We present the NEFOCAST project , funded by the Tuscany Region, about the feasibility of a system for the detection and monitoring of precipitation fields over the regional territory based on the use of a widespread network of new-generation Eutelsat “SmartLNB” (smart low-noise block converter) domestic terminals. Though primarily intended for interactive satellite services, these devices can also be used as weather sensors, as they have the capability of measuring the rain-induced attenuation incurred by the downlink signal and relaying it on an auxiliary return channel. We illustrate the NEFOCAST system architecture, consisting of the network of ground sensor terminals, the space segment, and the service center, which has the task of processing the information relayed by the terminals for generating rain field maps. We discuss a few methods that allow the conversion of a rain attenuation measurement into an instantaneous rainfall rate. Specifically, we discuss an exponential model relating the specific rain attenuation to the rainfall rate, whose coefficients were obtained from extensive experimental data. The above model permits the inferring of the rainfall rate from the total signal attenuation provided by the SmartLNB and from the link geometry knowledge. Some preliminary results obtained from a SmartLNB installed in Pisa are presented and compared with the output of a conventional tipping bucket rain gauge. It is shown that the NEFOCAST sensor is able to track the fast-varying rainfall rate accurately with no delay, as opposed to a conventional gauge. Rainfall is a critical factor of water cycle dynamics as it is a vector for energy exchange between atmosphere, sea and land. Moreover, it has a key role for water supply; rainfall monitoring is an important tool to be used for water management, especially in areas characterized by water scarcity. Some other important practical applications also concern agriculture and human welfare. Finally, the measurement, the monitoring and the forecasting of rainfall are different phases of meteorological studies substantial for the management of alerts and the assessment of environmental risks due to floods and landslides. They also play a key role in climatological studies, as the rainfall amount is an important climate index. The knowledge of the instantaneous rainfall intensity during precipitation events is very useful in urban areas as it allows a better understanding of hydrological dynamics for the correct interpretation of the complex infiltration and runoff processes. Urban hydrological flows are constrained by the drainage system and highly dependent on the rainfall intensity. In order to produce current estimates of the system conditions, the real-time rainfall data are very useful; they are also able to highlight short and very intense events.Several methods for measuring precipitation exist, based on different physical principles, direct and indirect methods, and ground and space-based systems. A complete up-to-date review regarding the fundamental and technical aspects of rainfall estimation is offered by , togetheThe combination of remote sensing and in situ observations for precipitation estimation is particularly suitable for now-casting purposes , as the Several ground-based instruments exist  which taRegarding the types of error sources, the main problem for point measurements is the difficulty of extrapolating the representativeness to an area, due to the high spatial variability of rainfall. During the measurement process, both systematic and random errors can occur. Errors due to the effect of wind, the evapotranspiration losses, the site-dependent instrument exposure, and the incorrect calibration fall within the first type. Malfunctioning problems, instrumental errors and observational effects can vary depending on the specific case, and therefore produce random effects. Some solutions exist for reducing the errors of the measuring instrument and the correction accuracy can be dependent on the observed phenomena . TippingAn in-depth literature review of the issues and problems pertaining to the use of TBRs, featuring laboratory testing and field evaluation, is reported in . TippingThe major problems of the TBRs are that they cannot measure instantaneous rainfall, but provide, at discrete-time instants, measurements of the water quantity relative to a time interval. For this reason, the information about rainfall spikes and peaks, essential in hydrological applications to solve water balance, is not given in the raw measurements. This is particularly critical, especially in very small catchment areas, such as urban ones, which are vulnerable from the hydrological point of view, as the hydrological processes develop very fast. In order to have continuous-time rain-rate estimates, algorithms must be applied to the measured data for the reconstruction of an instantaneous rain rate from the tipping bucket measurements. The simplest way is a linear interpolation based on the ratio between the bucket size and the time intervals between two tips. Unfortunately, this method only provides an averaged value and cannot reconstruct the instants of zero rain. In , a cubicA survey on the state-of-the-art rainfall intensity gauges, with the relevant physical principles, is presented in Section 2.2 of . The resZ), which depends on the number and size distribution of hydrometeors and their absorption and scattering properties related to the density and shape of the hydrometeors, radar wavelength and temperature. Most of the operational weather radars have adopted the dual polarization technology. Such radars are capable of transmitting pulses on both horizontal and vertical planes , providing additional information related to the shape and size of the hydrometeors, which can be used to improve the accuracy of the rainfall estimation algorithm and to obtain information on the precipitation microphysics [Weather radars are used for monitoring precipitation by most weather services. They are able to detect, quantify and monitor the evolution of precipitation events over a wide area  with a high spatial  and temporal (5–10 min) resolution. Furthermore, they can provide a 3D representation of the precipitation event, therefore allowing us to get a deep insight into the characteristics of rainfall and in general of the ongoing microphysical processes governing precipitation. Typically, weather services use radars by arranging them in a networked configuration, in order to obtain seamless coverage of nation-wide areas for meteorological and hydrological applications. However, weather radars perform indirect measurements of rainfall, obtaining precipitation estimates by converting radar measurements into rainfall rate using appropriate conversion algorithms . In the ophysics ,14. Quanophysics ,16 and tRecently, the use of microwave (MW) links has been introduced in several studies for the operational estimation of precipitation from tropospheric radio links . ReceiveNEFOCAST  is a research project funded by the government of the Tuscany Region . Started in September 2016 for a duration of 24 months, NEFOCAST is based on an innovative solution: It uses a dense population of interactive satellite terminals (ISTs) that serve as both weather sensors and modems to send the measurements to a dedicated now-casting platform to receive back rainfall information and potential alerts. The IST used for the project is named SmartLNB (smart low-noise block converter) and is an innovative product, introduced by the satellite operator EUTELSAT with the ambition to replace the traditional direct-to-home (DTH) receivers, providing at the same time additional interactive services through a narrowband return channel. The SmartLNB is a new-generation electronic feed connected to an antenna with an embedded transmitter for interactive applications. Such terminals serve as both weather sensors and modems to send the measurements to a dedicated center (the NEFOCAST service center) that generates precipitation products and eventually related weather warnings. Since ISTs are low-cost and low-power RF transceivers that are also equipped with a traditional satellite television (TV) decoder, they can replace the current population of DTH receivers. The NEFOCAST precipitation maps will be therefore based on capillary measurements, constantly and rapidly updated. Such system presents interesting aspects when compared to other consolidated precipitation measurement instruments.Due to its promising results, the NEFOCAST project received the endorsement from EUTELSAT, a leading satellite operator, and Météo France, a big player in the weather forecast market, which are both interested in setting up a collaboration based on the project results to develop new services. The business related to weather data has undergone an exponential growth in the last few years and, accordingly, provider companies of weather data grew very fast in terms of value and proposition.The NEFOCAST Service Center collects information from the satellite network and the rain gauges, generating rain field maps that are then shared with a number of value added service providers (VASPs) that use them to offer dedicated services to end users.The SmartLNB  is an inThe unit, composed of an indoor unit (IDU) and an outdoor unit (ODU), is formed by a 70 cm-diameter satellite dish and the actual SmartLNB appliance see .The IDU will provide electrical power to the whole system, and can be interconnected to a local network to exchange data via satellite and optionally to a satellite set-top box to receive standard broadcast channels. The ODU is interconnected to the IDU using a coaxial cable. It has an optional RF input for an external LNB, to be used in conjunction with another existing satellite receiver .The SmartLNBs used for the experimentation operate in Ku-band for both the forward and return links. The quality of these links is affected by weather conditions: Rain rate and SmartLNB signal attenuation (both transmitted and received) are highly correlated. The algorithms studied in the project allow the translation of signal attenuation measurements into rain rate estimates, which means that the SmartLNB can be used also as a weather sensor.In fact, it can measure the power of the received DVB-S2 signal and the associated signal-to-noise ratio with a resolution of 0.1 dB in real time. Regarding the network, the hub is able to measure the power level and the signal-to-noise ratio of the F-SIM traffic sent by all the SmartLNBs composing the network. Both measurements are stored in the hub database and accessed by the NEFOCAST Service Center for further processing.At any time, the satellite hub stores information on the signal attenuation on both forward and return links for all the SmartLNBs. Forward link attenuation is measured by the SmartLNBs and transmitted to the hub, while return link attenuation is directly measured by the hub subsystems.The hub database also stores geographic coordinates of all the SmartLNBs in the network, which are provided during their installation and commissioning phase.The SmartLNB is able to send weather information with a very dense granularity in the time domain  and to receive feedbacks simultaneously from the NEFOCAST service center, such as weather alerts. This significantly simplifies and optimizes the now-casting network architecture, as the SmartLNBs can simultaneously serve as both dense and scalable weather sensors, and communication nodes.The network of Smart LNBs deployed for the experimentation serve as both weather sensors and modems to send the rain gauge measurements to the NEFOCAST service center.After a pre-set amount of precipitation fall, the rain gauge lever tips and sends an electrical signal to the data logger. Periodically, the data logger sends the log of the received data to the NEFOCAST service center using the satellite network. For each tip, the rain gauge collects an amount of water equivalent to 0.2 mm rainfall. Tips are generated by a reed switch within the rain gauge. The data logger keeps track of each tip: These data are then integrated over a configurable time interval in the NEFOCAST Service Center. Debouncing is applied to the rain gauge signal in order to avoid possible false detections. The data logger is divided in two parts: A probe and a core module. The probe is installed inside the rain gauge and communicates with the core module using a dedicated Wi-Fi link. This probe is implemented using a NodeMCU ESP8266 microcontroller. Signals from the rain gauge are read on one of the probe’s general purpose input output (GPIO) pins and a multicast user datagram protocol (UDP) message is generated for each of them. Each data logger has an associated unique ID that is transmitted within the messages.This choice allows the use of the same data logger to collect statistics from multiple probes at the same time. The core module listens for multicast UDP packets coming from the probes, aggregates and forwards them to the NEFOCAST service center using the satellite link provided by the SmartLNB. Messages are also stored within the data logger: In the case of communication issues with the NEFOCAST service center (e.g. no satellite link available due to heavy rain), messages that have not been yet delivered will be sent as soon as the connection will be restored.The NEFOCAST system uses a bi-directional geostationary satellite network. The link connecting the ISTs to the gateway is used by the ISTs to access the terrestrial infrastructure via the satellite. The forward link transports the traffic generated by remote servers on earth and addressed to the ISTs via the satellite. EUTELSAT 10A (EUT 10A) geostationary satellite is used by NEFOCAST SmartLNBs for both the return and the forward links. The satellite is located at ten degrees east longitude and provides Ku-band widebeam footprints serving Europe. Measurements of SmartLNB power levels on both the forward and the return links are periodically collected by the NEFOCAST service center, which interacts with the satellite hub management system using a dedicated application programming interface (API). These data are processed to get the signal attenuation on the path between each SmartLNB and the satellite, which will be then translated into rain rate estimates. The NEFOCAST Service Center also stores data coming from the rain gauges of its network. It is possible to compare rain rates observed by the Smart LNBs with the values measured by the rain gauges.Data coming from the sensor network are further processed using a specific algorithm that generates real time rain field maps. These output data  will be available to service integrators through a public API. It will then be possible to show them in end-user applications or integrate them in other more complex systems . In both cases, these activities are developed by VASPs. In the context of the experimentation an existing alerting application, developed by one of the project partners, has been selected to be used for data presentation and alerting.The technologies developed within the project will be used to obtain very detailed estimates of precipitation. The NEFOCAST Service Center is able to provide real time precipitation data for now-casting applications, since it is primarily thought of as a tool for monitoring and detect precipitating events, even severe events.Higher accuracy, frequency and detail for the provided information, especially when combined with other forecast systems;The availability of all information in one single data center;The possibility to serve a large number of professional users using the same technological platform.In particular, it will be possible to obtain information with a temporal resolution much higher than what provided by other monitoring systems. These results will be valuable and significant for the prevention of natural disasters and for the continuous monitoring of basins and their precipitation status, as well as for other applications in the productive and civil fields. A considerable number of companies provide weather data in XML or CSV format at very convenient prices. Compared to existing market solutions, the main advantages of the NEFOCAST solution are:The NEFOCAST solution could provide interesting perspectives in reducing costs and having a high quality of the provided data at the same time. The prospective is to expand the covered area from one single country in one year after the project’s end to ten European countries in the forthcoming five years. The higher the number of installed SmartLNBs, the more accurate and detailed the precipitation estimation is. A very dense network of sensors, such as the one that could be available using home satellite receivers, could lead to a downscaling of the field’s coverage. Such a resolution increase will be beneficial when dealing with extreme events such as sudden flooding in urban areas to mitigate the exposure to risk for the population.D << λ, where D is the diameter of the drops), non-absorbing and spherical drops, while the Mie theory is applicable to spherical raindrops with D ≅ λ. Finally, the scattering amplitudes of non-spherical drops cannot be computed analytically. However, several numerical techniques are available for calculating the scattering properties, such as the T-matrix method [k (dB/km) due to the presence of precipitation can be obtained asEσ is the extinction cross section  that depends on the polarization , wavelength (λ) of the incident waves, diameter (D), type of the particles  and on the temperature (T), while N(D) is the DSD. The ITU-R P.838-3 recommendation [k vs. rain rate R given in the form of an approximate power law, for horizontal and vertical polarizations. R > 100 mm/h) ranges from 3.6 to 11.3 dB/km, depending on frequency and polarization. Similar results can be obtained considering measured DSDs , the electromagnetic wave that propagates from satellite to the Earth interacts with atmospheric gases and hydrometeors . It has x method . Therefox method  and the endation  providesDSDs see . The advendation .γ is the elevation angle (about 40° in this case). The smart-LNB provides the total attenuation (in dB) along the radio path between satellite and the ground. As mentioned before, the attenuation due to frozen hydrometeors can be neglected, and the majority of the attenuation is due to rain  = Pr(R > x)  that will be experienced on the satellite link. Summarizing, both models yield a relationship p = RF of the rain rate Though adequate for the prediction of the rain fading attenuation when dimensioning an operational margin of a satellite link, the above models definitely reveal themselves as not suitable for the inverse task; i.e., the derivation of an accurate rain rate estimate starting from signal attenuation measurements. Actually, customary statistical models only yield a relationship between the CCDF of the rain rate and that of the signal attenuation, i.e., By the “direct method” we mean a direct mapping rule dels see . In compRain height is a key parameter for both direct and statistical models. Through weather radar data, one can estimate the actual height and width of the melting layer. Different signatures of radar measurements can be used, depending on the available measures and the observation geometry. The most known signature is the “bright band”, a layer of enhanced reflectivity below the 0 °C isotherm that is due to large and wet snowflakes that melt during their fall. This signature can be observed both at vertical incidence and in the quasi-horizontal scan performed by operational radar systems, where it appears as a circular band with greater reflectivity. The Doppler velocity signature reflects the increase of velocity that takes place during melting: In vertically pointing measurements, Doppler velocity exhibits a sudden increase that ends where melting of particles is complete . TherefoAlthough based on empirical observations, there is extensive literature ,40,41,42For the direct model presented in this paper, we instead resort to the more accurate instantaneous rain height arameter ,45,46, wIn the perspective of a practical implementation, the instantaneous value of nditions . Alternanditions  global rnditions .For example, R-k relations that are more representative of the climate of the area in which the disdrometer measurements are collected. Since such a database is unique in Italy, it is not currently possible to quantify at what extent such relationships are representative for different regions. However, we can reasonably assume that they are valid at least for the climatic region in which Rome is included, which actually include almost all the regions of West Italy, like Tuscany [N(D); drop shapes have been modelled with the [k (in dB/km) and R (in mm/h) are known for a given DSD, the coefficients α and β of the following relation have been determined by performing a nonlinear regressionMore than 6 years of DSDs collected each minute by using a Parsivel disdrometer made by OTT Hydromet Deutschland  in the area of Rome  have been used as input of the T-matrix electromagnetic simulation method to compute the specific attenuation, according to the integral in (1), at different frequencies and for different polarizations. The used dataset is one of the longest time-series of measured DSD in Italy and include a huge amount of different types of precipitation events. The choice of using relationships derived by DSDs, instead of others available from the literature , is sup Tuscany ,50. The  Tuscany ; fall vewith the  relationR and k for the forward link  and the return link , both in Ku-band, but with different polarizations. Finally, R-k algorithms, namely the normalized mean absolute error (NMAE), normalized bias (NB), root mean square error (RMSE), and correlation coefficient (CC). NB is an index of the systematic error: Negative values means that the R-k relation slightly underestimates the rainfall rate with respect to disdrometer measured values. This statement is particularly valid for high rain rates (R > 80 mm/h). RMSE is a measure of the accuracy of the proposed algorithm; the obtained low values indicate an overall good performance of the R-k relation. NMAE values indicate the possible influence of the DSD variability on the accuracy of the rain rate estimates. The values of 17.9% and 20.6% indicates a limited impact of DSD variability. L of the slant path affected by rain is calculated by exploiting the knowledge of rain height and link geometry; (iv) the specific attenuation k is evaluated as The direct method utilizes (5) with coefficients given by s/N0 see , due to ) as see (6)R^=α Further details are provided in the next section. A variant of the foregoing procedure consists of replacing the analytical relationship (5) with experimental curves or nomograms available in the literature , which pη can be expressed asmT is the mean thermodynamic temperature of the meteorological formation, such as clouds and rain, which constitute an absorbent, and consequently emissive, medium  has no ectively ), while mosphere , which iη, which can be obtained letting η inferred from the received signal , notably when they are derived by means of global models such as [In this respect, it is worth recalling that the proposed rainfall estimation technique is affected by many sources of error, a few of which were mentioned earlier. They can be roughly classified as (i) errors in the  such as ; (ii) erk (dB/km) and the rainfall rate R (mm/h); the coefficients in the model being related to the specific geographic zone, to the operating frequency and to the signal polarization. Numeric values for these coefficients were numerically obtained by fitting the above exponential law with extensive experimental data. The algorithm computes the specific signal attenuation starting from the total rain-induced attenuation provided by the NEFOCAST terminal, using a few geometric link data and the rain field height. This latter can be derived either from short-term forecasts of the 0 °C isotherm height provided by a local area model, or  it can be replaced by a statistical estimate based on long-term observations. Some preliminary results obtained from a SmartLNB operating in Pisa during precipitation events occurred in May 2017 were presented and compared with the readings of a conventional TBR. The results indicate that the NEFOCAST sensor, thanks to its short sampling interval (of the order of a few seconds), is able to track and monitor accurately the fast and random evolution of the rainfall rate during a precipitating event and has a much faster response than a conventional tipping bucket gauge.In the framework of the NEFOCAST project, we have investigated the feasibility of using a network of new-generation Eutelsat SmartLNB interactive satellite terminals for widespread and capillary monitoring of precipitation fields throughout the Tuscan Region. In addition to operating as a terminal for interactive domestic DVB-S services in the Ku and Ka bands, each of these devices can serve also as a weather sensor. They have a fine capability for measuring rain-induced instantaneous attenuation on the signal received from the forward downlink and relaying these attenuation data over a narrowband satellite return link to the NEFOCAST service center, gathering real-time information from all the SmartLNBs active in the territory. The service center processes the collected attenuation data to reconstruct, and thus monitor, the precipitation field on the territory, also presenting the ability to alert civil protection services in the presence of potentially critical meteorological situations. In particular, we discussed some methods to convert the signal attenuation measurements into corresponding instantaneous rainfall rates. The most reliable among the assessed techniques is based on the use of an exponential model describing the dependence between the specific rain attenuation Subsequent refinements of the algorithms should be implemented to reduce some source of the errors; for example, the introduction of ancillary data  for discriminating stratiform and convective systems could improve the results.Although these are preliminary outcomes obtained for a single terminal in the experimental area, the results are encouraging for the future activities of NEFOCAST, which aims to set up a scaled demonstrator of the NEFOCAST network, including the service center, with a sufficiently wide set of terminals to cover a significant portion of the territory. This network will be devoted not only detect, monitor and map the instantaneous precipitation field, but also to nowcasting applications regarding surveillance and alerting activities in case of potentially dangerous meteorological events.


Our approach enabled the identification of different empirically estimated families of probability distributions to facilitate inference regarding the continuous physiological phenomena underlying cognitively driven decision-making. We found that the same pointing task revealed shifts in the probability distribution functions (PDFs) of the hand kinematic signals under study and were accompanied by shifts in the signatures of the heart inter-beat-interval timings. Within the time scale of an experimental session, marked changes in skewness and dispersion of the distributions were tracked on the Gamma parameter plane with 95% confidence. The results suggest that traditional theoretical assumptions of stationarity and normality in biophysical data from the nervous systems are incongruent with the true statistical nature of empirical data. This work offers a unifying platform for personalized statistical inference that goes far beyond those used in conventional studies, often assuming a “one size fits all model” on data drawn from discrete events such as mouse clicks, and observations that leave out continuously co-occurring spontaneous activity taking place largely beneath awareness.The field of enacted/embodied cognition has emerged as a contemporary attempt to connect the mind and body in the study of cognition. However, there has been a paucity of methods that enable a multi-layered approach tapping into different levels of functionality within the nervous systems . The present study introduces a new theoretical and statistical framework to characterize the influences of cognitive demands on biophysical rhythmic signals harnessed from deliberate, spontaneous and autonomic activities. In this study, nine participants performed a basic pointing task to communicate a decision while they were exposed to different levels of cognitive load. Within these decision-making contexts, we examined the moment-by-moment fluctuations in the peak amplitude and timing of the biophysical time series data . These spike-trains data offered high statistical power for  Such classes of actions contrast with signals obtained during naturalistic and self-generated continuous behaviors.Cognitive Science as a field has focused primarily on the study of the mind, with few studies addressing the mind-body interactions. In recent years, the field of embodied cognition has emerged to fill this gap and try to connect mental representations with physically enacted actions Wilson, . HoweverIn the naturalistic case, spontaneous movement segments coexist with deliberate ones and are performed largely beneath the person’s awareness Torres, . Indeed,Voluntary movements show themselves to be dependent on the returning stream of afference which they themselves cause.” Our work expands the use of this principle to other non-voluntary movements’ functionalities and to movements that may be independent of the returning afferent stream but coexisting within voluntary actions. These include supportive motions that occur spontaneously and do not pursue a goal, involuntary motions inherent in the person’s system, automated and autonomic motions. These motions have different dynamics and funnel differently the influences of dynamics on the geometry of the paths their trajectories describe—as compared to those intended to a goal, i.e., deliberately performed with intent or purpose  co-exist with, and are instrumental to the goal-directed segments of complex motions, as they provide fluidity to behavior at large Torres, . Along tdeliberate autonomy .We posit that interactions among signals from the full range of functionalities and from different nervous systems are necessary for the development and maintenance of Under the lens of this framework, to examine how increase in cognitive demands are manifested across different nervous systems, we assessed the variability inherent in the biophysical rhythms that we harnessed noninvasively from the various layers of the nervous systems. We characterize the influences of increases in cognitive demands on the hand movement kinematics and the heart signals, using new statistical methods under the renovated kinesthetic reafference framework, as applied to the multi-layered and multi-functional nervous systems. Here, we vary the level of cognitive demands during a pointing task to communicate a decision. Under those conditions, we examine: (1) the goal-directed segment of the pointing motion; (2) the supplemental segments of the retracting motions; and (3) the heart rate variability, as these provide a window into the individual’s mental states during cognitive decisions, in an interactive closed-loop between the central and the peripheral nervous systems.Nine undergraduate students  between the ages 18 and 22 were recruited from the Rutgers human subject pool system and received credit for their participation. This study took place at the Sensory Motor Integration Laboratory of Rutgers University. All participants signed the consent form approved by the Rutgers University Institutional Review Board (IRB). The entire study protocol was approved by the Rutgers University IRB. The study conforms to the guidelines of the Helsinki Act for the use of human subjects in research. Two participants were left-handed, and all had normal or corrected-to-normal vision.During the experiment, the motor and heart signals were recorded from each participant. However, one participant’s heart signals did not record successfully due to instrumentation malfunctioning, resulting in an analysis on motor data for nine individuals and heart data for eight individuals.In this study, two sensor devices—motion capture system and a wireless heart rate monitor—were used to record the signals coming from the bodily movements and the heart. The data obtained from these two devices were analyzed separately.Fifteen electromagnetic sensors at a sampling frequency of 240 Hz  were used to continuously capture the participant’s movements across the upper body. Nine sensors were placed on the following body segments using sports bands to optimize unrestricted movement of the body: center of the forehead, thoracic vertebrate T7, right and left scapula, right and left upper arm, right and left forearm, the dominant hand’s index finger. An additional sensor was used to digitize the body in constructing a biomechanical model using the Motion Monitor  software. One sensor was placed at the backside center of the iPad  display screen. This sensor served to measure the physical position of the fixed target, to help obtain a distance-based criterion to automatically classify motions into forward (from the resting position of the hand to the target) and backward (from the target to the resting position). There were also four positional sensors placed at the four corners of the table on which the iPad was standing. This physical information enables us to build computational models of these movements to study Bernstein’s degree of freedom problem  from a wireless Nexus-10 device  and Nexus 10 software Biotrace (Version 2015B) at a sampling rate of 256 Hz. Three electrodes were placed on the chest according to the standardized lead II method and were attached with adhesive tape. A typical ECG data includes a set of QRS complexes and detecting R-peaks (within the QRS complex) is essential, as the heart rate metrics needed for this study focuses on the oscillation of intervals between consecutive heartbeats. To remove any baseline wandering and to accurately detect the R-peaks, ECG data were preprocessed using the Butterworth IIR band pass filter for 5–30 Hz at 2nd order. The range of the band pass filter was selected based on the finding that a QRS complex is present in the frequency range of 5–30 Hz  program controlled the presentation displayed on the touchscreen display and recorded the timing and location of the touches made by the participant. The MATLAB program was presented on the touchscreen display using the TeamViewer (Germany) application.As shown in the schematics of Figure The experiment consisted of three conditions—control, low cognitive load and high cognitive load condition. Under the control condition, the participant simply performed this task for 60 trials. Under the low cognitive load condition, the participant performed these tasks for 60 trials, while repeatedly counting out loud one through five. Under the high cognitive load condition, the participant performed these tasks for 60 trials, while counting backwards from 400 subtracting by 3.Participants performed the conditions in the order of control-baseline, low cognitive load condition, and high cognitive load condition. Note, the order was not counterbalanced, because performing high cognitive load tasks prior to low load tasks would have caused cognitive load and fatigue to be carried over to the low cognitive load condition. This might have influenced the effect of cognitive load to be mixed with fatigue, but this was necessary to keep the low cognitive load tasks to be minimally taxing as possible. For both low and high cognitive load conditions, the participant was instructed to count at a comfortable pace. Participants took breaks in between conditions, and the entire experiment took about 40 min.To illustrate the effects of subtle increases in cognitive demands on the hand kinematics, we use Figure To justify the use of this paradigm to test influences of cognitive demands on movement kinematics, we evaluated the number of peaks in the angular acceleration waveform for both the deliberate portion of the reach (forward to the target) and the spontaneous retraction (backward to rest).t(8) = 0.15, p < 0.01) explained by the statistically significant increase in the number of angular acceleration peaks as the cognitive demands increased. The accumulation of peaks in the rates of hand angular speed with higher cognitive load resulted in higher physical effort, as the participants had longer angular excursions with higher cognitive demands. The insets in Figure t(8) = 4.21, p < 0.01). All these preliminary tests confirmed that the motor task we designed was adequate to assess variations in cognitive load and their potential effects on physiological parameters of interest. We then proceeded to examine these physiological waveforms’ peaks in terms of spike trains under the general rubric of continuous stochastic processes.The effects of the increase in cognitive demands manifested in statistically significant changes in the accuracy of the task and the time of performance. The group incurred a significant increase in the time to point , was precisely designed to longitudinally tackle the emergence, dynamic development, maintenance and degeneration of the signals produced by the multi-layered nervous systems, including those with different pathologies over the human lifespan  motions themselves cause, from the independent processes. The latter are those for which the present events are independent of the past events. All fluctuations treated as standardized spikes in the 0–1 unit-less real number range are the “the micro-movements” of biophysical signals. To model them, we build on our original work  give rise to time series of peaks and valleys, which vary in amplitude and timing Figure . The fluFor the current study, the goal is to show an example of using SPIBA and micro-movement data involving signals harnessed in tandem from the PNS and ANS while performing CNS driven decisions. To that end, we will examine biophysical data from body movements and the heart activities in a personalized fashion, as each participant is exposed to a decision-making task with different levels of cognitive load.The continuous positional trajectory of the participant’s dominant hand index finger was decomposed into forward and backward movements .As explained above, the rationale behind the separation between forward and backward movement is that one is instructed and goal-directed, while the other is not, thus differing in their levels of intent. The latter is spontaneously self-initiated by the person without instruction. The statistical characteristics have been shown to differ between forward and backward movements  during reaching, pointing, and grasping actions among different patient populations and across the general human population  and gathered across all trials. Among the four types of parameters, for both forward and backward movements, angular acceleration was analyzed, as it has the largest number of peaks and provides the signal with the highest statistical power (hundreds of peaks per person) to carry on our stochastic estimation with high (95%) confidence.angular acceleration, as this provides the most power in the statistical estimation within the shortest time. The tradeoff here is that higher order derivatives of the position/orientation data (such as angular acceleration) can introduce large fluctuations from instrumentation noise. However, we have developed in house filtering/smoothing methods  so the higher the number of samples used to make an empirical estimation for a given person, the less taxing the experiment is to the participant, as it takes less time to attain a robust estimate. For instance, during a typical point-to-point reaching action, which consists of a single forward and backward movement, the linear velocity would typically provide at least two salient samples , Torres et al., Normalized peak amplitude (coined timing TM) and normalizing the array of these TM values using Equation 1 (coined timing micro-movements NTM). The two types of normalized, unitless spike-dependent data  can be visualized in a spike train format as shown in Figure 2 and seconds) of the original peaks can be used to color code the graphs and show the range of parameters of each participant as shown in Figure Besides the amplitude information, peak data can provide estimates related to the motion’s temporal dynamics. To that end, normalized inter-peak interval timings were computed by extracting the time elapsed between consecutive peaks  are on the order of approximately 1500 ms each (see Supplementary Table S1). As such, we have many sample peaks within a single minute. Usually, we set the size of the sampling window to 1 min  and additive  random processes of the micro-movement spike trains during voluntary, automatic and involuntary motions Torres, . Among ta is the shape parameter, b is the scale parameter, and Γ is the Gamma function  and scale (b)—were estimated for each histogram of the micro-movement data, as mentioned, using MLE with 95% CIs. The estimated parameters with their CI were plotted on a Gamma parameter plane, where the x-axis represents the shape parameter value and the y-axis represents the scale parameter value  since the Gamma mean a = 1 are found in autism cases , the scale axis of the Gamma parameter plane allows us to infer behaviors leading to higher noise levels vs. lower noise levels. Along the shape axis, the Exponential distributions at  Torres, , 2013c.  Torres, .2) and NTM (expressed in second), giving us the change in physical units along this color gradient for each participant. The marker’s face represents the median of the physical values within a condition, and the marker’s edge is used as another feature to represent the condition . This visualization tool allows us to see the physical ranges of each individual person in transition from one condition to another, while expressing all parameters along a common unit-less standard scale. Note that reporting on the physical parameter ranges of each instrument while maintaining the standardized unit-less scale for statistical estimation and inference is amenable for data exchange and reproducibility of results in our fields of study.Additionally, the estimated Gamma moments were obtained and plotted in a four-dimensional graph Figure . Here, t a priori hand-picking homogeneous groups for significant hypothesis testing comparison . This is very important because the patterns that we uncover are entirely data-driven, as the patterns self-emerge from the inherent variability of the nervous systems signals.Graphs such as Figures empirically characterized in prior work , we applied the distributional analyses on the IBI data for each condition. As with the hand kinematics, we fitted the PDF using MLE . Histograms for the IBI data were fitted among the Gamma, exponential, lognormal, and normal for each condition, and we determined that the continuous Gamma family of distributions would be appropriate for fitting the IBI data. For that reason, the parameters of the Gamma PDF were estimated for each histogram of the IBI data, and the shape and scale values were plotted on the Gamma parameter plane with 95% CIs, and the Gamma moments of the estimated PDFs were plotted on a 4D graph. Through this analysis, we could examine the inevitable processes emerging from the ANS.Given the preliminary analyses of Figure The estimated Gamma parameters characterizing the PDFs of the IBI showed a distinct trend in the separation between the two conditions at 95% CI. Figure The increase in the IBI’s timing variance as the cognitive load increases is reflected in the increase of the NSR  across all participants .The PDFs that we empirically estimated for each participant were skewed, as is shown in the insets of Figures Furthermore, comparisons of the parameters of the estimated Gamma PDFs and moments yielded differences in skewness and dispersion with the task. In the forward case of Figure The results of assessing these stochastic transitions with the Kolmogorov Smirnov test are detailed for each participant in Supplementary Figure S5A. Importantly, besides the shifts in PDFs, we also quantified shifts in the physical range of the parameters underlying the NMT . These are appreciated in Figures To further quantify the shifts in PDFs between forward and backward cases, we used the line fitting the scatter represented in log-log transform of the Gamma parameter plane. These are depicted in the insets of Figure grand average treatment to these biophysical data. Each participant manifested a different stochastic shift. Further, there were no visible patterns across all participants. Here, both the forward and backwards cases showed unique shifting patterns for each person’s stochastic signatures. The trend was rather in the physical ranges of angular acceleration, which tended to decrease with the increase in cognitive load for the forward reaches. This trend in reduction of angular acceleration amplitude  of Figures The analyses of the fluctuations in the amplitude of the angular acceleration, as normalized by the micro-movements data type (AM) using equation (1) show departure from 0-change in PDF for all participants. As with the TM and NTM cases, these results also advise against the use of a e Figure  was genee Figure , with soOf note is the skewed  distributions of the original peaks of the angular acceleration shown in Figures As with the NTM parameter, here, besides uncovering individual shifts between high and low cognitive loads for each movement type, it is also possible to ascertain the overall shifts of the group scatter between the deliberate and spontaneous movements. In the log-log Gamma parameter planes of Figure Deliberate forward and spontaneous backward reaches revealed systematic shifts in PDFs for all participants and parameters under examination, when comparing the basic pointing task to the pointing task under time estimation. Several features for each parameter are reported below.A trend across all participants in the deliberate forward reaches was a marked decrease in parameter range (time in seconds) underlying the NTM data. Namely, basic pointing on average took longer time between peaks . We obtained the slope and intercept of the line fitting the log-log transform of the scatters .A change in the estimated PDF from basic pointing to pointing during time estimation was registered for the fluctuations in the amplitude of the angular acceleration peaks, AM, as scaled by equation (1). The individual shifts in the empirically estimated Gamma moments were registered for both the forward and backward reaches. The overall trend in the scatter of forward reaches of Figure Comparing between the movement classes, forward reaches tended to have distributions with higher skewness as quantified in the moments graphs of Figure In the forward goal-directed motion, the stochastic signatures had higher NSR and lower shape parameters than the spontaneous backward motions. The lower shape corresponds to the higher positive skewness of Gamma moments plot in Figure deliberate, spontaneous and inevitable. These proposed processes have specific characteristics and can be studied (non-invasively) through the variability of various somatic-sensory-motor and heart signals harnessed in tandem  autonomic processes.Of relevance here, we highlight the marked differences we found in IBI with changes in the cognitive demands of the task, transitioning from low to high cognitive loads. Changes in PDF of the IBI were not as marked with the time estimation task, perhaps inviting thoughts about differences between a task with higher cognitive demands (counting backward) and one with lower demands (estimating time). Indeed, the mere quantification of the number of angular acceleration peaks during the higher cognitive loads denoted higher demands in bodily motions: i.e., the hand moved significantly more at the micro-level with higher cognitive demands. As such, when viewed cumulatively over the timespan of the task, the system overall required more energy. This may be reflected as well in the shifts in IBI with higher cognitive loads. In this sense, we found a statistically quantifiable link between cognitive loads and physical motions whereby differences are detectable and have characteristic values that we summarized in various ways. Among these, the slope and intercept of the log-transform of the scatter points on the Gamma plane was similar for each experiment , denoting a power-law relation between the shape and scale estimated parameters for each participant. Yet the location of the scatter along the fitting line of these points representing the personalized family of PDFs changed across conditions and between the deliberate and spontaneous classes of motions. They also changed for the IBI timings of the autonomic motions. The main shift from deliberate to spontaneous mode was down and to the right on the Gamma parameter plane, consistently denoting distributions with lower NSR and more symmetric shapes. During these tasks, across all parameters, the spontaneous retractions were unexpectedly more controlled (lower noise and higher predictability) than the forward ones. Yet it was the forward motions that broadcasted more clearly the shifts across conditions in the signatures of variability of the kinematic parameters. These shifts were also noted in the IBI activity.One limitation of the present methods is that they depend on the sampling resolution of the sensors and accordingly, on the time length of the task. In this study, due to time constraint of the experiment (to avoid fatigue) we were only able to examine angular acceleration as a kinematic parameter. As explained in the methods and Supplementary Figure S2, within the time constraints of this task, the angular acceleration provided enough peaks in its waveform for statistical power in our distribution-parameter estimation (we needed above 100 peaks for tight CIs). If we were to conduct this experiment for a longer period, we could examine other position-related parameters, such as linear speed and hand trajectory curvatures. However, this would have caused participants to experience fatigue during a prolonged experiment with conditions involving multiple levels of cognitive loads. The linear speed has fewer peaks-though we have recently studied the micro-movements in the context of basic pointing in autism . The shifts in the empirically estimated parameters of the continuous Gamma family of probability distributions, that we quantified here, occurred on the time scale of minutes, i.e., the duration of the experimental session. They strongly suggest that prior assumptions involving kinematics data analyses may be insufficient to capture the richness of cognitive phenomena, pertaining to their effects on the somatic-motor signals. Here, we showed that cognitive phenomena do not merely elicit a change in the mean or variance of somatic-motor related variables under a single PDF. Rather, different PDFs are needed altogether to better characterize cognitive phenomena for each person under examination, as it is continuously funneled through physical activity that leads to shifts in the signatures. The process changes dynamically along the multiple layers of the nervous systems.We underscore here that these stochastic shifts in the biophysical parameters were empirically characterized. We did not assumeAnother aspect of the results alludes to the motor control literature examining pointing behavior. There, the uninstructed retraction segments, during which the hand automatically returns to rest , are hardly ever considered as part of the overall behavior. However, when we examined those retraction segments, we quantified the effect of cognitive load on biophysical signals from spontaneous processes in the moment-by-moment variations of the angular acceleration NTM. Indeed, their stochastic signatures showed statistically significant shifts in the empirically estimated parameters of the Gamma PDF family .inevitable (autonomic) afferent processes feeding back to the cognitive systems. As such, we provide a new experimental paradigm and a unifying statistical framework to study embodied cognitive decision-making under a renewed theoretical construct of multi-modal, multi-functional recursive kinesthetic afference.Pointing is a very automatic task, and yet several motor signals from the peripheral end-effector were significantly affected by simply adding an additional task requiring decision-making . This result implies that decision-making processes driven by central controllers at the CNS level can be quantified using the continuous flow of the motor signal, as the voluntarily generated bodily motions unfold to communicate the decision; and as the fast-automatic segments of the motion spontaneously unfold. In this sense, a parallel between slow-fast  scale, using different levels of cognitive loads (driven by the CNS), thereby allowing us to gain a glimpse into the brain-body coupled stochastic dynamics. In this sense, we have characterized cognitive load with sensory and somatic-motor signals, alluding to processes that occur in a closed (recursive) loop between the many layers of the brain and the body (the body that the brain aims to control at will); including also those spontaneous processes that fall largely beneath observational and/or sensing awareness. For instance, the input signals from the micro-movements of the movement-kinematics and the heart signals can be thought of as fluctuations providing an important source of guidance to the brain. They may be a form of re-afferent feedback, to help the brain compensate for synaptic transductions and transmission delays. By selectively shifting the signatures of statistical variability under different levels of cognitive load, different functional relations (in terms of probabilistic maps) between bodily responses and environmental demands (including cognitive loads) may be built, to be able to predict ahead the sensory consequences of bodily actions, even in the absence of, or the intermittent availability of relevant sensory information.The current study employs a novel methodology to assess features ofThis multi-layered, multi-modal and multi-functional embodied approach to the study of cognitive processes has the potential to provide a more holistic perspective on our overall understanding of cognition and its development. Indeed, this simple paradigm was useful to examine the changes in bodily signals across multiple layers of the nervous systems and characterize the sensory-motor behavior that underlies cognitively driven performance. Furthermore, by adopting the renovated kinesthetic reafferent framework in this study, we could capture the variations of motor and multifaceted sensory inputs that must be integrated to drive cognitive processes  under varying levels of control, ranging from voluntary to automatic to autonomic.The current study provides important evidence to justify an embodied and personalized approach to studying cognition (Gallagher, JR designed experiment, collected and analyzed data and wrote the article. EBT designed experiment, designed analyses and wrote the article. Both authors agreed to the final version of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Wind turbines usually operate under nonstationary conditions, such as wide-range speed fluctuation and time-varying load. Its critical component, the planetary gearbox, is prone to malfunction or failure, which leads to downtime and repair costs. Therefore, fault diagnosis and condition monitoring for the planetary gearbox in wind turbines is a vital research topic. Meanwhile, the signals measured by the vibration sensors mounted in the gearbox exhibit time-varying and nonstationary features. In this study, a novel time-frequency method based on high-order synchrosqueezing transform (SST) and multi-taper empirical wavelet transform (MTEWT) is proposed for the wind turbine planetary gearbox under nonstationary conditions. The high-order SST uses accurate instantaneous frequency approximations to obtain a sharper time-frequency representation (TFR). As the acquired signal consists of many components, like the meshing and rotating components of the gear and bearing, the fault component may be masked by other unrelated components. The MTEWT is used to separate the fault feature from the masking components. A variety of experimental signals of the wind turbine planetary gearbox under nonstationary conditions have been analyzed to demonstrate the effectiveness and robustness of the proposed method. Results show that the proposed method is effective in diagnosing both gear and bearing faults. Wind energy is the fastest growing renewable energy source due to its cleanness and reproducibility . HoweverA planetary gearbox is widely used in wind turbines to meet the requirements of smaller size or higher torque output. In a wind turbine, the planetary gearbox transfers the mechanical energy from the rotor hub with a low rotational speed to the generator with a high speed. The planetary gearbox malfunctions easily due to severe working conditions, such as wide-range speed fluctuation, time-varying load, extreme operational temperature, and humidity changes . The dowThe industrial trend of wind energy leans towards multi-megawatt and large wind turbines, whose size has increased from 20 kW to 5 MW during the last two decades ,27. To cRecently, Daubechies  proposedIn this study, a time-frequency method based on high-order synchrosqueezing transform and multi-taper empirical wavelet transform is proposed for the fault detection of wind turbine planetary gearboxes under nonstationary conditions. The high-order SST produces a highly concentrated TFR. The signals of a wind turbine exhibit typically time-varying features due to the complex operating conditions, such as speed fluctuation and load variation. The original signal is resampled with the shaft speed to avoid the speed fluctuation and spectrum smearing. Generally, a tachometer is required to obtain the instantaneous speed to sample signals equi-angularly. This requirement is barely satisfied in many applications due to limited space and cost . The insThe rest of this paper is organized as follows. As a post-processing method, SST has been used for other TFRs ,49,55. IThe signal acquired by the vibration sensor mounted in the wind turbine planetary gearbox can be modeled as a typical amplitude-modulated and frequency-modulated (AM-FM) signal. The high-order SST achieves a highly energy concentrated TFR for an AM-FM signal by using accurate approximations of the amplitude and phase.A(τ) and φ(τ) are the amplitude and phase functions; both are real functions.An AM-FM signal is modeled as:t and frequency f is defined as:g is the window function and g* is the complex conjugate of g.Then the STFT of this signal at time ε is the threshold and δ is the Dirac distribution. R{Z} represents the real part of Z and t.The traditional SST is defined as follows:In SST, the coefficients τ close to t is given as:Fk)((t) denotes the kth derivative of F at t.The Taylor expansion of the signal in Equation (1) for Then Equation (2) is written as:t and divided by s(t) computed with window kt−1g(t).The STFT Nth-order complex IF The Its real part The modulation operator Nth-order complex IF Then the Furthermore, Nth-order SST (SSTN) is defined by replacing Then the A simulated signal The signal and its IF are shown in The TFR provided by different time-frequency methods are compared in SST3 and SST4 seem to behave similarly in terms of the energy concentration of the TFR. Furthermore, computational costs of four time-frequency methods are considered. The algorithms are run on a computer with an Intel Core i5-4460 CPU and 8.0 GB RAM. Then results of the computational costs are listed in The multi-taper empirical wavelet transform algorithm is proposed to identify the fault features from a planetary gearbox vibration signal. As the original empirical wavelet transform (EWT) method yields unexpected segmentation due to false peaks and burrs induced by noisy and non-stationary factors, the multi-tapering is used to overcome these shortcomings. The multi-tapering approach can reduce the variance and improve the accuracy of the power spectrum estimation. In this approach, several orthonormal functions are used as tapers to estimate the corresponding power spectrum. The multi-taper spectral estimate is defined as:kh(n) is the kth taper orthogonal to other tapers:And In the spectrum segmentation part, boundaries of each segment are determined by the spectrum peaks indicating dominant components. These peaks are picked out based on the spectrum shape. Then the boundary is described as the minimum in two consecutive frequency peaks. Details of the spectrum segmentation can be found in References ,57.Inspired by the construction of Littlewood-Paley and Meyer’s wavelets, the empirical wavelets are constructed as bandpass filters. The empirical scaling function and empirical wavelets are given by the following expressions:nτ satisfies the following equation:To obtain a wavelet tight frame, the parameter According to the traditional wavelet theory, both approximated coefficients and detailed coefficients are given by the inner products:Then the empirical modes are defined as:An example is given to compare the performance of the EWT and the MTEWT method. The test signal is defined as:This signal and its constituents are shown in In In To detect the faults of the wind turbine planetary gearbox under nonstationary conditions, a new time-frequency method based on high-order SST and MTEWT is proposed in this study. The fault features are separated from masking components or speed-related components. The procedure of the proposed method is summarized as follows:(1) Obtain the time-frequency representation via the high-order SSTA sharpened TFR is obtained via the high-order SST. Compared with other time-frequency methods, the high-order SST provides a highly concentrated time-frequency representation, which guarantees the precision of IF estimation.(2) Estimate the IF and resample the signal synchronous to the shaft instantaneous speedThe IF is a crucial feature to recognize the time-frequency pattern of nonstationary signals in the wind turbine. In the present study, the IF is estimated directly from the vibration signal, as the provision of a tachometer with sufficient resolution is not always possible due to technological or cost reasons. The IF is estimated based on the DPORD algorithm. Details about the DPORD algorithm can be found in References ,58.Under nonstationary conditions, the fault features of the vibration signal vary with time. Therefore, the direct application of spectrum-based methods leads to spectrum smearing and false diagnosis. The original signal is resampled at constant angular increments of the estimated shaft instantaneous speed. In this way, the spectrum smearing phenomenon is avoided and speed-related components are separated.(3) Apply the MTEWT algorithm to extract the fault featureThe wind turbines exhibit complex dynamic responses due to extreme loading and widely varying operating conditions. The fault features are masked by unrelated components originating from other machine elements like shafts or gears. The resampled signal is decomposed by the MTEWT method and the fault features are separated from masking components.The effectiveness of the proposed method is validated by vibration signals collected from two experiments. The first experiment is carried out on a drivetrain dynamics simulator. The second experiment is performed on a wind turbine planetary gearbox of an actual wind turbine. Meanwhile, the proposed method is also compared with the fast kurtogram method to show its effectiveness.The vibration data are collected from a Spectra Quest’s drivetrain dynamics simulator, which is used as a fault simulation of the wind turbine planetary gearbox. As shown in The effectiveness of the proposed method is verified by detecting the tooth crack in a sun gear which is given in The collected vibration signal and its spectrum are depicted in To reveal the crack fault, the proposed method is employed to analyze the vibration signal. Firstly, the TFR of the signal is calculated via the high-order SST and shown in Secondly, the IF is estimated via the DPORD method based on the calculated TFR. Thirdly, the original signal is resampled synchronous to the estimated IF. The resampled signal and its order spectrum are shown in Finally, the resampled signal is decomposed into 13 empirical modes via the MTEWT method. As shown in The second set of experimental data is collected from a wind turbine planetary gearbox and is provided by the diagnosis contest during the International Conference on Condition Monitoring of Machinery in Non-Stationary Operations (CMMNO) in 2014.The vibration signal is measured on the gearbox casing of a wind turbine in the radial direction. The kinematics of the wind turbine planetary gearbox is described in The first goal is to estimate the instantaneous angular speed of the high-speed shaft directly from the vibrational signal in order to address the case where no provision of a tachometer with sufficient resolution is made available for technological or cost reasons. The estimated result is compared with the reference speed signal. The second goal is to diagnose the bearing faults in the wind turbine planetary gearbox under nonstationary working conditions in the industrial field. In this realistic case, fault features do not correspond to priori expectations, leading to potential misinterpretation or false diagnosis.The vibration signal and its spectrum are given in Then the DPORD algorithm is employed to estimate the IF. Furthermore, the signal is resampled in an angular domain to avoid the influences of speed fluctuation. The resampled signal is shown along with its envelope order spectrum in For comparison, the fast kurtogram method is also used to analyze the resampled signal to extract the fault feature. The kurtogram is shown in In this study, a novel time-frequency method based on high-order SST and MTEWT is proposed for the fault diagnosis of a wind turbine planetary gearbox under nonstationary conditions. The high-order SST defines new synchrosqueezing operators based on high order amplitude and phase approximations. Compared with other time-frequency analysis methods, the high-order SST produces a highly concentrated TFR for both signals with fast varying IF and slowly varying IF. Meanwhile, the MTEWT method is proposed to separate the fault feature from masking components originating from other machine elements such as shafts or gears.The effectiveness of the proposed method is validated by a variety of time-varying experimental signals measured by the vibration sensors mounted in the wind turbine planetary gearbox under nonstationary conditions. The calculated TFR is highly energy-concentrated and the estimated IF matches very well with the actual IF. The proposed method can successfully detect the sun gear crack fault, the planet gear crack fault, multi gear faults, and the planet bearing fault. Results indicate that the proposed method is a promising tool for the fault diagnosis and condition monitoring of a wind turbine planetary gearbox.


In this paper, we investigate the capability of an axle box acceleration (ABA) system to evaluate the degradation at railway crossings. For this purpose, information from multiple sensors, namely, ABA signals, 3D rail profiles, Global Positioning System (GPS) and tachometer recordings, was collected from both nominal and degraded crossings. By proper correlation of the gathered data, an algorithm was proposed to distinguish the characteristic ABA related to the degradation and then to evaluate the health condition of crossings. The algorithm was then demonstrated on a crossing with an unknown degradation status, and its capability was verified via a 3D profile measurement. The results indicate that the ABA system is effective at monitoring two types of degradations. The first type is uneven deformation between the wing rail and crossing nose, corresponding to characteristic ABA frequencies of 230–350 and 460–650 Hz. The second type is local irregularity in the longitudinal slope of the crossing nose, corresponding to characteristic ABA frequencies of 460–650 Hz. The types and severity of the degradation can be evaluated by the spatial distribution and energy concentration of the characteristic frequencies of the ABA signals. A railway crossing is one of the fundamental components of track infrastructure because it intersects different tracks at the same level. Currently, the monitoring of crossings highly relies on human visual inspection, that is, technicians visit the tracks or watch videos of tracks to identify degradation. This task is labor-intensive and inefficient, and the detection results may be subjective and erroneous. Consequently, most degraded crossings are reactively replaced when they reach severe degradation. The limitations of manual inspection motivate the development of on-board monitoring technologies, such as ultrasonic measurement ,5, eddy Each of these technologies is adept at detecting certain defects but suffers from certain limitations. Ultrasonic measurement shows the best performance in detecting cracks, whereas it is not adept at detecting surface detects. Eddy current testing is able to detect surface defects. However, the probe in the eddy current system must be positioned at a constant distance from the rail head, making it unavailable at geometric discontinued crossings. The magnetic induction method, which can be used for near-surface or surface transverse defects, also suffers from the restriction of a constant distance between sensors and rail surfaces. The image recognition method can detect visible defects on rail surface and other track components , whereas it is adversely affected by illumination inequality and inconsistent reflection properties on plain tracks and by the complex structure and discontinued geometry at crossings. Vibration-based inspection can be used for several purposes, such as monitoring track irregularity and detecting train derailment, whereas some of its applications (such as detecting long wave rail irregularity) require moderate train speeds. Guided-wave inspection is capable of detecting several defect types, such as cracks and corrosion, but is limited by the critical size of defects. Radio detection and ranging sensors are able to detect obstacles endangering railway operation . Acoustic emission systems can detect several defects, such as poor track alignment and squats, but its on-board implementation is disturbed by the noise generated by airflows. The thermography method can detect cracks and ballast conditions, but the method is disturbed by fluctuations in weather conditions. Ground-penetrating radar is adept at monitoring track substructure components such as ballasts and subgrades. Among the abovementioned inspection methods, those that can be applied at geometric discontinued crossings  are adept at crack detection. Regarding the numerous crossings without cracks yet with significant profile degradation because of plastic deformation and wear, an effective diagnostic method is required for prompt detection.In this study, we investigate the feasibility of the axle box acceleration (ABA) system for the condition monitoring of railway crossings. ABA measurement is a vibration-based inspection method, and its detection algorithm relies on extracting changes in dynamic responses with respect to the nominal condition. On plain tracks, the ABA system has been used to detect isolated defects  occurred in the facing direction, namely, from closure rail to crossing nose.The ABA system is composed of accelerometers, a GPS antenna and a tachometer; see When a train passes over ordinary tracks under nominal conditions, the ABA signal fluctuates because of the natural response of the vehicle-track system. The presence of undesired degradation  or intrinsic geometric discontinuity  can significantly affect the vehicle-track interaction, which is captured in the ABA signal. The continuous wavelet transform (CWT) method has been effectively used to identify the characteristic vibrations of ABA at squats and worn insulated joints ,32. With follows :(1)Wn(s) wavelet .f1 to f2 :(2)W¯n2[The crossing profile was measured in 3D using the laser-based non-contact apparatus HandyScan; see To gain insight into the measured profile, two longitudinal-vertical cross sections are selected from the wing rail and crossing nose; see On the crossing nose, wheel-rail contact occurs from 235 mm onward, as indicated by the shiny running band in Based on the measured crossing profiles shown in The characteristic vibrations of ABA related to the degradation are extracted by comparing the measured ABA and 3D profiles of nominal and degraded crossings. With this information, an algorithm capable of detecting crossing degradation is proposed.To demonstrate the repeatability of the measured ABA, the measurements were performed three times using the same train at the nominal crossing. In each measurement, the train passed over the crossing at a speed of 26–28 km/h in the facing direction.In a and b in In the nominal state, most of the vibration energy is localized around arrow A, which is induced by the intrinsic geometric discontinuity of the crossing, and thus the wheel-rail impact. At the arrow, two major characteristic frequencies appear at 230–350 and 460–650 Hz; see rectangles c) localize within a short duration such that both the train bogie and the track superstructure components are only minimally affected [In the degraded state, the vibration energy distributes at two regions, as denoted by arrows A and B. At arrow A, the major frequencies occur at 230–350 and 460–650 Hz. Because these characteristic frequencies take place in both nominal and degraded states, they should depend on the natural responses of the system rather than the wheel-rail contact geometry. The high-frequency components at arrow A . It exacerbates the wheel-rail impact and enlarging the energy concentrated at the characteristic frequencies of 230–350 and 460–650 Hz. The severity of the degradation can be evaluated by the values of Degradation type 2 . It increases the vibration energy at 460–650 Hz. Thus, the location of the irregularity can be determined by the spatial distribution of the 460–650 Hz components, while the severity can be evaluated by the value of By comparing the gathered data in the nominal and degraded states, the following relation between the characteristics of ABA  and the c and e) shows that the high-frequency components at 650–1200 Hz become more pronounced in both degradation types. Because these components distribute with relatively short duration, they can be used to better locate the crossing degradation.By proper correlation of the gathered data from multiple sensors, an algorithm for the detection of crossing degradation is proposed. In the algorithm, the SAWP is calculated using the values Step 1: Detection of uneven deformation between the wing rail and the crossing nose .If Otherwise, the crossing does not exhibit significant uneven deformation.Step 2: Detection of local irregularity of the crossing nose .If there is more than one position with Otherwise, the crossing does not exhibit significant local irregularity at the nose.In this section, the ABA measurement is performed on a crossing with unknown degradation status as a trial detection, and the capability of the proposed detection algorithm is verified via in situ profile measurement and field observation.Because the concerned crossing had degraded significantly, repair maintenance in terms of grinding and welding was performed to extend its service life and avoid sudden failure. The repair procedure was as follows: first, the crossing rails were ground to remove surface damage ; second, the hollow regions caused by grinding were filled by welding; finally, the crossing rails were ground again to the desired profiles. At arrow A, the value of To examine the evaluation results, a 3D profile measurement was performed on the repaired crossing. In this study, a detection algorithm is developed and verified relying on in situ ABA and 3D profile measurements taken at a single track site. At the site, two crossings with three different health conditions were measured: the first measurement occurred on a degraded crossing, the second measurement was performed shortly after repair, and the third measurement was performed on a new crossing at the same site after the repaired crossing was replaced because of severe cracking.The advantage of focusing on a single site is that the disturbance of non-uniform track conditions on the characteristic vibrations of ABA can be minimized. It would be highly beneficial to demonstrate the detection algorithm on additional crossings. However, access to additional track sites is strictly limited by the safety regulations of the Dutch railway network authority. In this study, we were allowed to perform measurements at only one site, and it required 1.5 years to collect information for three different health conditions. For this feasibility study, the experiment was satisfactorily conducted and provided new information that is helpful for developing a better maintenance strategy. Signal processing together with physical insight into the system provided reliable information for verifying the quality of maintenance actions.The effect of non-identical wheel-rail trajectory on the characteristic frequencies of ABA. In the real-life implementation of the ABA system, it is impossible to keep the identical wheel-rail trajectory among measurements. On one hand, it is difficult to keep in-service trains with a controlled constant train speed; on the other, the wheel-rail trajectory is affected by the randomness of vehicle-track interaction . The effect of non-identical trajectory on the characteristic frequencies of ABA must be analyzed. In the literature, it is found that the characteristic frequencies of ABA are related to the natural response of the vehicle-track system , so thatThe effect of the crossing type on the characteristic frequencies of ABA. In this study, the proposed detection algorithm is demonstrated and verified on the crossing type of 54E1-1:9. Because the natural response of crossings may differ from one type to another, the characteristic frequencies of ABA on other crossing types should be extracted. To overcome the limitations on field track testing, computer-aided approaches . For example, it is possible to estimate the location and severity of the catenary degradation by collecting and correlating the data of the pantograph-catenary contact force  and the (1)The ABA system can identify two types of crossing degradation. The first type is uneven deformation between the wing rail and the crossing nose, and the second type is local irregularity in the longitudinal slope of the crossing nose.(2)Deformation of the crossing nose that is more severe than that of the wing rail exacerbates wheel-rail impact during the facing motion of vehicles, increasing the energy concentrated at the characteristic frequencies of 230–350 and 460–650 Hz. The severity of the uneven deformation can be evaluated by the energy concentration at these frequencies.(3)The presence of a local irregularity at the crossing nose increases the vibration energy at the characteristic frequencies of 460–650 Hz. The location of the irregularity can be determined by the spatial distribution of these frequencies, while the severity can be evaluated by the energy concentration at these frequencies.(4)The ABA system can detect crossing degradation at measuring speeds as low as 26–28 km/h. Therefore, the capability of the method in large-scale networks is not restricted to the low operational speed often specified at crossings (40–80 km/h on the Dutch railway).In this study, the capability of the ABA system to detect crossing degradation was investigated. For this purpose, in situ ABA and 3D profile measurements were conducted on both nominal and degraded crossings to extract characteristic vibrations related to the degradation. ABA measurements were then performed on a crossing with an unknown degradation status condition as a trial detection, and the capability of the method was verified using 3D profile measurements and field observations. The following conclusions are drawn:Planned future work includes investigating the characteristic vibrations of the degradation at various crossing types and over a broad range of measuring speeds. Possible future studies also include integrating the ABA system with other nondestructive testing technologies  such that infrastructure managers can be provided with more comprehensive information for decision making on maintenance work. In addition, a numerical model will be developed for virtual testing to analyze the characteristic signals of various degradation types.