Auroral zones are regions where, in an average sense, aurorae due to solar activity are most likely spotted. Their shape and, similarly, the geographical locations most vulnerable to extreme space weather events (which we term ‘danger zones’) are modulated by Earth’s time-dependent internal magnetic field whose structure changes on yearly to decadal timescales. Strategies for mitigating ground-based space weather impacts over the next few decades can benefit from accurate forecasts of this evolution. Existing auroral zone forecasts use simplified assumptions of geomagnetic field variations. By harnessing the capability of modern geomagnetic field forecasts based on the dynamics of Earth’s core we estimate the evolution of the auroral zones and of the danger zones over the next 50 years. Our results predict that space-weather related risk will not change significantly in Europe, Australia and New Zealand. Mid-to-high latitude cities such as Edinburgh, Copenhagen and Dunedin will remain in high-risk regions. However, northward change of the auroral and danger zones over North America will likely cause urban centres such as Edmonton and Labrador City to be exposed by 2070 to the potential impact of severe solar activity. Accurate determination of the future locations where, on average, aurorae sightings are most likely in the future also has consequences for the tourism industry and aurora-watching trip planning.Aurorae are the best known visual expression of space weather activity. They are caused by ionisation in the upper atmosphere by charged magnetospheric particles, accelerated during periods of enhanced geomagnetic activity. These charged particles travel along magnetic field lines and because of the primarily dipolar nature of the geomagnetic field, aurorae are preferentially observed at high latitudes in approximately oval-shaped regions  surrounding the geomagnetic poles (the intersection points of the geomagnetic dipole axis and the surface of Earth). The auroral ovals are important features of the magnetospheric response to space weather phenomena, as they are associated with increased electromagnetic disturbances, visible in both ground- and satellite-based observations7. Using this definition, the auroral zone location and shape do not depend on instantaneous solar wind conditions and their temporal evolution can be solely linked to the changes in the geomagnetic field. This allows us to consider space climate, a moving average of space weather conditions over the decadal timescales dictated by the evolution of the geomagnetic field of internal origin. Previous studies estimated the past evolution of these low-solar-activity auroral zones10 or of their poleward edges alone 11 and found significantly different shapes and temporal changes for the Northern and Southern zones. In particular, since the beginning of the 20th century, the evolution of the Northern auroral zone can be essentially described by a drift from North America towards Siberia11, in qualitative agreement with the recent rapid motions of the North Magnetic pole17. At the same time, the Southern auroral zone evolution is better described by an elongation towards the equator in the Atlantic Hemisphere11. The auroral zones and polar cap surface areas have been decreasing since 194011 for the Northern Hemisphere and increasing since at least the beginning of the 20th century for the Southern Hemisphere. This asymmetric behaviour is at odds with expected scaling laws valid under the assumption of a dipole-dominated main field20, according to which both polar cap areas should increase as the dipole intensity decayed23.11 suggested that the shrinking of the northern auroral zone is due to a local strengthening of the high-latitude geomagnetic field intensity in the Northern Hemisphere, contrary to the geomagnetic field evolution in the Southern Hemisphere. Similarly, the recent rapid drift of the North Magnetic Pole can be explained by the weakening (strengthening) of the patch of high magnetic field intensity above Canada (Siberia) and the concurrent drift towards Siberia of the whole magnetic pattern17.The exact shape of the auroral ovals is controlled by the instantaneous position of Earth with respect to the Sun, the physical conditions of the solar wind and the configuration of the geomagnetic field. Over longer timescales, e.g. longer than the 11 years of a solar cycle, the auroral ovals can be approximated by the auroral zones, which, for low-to-moderate solar activity, are traditionally represented by quasi-circular belts centered around the geomagnetic poles and located between 65 and 7024. In extreme cases, such as during the 1859 Carrington event, aurorae and electromagnetic disturbances were detected as far south as 10 degrees latitude25. Using extreme event statistics informed by available ground-based geomagnetic field observations,26 estimated that the largest geomagnetic field perturbations for extreme space weather events (100 and 200 years return period), can be expected in a range between geomagnetic centered-dipole latitudes28 of about Under the influence of severe solar activity, the auroral oval is pushed to lower latitudes and the electromagnetic disturbances associated with it increase in magnitude, with damaging effects on ground-based technology29, in which a simple description for the centennial evolution of the geomagnetic field coefficients  is extrapolated over a 1000 years temporal window. However, new physics-based forecasts are available, which model the expected dynamics within the core31 to predict the evolution of the internally generated geomagnetic field over decadal timescales. We will use these to produce new and likely much better forecasts of the auroral zone shape and location.Predictions of the future location of the auroral and danger zones can help inform industry and policy makers, and feed into the timely development of effective space weather mitigation strategies. To our knowledge, the only auroral zone forecast available in the literature is presented in32 and has been corroborated by complementary magnetospheric simulations with the global magnetohydrodynamic code Gorgon, for various choices of interplanetary magnetic field (IMF) intensity (see Methods). We find that for a wide range of IMF strengths typical of low-to-moderate solar wind conditions, the poleward bound of the auroral zones can indeed be effectively described by a geomagnetic latitude of 23. Note that the conversion between AACGM and geographic coordinates depends on the full set of Gauss coefficients describing the geomagnetic field and its temporal evolution. The auroral and danger zones for the year 2020 are illustrated in Fig. 29.We consider the auroral zones as a climatological average of the auroral ovals for low-to-moderate solar wind conditions, which are defined by the latitudinal bands between 65 and mentclass2pt{minim26). For such events, we do not have access to a wide enough set of of reliable GIC observations upon which the climatological meaning of the danger zones can be justified. We can, however, corroborate the danger zone definition by comparing its location with electromagnetic disturbances reported during severe events for which written records exist. Furthermore note that the bounds reported in26 (see Methods) are expressed in geomagnetic, dipole-centered coordinates, which only depend on the inclination of the geomagnetic dipole. It is therefore necessary to test whether the generalisation to AACGM coordinates is appropriate. The most severe geomagnetic storm in recent history was the 1859 Carrington event33; in Fig. 25 together with our reconstruction of the danger zones in 1859. For this epoch, we used the gufm1 model to describe the magnetic field coefficients34. Other models for the 1859 are available, such as the COV_OBSx.2 field model35. The danger zones locations reported in Fig. 36, associated with a phenomenology that is not included in our danger zone definition.In contrast to the auroral zones, the regions that we here term danger zones cannot be rigorously defined in terms of long-term averages of observed quantities. We defined them based on extreme events with estimated return period of 200 years (see Methods and31 (see Methods). The MPG forecast describes the evolution of the geomagnetic field over the entirety of the current century. Its ensemble nature allows us to estimate auroral and danger zone location uncertainty (see below). To our knowledge, the only other available physics-based prediction of the geomagnetic field over the same period has been presented in30. This prediction, that we refer to as the ‘IPGP forecast’, is produced by a geodynamo simulation initialised from a state given by a single-epoch inversion of geomagnetic observations in 2015. For comparison, we also consider a non-physical, IGRF-based forecast for which the IGRF-13 model predictions for the 2020-2025 coefficients are extrapolated to future epochs (see Methods). As suggested by Gauss coefficients evolution  predict that the recent evolution of the high-intensity patches will continue over the next 5 decades, with the Canadian patch weakening and drifting towards Siberia, while the Siberian patch strengthens  as the geographical regions of Earth’s surface where the highest geomagnetically induced currents (GIC) are expected to be driven by temporal geomagnetic variations. For catastrophic space weather events with 200-years return period,26 estimated that the auroral zones can be defined by the geomagnetic latitudinal band between 50 and 26). We therefore define the danger zones as being bound by AACGM latitudes We identify the auroral zones under low-to-moderate solar wind conditions  by the geomagnetic latitudinal bands between 65 and https://github.com/aburrell/aacgmv2, see also40), which allows conversion between geographical and AACGM coordinates in accordance to a given geomagnetic field model, for a specified epoch and a given altitude above Earth’s surface. Since our focus is on the variations in geomagnetic latitude caused by decadal changes in the internal geomagnetic field, the epochs for which AACGM coordinates are calculated are defined by the year alone and we fix the day of the year to be the first of January. Considering a different day of the year would not alter the results presented here.In order to calculate AACGM latitude, 28. The advantage of AACGM coordinates over Magnetic Apex coordinates is the availability of fast routines to calculate the conversion from and to geographic coordinates. For more details on the AACGM coordinate system, the reader is invited to consult40 and references therein.AACGM coordinates are used to calculate geomagnetic latitude and longitude of a given geographic location making use of a full description of the geomagnetic field, including its non-dipolar components. The AACGM coordinates corresponding to a given geographic location at the surface of Earth are calculated by following the geomagnetic field line from the geographic location to the magnetic dipole equator, then following back to the surface of Earth along the dipole field line intersecting the point on the magnetic equator. The AACGM coordinates are then given by the latitude and longitude of the intersection of the dipole field line with the surface of Earth. Because all points along a magnetic field line have the same geomagnetic latitude and longitude, AACGM coordinates are widely used in magnetospheric studies since they allow researchers to naturally track particle precipitation along these lines. By construction, AACGM coordinates are not well defined in an equatorial region making this coordinate system unreliable for equatorial and low-latitudes application. For high-latitude applications , with which we simulate the coupled magnetosphere-ionosphere system under different strengths of solar wind driving. We employ a high resolution  46. A dipole magnetic field is placed at the origin, with moment To further place into context our definition of typical auroral zone latitudes, we perform a comparison to predictions from a global magnetohydrodynamic (MHD) model, Gorgon(n = 5 cm47:49). Using the values for our simulated solar wind conditions we would thus expect substorm activity (and enhanced space weather risk) for IMF strengths of The solar wind has steady synthetic conditions of velocity 50. The OCB is identified by sampling magnetic connectivity near the inner boundary (see51). We then map the OCB coordinates down along dipole field lines to the ground at a radius of 1 The magnetosphere is initialised up to 2 h with each set of driving conditions, such that it enters a quasi-steady state. Note that we use a uniform ionospheric Pedersen conductance of 10 mho and zero Hall conductance; whilst this does not consider ionisation effects such as auroral precipitation, we are only interested in identifying the average location of the auroral zone rather than exploring any local time-dependence or more complex ionospheric electrodynamics. After 2 h of simulation time we locate the open-closed field line boundary (OCB) which encloses the ionospheric polar cap, corresponding to the poleward boundary of the auroral ovalWe show the resulting polar caps in Supplementary Fig. 52). However these latitudes are still poleward of our defined danger zone of 53. This would correspond to much more extreme upstream solar wind conditions than used in our runs . The reason for this is that a constant reconnection voltage (i.e. rate of magnetic flux opening) across the dayside magnetopause will generate a fixed amount of open flux in the steady-state magnetosphere. For a weaker (stronger) dipole and given the same external solar wind driver, this would result in a larger  polar cap which encloses the same magnetic flux. However since M predicted by the 2070 MPG forecast  to the strength of the geomagnetic dipole; arguments based on changes in the size of the magnetosphere yield a theoretical dependence of 55, we describe the evolution of the geomagnetic field, l and order m, L is the maximum degree of expansion and As input to the aacgmv2 algorithm, a geomagnetic field model is required. As is commonplace23, which contains a description of the Gauss coefficients from 1900 to 2020, at 5 years of interval, and a forecast that is distributed for use between 2020 and 2025. For the years after 2020, we consider two state-of-the-art forecasts which we refer to by the principal home institution of the authors: one is presented in31 and we refer to it as the MPG forecast, and the other is presented in30, referred to as the IPGP forecast. Both MPG and IPGP estimations are based on convection-driven dynamo simulations using the PARODY code57. The dynamical MPG forecast is based on an ensemble Kalman filter approach, described in58, combined with localization techniques that allowed the authors to obtained converged results with a limited number of ensemble members. The background dynamo model used by the MPG forecast is of moderate complexity, with homogeneous heat flow boundary conditions. The observations assimilated consisted of the main field from the COV_OBS.x1 model59 for the epochs between 1840 and 2000 and from the Kalmag model60 for the epochs between 2001 and 2020. The MPG forecast, which starts in 2020, was a candidate model for the IGRF-1323. Together with the mean MPG forecast (obtained by averaging the coefficients of the 256 ensemble members) we consider 64 random members of the ensemble. This reduced ensemble size has been chosen as a compromise between the number of additional forecasts  and the capability of the reduced ensemble to meaningfully capture the spread of the total ensemble (see31).For the years before 2020 we describe the geomagnetic field via the IGRF-13 model61. As background state for the inversion and to evolve the initial condition forward in time, the IPGP forecast makes use of the Coupled Earth dynamo model62, which employs a more involved physical setup  that helps better explain the observed field. Since the IPGP forecast starts in 2015 there is a potentially severe discontinuity between the IPGP and the IGRF-13 models for the years between 2015 and 2020. However, for the purposes of the present paper we could not find any significant discrepancies between the two  data for the 2015 epoch from the CHAOS-5 modelFor comparison, we consider a third, simple forecast given by a linear extrapolation of the IGRF-13 coefficients past its epoch of validity according to the IGRF consortium . We acknowledge that extrapolation past the 2025 epoch is beyond the scope and purposes of the IGRF model. This forecast has no particular physical meaning and merely serves to compare the MPG and IPGP forecast with future scenarios derived with no consideration of the non-linear dynamics of the geodynamo. We refer to this forecast as the IGRF forecast.31, as are the forecasts of l we can see either agreements or significant departures, depending on the specific coefficient we consider. For most of the coefficients and quantities displayed in Supplementary Fig. In Supplementary Fig. Although we made use of the set of Gauss coefficients up to degree Supplementary Figures.


Existing guidelines recommend statisticians remain blinded to treatment allocation prior to the final analysis and that any interim analyses should be conducted by a separate team from the one undertaking the final analysis. However, there remains substantial variation in practice between UK Clinical Trials Units (CTUs) when it comes to blinding statisticians. Therefore, the aim of this study was to develop guidance to advise CTUs on a risk-proportionate approach to blinding statisticians within clinical trials.This study employed a mixed methods approach involving three stages: (I) a quantitative study using a cohort of 200 studies (from a major UK funder published between 2016 and 2020) to assess the impact of blinding statisticians on the proportion of trials reporting a statistically significant finding for the primary outcome(s); (II) a qualitative study using focus groups to determine the perspectives of key stakeholders on the practice of blinding trial statisticians; and (III) combining the results of stages I and II, along with a stakeholder meeting, to develop guidance for UK CTUs.After screening abstracts, 179 trials were included for review. The results of the primary analysis showed no evidence that involvement of an unblinded trial statistician was associated with the likelihood of statistically significant findings being reported, odds ratio (OR) 1.02  0.49 to 2.13). Six focus groups were conducted, with 37 participants. The triangulation between stages I and II resulted in developing 40 provisional statements. These were rated independently by the stakeholder group prior to the meeting. Ten statements reached agreement with no agreement on 30 statements. At the meeting, various factors were identified that could influence the decision of blinding the statistician, including timing, study design, types of intervention and practicalities. Guidance including 21 recommendations/considerations was developed alongside a Risk Assessment Tool to provide CTUs with a framework for assessing the risks associated with blinding/not blinding statisticians and for identifying appropriate mitigation strategies.This is the first study to develop a guidance document to enhance the understanding of blinding statisticians and to provide a framework for the decision-making process. The key finding was that the decision to blind statisticians should be based on the benefits and risks associated with a particular trial.The online version contains supplementary material available at 10.1186/s13063-022-06992-5. There is limited empirical evidence to guide trial teams within UK Clinical Trials Units (CTUs) about the practice of blinding statisticians. Although there are examples of published guidance on blinding statisticians in clinical trials in the US, they are not internationally adopted , 2. A suCTUs can be broadly split into those that always blind the statisticians and involve a second statistician for unblinded/disaggregate analyses  and thosThere are clearly benefits to developing an evidence-based risk-proportionate approach to blinding statisticians in clinical trials, in line with other areas of clinical trial conduct . The lacCompare the outcomes of recently published randomised trials where the statistician was blinded prior to the final analysis versus those where the statistician was notFurther explore current practice in academic CTUs, and reasons for these practicesUnderstand stakeholder views on important risks and benefits to consider when deciding on blinding practiceProvide recommendations and a practical tool to enable CTUs to utilise a risk-based approach when considering blinding of the TSThe objectives of BOTS were to:Objectives 2 and 3 are the focus of another qualitative study .Stage I: Quantitative data was obtained from randomised trials funded by the UK National Institute for Health and Care Research (NIHR) Health Technology Assessment (HTA) and the MRC-NIHR Efficacy and Mechanism Evaluation (EME) programmes to assess the impact of statistician blinding on the proportion of trials reporting statistically significant findings for the primary outcome(s).Stage II: Qualitative data was collected by conducting focus groups with key stakeholders who work in the delivery and oversight of clinical trials, in order to explore their perspectives on when/how to blind TSs.Stage III: This consisted of two parts:  A first BOTS employed a mixed methods approach conducted in three stages.To develop a guidance document for blinding TSs in clinical trials, a triangulation design was used . TrianguThe NIHR Evaluation Trials and Studies Coordinating Centre (NETSCC) database was searched to identify publications of randomised controlled trials in the NIHR Journals Library between 1 January 2016 and 31 December 2020. Studies classified as pilot or feasibility were excluded. This cohort was chosen as it contained recently reported high-quality randomised trials with minimal potential for publication bias or other methodological deficiencies that could confound the comparison of interest.The abstracts of potentially eligible studies published in this period  were reviewed independently by two authors (CP & MI) to confirm eligibility.p-value).A data extraction form  was invited to arbitrate.For trials with a single primary comparison , the reported Where the blinding status of the TS was not clear in a monograph, the research team contacted the named statistician(s) and/or manager to provide information about the blinding status of the TS in the clinical trial.Descriptive statistics describing the study characteristics were presented by blinding status of TSs. Continuous data were summarised in terms of the mean, standard deviation, median, lower and upper quartiles, minimum, maximum and number of observations. Categorical data were summarised in terms of frequency counts and percentages. No formal statistical comparisons were made.The proportion of statistically significant findings for the primary outcome was compared between the included studies where TSs were blinded versus not blinded, using a logistic regression model, adjusting for whether there were multiple comparisons, whether the target sample size was achieved, and the blinding status of participants, clinicians and outcome assessors. These covariates were included based on the prior belief that these factors might plausibly influence the likelihood of statistically significant findings being reported and might also be associated with the blinding status of the statistician (thereby confounding the association of interest). A trial was determined to include multiple comparisons if the trial included either (a) more than two treatment groups or (b) multiple co-primary outcomes. In the primary analysis model, a trial was determined to be not blinded if any of the participant, clinician or outcome assessor were not blinded. To facilitate inclusion in the statistical model, where the blinding status of any of these groups was unclear, this was assumed as not blinded. A secondary analysis model included blinding status of each of participants, clinicians and outcome assessors, as separate covariates. In addition, the sensitivity of the findings to alternative model specification was also explored. In particular, the primary analysis was repeated using models that additionally adjusted for the proportion of missing data for the primary outcome, as well as models determined using forwards selection and backwards elimination of covariates.p-value and a corresponding 95% confidence interval. The primary analysis included only those studies where the blinding status of the TS could be confirmed. However, a sensitivity analysis included all studies, by assuming that the TS was not blinded for those studies where the blinding status was unclear.The between-group effect was reported using an adjusted odds ratio along with a p-values were compared between groups by using a beta-regression model, adjusting for whether the target sample size was achieved and the blinding status of participants, clinicians and outcome assessors.For trials with a single primary comparison, the reported The aim of the qualitative stage of BOTS was to explore the experiences, opinions and ideas of key stakeholders on blinding statisticians in clinical trials. Therefore, it was relevant to conduct focus groups with key stakeholders including statisticians, Trial Steering Committee (TSC) and DMC members and those working within trial management who have experience in the delivery and oversight of clinical trials. Further details about the methods of this stage are the focus of a separate publication .The results from stages I and II were triangulated to develop provisional statements to advise CTUs on a risk-proportionate approach to blinding statisticians within trials. The provisional statements were developed by the research team using an iterative process in partnership with a stakeholder group, comprised of the BOTS study co-investigators and an invited multidisciplinary group of experts. Figure The research team sent an invitation letter to potential participants of the stakeholder group via email to the UKCRC, the Trials Methodology Research Partnership (TMRP) and UK Trial Managers’ Network (UKTMN), supplemented by personal invitations suggested by the study co-investigators.Prior to the meeting, the research team circulated a survey to the stakeholder group members containing provisional guidance statements , facilitated by CP, AM and EJ. Each room started and finished on a different topic to ensure that at least one survey section was covered comprehensively by each group. Verbal consent was obtained from participants before starting to record the meeting.The statements were organised under two themes originally identified from the qualitative study (Stage II). The ‘Processes’ theme included statements related to the timing of unblinding, impact on statistician interaction with other groups and practicalities. The ‘Trial design and conduct’ theme included statements focused on study design, type of analysis, interventions and outcomes.Statements where there was high agreement were presented to the participants but not discussed during the meeting. All other statements were discussed to determine whether the statements should be refined and added to the guidance or omitted completely. The stakeholder group were also invited to discuss and agree what factors (if any) would change the participants’ initial score. Feedback on the main discussion points raised during the meeting were tabulated and iterative meetings between the research team  were conducted to discuss the participants’ feedback in order to rephrase, refine or remove statements. The revised statements were circulated to the BOTS study co-investigators for them to comment and agree on the final statements’ structure and clarity.After screening the abstracts of the 200 studies, 21 studies were excluded leaving a total of 179 trials appropriate for inclusion in the review. The study flow diagram is shown in Fig. The characteristics of the trials included in the review are described in Table Table n=152), there was no evidence that involvement of an unblinded trial statistician was associated with the likelihood of significant findings being reported, odds ratio (OR) 1.02  0.49 to 2.13). However, there was strong evidence that failure to blind any of clinicians, participants and outcome assessors increased the likelihood of statistically significant findings being reported, OR 3.00 (95% CI 1.16 to 7.78). The findings remain consistent when imputing missing data for the blinding status of the statistician.The results of the primary analysis, investigating the influence of the blinding status of the statistician on the reporting of statistically significant findings, are presented in Table The sensitivity of the findings to alternative model specification was also explored and conclusions were found to be consistent. Table A1 in the Additional file p-value (n = 110). There was little evidence to suggest that the blinding status of the statistician was associated with the reported p-value.Table A2 in the Additional file Statistical models of work: six models were identified where all models shared the involvement of at least two statisticians, one typically more junior TS and one more senior.Factors affecting the decision to blind or not blind statisticians: a range of factors were highlighted such as types of data, study design, outcomes, analysis, interventions and some external factors, e.g. funder limitations and expectations and personal relationships with sponsors and chief investigators.Benefits of blinding versus not blinding TSs: The benefits of blinding the TS suggested by the FGs participants included reducing the perception of bias, and reducing pressure on statistician to reveal data. The main benefits of not blinding were understanding data in context which leads to higher quality analysis and reduces the risk of incorrect decision-making and erroneous assumptions about the data.Practicalities: How to maintain the blind of the statistician during trial delivery, issues of staffing and unit capacity and the level of statisticians’ experience and knowledge about blinding were challenging factors raised by participants across all the FGs that might influence the practicality of blinding the TS.Six focus groups were conducted with 37 participants taking part (average of 6 per group). FGs included a mixture of statisticians, trial managers, data managers and data coordinators. Four themes were identified from the analysis of the FGs’ transcripts:More detailed results of this stage can be found in a separate publication .The triangulation between stage I and II findings resulted in the highlighting of two main themes: the influence of statisticians’ blinding status on trial findings, and the association of statisticians’ blinding status with trial characteristics, e.g. study design, type of intervention. Interestingly, there was convergence between the quantitative and qualitative findings when it came to the impact of blinding of statisticians on findings. The statistician’s blinding status had no significant impact on trial outcomes. Almost all participants in the FGs’ study agreed that they did not feel statisticians knowingly introduced bias to the clinical trial . AnotherThe triangulation method led to a better understanding of the research question and resulted in the development of 40 draft provisional statements, which were sent to the stakeholder meeting participants for them to independently rate prior to the meeting day. All stakeholder attendees were invited to rate the provisional statements. The overall response to the survey was good with 80% of the participants independently rating the provisional statements. Table The majority of the statements did not reach agreement in either direction; however, there was unanimous agreement that the decision to blind or not blind the statistician should be based on the benefits and risks associated with a particular trial. It was clear from the free text feedback that agreement or disagreement with the proposed statements on blinding TSs was dependent on contextual factors, i.e. trial-specific and CTU-specific factors. Although the importance of contextual factors was the prominent issue raised by the participants in the free text feedback, analysing participants’ feedback identified other important themes to be discussed in the stakeholder meeting. For example, practical mitigation strategies against the risks of blinding or not blinding the statistician, blinding statisticians in adaptive designs, credibility of pseudo-blinding/partial blinding (i.e. using coded groups) and issues related to the marketing authorisation and whether it should be used as a consideration to blind or not blind statisticians.The stakeholder meeting was held in November 2021. A virtual stakeholder meeting via Microsoft Teams was held with 16 stakeholders from the following roles: statisticians, methodologists, trial management and data management professionals, CTU directors and unit managers, as well as members of independent trial oversight committees and representatives from the NIHR and the MHRA. A list of stakeholders’ names, organisations and roles is detailed in Additional file The responses to the provisional statements from the online survey provided a rich source of material for further discussion with the participants in the stakeholder meeting. During the meeting, there was a general feeling between the participants that the provisional statements in the survey were broad and not specific. Almost all participants agreed that it was crucial not to use definitive statements but to favour softer ones to accommodate flexibility. The stakeholder meeting was in many ways successful, with agreement emerging about the various factors that could influence the decision whether to blind the statistician. These factors, also identified during the qualitative phase, were categorised under seven broad themes: ‘timing of unblinding’, ‘ impact on statistician interaction with other groups’, ‘study design’, ‘types of intervention’, ‘types of outcome’, ‘additional roles and responsibilities’ and ‘practicalities’.Participants agreed that timing of unblinding is a key factor; for example, unblinding the TS after the statistical analysis plan (SAP) has been approved mitigates against some of the risk of the TS introducing any bias, while maintaining the blind until after the final database lock and approval of the SAP almost completely eliminates the risk. It was also identified that the blinding status of TSs could impact on their interactions with other members of the trial team and oversight committees. Regarding study design, there was also agreement that the risk of bias associated with unblinding TSs was likely to be smaller for open-label trials, where the nature of the treatments under investigation may not permit blinding and other members of the research team are unblinded . FinallyThe revision of the provisional statements, in line with the stakeholders meeting output, resulted in developing a guidance document for achieving a risk-proportionate approach to blinding statisticians within clinical trials. The guidance document consisted of 21 final recommendations/considerations categorised under seven sections. Further justification and explanation are included for each recommendation/consideration in the guidance document  in superiority trials is contrary to previous studies that have suggested that the methods of blinding in equivalence or non-inferiority trials should mirror as much as possible those used in superiority trials, in order to remove factors that may obscure any differences between the study arms , 19.There was strong agreement within the stakeholder group on the need for a risk-proportionate approach to deciding whether to blind TSs. Specifically, it was agreed that the decision should weigh up the benefits and risks associated with a particular trial. The importance of this concept is substantiated by other empirical evidence of the MHRA initiative for CTIMP trials, which highlighted that not all trials are equal and some clinical trials pose only a minimal additional risk in relation to safety and data integrity . This inLittle evidence was found in the literature search on the question of when and how to blind statisticians in clinical trials. Researchers have previously advocated blinding statisticians by using the independent statistician model  or by keIn response to these findings, guidance was developed based on the experiences of stakeholders and the findings from the quantitative and qualitative data, encompassing recommendations and considerations on when and how to blind TSs in clinical trials.The recommendations and considerations, along with the BRAT, are designed to be flexible and can be implemented at different stages throughout the life cycle of a trial. For example, one could implement at either (a) the grant application stage to ensure appropriate funding is requested for the trial, or (b) during the trial set-up phase to determine the appropriate allocation of statistical resources. The BRAT could also be applied mid-study when determining the advantages and disadvantages of unblinding the TS . Both the guidance document and BRAT are designed to be used by the TS, preferably with input from the wider trial team.While it is possible that the BRAT may not eliminate variation in practice, nor is it designed to, it will hopefully serve to ensure that the practice is justified and carefully considered. Crucially, it should also reduce the implementation of unnecessary procedures that cost money and time and can have unintended consequences.The trials included in the quantitative study were limited to a cohort of the HTA and EME-funded trials, published between 2016 and 2020; however, this cohort provided high-quality trials that should be less prone to methodological deficiencies that could confound the comparison of interest.A persistent challenge was achieving consistency in definition of statistician blinding. For instance, although guidance was issued by the BOTS study team, heterogeneity in the definition of statistician blinding applied by individual trial teams in the quantitative included studies was inevitable. Similarly, although the research team provided FG participants with a clear definition of statistician blinding, achieving consistency between participants within and across FGs remained a challenge.The use of a mixed methods approach provided a comprehensive insight into the impact of the blinding status of TSs as the data was collected and triangulated from two sources. The qualitative data is likely representative of practice in UK CTUs as it was collated from a multidisciplinary and geographically diverse sample of key stakeholders, who had extensive experience in the delivery and oversight of clinical trials. Consequently, the findings are likely to be readily generalisable to practice within UK CTUs; however, it is unclear the extent to which these findings are applicable to other settings. For instance, within pharmaceutical-led trials  or in low-resource settings, a risk-proportionate approach to blinding may not be appropriate. This is because the decision to blind or not may be pre-determined by other circumstances (e.g. regulatory or resource constraints). Nonetheless, in such settings, a careful exposition of the risks (and associated mitigation strategies) of blinding or not blinding remains valuable.The overarching purpose of the BOTS study was to develop guidance for CTUs to utilise a risk-based approach when deciding whether to blind statisticians in clinical trials. The blinding status of the statistician appeared to depend on certain trial characteristics, e.g. study design, type of comparison and the blinding status of other groups within the trial. No evidence was found to support the assertion that the blinding status of the statistician influenced reported findings. However, the risk of bias certainly appeared lower compared with unblinding participants, clinicians or outcome assessors, who perhaps have a greater opportunity to influence the findings. The guidance should prove useful in expanding the understanding of how and when to blind TSs and to help trial teams to use the BRAT in the decision-making process. We believe that using the guidance along with BRAT lays the groundwork for clinical trialists to apply evidence-based decision-making regarding blinding of statisticians.Additional file 1. Data extraction form.Additional file 2. Online survey. Additional file 3. A list of the included/excluded studies in the quantitative study.Additional file 4. Additional analyses.Additional file 5. BOTS stakeholder survey responses.Additional file 6. BOTS stakeholder group membership.Additional file 7. BOTS guidance. Additional file 8. BOTS Risk Assessment Tool (BRAT).


Background and objective: Nowadays, foodborne illness is considered one of the most outgrowing diseases in the world, and studies show that its rate increases sharply each year. Foodborne illness is considered a public health problem which is caused by numerous factors, such as food intoxications, allergies, intolerances, etc. Mycotoxin is one of the food contaminants which is caused by various species of molds (or fungi), which, in turn, causes intoxications that can be chronic or acute. Thus, even low concentrations of Mycotoxin have a severely harmful impact on human health. It is, therefore, necessary to develop an assessment tool for evaluating their impact on the immune response. Recently, researchers have approved a new method of investigation using human dendritic cells, yet the analysis of the geometric properties of these cells is still visual. Moreover, this type of analysis is subjective, time-consuming, and difficult to perform manually. In this paper, we address the automation of this evaluation using image-processing techniques. Methods: Automatic classification approaches of microscopic dendritic cell images are developed to provide a fast and objective evaluation. The first proposed classifier is based on support vector machines (SVM) and Fisher’s linear discriminant analysis (FLD) method. The FLD–SVM classifier does not provide satisfactory results due to the significant confusion between the inhibited cells on one hand, and the other two cell types (mature and immature) on the other hand. Then, another strategy was suggested to enhance dendritic cell recognition results that are emitted from microscopic images. This strategy is mainly based on fuzzy logic which allows us to consider the uncertainties and inaccuracies of the given data. Results: These proposed methods are tested on a real dataset consisting of 421 images of microscopic dendritic cells, where the fuzzy classification scheme efficiently improved the classification results by successfully classifying 96.77% of the dendritic cells. Conclusions: The fuzzy classification-based tools provide cell maturity and inhibition rates which help biologists evaluate severe health impacts caused by food contaminants. Food quality and safety are among the most important worldwide concerns, especially in France ,2. MycotRecent studies in vitro have revealed that many mycotoxins possess immunosuppressive effects, which are currently considered their most important effects ,14,15,16They revealed that DCs can potentially be a target, which inhibits the primary immune response ,20,21,22In typical cases, expert biologists adopt an assessment approach that focuses on the visual analysis of microscopic DC images. Indeed, they try to detect significant cell morphological changes between toxin-exposed and the control DC cultures. To reliably assess the undesirable effects of mycotoxins on DCs, the expert biologist must detect these cells’ most subtle morphological changes to accurately discern the different states of DCs  ,23. TherNowadays, computer vision systems’ design for automating the cell culture analysis process requires special attention. An automated analysis would allow expert biologists to facilitate the evaluation of food contaminants on human health. Indeed, these automated systems would overcome several limitations of the visual image analysis methods used until now. In particular, they would ensure speed, reproducibility, objectivity, and non-fatigability. In this context, the characterization of potential dangers caused by the presence of mycotoxins in food chains by using an automatic analysis method of microscopic images of DCs could be a reliable and efficient evaluation tool. This involves automatically counting and characterizing DCs in control and exposed cultures to collect quantitative data and relevant information that can be used for assessment. The desired automatic analysis consists of identifying, on the microscopic images of DCs, the different types of DCs  to determine if there are significant differences between the morphological characteristics corresponding to the different classes. It, therefore, allows for an observation of changes in cell morphology between these classes. This description is necessary because it will enable biologists to make a relevant assessment.The problem of automatic cell classification from segmented microscopic images is becoming more and more common in medical image fields because the recognition of these cells in the visual examination of bone marrow and blood smears is an essential tool for identification, diagnosis, treatment, and prevention of various diseases. In our study, the classification procedure aims to discriminate the state of the dendritic cells DCs . Once the cells’ relevant characteristics (attributes) are extracted, they could be integrated into a classification process categorizing them. Indeed, based on the extracted features, the classifier categorizes or recognizes different image components. The efficient procedure of segmentation and feature extraction could greatly simplify the classifier design.It should be noted that automatic white blood cell classification is a very complicated process compared to the human observer’s capabilities concerning regular, variable, and complex cell shapes. Given the importance of this field, various recent research has focused on providing insights into this issue ,25. Sevea training database. This thus ensures the learning of the classifier. Then, a new database called the test database can be processed once the classifier parameters are determined. Among these algorithms, we can cite, for example, naïve Bayesian classifier (NB), Support Vector Machine (SVM), k-Nearest Neighbors (k-NNs), and Multilayer Perceptron (MLP).For supervised classification, it is imperative to have a database of already labeled samples (examples of cells of each class), called a posteriori rule. The NB classifier is widely used to effectively recognize cells in microscopic blood images 60], ANFIIn contrast to supervised classification approaches, unsupervised classification methods do not require a database of labeled examples. Thus, these approaches learn by themselves and alternatively, class characterization is done from the available dataset. Among these algorithms, we can cite the K-means algorithm, the fuzzy C-means algorithm (FCM), the Expectation-Maximization (EM) algorithm, and the Mean-Shift algorithm (MS). K-means and FCM algorithms use the criterion of maximizing inter-class distances and minimizing intra-class distances to search for classes of similar objects.We conclude the state-of-the-art classification methods used in the field of microscopic cell image analysis by giving in In this work, we develop classification techniques that accurately recognize DCs in microscopic images. Our approaches involve three main steps: (1) Shape characterization, (2) Dimensionality reduction, and (3) DCs classification.The main contribution of this work is to have proposed an automatic classification of dendritic cell images. According to our knowledge, this subject has not been treated before in the literature. We first propose the SVM classification, which is classically used in studies of microscopic images of cells. Then, we propose other methods using fuzzy logic. We demonstrate that fuzzy logic is best suited for this problem. We show also that the features of the different classes of DCs often overlap and are difficult to distinguish. Consequently, the choice of descriptors is very crucial for classification, even when using automatic feature selection methods. Finally, we proposed to use fuzzy logic to propose an interpretation tool to let the biologist or the physician say the last word in the classification of doubtful cells.The remaining sections of the paper are structured as follows: In this work, we utilize the dataset described in previous work . It consThe shape characterization step aims to obtain descriptors or attributes describing the shape of segmented cells. These attributes will be used as input for the classification process. Formally, shape characterization can be defined as a function ted cell . The mosted cell ,64. To c-Class IM: immature DC.-Class MA: mature DC.-Class IN: inhibited DC.Therefore, depending on the deformation of the cell contour, it could be assigned to one of the three following classes:within-class scatter matrix and between-class scatter matrix, are given by Equations (1) and (2), respectively:The dimensionality reduction step aims to reduce the dimensionality of the vectors associated with the segmented cells by determining the most relevant, discriminating, and uncorrelated attributes. This step is a commonly used process in machine learning and pattern recognition. Dimensionality reduction techniques can be categorized into filter methods, wrapper methods, and embedded methods ,65. Indewithin-class (intra-class) measure while maximizing the between-class (inter-class) measure by maximizing the following ratio:FLD aims to minimize the The linear transformation The originally considered attributes  may be cFor DC classification between the different classes , we propose first to use the support vector machine (SVM) classifier in two different ways: with and without dimensionality reduction. SVM has been an efficient and powerful tool for solving many classification problems, particularly cell recognition in microscopic images ,54,66,67Fuzzy logic could be defined as the continuity of the Boolean logic that Lotfi Zadeh developed in 1965 . The latA fuzzy classification system consists of three main stages  illustra◾FuzzificationThe first step of fuzzification is to determine the degree of membership of a morphological feature value to a fuzzy set. Indeed, this value provides a way to convert the real domain into a fuzzy domain. The degrees of membership values range from 0 to 1. The membership functions are among the most important elements to find in the fuzzification process. In fact, many types of membership functions can be found in the literature, with the Gaussian, the trapezoidal, and the triangular functions being the most common and most used membership functions .◾Fuzzy inferenceFuzzy inference, also called inference engine, is the fundamental block of the fuzzy system. The inference engine emulates the behavior of the human expert by using his knowledge to interpret the classifier better and thus control it well. Once the rules to be applied have been decided, this step consists of defining the degrees of membership of the output variable to the fuzzy sets. The two most commonly used fuzzy inference systems in the literature are Mamdani  and Suge(1)max min inference method)The Mamdani method (The Mamdani fuzzy model is composed of fuzzy rule bases of the following form :(5)If x1min and max functions.In the case of inference engines based on the Mamdani method, the degrees of membership of the output variable are computed through the AND and OR operators using the (2)The Takagi–Sugeno method (sum-prod inference method)Similar to the previous method, the Takagi–Sugeno fuzzy model uses conditional clauses in which the premise is imperatively a linguistic variable, but the conclusion is a numerical variable. The conclusion could be calculated using any formula or mathematical function depending on the result and desired behavior .In the literature, unctions .◾Defuzzification-Center of gravity method;-Maxima method;-Bisector method.This is, in fact, the last step of the fuzzy system. Certainly, the outputs of the inference engine represented as degrees of membership to the functions of the output must be converted and thereafter applied on the classifier. In this case, we can talk about defuzzification which is the conversion of these fuzzy values into usable real variables. There are three basic methods of defuzzification depending on the shape of the desired output and the type of membership functions of the output:We propose two fuzzy DC classification approaches based on the FIS structure shown in For a first system (FIS1), we used a single FIS to identify the three classes . Then, wThis section presents a comparative study of the classification results using the SVM method with those obtained by the FLD-SVM classifier. FLD-SVM is a combination of the FLD feature extraction method and the SVM classifier. FLD is used to generate new uncorrelated and relevant features from the input dataset, and then, SVM is used to classify these newly obtained components. SVM is the classical support vector machine trained with the original DC features extracted from a set of training images. In our experimental study, three binary SVMs, with Gaussian kernel function are designed to estimate the cell class. To evaluate the performance of the used recognition method, we use a cross-validation technique . This laWe used Matlab’s Fuzzy Toolbox to generate the fuzzy inference systems. In the fuzzification step, we estimated the membership functions from the feature histograms. We implemented Mamdani FIS. To automatically generate the fuzzy rules of the system, we also used the FCM method. The defuzzification method used is the maxima method for the FIS1 system and the center of gravity method for the FIS2 system, with Gaussian membership functions for the output .within-class measure while maximizing the between-class measure. This resulted in the selection of two features, circularity and convexity. We show the corresponding membership functions in The cross-validation method is used to find the optimal training data for the construction of the FISs. For the input features, we experimented with three scenarios. For the first scenario, we used all original features at the classifier’s input. Then, in the second one, we used the FLD technique to select the relevant features. Finally, we analyzed the membership functions of different features and found that they overlap more than some individual features. For this reason, we experiment the feature subset selection in order to improve the results. Indeed, in order to reduce the dimensionality, we can proceed in two ways. Feature extraction is the first way, it aims to provide new features from linear or non-linear transformations of the original features, and such is the case of the FLD method. The second way is to select the optimal subset of features from the original attributes. To reduce the dimensionality to two (as with FLD), we chose the two original features corresponding to the maximum eigenvalues of the Fisher matrix First, we will consider the FIS1 system which is configured to classify cells into the three classes directly. Using all the features described in The FIS2 classification system is made up of three classifiers which separate the three classes from one another each time. Classification rates with this system were better than with the first system. With all original features given in the input, 82% of cells are classified correctly. With the FLD extraction, the correct classification rate is 78.86%. Finally, using FSS, the correct classification rate rises to 96.77%. The different rates obtained with the SIF2 system are given in Our proposed model (FSS + fuzzy classification) brought the best performance to the problem posed. The features of the different classes of DCs often overlap and are difficult to distinguish. For this reason, classical classification methods such as SVM did not provide reliable cell recognition. However, the classification based on fuzzy logic allows us to take into account the uncertainties and inaccuracies of insufficiently known data. Since the features had very large intersection areas, especially with the inhibited class, the fuzzy system with FSS was best suited for separation.The first limitation of the proposed method is that it failed to classify all cells correctly. There is still confusion between inhibited and mature cells. With FIS2 + FSS, we reached better performances, but these two most difficult classes were not totally differentiated. For this reason, we propose in the next section a help tool that would present the unclear results to the biologist who will decide at the end in case of doubt. Another limitation of the proposed method is that we have chosen the shape characteristics ourselves. We then showed that some features had no contribution; on the contrary, some of them deceived the system. It would be interesting to exploit deep learning methods that extract relevant features automatically. It is regretful that we could not experiment the methods on our base which is composed of a very limited number of images. In future, we could study the combination of deep learning classification and fuzzy logic for parameter control as done in ,76.In our study, the features of the different classes of DCs often overlap and are difficult to distinguish. For this reason, classical classification methods such as SVM do not provide reliable cell recognition . Therefore, we have proposed the classification based on fuzzy logic which allows us to take into account the uncertainties and inaccuracies of insufficiently known data. Fuzzy classification can also be used to propose a system to help in the evaluation of the harmful effects of food contaminants with confidence indices. In other words, we will take from the outputs of the inference systems the values of the membership functions of each class and let the biologist make the final decision on the class of the cell. The values of membership to the three classes can be interpreted as a degree of immaturity, degree of maturation and degree of inhibition. The degree of inhibition will be used, for example, by the biologist to assess the effects of toxic products on the immune system.We illustrate in The outputs of the three FIS2 inference systems for the same input cell are shown in This paper has designed and experimented with classification techniques to recognize dendritic cells based on extracted and selected morphological cell features. Classification is addressed to identify immature, mature, and inhibited cells for a posteriori evaluation of the toxic effects of some contaminants on the immune system. The first proposed classifier is based on SVM and FLD to select uncorrelated and relevant attributes. The FLD-SVM classifier does not give satisfactory results due to the significant confusion between the inhibited cells on one side and the other two cell types (immature and mature). Subsequently, a second strategy was developed to improve dendritic cell recognition results in microscopic images. This one is based on fuzzy logic, which allows us to consider the uncertainties and imprecision of the data. The classification results were much improved with the fuzzy classification system (FIS2 + FSS), which successfully classified 96.77% of the cells. Classification results could be improved by combining fuzzy logic with a deep learning classifier, but to do so, we will need a larger image base. The constructed fuzzy classification system has also been proposed to provide biologists with decision support tools for dendritic cell recognition in uncertainty-type cell identification. These fuzzy classification-based tools also provide cell maturity and inhibition rates to help biologists evaluate the severe health impacts of food contaminants.Finally, we note that this work is proposed in the context of processing and analyzing 2D microscopic images of dendritic cells. However, 3D image analysis could be considered to provide biologists with additional clues about the toxic effects of food contaminants. The analysis of the three-dimensional aspect of dendritic cells that starts with the 3D acquisition of these cells is the perspective of the work presented in this paper.


Aimed at the problem of fault characteristic information bearing vibration signals being easily submerged in some background noise and harmonic interference, a new algorithm named enhanced differential product weighted morphological filtering (EDPWMF) is proposed for bearing fault feature extraction. In this method, an enhanced differential product weighted morphological operator (EDPWO) is first constructed by means of infusing the differential product operation and weighted operation into four basic combination morphological operators. Subsequently, aiming at the disadvantage of the parameter selection of the structuring element (SE) of EDPWO depending on artificial experience, an index named fault feature ratio (FFR) is employed to automatically determine the flat SE length of EDPWO and search for the optimal weighting correlation factors. The fault diagnosis results of simulation signals and experimental bearing fault signals show that the proposed method can effectively extract bearing fault feature information from raw bearing vibration signals containing noise interference. Moreover, the filtering result obtained by the proposed method is better than that of traditional morphological filtering methods  through comparative analysis. This study provides a reference value for the construction of advanced morphological analysis methods. The assessment of bearing faults is an essential part of condition monitoring for the pieces of rotating machinery inside a wind turbine ,2. If beAs a nonlinear signal processing method proposed by Serra and Matheron, mathematical morphology (MM) was originally utilized to predict the value of an area’s mineral resources ,13,14. NConsidering the above-mentioned situations, to improve bearing fault feature extraction ability and avoid the problem of empirical selection of parameters of morphological filtering, this paper proposed a bearing fault feature extraction method based on enhanced differential product weighted morphological filtering (EDPWMF), where its combination parameters can be automatically determined by using fault feature ratio (FFR). The effectiveness of the proposed method for bearing fault feature extraction is demonstrated by simulation analysis and two experimental case studies. Moreover, quantitative comparative analysis is also performed to validate the superiority of the proposed method.The rest of this paper is organized as follows: Morphological filtering is a nonlinear filtering method based on mathematical morphology theory, which can effectively eliminate noise and retain some shape feature information in the original bearing vibration signal. The basic principle of applying morphological filtering for signal analysis is to use a structuring element (SE) with a specific shape to detect the feature information of a signal. Four common morphological operators include dilation, erosion and opening and closing operations .M of SE is less than that of Assuming that The opening operation and closing operation are essentially the combined results of the dilation and erosion operation. The opening operation and closing operation are respectively defined as:The erosion operation can filter out unnecessary noise, smooth the negative impulse of a signal, and eliminate the positive impulse of a signal. The dilation operation has the opposite effect on the signal as the erosion operation. Similarly, the function of the opening operation is to filter the peak noise of a signal and remove edge burr of the signal. In contrast to the opening operation, the closing operation can be utilized to smooth or suppress the noise in the trough of the signal and fill in the holes and gaps in the signal.To ensure that the shape characteristics of the original bearing vibration signal are not damaged, the closing operation and dilation operation are combined to enhance the feature extraction ability of the morphological operator, which can suppress the negative impulse and retain or expand the positive impulse. However, considering that the combination morphological operator may damage the negative impulse, it is necessary to conduct the erosion operation after the closing and dilation operations, so that the negative impulse in the bearing vibration signal can be amended. Therefore, two combinations morphological operators can be defined as follows:Similarly, the feature extraction ability of the morphological operator is enhanced by combining the opening operation and erosion operation, which can suppress the positive impulse and retain or enlarge the negative impulse. However, considering that the combination operator may destroy the positive impulse, it is necessary to conduct the dilation operation after the opening and erosion operations, so that the positive impulse in the bearing vibration signal can be amended. Therefore, another two combinations of morphological operators can be defined as follows:To further extract the positive and negative impulses from the bearing vibration signal simultaneously, two new weighted synthetic morphological operators  is largely related to the analysis performance of morphological filtering. Due to the fact that the flat SE has the advantages of simple structure and fast operation, this paper intends to adopt the flat SE for analysis. The length is the main parameter of the flat SE. If the length of flat SE is very short, morphological operators can extract more impulse features from the bearing vibration signal, but will retain a lot of noise interference and make it difficult to extract bearing fault features. On the contrary, if the length of the flat SE is too long, some useful fault information will be filtered out and only a few impulse features can be extracted. Therefore, the selection of the length of the flat SE has a great influence on the performance of the morphological operator.x(t), the FFR can be defined as:x(t). x(t), respectively. Generally speaking, the higher FFR is, the better the effect of morphological filtering is, and it is more advantageous to extract bearing fault characteristics. Therefore, in this paper, FFR is employed to carry out adaptive selection of the length of flat SE of the proposed EDPWO. Meanwhile, the weighting correlation factors Fault feature ratio (FFR) has been proven to be an effective sensitive index in describing bearing fault information ,31. For In order to obtain useful bearing fault feature information and improve fault diagnosis accuracy, a novel approach based on enhanced differential product weighted morphological filtering (EDPWMF) is proposed for bearing fault feature extraction. Step 1: The bearing vibration signal is collected by installing the sensors on the mechanical fault simulator.Step 2: Set the search range of parameters  is constructed as follows:x(t) is composed of three parts , sinusoidal harmonic interference signal y(t) and Gaussian white noise). The harmonic interference signal y(t) is composed of two sinusoidal waves s(t) by using MATLAB function C is 800, the resonance frequency T = 110 Hz, i-th shock relative to the period T, and it follows normal distribution with the mean value of 0 and the standard deviation of To study the effectiveness of the proposed method, the bearing fault simulation signal terature , the GauM, the optimal weighting correlation factors The proposed method is utilized to analyze bearing fault simulation signals. Firstly, set the search range of parameters  obtained by the proposed method with increasing levels of noise, as shown in To further show the feature extraction ability of the proposed method, the proposed method is compared with three typical morphological operators  to verify the effectiveness of the proposed method. Specifically, the QPZZ-II rotating machinery fault simulation test bench is adopted to collect experimental bearing vibration data induced by the local fault. The photo of the experimental system is illustrated in M of flat SE, the weighting correlation factors M of flat SE, the weighting correlation factors Firstly, based on the largest FFR criterion and the iterative search operation, the optimal combination parameters In this section, to demonstrate the effectiveness and advantage of the proposed method in bearing fault feature extraction, comparisons between the proposed method and several representative morphological filtering methods  are conducted. Bearing benchmark data from Case Western Reserve University (CWRU)  is introDue to the CWRU benchmark data having different fault data, including four fault diameters and four load values, this section takes the 12 k drive end bearing fault data as an example for statistical analysis. Due to space limitations, this paper only plots the analysis results of four datasets  using different methods . The specific analysis results are shown in To more intuitively evaluate the performance of various methods, Experimental data from the mechanical fault diagnosis laboratory of Southeast University (SEU) is adopted to validate the effectiveness of the proposed method. The collected bearing outer race fault signal in case 3 is processed by using direct envelope spectrum analysis and four methods . Similarly, direct envelope spectrum analysis and four methods  are adopted to deal with the collected bearing inner race fault signal in case 3. (1)Due to the performance of the proposed method will be significantly affected by the lower SNR, especially below the SNR of −6 dB. Therefore, in future work, in order to satisfy bearing fault feature extraction with lower SNR, we will combine the proposed method with other advanced filtering methods Considering that some prior knowledge of bearing fault characteristic frequency is required in the calculation process of FFR of our proposed method, this tends to hinder the application of the proposed method in real engineering. That is, this prior requirement is regarded as the disadvantage of our proposed method. Therefore, in our future work, to satisfy the actual requirements, we will explore some effective indexes  without prior knowledge instead of FFR to select the optimal combination parameters of the proposed EDPWO. Specifically, to improve the fault feature extraction ability of our proposed method and avoid the dependence on prior knowledge of bearing fault frequencies, we will work on a new indicator named integrated measure of sparsity-impact (IMSI) to replace FFR to select the optimal SE length of our proposed method. Moreover, the effectiveness and superiority of this IMSI index in bearing fault feature extraction will be launched and promoted steadily in the follow-up work.(3)In this paper, the proposed method is used for analyzing bearing single faults, but its performance is unknown for multiple fault detection. Hence, in order to meet the requirements of the proposed method for synchronous intelligent online diagnosis of multi-bearing faults, the proposed EDPWO will be fused with deep learning models  obtained by various methods for simulation signals and different experimental fault data. All experiments are conducted on a computer configured with Intel(R) Core(TM) i7-9750H, CPU 2.60 GHz and RAM 8 GB. The detailed calculation results of statistical indicators of different data are shown in (1)An enhanced differential product weighted morphological operator (EDPWO) is presented by integrating the differential product operation and weighted operation into four basic combinations of morphological operators.(2)To avoid the problem that EDPWO selects parameters according to artificial experience, the fault feature ratio (FFR) index is adopted to automatically determine the optimal combination of parameters  of EDPWO.(3)Through the analysis of simulation signals and two experimental cases, the effectiveness of the proposed method in bearing fault feature extraction is verified. In addition, compared with the traditional morphological filtering method , the proposed method can obtain the larger FFR values, which is more conducive to the extraction of bearing fault feature information.In this paper, a novel method praised as enhanced differential product weighted morphological filtering (EDPWMF) is proposed for bearing fault feature extraction, which can not only suppress noise interference effectively but also retain the detailed information of the signal. Simulation and experimental signal analysis verify the effectiveness of the proposed method in bearing fault feature extraction. The detailed contributions and innovations of this paper are as follows:A point worth mentioning is, to preferably conform the actual engineering needs, in future work, we will also focus on integrating morphological filters with transfer learning or meta learning to achieve health status assessment and life prediction of large-scale industrial equipment .


Volunteered geographic information is often generated as voluminous point data, leading to geometric and thematic clutter when presented on maps. To solve these clutter problems, cartography provides various point generalization operations such as aggregation, simplification or selection. While these operations reduce the total number of points and therefore improve the readability, information preservation could be harmed when specific spatial patterns disappear through the generalization process, possibly leading to false interpretations. However, sets of map generalization constraints that maintain spatial pattern characteristics of point data are still missing. To define constraints that support synoptic interpretation tasks, user behaviour while solving these tasks has to be analysed first. We conduct a study where participants have to perform such interpretation tasks, using a new method that combines think-aloud interviews and techniques from visual analytics. We reveal that the point density of a dataset has the biggest impact on the user behaviour and the respective task-solving strategy, independently from the actual task type executed. Furthermore, our results show that the graphical map complexity only has a minor impact on the user behaviour, and there is no evidence that point data cardinality influences task execution and the solution-finding strategies. Volunteered geographic information (VGI), as a special case of the more general web phenomenon of user-generated content  and related quantitative measures are defined for guiding the generalization process, considering the contradicting aspects of information preservation (preservation constraints) and readability (legibility constraints).With regard to information preservation, many applications require to maintain specific spatial patterns such as extreme values, clusters or hot spots. If generalization is applied rather general and without considering the actual map use, these patterns could disappear and mislead the user to false results of respective synoptic interpretation tasks that—in contrast to elementary tasks—include pattern identification, pattern comparison or relation seeking :To answer these questions, we introduce relevant literature Sect.  and condIn their work on display clutter and respective measurement techniques, Moacdieh and Sarter  refer toaggregation operations, point clusters based on geometric and/or semantic criteria are identified and replaced by aggregator markers. The cluster initialization method  thereby influences the final result  the eBird Basic Dataset and from (2) the iNaturalist database.Antelope sightings at Kruger National Park, South Africa, retrieved from the iNaturalist database.To examine the different types of tasks, we created various maps using VGI point data sets from different sources:For all datasets retrieved from the Flickr API, we created smaller subsets for examining the influence of the point cardinality on user behaviour. To preserve the initial clusters, we reduced the number of points incrementally and analysed after each step if all clusters are still identified by the HDBScan algorithm.Goals of the preliminary study were to identify and select relevant interpretation tasks for our datasets, to get a first impression of the user behaviour and confidence while solving these tasks, and to evaluate the suitability of the datasets for the purpose of overall study objectives. Beyond that, we wanted to find manually defined patterns in our datasets, which we used during the encoding process of the following interviews.The preliminary study was conducted as a postal questionnaire with 25 participants, all of them professionally working with maps. For the first part of the study (Part A), a printed map of the Italian restaurants in the inner city of Hamburg, Germany, was provided. The dataset was also used for the second part (Part B) but is now extended with randomly generated information about the price level of each restaurant, which was symbolized with different colours. The map for the third part (Part C) showed the distribution of sightings of four different antelope species in the Kruger National Park, indicated with different colours. Based on the aforementioned task typology, we generated three elementary and nine synoptic tasks, and increased task difficulty (elementary vs. synoptic tasks) and complexity  from part to part .The main study focused on the overall objective—the analysis of user behaviour while solving synoptic interpretation tasks. We also wanted to find out whether the cardinality of the point data set, as well as the graphical map complexity of the background map, have an influence on the task-solving strategy of the participants. Figure Originally, we planned an eye-tracking study, but due to the ongoing COVID-19 pandemic, the study design changed to an online study. First, we sent a questionnaire to the participants and asked for their gender, age, education, their experiences and skills with maps and their geographic knowledge . The interview guidelines included a list of questions regarding the different actions a participant made to solve the task, their order, the decision-making process, and if special characteristics of the map had influenced their strategies. With the guidelines, we made the interviews comparable and ensured that each question was answered by the participants, either directly while thinking aloud, or on request afterwards (retrospective Think Aloud).We chose a between-subject design for our study, where each participant had to solve five tasks, and examined the user behaviour through a set of ordered task-solving actions. Every task was introduced with an explanation about the map, the underlying data and the task, and participants could decide when to start. While solving the task, each participant described her or his behaviour and answered questions from the interviewer. With that, the method is a mixture of concurrent and retrospective Think-Aloud as described by Häder . AlthougTwenty-one people  participated in the main study voluntary, with none of them already participating in the preliminary study. All of the participants were either students or postgraduates from the HafenCity University Hamburg, Germany. Regarding geographical knowledge, two participants rate themselves as experts, 15 participants as advanced, and four as a layman. All participants rate their experience in using maps as either average or expert. The questionnaire further revealed that two of the participants use satellite data every day, eleven often and eight rarely.Nineteen of the twenty-one participants provided their results of the Navon test. The Navon test is a method to define the cognitive style of a person, which can be holistic or analystic. Holistics tend to focus on the large-scale patterns . Then we encoded each clip twice .The map for task 2 visualized the point locations of Flickr photos taken in Rio de Janeiro which were either tagged with “Cristo Redentor” (orange dots) or “Sugarloaf Mountain” (blue dots), and participants had to compare the two-point distributions. We suppose that the landmarks were present on the majority of these respective tagged photos, so after the initial task, participants guessed the exact location of each landmark based on the potential line of sights.Even though the orange point set was the first listing in the legend, 18 out of the 21 participants started with the description of the blue points, following the coastline from cluster 1 see Fig.  to the bIn contrast to the first task, participants referred frequently to the background map during their reasoning, describing the coastline, the harbour, built-up areas, and the mountainous region in the west. Again, the differentiation between dense and sparse areas was highlighted by most of the participants, this time in combination with the different colours. As shown in Fig. For the third task, participants had to describe the relative positions of the sightings of two different antelope species on a map of Kruger National Park, with one specie (orange) sighted more frequently in the northern part, and the other (blue) more southwards.When comparing the distributions, participants focused mainly on two aspects. First, they compared the location of the clusters of each antelope specie. Most of them described the north–south differentiation explicitly or implicitly correct, which can also be seen in the colour distribution in Fig. In general, the task-solving behaviour of the participants was very heterogeneous for this task. In contrast to the previous task, this time more participants started with the orange category, which again can be explained by the higher saliency from the background map. But other than in task 2, there was no particular starting cluster the majority of participants chose see Fig. . They stFurthermore, we varied the background map for this task. While this had no effect on the overall task-solving strategies, the subgroup using the stamen background map focused much less on a central cluster close to a river. We argue that the characteristics of the other two background maps guided the users to this cluster, while the low visibility of the river hamper this effect on the stamen map.For task 4, participants had to find similar distributions of other antelope specie sightings compared to the ones in task 3. The overall strategy of the participants was quite similar between all. 14 of them focused on the distribution of the black points from the start, arguing that these black points stand out against the rest due to their colour saliency and the low density in the areas the points appear. After choosing their first antelope specie, 18 of the 21 participants described the point distributions of at least two other species, before making their decision. In comparison to the previous task, there were two inherent differences, which can be explained by the repetition of the map topic and the relation to the task before: First, the background map was not part of the reasoning anymore. Second, participants generalized much more in their statements by just distinguishing between distributions appearing “more in the South” or “more in the North”, as about one-third of all statements referred to these broad areas. Apart from that, the high number of transitions between the northern and southern parts of the map was still present during this task, and again with no dominant connection between two certain clusters.For the last task, participants had to find city districts that have a similar price level of Italian restaurants (marked as points) compared to a reference district.Other than before, the first part of the task-solving strategy was similar between all participants, as they searched for the reference district on the map, and defined their individual comparison criteria by describing the distribution of different price levels in this district. After that, they moved over the map to identify the most suitable candidates of similar districts and made their decision based on the comparison criteria and the best candidates they have found.The content analysis of the statements revealed that there were four different comparison criteria used by the participants, with 14 of them using at least two of these criteria during the task-solving process. The comparison criteria regarding the reference district were an overall number of points (named 13 times), point proportion between the different price level classes (11 times), mean price level (10 times), and absence of the highest price level class (10 times).sequential strategy). The second approach represents the opposite characteristics, with more of the longer trajectory paths: Starting from the reference district, these participants moved less strategical through the map, focusing only on selected districts, and moved back to the reference district several times (star strategy).After defining the comparison criteria, the next step was to search for suitable candidates. Figure central cluster strategy), the other group focused more on a cluster in the north of the map and much less on the most-dense areas further south (north cluster strategy). Figure Within participants not following one of the approaches described above, we find two more search strategies using the MultiMatch algorithm for position similarity: One group of participants tended to move towards the area of the map with the highest point density , followed by point colour (see tasks 2 to 4). While the density of points is a data-related factor, we introduced the second factor with our colour choice and the respective contrast and visual saliency. Beside these two aspects, a unique cluster shape was the only other characteristic attribute attracting participants from the beginning. For the fifth task, all participants started their task-solving by searching for the explicitly given reference district.The point density of clusters was also the most important factor during the following process of obtaining information. If there was more than one alternative category to deal with—as in the tasks 1, 3 and 4—the one with a denser cluster was described and analysed earlier and more often, while sparse distributions were ignored by many participants. For comparison tasks, density was also the main evaluation measure that participants used to describe and distinguish clusters, and an important factor influencing their respective search strategy in task 5.RQ1.In general, we can distinguish different task-solving strategies; however, these strategies do not differ significantly between the different task types. Within our study focusing on VGI point data, we can state that the point density has the biggest impact on the user behaviour during the task-solving process. This answers our research question open landscape, so adding more bird observations and photos introduces more locations and possible clusters on the map. Task 2 shows much more concentrated photo locations in a city, as the two landmarks cannot be seen from everywhere in the city. Therefore, increasing the size of the dataset primarily adds more photos to the existing sightseeing spots. However, for both tasks, the task execution strategy itself and the solution-finding were not influenced by the point cardinality. In summary, we can state that user behaviour and solving strategies did not change significantly with higher point cardinality, which answers our research question RQ2.Concerning the influence of the point cardinality on the task solving process, we varied the amount of points on the map for both tasks 1 and 2, and compared the respective user behaviour for each step of the solving process. As described in Sect. The second variable we changed within our study was the graphical complexity for tasks 1 and 3. As shown for task 1, the vast majority of the participants referred to the background map only on request. However, as the focus maps differ slightly, an implicit effect on the task execution process is possible. Between the three background maps used in task 3, the only significant difference was the low frequency of participants focusing on the central cluster at the river while using the stamen background map. As stated in Sect. In general, we see both an implicit and explicit influence from the background map on the participants’ reasoning for all the five tasks: On the one hand, participants explained the cluster characteristics referring to the background map. On the other hand, frequently identified clusters were implicitly supported by background map characteristics, even if not explicitly mentioned in the statements during the interviews. Although the background map can be part of each step of the task-solving process, we found no evidence that the graphical complexity of a map influences the overall strategy to solve the given task.RQ3, we state that the graphical complexity in general, and the background map in particular, have an implicit and explicit influence on the participant’s reasoning, but do not change the overall task-solving strategy.The only task execution strategy we identified throughout our study which is clearly defined by the background map is the sequential strategy during task 5 when the order of districts was defined by neighbourhood and not by point density. Answering our research question Both preservation and legibility constraints in map generalization have to address point density in the first place. In the following, we provide recommendations for defining constraints that shall be used for guiding the point generalization process.similarity, and the criteria most frequently used was the total number of points within a district. Moreover, our results reveal that the point density of clusters or classes was the main attractor to the participants, and the point density predominantly defined the order of areas recognized. A potential solution for this demand is constraints preserving the ranking of densities between focus areas.For the preservation of spatial pattern, two aspects have to be considered. First, the proportion of points between the different patterns, as well as between dense and sparse areas, has to be retained. As the solving strategies for comparison and relation-seeking tasks show, it is of major importance that generalization operations fulfil constraints by preserving the proportion of objects under consideration. For instance, in task 5 of our study, the individual pattern definition depended on the user’s interpretation of The second aspect is the proportion of points of different classes within an area. For all tasks, the participants compared the characteristics of different clusters, classes or city districts. If there were different classes present within the same cluster, the proportion between them was described frequently. Furthermore, the absence of classes was also part of cluster characterisation. Consequentially, defining constraints to preserve proportions between classes while maintaining at least one point per class is the second requirement.Beside density, the colour of points was the second most important factor influencing the task-solving strategies of the participants. As the use of specific colours to draw the map readers’ attention is a common technique in cartography, this can be adopted by point generalization algorithms. Especially with datasets where pattern preservation is difficult to manage, using style elements like colour and opacity could extend the variety of generalization techniques. Of course, any obvious thematic correlations for the specific applications have to be considered . Furthermore, the Gestalt Laws regarding similarity and proximity should also be taken into account when using colors.Another cartographic solution to help pattern recognition is an adjustment of the background map. As discussed in Sect. VGI often shows an enormous data volume in combination with semantic and temporal heterogeneity, often leading to undesired clutter effects. While existing cartographic generalization operations improve the readability of the map, specific spatial patterns in the data such as extreme values, clusters or hot spots, are rarely considered and can disappear through the generalization. To prevent users from being misled to false interpretations, map generalization constraints to maintain spatial pattern characteristics of point data are needed. To provide such a set of constraints, we first have to empirically analyse the user behaviour while interpreting point data sets.We developed a new method, which adapted Think Aloud interviews and uses visualization techniques from eye-tracking analysis. Based on the results of our study, we can state that the point density of a dataset has the biggest impact on the user behaviour and the respective task-solving strategy, independently of the actual task type which is executed. We further examined the influences of point data cardinality and background map and identified only small impacts on the user behaviour when using background maps of different complexity.Preparing the next step of our proposed research process, we further developed recommendations for constraint definition regarding the preservation of pattern proportions and the usage of cartographic techniques. Future work will further develop, implement and test respective constraints into generalization workflows. At this point, it could also be useful to conduct a follow-up study to the one presented here, focusing on a specific synoptic task with different complexity conditions and data sets. In addition, we will extend the focus of the present work: First, we want to apply our method to multiscale and multi-temporal displays. Second, we consider to broaden our work to more complex geometries, e.g. trajectories or buildings.