cannot provide a sufficient remedy here, as many children are not cared for in the companies. Only a small number of doctors were able to achieve flexibility through private childcare, the financing of which was not recorded. The majority of the doctors were completely dependent on emergency childcare from public institutions. It is not surprising that the majority (>78%) estimated the professional and private double burden to be higher or significantly higher than before the COVID-19 pandemic. This problem is exacerbated by the combination of inadequate childcare and little or no possibility of adapting working hours in an occupation requiring attendance. In both groups , similar demands for improvement were made regardless of gender. The support factors favored in this survey were better-adapted childcare and schooling, as well as flexible options for organizing work and taking advantage of offers of assistance. These are already part of the recommendations for reducing stress and psychological distress for health professionals during the current COVID-19 pandemic .Male doctors also rated the childcare situation as inadequate and the double burden as high. However, female doctors were more affected, due to their higher burden of family care-work ,18. Due In particular, female interns and senior physicians feel that their career development is more impaired than their male colleagues do. This finding is underlined by the literature: after an analysis of 60,000 articles in international journals, the proportion of scientific articles by female first authors decreased considerably . The herBoth female and male doctors desire more flexible working hours so that they can better adjust to the requirements of their families. The focus is explicitly on more flexibility in working hours and not on reducing them. It is well known that the adjustment of working hours is more common and more recognized for female doctors than for male colleagues, who, as our data show, often have even greater difficulties in terms of flexible organization. This becomes much clearer under the intensified conditions of the pandemic, but should also be relevant under normal circumstances.The early phase of the COVID-19 pandemic already revealed the insufficiency of the emergency childcare system created. This is an issue of particular importance as it further undermines the already insufficient measures to promote equality and work-family balance for female doctors. Female doctors are more affected, due to their higher burden of family care-work ,18, whicThe aim of not pushing a health system to its limits includes, in addition to (intensive) medical capacity increases, maintaining the workforce and health of indispensable actors ,25,26. TMore flexible working hours for both genders and their implementation and acceptance as an explicit option for male colleagues may also be a way of relieving and thus promoting the careers of female doctors.Overall, the COVID-19 pandemic demands the adaptability not only of individual employees in the health system but also of employers to maintain the ability of employees to work. The explicit promotion of opportunities for the development of scientific careers for female doctors with families also appears necessary. Adaptable childcare concepts, especially during the COVID-19 crisis, but also beyond it, are still an important component in promoting employees with families.Gender analyses during the COVID-19 pandemic are useful in order to uncover structural deficits that have become more apparent during the crisis and to make them public. Although our study mainly focuses on the specific aspect of work-family stress during the COVID-10 pandemic, concrete research and knowledge of the deficits offers the opportunity to find new solutions and to transform the initially negative consequences of the pandemic into a structural improvement.


We present a novel computational model of the human skin designed to investigate dielectric spectroscopy electrodes for stratum corneum hydration monitoring. The multilayer skin model allows for the swelling of the stratum corneum, as well as the variations of the dielectric properties under several hydration levels. According to the results, the stratum corneum thickness variations should not be neglected. For high hydration levels, swelling reduces the skin capacitance in comparison to a fixed stratum corneum thickness model. In addition, different fringing-field electrodes are evaluated in terms of sensitivity to the stratum corneum hydration level. As expected, both conductance and capacitance types of electrodes are influenced by the electrode geometry and dimension. However, the sensitivity of the conductance electrodes is more affected by dimension changes than the capacitance electrode leading to potential design optimization. Commercially available and well-established instruments, such as the MoistureMeterD (Delphin Technology AG), the Corneometerherapies ,2,3. Mucherapies ,5,6.A numerical model simulating the dielectric properties of human skin can help to understand the effects of dielectric spectroscopy within the skin and to study the influence of skin hydration. Various publications characterize biological tissues ,8,9 and The outermost layer of skin, the stratum corneum (SC), functions as a barrier to water loss and as a barrier to exogenous chemical penetration. SC water content is known to reflect skin health, and is related to changes in elasticity, flexibility, and surface morphology ,17,18. LThe objective of this work consists of the development of a reliable, computationally efficient numerical model for the hydration-dependent dielectric behavior of the human skin. A multilayer skin model was set up, each layer characterized with its dispersive dielectric properties, in combination with a SC hydration model. Focusing on the SC layer, the dispersive dielectric parameters were fitted to estimate the dielectric properties under the influence of hydration. To further investigate hydration influences on dielectric spectroscopy, the SC thickness was set up to be hydration-dependent as well.With the SC hydration model, the range of water concentration was investigated by exposing the skin surface to air at various relative humidities. Three different fringing-field electrodes were employed on the skin model in order to investigate the influence of the hydration-dependent SC thickness on the dielectric spectroscopy. Finally, a sensitivity analysis was performed with the three different fringing-field electrode types with various geometries.Different physical models are combined to simulate the behavior of the human skin under dielectric spectroscopy measurements. Various work investigated the SC’s hydration influences. The hydration dependency of the dielectric properties is reported in , and theThis section introduces the stratum corneum model, as proposed by . The finv the convective velocity in D is the diffusivity at depth in The hydration model of the stratum corneum describes, on one hand, the hydration profile and the water gradient, and on the other hand, the change in the thickness (swelling and shrinking) with varying hydration. The convection–diffusion PDE with a moving boundary sufficiently describes the swelling model of the SC, that is,The convective velocity is caused by the flux at the lower boundary. It can vary with time, but is not depth-dependent because it is assumed that the water partial molar volume in the SC is equal to the pure water molar volume. We haveposed in .The moving boundary describes the swelling and shrinking of the SC, where its thickness −1 is the mass transfer coefficient [−1 is water molecular weight, and If the skin is in contact with air, the flux at the upper boundary is dependent on the relative ambient humidity, and can be described byfficient , aw the V (g water/g dry tissue) can be determined by the Guggenheim–Anderson–deBoer (GAB) isothermV according to Equation  . The ass density . With thmined in  from the[43.4 μm .n is the number of dispersions, nth permittivity increment, nth relaxation time, nth broadening parameter, Biological tissue is a very heterogeneous material, and various components influence the dielectric properties, such as concentration of free water, bound water, and molecular compositions. The dielectric dispersion characteristics (or Debye-type dispersion) of biological tissues are commonly approximated by a Cole–Cole model ,21,22,26The frequency-dependent relationship between the conductivity and relative permittivity isantities .free parameters are caused by the free water in SC and the slow parameters are assumed to be caused by protein polarization.The optical permittivity directly depends on the permittivity increment of free waterIn , it was The value 3.3 in  represenAs stated in , the dieers from  undergo quations  and 8)..Δεfree wWe obtainThe interpolation equations take the formThe final estimated relative permittivity for the SC is formulated asFor dielectric spectroscopy, sensors with different electrode geometries and different electrode setups are available . These sensors can be categorized according to their measurement principle as a conductance sensor and capacitance sensor. For the conductance measurement, the electrodes are in direct contact with the skin, whereas for the capacitance measurements, the sensors have an insulating layer between the electrodes and the skin .C of the skin can be calculated by solving the current conservation equationsThe dimensions of the electrodes and the skin are much smaller than the smallest wavelength of the applied signal. Therefore, a quasi-static approximation of Maxwell’s equations can be applied with Q the charge density, V the applied electric potential, Here, ® version 5.6  was used.For the numerical computation of the above-listed models, the finite-element method (FEM)-based simulation software COMSOL MultiphysicsAs explained in For the evaluation of the water concentration in the SC and the reproduction of the measurements in , the dynUnder the assumption that the model resembles realistic dispersive dielectric skin behavior, various influences on the electrodes’ measurements were investigated. The skin model was dimensioned  so that the boundaries of electric insulation As mentioned in 3 is proposed in [3 and within the linear relation. This justifies the linear approximation of the dielectric parameters in For a better insight of the stratum corneum water concentration range under conditions without special influences , the boundaries were evaluated by exposing the SC surface to air with a humidity level of 0% and 100% by means of the dynamics of water transport in SC . The simposed in . The meaWith the changing dielectric SC properties depending on the water content, the question arises as to what influence the SC thickness, also depending on the water content, has on the measurement. The influence of the varying thickness has been investigated per electrode type at a measurement frequency of 1 The following points must be considered when interpreting the simulated effects of the comparison of skin with SC swelling with skin with constant thickness. The major component of simulated capacitance is due to the electric field that penetrates into the epidermis/dermis layer because it has higher relative permittivity than SC, see The increase of the capacitance for water activity The magnitude difference between the variable and constant thickness is again due to the influence of the epidermis/dermis layer. At constant thickness (here at dry thickness According to this model, varying the thickness depending on the hydration level has a significant impact on the calculated capacitance that cannot be neglected. The penetration depth of the electric field could also be investigated by increasing the SC thickness until the capacitance converges and the influence of the epidermis becomes negligible.This effect is as expected. The drop in the magnitude of the capacitance with increasing frequency can be explained with the SC dielectric spectrum, see The sensitivity analysis was performed at different SC hydration levels within a water activity range of For the analysis, we define the relative capacitive electrode sensitivity asr=Caw−C0.In Comparing the values of three electrodes’ relative sensitivity, in the hydration range The current density of the circular conductance electrode in An optimum of the electrode becomes visible in This work will enable better electrode designs and will be beneficial to several applications. In the fields of cosmetics and drug delivery, it will allow to improve upon current methods used to investigate and characterize SC hydration ,30. For In this work, we reported a computational model simulating the human skin for dielectric spectroscopy applications. The skin is modelled as a multilayer system, each layer exhibiting different dielectric dispersive parameters. In addition, the outer skin layer, i.e., the stratum corneum, implements a swelling model with hydration-dependent thickness.3 and 3, or expressed in term of water activity between 0.9745 and 0.996, the stratum corneum is always fully hydrated.The exposition of the skin surface to dry air with ambient relative humidity of 0% and humid air with ambient relative humidity of 100% allowed to retrieve the physiological ranges of water concentration and water activity. With a water concentration between The more the electric field penetrates into the epidermis/dermis layers, the higher the resulting capacitance due to the high dispersive dielectric parameters of those layers in comparison to the stratum corneum. Varying the stratum corneum thickness with hydration impacts the penetration depth into the lower skin layers. At high water activity, a thicker stratum corneum reduces the penetration depth of the electric field into the epidermis/dermis layer and as a result, the capacitance decreases.In addition, we examined the sensitivity of three different fringing-field electrode types. The analysis demonstrated that, as expected, the sensitivity is geometry and dimension dependent. Nonetheless, as conductance electrodes exhibit two orders of magnitude higher sensitivity, they are more affected by a change in dimension than capacitance electrodes.The presented model opens many potential applications in terms of electrode design optimization or to provide a deeper understanding of the variations observed experimentally when using different skin hydration sensors.


Background: Neuroscience lacks a reliable method of screening the early stages of dementia.Objective: To improve the diagnostics of age-related cognitive functions by developing insight into the proportionality of age-related changes in cognitive subdomains.Materials and Methods: We composed a battery of psychophysiological tests and collected an open-access psychophysiological outcomes of brain atrophy (POBA) dataset by testing individuals without dementia. To extend the utility of machine learning (ML) classification in cognitive studies, we proposed estimates of the disproportional changes in cognitive functions: an index of simple reaction time to decision-making time (ISD), ISD with the accuracy performance (ISDA), and an index of performance in simple and complex visual-motor reaction with account for accuracy (ISCA). Studying the distribution of the values of the indices over age allowed us to verify whether diverse cognitive functions decline equally throughout life or there is a divergence in age-related cognitive changes.Results: Unsupervised ML clustering shows that the optimal number of homogeneous age groups is four. The sample is segregated into the following age-groups: Adolescents ∈ [0, 20), Young adults ∈ [20, 40), Midlife adults ∈ [40, 60) and Older adults ≥60 year of age. For ISD, ISDA, and ISCA values, only the median of the Adolescents group is different from that of the other three age-groups sharing a similar distribution pattern (p > 0.01). After neurodevelopment and maturation, the indices preserve almost constant values with a slight trend toward functional decline. The reaction to a moving object (RMO) test results (RMO_mean) follow another tendency. The Midlife adults group's median significantly differs from the remaining three age subsamples (p < 0.01). No general trend in age-related changes of this dependent variable is observed. For all the data , Levene's test reveals no significant changes of the variances in age-groups (p > 0.05). Homoscedasticity also supports our assumption about a linear dependency between the observed features and age.Conclusion: In healthy brain aging, there are proportional age-related changes in the time estimates of information processing speed and inhibitory control in task switching. Future studies should test patients with dementia to determine whether the changes of the aforementioned indicators follow different patterns. Neuroscience lacks a reliable means for screening patients in the early stages of dementia   investigating possible new causes of brain aging; 2) testing the reliability of the test in a healthy population; and 3) testing the reliability in patients with dementia.There are several ways to improve the diagnostics. The first one is brain reserve and cognitive reserve both mitigating consequences of traumas to the head, aging, and neurodegenerative diseases  as predictors of the brain reserve   and Cognitive Control. Cognitive control is the ability to orchestrate our thoughts and actions per internal goals. EF is commonly used as an umbrella term that covers both EF and cognitive control and applies to a set of higher-order (cognitive) processes involved in organizing intentional behavior in a novel situation  and sustained attention or vigilance  . Working memory is more age-sensitive regarding spatial rather than verbal material  and construction  may be impaired in severe cases of dementia, damage to the nondominant hemisphere, or lesions to the parietal cortex . The task estimates mean reaction time recorded as a result of subsequent attempts in the task with the only type of stimuli and the only way to respond to them. Reaction time (ms) is a major dependent variable. Typically, the test contains over 30 trials  with unequal intervals of time between them. One can calculate the mean value of reaction time out of subsequent episodes of testing (SVMR_mean). By making a set of trials, researchers improve the accuracy of assessing information speed processing. They also count the number of mistakes made by the examinee (SVMR_mistakes). The mistakes can be either missing the targeted events (SVMR_passes) or preliminary responding .SVMR time reflects the mobility of the examinee. The mean reaction time under 177 ms accounts for the pronounced mobility of the nervous processes. The range of values from 177 to 200 ms is characteristic of a mobile type of the processes. Its length within 200–210 ms depicts an average type of the nervous processes. SVMR_mean value of 210–233 ms indicates the inertial status of the nervous system. After reaching the threshold value of 233 ms, the pronounced inertia is diagnosed. The SD (SVMR_variance) is a measurement that shows how the length of the reaction is scattered in time.Complex visual-motor reaction (CVMR) is a variant of the “go/no-go” test in which the examinee is to respond to one of the two possible types of triggering stimuli. We asked the examinee to respond by pushing the button when the green indicator light appears (see ears see . In reveears see . The sysdecision-making time (DMT) (see Equation 1). It reflects the time cost of response selection  (see Equation 2).Reaction to a moving object (RMO) allows us to estimate a balance or predominance of either excitation or inhibition in the central nervous system. At the time of the test, a circle, a starting point and a finishing line appear on the screen. The circle is quickly filled at a constant radial pace with a color, from some starting point to the finishing line in a clockwise direction as shown on There are a total number of over 30 trials . The system calculated the mean value (RMO_mean) of positive (the time delays) and negative values (the premature responses). If the RMO_mean value is positive, it reveals the predominance of inhibition over excitation. When negative, RMO_mean indicates the predominance of excitation over inhibition.The application sums up the number of the delayed responses (RMO_delays), the false starts  and the total number of responses that were accurate in time (RMO_acc). Also, the tester records the time length of the responses .Attention study technique: To test attention, identical triggering stimuli are presented subsequently in different locations on a computer screen  overlapping each other and the targeted stimuli, which requires additional time for the participant to notice the triggering signal and respond (see pond see . The syswrist dynamometry to measure the maximum muscular strength of the right (WDR_MMS) and left hand (WDL_MMS). Asymmetry coefficient (AC) is calculated as the ratio of the maximum muscular strength of the wrists (see Formula 4).We used We analyzed the data from a publicly available dataset named after the title of the project Psychophysiological Outcomes of Brain Atrophy (POBA). The dataset contains about 100 features reflecting the overall psychophysiological status of 231 people of different age . Written patient consent or parental consent with assent from minors for testing and scanning was obtained in each case. The examinees were scanned to exclude brain pathology. Some of them suffered from periodic headaches. The others started their professional sports career. Not to impact the study outcomes, the examinees were not paid for participation or being tested.The inclusion criterion was literacy, i.e., only those adults who indicated that they did at least professional courses after finishing general education took part in the study.The exclusion criteria were as follows: organic brain pathology, mental disorders, and recent or past injury to the head. All the participants were examined by a qualified neurologist. They were found healthy based on the clinical examination and the negative results of MRI which was conducted to rule out any underlying pathology. In this way, we followed the recent practice parameters of the American Academy of Neurology that recommend neuroimaging  to detect neurodegenerative conditions in early stages , which is also commonly called the choice reaction. Similar to the simple visual-motor reaction, the choice reaction includes such components as sensory acquisition  and motor responding. Additionally, CVMR encompasses the decision-making component required to process an inhibitory condition present in the task (see task see . This prreaction to a moving object test (RMO_mean) reflects the cooperative involvement of different cognitive domains.We also found the analysis of RMO_mean variable relevant to this study. In the RMO task, the examinee is supposed to respond subsequently to a set of expected events accurately at the anticipated moments when the events occur. To perform the test, the individual employs such cognitive domains as attention, inhibitory control, and task switching. Thus, the dependent variable of the The second objective was to find the optimal number k of distinct nonoverlapping subgroups with regard to age. For this, we used a heuristic approach based on the elbow method. We utilized the K-means algorithm and evaluated the distortion score or the sum of squared distances from each point to its assigned centroid as a performance metric of each chosen k. The optimal cutoff k value corresponded to the minimal distortion score. When the optimal k was set, we utilized the K-means clustering method to assess the separability measure with regard to the age group by finding a centroid for each cluster and counting the number of relevant and irrelevant data points in the groups.To address the third objective, we analyzed the charts that describe age-related changes of the aforementioned indices and dependent variables. Using the bootstrap method with regard to age, we built the linear regression model fit and 95% CI for the regression estimate. Then we analyzed the progression or dynamics of the proposed indices. To compare lifelong changes of the variables in different age-groups, we used descriptive statistics and the Kruskal-Wallis test  curve averaged over 10 times. We also calculated the mean sensitivity, specificity, accuracy (ACC), and area under the curve (AUC) values. These performance measures were suitable as the dataset was balanced across the age attribute. Then, we averaged the accuracy of the models by calculating Mean ± SD for each index used as a predictor (see the left columns of Table 5). Finally, with the Kruskal-Wallis test we tested whether the variance of the accuracy differs significantly (p > 0.05) for an index compared to other indices.Working on the second part of objective four, we figured out whether the proposed indices provide a summary of the findings obtained while testing individuals. To address the task, we used ML regression models forecasting values of the newly proposed indices. As predictors, we utilized the features comprising POBA dataset with an exception of those from which the values of the indices can be calculated. Specifically, to predict the values of ISD and ISDA indices we used the variables listed in the middle column of Table 5).All the experiments were conducted with the Linux Ubuntu 18.04 workstation with 24 CPU cores and two NVIDIA GeForce GTX 1080 Ti GPU with 11 GB GDDR5X memory each using programming language Python, and its libraries for data processing, ML, and data visualization, such as scikit-learn, NumPy, Pandas, Matplotlib, Seaborn, and Yellowbrick.index of simple reaction time to decision-making time (ISD). It provided us with the ratio of processing speed to decision-making time (see Equation 5). Both the time estimates were vulnerable to age-related neurocognitive slowing; however, there are no clear data supporting the assumption that the pace of decline is equal in diverse cognitive domains. Therefore, the derivative variable may serve as a marker of their disproportional decline.Based on the analysis described in section 3.3, we came up with the index of simple reaction time to decision-making time with the accuracy performance (ISDA). If compared with the previous one, the index includes the percentage of correct responses in the denominator (see Equation 6).ISD index considers two indicators that constitute the reaction time of the visual-motor task with the switching condition in it. The weak point is that it does not take the performance accuracy into consideration. For this reason, we proposed an additional derivate variable, which was the index of performance in simple and complex visual-motor reaction with account for accuracy (ISCA) calculated as it is seen in Equation 7.Another way to combine the speed and accuracy estimates of SVMR and CVMR is to calculate the IES score for each of the tests separately and then find the ratio between them. This solution leads us to the In this research, we did not intend to test all the possible ratios of the performance metrics in different cognitive tasks. Our goal was to show the utility of the approach when cognitive testing covers several domains and estimates their interrelated divergent changes.index was set to ISD, ISDA, or ISCA.In the cluster analysis, we used two variables (age and a proposed index) and employed K-means method to segregate the data points between groups. We utilized the unsupervised learning clustering K-means method to find the optimal number of homogeneous groups of data points. With the elbow method, we found the most appropriate number of clusters. It was justified by the separability measure based on a distortion score. The score is the sum of squared distances from each point to its assigned centroid. All centroids are obtained iteratively by minimizing the intracluster proximity while maximizing the distance between clusters. We applied the elbow method to two-dimensional data points composed of the age of the subjects and corresponding index values, where the age, ISCA), the optimal choice is annotated with a black dashed line. The blue line on the graph is plotted from the values of distortion scores with regard to the number of clusters, whereas the green dashed line displays the amount of time needed to train the clustering model per k.The knee point detection algorithm , we utilized nonparametric statistics. First, we checked the hypothesis that the population medians of all the groups were equal to the Kruskal-Wallis test, which showed significant changes in the distribution of the four groups (p < 0.05).To compare the distribution of the indices over the age-groups, we applied statistical significance tests. Because none of our indices data underwent Gaussian distribution according to the Shapiro-Wilk test for normality (post hoc Dunn test with the step-down method. We used Bonferroni adjustments (Holm's step-down procedure) to control the family-wise error rate. Regarding the indices values, only the median of the Adolescents group differed from those of the other three groups in the indices values. The three remaining groups shared a similar distribution pattern (p > 0.05). After a period of neurodevelopmental changes and maturation, the indices preserve almost constant values with a slight trend toward functional decline.To study which groups differed in their medians, we ran p < 0.01). No general trend in age-related changes of this dependent variable is observed  in the variances among age-groups for the aforementioned values. Homoscedasticity also supports our assumption about stable linear dependency between the observed features and age.Finally, we investigated the variances of the proposed indices and selected psychophysiological attribute values for different groups. Levene's test reveals no significant changes  between women and men with an exception of the group of Midlife adults.It is interesting to note that performance in the majority of the PTs does not differ significantly (p = 0.034). However, the variance of the reaction time and the number of errors was significantly lower in men .In the age interval [40, 60) years, women seem to spend more time on the task on average to compensate for a better accuracy in both SVMR and CVMR tests. Women were also more accurate in responding to RMO test stimuli . However, this difference does not seem to be considerable as the mean values for both sexes stay close within the interquartile range. No other essential differences were found between the values of the indices for men and women of any age group.In the same age group, ISCA index was significantly higher in women compared to men . In The performance metrics of the regression model such as mean absolute error (MAE), root mean squared error (RMSE), and the coefficient of determination (R2) are presented on the right side of In this study on aging, we resorted to psychophysiological tests. This goes in line with the recent publications  slow to the same degree. The ISD index remains unchanged as the time spent on reasoning in CVMR retards across the years of life at the same pace as the summary length of receiving, encoding, and responding components. This makes the ratio between DMT and SVMR_mean stable throughout years on a population scale.The strong version of the complexity hypothesis offers distinct advantages. It supports the idea that age-related retardation is associated with the general slowing in the processing speed rather than in components of information processing. It also vastly simplifies the tasks of neuroscientists searching for brain structure-functional associations while aging  or involves both intellectual and non-intellectual functions .To get the overall efficiency of the examinee in the test, we supplied ISD index with the accuracy metric see . The ideThe last index presents the IES ratio between simple and complex visual-motor reactions. IES score summarizes the overall efficiency of decision-making. IES accounts for different cognitive subdomains and may reflect their disproportional changes throughout the lifespan    and information processing speed . We claim that this is a feature of normal brain aging because we did a cross-sectional study of the healthy participants. In accelerated brain aging, the pattern of the changes may differ, in which case the proposed indices may serve as a screening tool for detecting such conditions. To verify this, a comparison study of the cohort of patients with dementia is required.We do not see a significant accuracy decline in the relative CI of the performance of RMO technique across the lifespan. This is consistent with the origins of the Cognitive Aging Theory according to which intelligence does not decline with age. At that time, this pushed neuroscientists to correct the intelligence test data for the speed of processing  may substitute the dependent variables of the battery of PTs. In this way, it may serve as a marker of the psychophysiological status. If so, machine learning algorithms are capable to calculate its value out of other PT results. The potential of PTs to predict the values of ISCA is illustrated in The predictive accuracy is almost equal in all the age-groups studied. In contrast to this, the performance of predicting IES varies regarding the age: It is maximal for Adolescents and a bit lower for Older adults . There is no agreement on the issue in the literature as well. While some authors counted the number of years of full education, other researchers justified that education slows the decline of crystallized intelligence rather than other cognitive abilities. This is why a lower educational level is not predictive of a decline of the cognitive speed, memory, or reaction time in tests , Young adults ∈ [20, 40), Midlife adults ∈ [40, 60), and Older adults ≥ 60 year of age.Our findings justify the strong version of the complexity hypothesis. The version assumes that all the elements of information processing  slow to the same degree. The ISD index remains unchanged as the time spent for reasoning in CVMR retards across the years of life with the same pace as the summary length of the receiving, encoding, and responding components. This makes the ratio between DMT and SVMR_mean stable throughout years on the population scale.To extend the utility of machine learning classification in cognitive studies, we proposed the estimates of the disproportional changes in cognitive functions . The distribution of the indices and the values of the RMO test over the age provide the evidence that diverse cognitive functions decline equally throughout life.The ISD, ISDA, and ISCA values are more stable across the lifespan than the major dependent variable of the battery of the psychophysiological tests we used. After neurodevelopment and maturation, the indices preserve almost constant values with a slight trend toward functional decline. A new study is required to determine the utility of the ratio for segregating the normal brain aging from the accelerated one.The results of other psychophysiological tests  did not demonstrate any general trend over age.p < 0.05). The accuracy of the models is higher than that of the models that we built recently for predicting IES score out of PT data (3.36−3.77% vs. 3.37−5.15%). In contrast to the models predicting IES score, the prediction performance on ISCA does not vary regarding the age. This reduces the reliability of IES and makes ISCA the most suitable index for assessing psychophysiological performance and comparing the results disregarding the age of examinees. As it is hard to segregate between the normal vs. accelerated aging, the index that is not sensitive to aging may improve the currently existing strategies for the early detection of dementia.The ISCA index for PT proved to be reliable: It reflects the overall psychophysiological status of an individual. We predicted ISCA values out of the results of other psychophysiological tests with high accuracy  at The study underwent ethical review by UAEU Human Research Ethics Committee (Notice Number: ERH_2019_4006 19_11) and got approval for the retrospective analysis of the data obtained as a standard of care. Written patient's consent or parental consent with assent from minors for being tested and scanned was obtained in each case.All authors contributed to the creation of the article as follows. YS and TH contributed to the conceptual idea of the manuscript. YS formulated the objectives and wrote the manuscript. TH performed the statistical analysis and prepared the figures and tables for data presentation, and illustration. KN-VG with NZ, TA, FA, ML, and MB contributed to the literature review and data analysis.This work was supported by Aspire grant AARE19-060 (PI: ML) and UAEU StartUp grant 31M442 (PI: YS).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Global localization is a fundamental ability for mobile robots. Considering the limitation of single type of sensor, fusing measurements from multiple sensors with complementary properties is a valuable task for study. In this paper, we propose a decoupled optimization-based framework for global–local sensor fusion, which fuses the intermittent 3D global positions and high-frequent 6D odometry poses to infer the 6D global localization results in real-time. The fusion process is formulated as estimating the relative transformation between global and local reference coordinates, translational extrinsic calibration, and the scale of the local pose estimator. We validate the full observability of the system under general movements, and further analyze the degenerated movement patterns where some related system state would be unobservable. A degeneration-aware sensor fusion method is designed which detects the degenerated directions before optimization, and adds constraints specifically along these directions to relieve the effect of the noise. The proposed degeneration-aware global–local sensor fusion method is validated in both simulation and real-world datasets with different sensor configurations, and shows its effectiveness in terms of accuracy and robustness compared with other decoupled sensor fusion methods for global localization. Precise global localization is of high importance in many applications, such as navigation and mapping. When there is no access to a pre-built environment map, the robot can only obtain the global positioning information via global-aware sensors like global positioning system (GPS) and ultra wide band (UWB). Generally these sensors can access global positional information with bounded error. However, due to the installation limitation of the ground stations and the signal block from obstacles, their measurements might be intermittent and suffer from large noise. Besides, the 3 degree-of-freedom (3D) positioning measurements are inadequate for some applications that require 6 degree-of-freedom (6D) global pose estimation. On the other hand, local sensors that measure the local environmental or kinematic information can achieve consecutive 6D pose estimation in real time ,2,3,4,5.In this paper, we set to integrate the global and local sensors to achieve 6D global drift-free localization. To do this, the extrinsic calibration between sensors is required, and so is the mapping that transforms the local estimations to the global coordinate. Besides, the scale of the local poses is also required since some local estimators such as monocular visual odometry can not recover it. Many researches investigate the sensor-fusion problem on specific sensor configurations, and the methods can be divided into two categories.One kind of fusing methods tightly couple the measurements from different sensors under the filtering or optimization based frameworks ,7. GenerHowever, few of these methods have analyzed the observability of the global–local sensor fusion system. As noted in , the senIn this paper, we propose a novel global–local sensor fusion framework that estimates the translational extrinsic calibration, the scale of the local poses, and the relative transformation from the reference frame of the local estimator to the global coordinate within a sliding-window, which are utilized to map the real-time local poses to the global frame for localization. We prove the full observability of this formulation under general motion patterns. To avoid the degeneration from deteriorating state estimation, we distinguish the degenerated subspace before each optimization, and add prior constraints specifically along with the unobservable directions. We validate the effectiveness of the proposed method in both simulated and real-world datasets with different sensor configurations. The experimental results also show that our method can effectively restrain the drift along degenerated directions and work out robust global localization results. To summarize, the contributions of the paper are listed as followA novel global-local sensor fusion framework is proposed which is applicable to arbitrary sensor configurations. The observability and degenerated motion patterns of the proposed system are detailedly analyzed;A degeneration-aware optimization approach is designed to avoid the sensor fusion framework being deteriorated by the noise on the degenerated directions;Both simulated and real-world datasets with multiple sensor configurations are utilized to validate the generalization and effectiveness of the degeneration-aware sensor fusion framework for global localization.The study in this paper is relative to multi-sensor fusion and degeneration-aware state estimation. Considering the limitation of the single type of sensor, multi-sensor fusion is a widely researched area in robotics. Generally, the sensors selected for fusion possess complementary properties. For example, the monocular visual inertial system fuses external visual information with internal inertial information to estimate 6D pose with scale. In this paper, we pay attention to the fusion between local-aware sensors , camera, inertial measurement unit (IMU)), and global-aware sensors  for localization. The fusion frameworks can be divided into filtering and optimization-based methods. Typically, most of the filtering-based frameworks are developed based on Extended Kalman Filter (EKF) ,16 and uObservability is the vital property of dynamic systems which reflects whether the inner states of the systems can be estimated from the observed measurements . In the Even though the fusion system is proved to be fully observable in general conditions, the observability would degenerate if the robot moves with insufficiently excited motion. Ref.  proves iIn this section, first the notations used throughout the paper are presented. Then we introduce the formulation of the global–local sensor fusion system and its detailed implementation for batch optimization. As a special discussion, we show that some commonly-appeared motions in robotics are actually degenerated for sensor fusion. Finally, we present our degeneration-aware optimization method that is designed to address the degeneration problem occurred during online localization.C to the reference frame of the odometry O. We assume that the global estimator outputs 3D positional measurement G on the robot with respect to a fixed world frame W. To fuse the outputs from the global and local estimators, we estimate the extrinsic calibration s of the local estimator, and the relative transformation s. We draw the relation of the frames in The nomenclature used throughout the paper is defined in n global sensor measurements and the related local sensor frames within the corresponding time duration, and we denote the first local sensor frame in the sliding-window as L. The length of the sliding-window in this work is maintained according to the distance, but can be modified by any other criterion. Upon the sliding-window based formulation, we change the estimated relative transformation from The proposed sensor fusion system is demonstrated in Generally, the global sensors possess lower frequency than the local estimators. Therefore, the system performs the fusion process each time it receives the measurement from the global estimator. As shown in We first align the global and local measurements according to the timestamps. The global measurement function .After aligning the newly received global measurement, the system state Summing up all the valid error functions in the sliding-window, the cost function for the general localization based optimization is defined asfunction  which cafunction ,29.t can be calculated asGiven the latest optimized state For the optimization formulated in Equation , we firsWe denote As the system state ollowing (9)M=⋮HkAs in general cases the columns in Equation  it can bIn this subsection, we summarize the common degenerated motion patterns in the robotics area and derive their corresponding unobservable directions.m is utilized to denote the beginning of the sliding-window. The translational measurement of the local estimator can be derived asThis is a common motion pattern in autonomous driving. When the robot moves along a straight line, This would occur when the robot performs pure translation in 2D/3D space without rotating. In this case, Equation  is violaWhen the robot turns along a fixed rotation axis The result is constant for any It should be noticed that when the robot performs uniform motion, more dimensions maybe unobservable. One case is that, when both the angular velocity and the translational velocity are constant, the dimension of the unobservable subspace is expanded to 2 as one direction of When there exists an unobservable subspace in the system, the related states are unconstrained and susceptible to measurement noise. To address this problem, we first detect the degenerated directions before the optimization process, then add prior constraints specifically along these directions.Similarly to , we calcAlgorithm 1: Detecting unobservable directions.We propose a heuristic method to detect the unobservable subspace as shown in Algorithm 1. The absolute thresholds r, we collect the corresponding eigenvectors s, respectively. ath to bth elements of After detecting out the degenerated subspace with dimension We validate the effectiveness of our degeneration-aware sensor fusion method through both simulated and real-world datasets. In simulation experiments, we first show the sensitivity of the eigenvalues with respect to the measurement noise. Then we create four sequences of simulated trajectories that correspond to the common degenerated motion patterns analyzed in In the simulation experiments, different motion patterns are controlled by setting different translational and rotational velocities for the local sensor. The minimum sampling interval is 0.1 s, and the ground truth of the trajectories can be integrated based on the velocities. The trajectories of the global sensor can be calculated based on the ground truth of the system state using Equation . The glot, we find its corresponding ground truth pose In real-world experiments, we evaluate the performances of different methods by the absolute trajectory error (ATE) and rotational error . For eacThe ATE error relates to the norm of the translational component in To quantitatively demonstrate the influence of the noise on the eigenvalues, we create simulated trajectories that are related to two types of the degenerated motion patterns shown on the first row of Based on our analysis in In this subsection, we utilize simulated data collected under degenerated movement patterns to perform ablation study on the effectiveness of the proposed degeneration-aware sensor fusion. Specifically, we evaluate the accuracy of the estimated system state optimized with general optimization formulated in Equation  and the r dimensions of unobservable directions would cause the divergence of more than r state variables.The estimation errors for the system state Equation , when thWe evaluate the global localization performance of our proposed method on sequences MH01–MH05 in EuRoC datasets and sequence Urban 38 in KAIST dataset.We implement the monocular visual odometry based on ORB-SLAM  to evaluIn EuRoC dataset we utilize monocular vision to perform local pose estimation. The output of the monocular visual odometry does not include the absolute scale, which can not be utilized for global localization in many other global–local fusion methods ,9,10. ThWe draw ATE errors evaluated by different methods in We also perform ablation study to evaluate the effectiveness of the degeneration-aware optimization. We first evaluate the localization performance tested on the general batch optimization formulated in Equation . The resIn KAIST dataset, we utilize the GPS as the global estimator, which is prone to drift when the car stops at the crossroads. Additionally, the GPS signal is inaccurate when the covariance is large. Therefore, during online localization, we drop the GPS messages with large covariance (the threshold is set as 60) and the drifted messages indicating that the car is moving while the local estimator denoting that the car does not move.We list the localization performance of GPS and the stereo-IMU version of Openvins  in TableCompared with EuRoC datasets, the robot performs planar movements in Kaist dataset, in which the degeneration would likely occur. Thus, the results of “no prior” are largely influenced by the degeneration and fail to perform the whole localization. The results also show that our method achieves better performance than the compared methods and could provide drift-free global localization results.To validate the ability of achieving real-time localization, we evaluate the computational time cost on the multi-sensor fusion process. The computational time is defined as the duration between the time at which a new global measurement is received and the time the system state is updated by the optimization results, which is independent with the processes in the front-ends. We collect the computational time tested on the KAIST dataset and draw the results in To achieve drift-free 6D global localization, in this paper we propose a general optimization-based framework that fuses the 3D intermittent global positioning information and 6D local odometry for real-time global pose estimation. The system state is specifically formulated to be fully observable under general motions. To address the impact from generated motion patterns, we propose a degeneration-aware solution to robustly detect the degenerated directions that are further utilized as indicators to add prior constraints. Though extra time is cost for degeneration detection, the whole processing time could satisfy the requirement of real-time sensor fusion. The effectiveness of our proposed method is validated on both simulated and real-world dataset. In the future work, we set to extend the configuration of our framework from 3D–6D global–local combination to multiple types of pose estimators with general degree of freedom, and utilize the multi-sensor information to further detect the failure in the local pose estimators for outlier rejection.


Due to planetary movement of planet gears, the vibration signal perceived by a stationary sensor is modulated and difficult to diagnose. This paper proposed a vibration separation methodology compensated by a time-varying transfer function (TVTF-VS), which is a further development of the vibration separation (VS) method in the diagnosis of non-hunting tooth planetary gearboxes. On the basis of VS, multi-teeth VS is proposed to extract and synthesize the meshing signal of a planet gear using a single transducer. Considering the movement regularity of a planetary gearbox, the time-varying transfer function (TVTF) is represented by a generalized expression. The TVTF is constructed using a segment of healthy signal and an evaluation indicator is established to optimize the parameters of the TVTF. The constructed TVTF is applied to overcome the amplitude modulation effect and highlight fault characteristics. After that, experiments with baseline, pitting, and compound localized faults planet gears were conducted on a non-hunting tooth planetary gearbox test rig, respectively. The results demonstrate that incipient failure on a planet gear can be detected effectively, and relative location of the local faults can be determined accurately. Planetary gear transmissions are widely used in industrial and military applications, such as wind turbine  and heliIn the past few decades, vibration-based analysis techniques have been developed successfully to detect weak fault characteristics and incipient damage in fixed axial gearboxes, but most of these techniques cannot be applied to a planetary gearbox directly. Researchers modified or adapted some techniques to diagnose planetary gearboxes. Kong et al.  establisAlthough plenty of researchers have shown that vibration-based analysis techniques are effective in diagnosing gearboxes, the aforementioned conventional signal processing methods usually require a high degree of expertise . The reqTo figure out more about the vibration mechanism of the planetary gearbox, a lot of dynamic-based or phenomenon-based models have been established to reveal the vibration characteristic and modulation sidebands generation mechanism. Inalpolat et al. The authors in  proposedAccording to the vibration models built above, it can be summarized that the description of the time varying transfer path is vital important. The periodic time-varying transfer path leads to complicated amplitude modulation, resulting in amplitude envelope and modulation sidebands. The vibration signal received by a stationary sensor is modulated by the effect of the time-varying transfer path. As a result, the modulated signal may mask the incipient fault characteristic or trigger a false alarm when using traditional signal processing methodologies and a health indicator. It is necessary to establish reasonable TVTF to reveal regularity of movement and overcome amplitude modulation effects.When analyzing a planetary gearbox vibration signal, it would be easier if the planetary gearbox signal could be converted into the fixed-axial gearbox signal. Based on this idea, McFaden et al. ,21 firstDue to the gearbox parameters and motion regularity, the complete VS signal can only be extracted from planetary gearboxes with a hunting ratio between the planet and ring gears, and the sun and ring gears . HuntingTo settle this problem, a vibration separation methodology compensated by a time-varying transfer function (TVTF-VS) is proposed in this paper to diagnose the non-hunting tooth planetary gearbox using a single transducer. In our methodology, the multi-teeth vibration separation (multi-teeth VS) algorithm is proposed to extract and synthesize the meshing signal of an individual planet gear in a non-hunting tooth planetary gearbox. Subsequently, TVTF is constructed using a segment of healthy signal to overcome the amplitude modulation effect existing in the multi-teeth VS waveform. After compensation of the TVTF, the resultant TVTF-VS waveform is obtained. Finally, the diagnosis conclusions are drown based on the resultant TVTF-VS. The main innovation of the proposed methodology is that the TVTF-VS algorithm can be applied to non-hunting tooth planetary gearboxes with only one transducer used. Two sets of planet gear fault-seeded experiments, pitting and compound localized faults, are conducted to verify the performance of proposed methodology. According to the experimental results, the TVTF-VS methodology proved to be effective in planet gear fault detection and location.The organization of this paper is as follows: In order to apply the VS method to the non-hunting tooth planetary gearbox, this paper proposes a modified VS methodology called multi-teeth VS. The multi-teeth VS mainly contains 3 steps and the schematic of multi-teeth VS is illustrated in Step 1: Interpolating and multi-teeth sectioning. The encoder pulse train and vibration signal are collected simultaneously. Then, vibration signal is partitioned into blocks every one carrier cycle. It should be noted that the location of blocks is decided by the encoder pulse train during the partition process. Since carrier rotates once, Step 2: Mapping and combining. After extracting the sections from vibration signal, the sections are mapped into assembly matrix according to the teeth meshing sequence, which will be introduced in Step 3: TSA. The TSA is applied to the meshing signal of several revolutions for The teeth meshing sequence of planetary gearbox follows some certain regularities. It is noted that the stationary sensor is usually fixed on the ring gear. When an individual planet gear passes by a sensor, one particular tooth on the planet gear meshes with the ring gear under sensor. At the end of next revolution of carrier, another tooth on the planet gear is in mesh with the ring gear. After several rotations of the carrier, the same tooth on the planet gear will mesh with the ring gear at the same position relative to the ring gear. Similarly for the sun gear, the same tooth on the sun gear will mesh with one particular planer gear aligning to the sensor (the same position relative to the ring gear) after several rotations of carrier.LCM denotes the least common multiple, In other words, the teeth meshing sequence will repeat periodically after several rotations of the carrier. The least number of carrier rotations can be modeled by:The extracted sections should contain more information about the objective planet gear. There are two methods to determine the location of sections. The first is tracking the location by calculating the phase difference between the section location and pulse train, but this method requires measuring the angle among encoder, planet gear, and accelerometer while setting up . CommonlTo implement the TVTF-VS in practical application, the second method to determine the location of sections is proposed in the following. First of all, the non-hunting ratio between the ring gear and the planet gear should be calculated by the given parameters of the planetary gearbox. As the When there is a localized fault on the planet gear, the meshing points of the fault tooth with the ring gear relative to the ring gear are fixed. The number of fixed fault meshing positions on the ring gear can be calculated byFor a planet gear with localized fault, the location of the first section can be obtained by moving the sensor. Move the sensor Taking the type 2 planetary gearbox given in The length of one section is then given byThe vibration signal collected from the planetary gearbox has unique characteristics distinguished from that from the fixed axis gearboxes. Multiple gear pairs simultaneous meshing coupling, multiple vibration transfer paths, and time-varying transfer path are the main features of planetary gearbox, which causes complicated amplitude and phase modulation. Summarizing the characteristics of the planetary gearbox can help us better make use of the vibration signal for analysis and diagnosis.As is well known, the structure of a planetary gearbox is much more complicated than a fixed-axis gearbox. Different transmission ratios could be achieved by fixing any one of the ring gear, sun gear, or carrier. Generally, the ring gear is stationary while the sun gear and the planet gears are rotating as input or output. Only this case is discussed in this paper.As the planet gear revolves around the sun gear, it also makes self-spinning motion at the same time. The planet gear meshes with the sun gear and ring gear simultaneously and there are a couple of planet gears in one planetary gearbox. Therefore, multiple gear pairs simultaneous meshing produces multiple vibration sources. The vibration signals coupling also increases the difficulties for vibration analysis.Assuming that the gears are isotropic, the length of path 2, path 3, path 5, and path 6 are all constant. The constant transfer path leads to constant energy loss, and hence the signals transmitted through these paths are time-invariant. However, the length of path 1 and path 4 are changed with the carrier rotation; therefore, the vibration signals transmitted through time-varying transfer paths are time-variant. This phenomenon leads to complicated amplitude modulation and phase shift. Hence, conventional vibration analysis methods, such as synchronous averaging (SA), cannot be applied to the planetary gearbox directly.As the planet gear approaches the sensor, the signal perceived by the fixed sensor increases and the signal reaches the maximum when the planet gear is just below the sensor. Vice versa, as the planet gear goes away from the sensor, the signal perceived by the fixed sensor decreases and the signal reaches the minimum when the planet gear is opposite the sensor position along the ring gear. The signal perceived by the fixed sensor is the superposition of signals transmitting through all the paths. As a result, the amplitude of the signal perceived by the sensor corresponds to the periodic change in the time-varying transfer path length due to the carrier rotation. Inalpolat  initiallFor a specific planetary gearbox, when the planet gear goes away from the sensor, the perceived signal by the sensor from the meshing point may attenuate to zero before arriving the farthest position. Based on this point, Liang et al.  proposedAs the ith data point, ND6, using the sixth moment normalized by the variance to the third power:N is the total number of data points in the time signal, ith data point, and ND6 is non-dimensional and more sensitive to the number and amplitude of peaks present in the signal due to the use of the sixth moment. Higher moment corresponds to higher sensitivity. It should be noted that a sharp increasing of sensitivity to the peaks is not desired because it may trigger a false alarm. The parameter of ND6.In order to evaluate the compensation effect of the target planet gear quantitatively and to seek the optimum parameters of the TVTF, an evaluation indicator is desired. Consider the classic damage detection metric Kurtosis  given asND6 of The TVTF is used to compensate the multi-teeth-VS waveform and the construction process of the TVTF is illustrated in In order to apply the VS to a non-hunting tooth planetary gearbox and diagnose the planetary gearbox effectively, the TVTS-VS is proposed in this paper. Monitoring signal is first processed by multi-teeth VS to get a multi-teeth-VS waveform in spite of a non-hunting ratio, then the TVTF is used to eliminate the amplitude modulation effect so that the incipient fault on the planet gear can be highlighted accurately. The technical route of fault detecting by the TVTF-VS is displayed in As previously illustrated, the proposed the TVTF-VS methodology can be formulated by:To implement the TVTF-VS methodology, the extracted multi-teeth sections should be dominated by the objective planet-ring pair. That is to say, the signal perceived by the sensor is dominated by the signal transmitted from path 1, as depicted in In addition, the angle Taking Equation (14) into the Equation (13), we can obtain:In order to reduce interference from other meshing pairs, a large ratio In this section, the effectiveness of the proposed TVTF-VS methodology is evaluated by experimental data. Details of experiment and discussion of results are as follows.Vibration signals under healthy condition and two faulty conditions are collected, respectively. In the two faulty conditions, one is the planet gear with intentionally created pitting using laser machining (LM). The pitting is processed into irregularly distributed points to simulate actual working conditions. The other is the planet gear with a compound fault containing both spalling and a root crack created by electro discharge machining (EDM). Spalling is about 25% of tooth width and the root crack is 25% depth closed when in mesh with ring gear. The two faulty planet gears are shown in An accelerometer was mounted on the external of ring gear. It should be mentioned that the encoder pulse train and vibration are picked up simultaneously by an acquisition card (NI 9234) with the sampling of 25.6k HZ. Experiments were carried out under different working conditions.The baseline signal is used to construct the TVTF and to verify the feasibility of proposed methodology preliminarily. Collected encoder pulse train and corresponding speed plots calculated by the intervals of the pulse train are shown in In the case of heathy planet gear, even though TVTF-VS waveform is compensated by the TVTF, the amplitude of signal near the connections of multi-teeth-sections is faint, such as tooth number 12, 24, and 36 in In order to verify effectiveness of the TVTF-VS under different speeds, three baseline experiments are conducted with the speed of 400 rpm, 800 rpm, and 1200 rpm, respectively. The vibration signal and resultant TVTF-VS waveform under 400 rpm and 800 rpm are given in In In order to test TVTF-VS’s capability of fault diagnosis in case of multiple faults, compound localized faults experiment are conducted. This paper presents a planet gear fault diagnosis methodology called vibration separation compensated by a time-varying transfer function (TVTF-VS), which makes the VS further developed in diagnosis of non-hunting tooth planetary gearboxes. Based on VS, multi-teeth VS is proposed to extract the meshing signal of a planet gear. Then, a parameter optimization algorithm is developed to construct the TVTF using a segment of healthy signal. The TVTF is used to overcome the amplitude modulation effect caused by planetary movements, and highlight weak characteristics induced by incipient local fault. Finally, the localized fault detection conclusions are drawn using the resultant waveform. A distinct advantage of the TVTF-VS is that only one vibration transducer is needed. Two sets of planet gear fault-seeded experiments with pitting and compound faults are conducted to verify the proposed methodology. Experimental results show that the proposed method can effectively detect and locate local faults on the planet gear and provide more details about the faulty planet gear in non-hunting tooth planetary gearboxes. Damage condition and location information of faults could be obtained by the TVTF-VS waveform. While applying the process of the proposed method, selection of the TVTF determines the compensation effect and diagnosis result. In the future, a more accurate TVTF should be modeled in order to match planetary gearboxes with different specifications.