TReaction is a mobile app developed to determine strike response time at low cost and with easy application in combat sports. However, the validity and accuracy of the response time obtained by the TReaction app has not yet been evaluated.This study aimed to test the validity and reliability of the TReaction app in measuring motor response time in combat sports.t test for dependent samples, and the Bland-Altman analysis were performed. Accuracy was verified using the intraclass correlation coefficient. Effect size (g) and the typical error of measurement (TEM) were calculated. The significance level was set at P<.05.A total of two athletes performed 59 strikes to assess the response time upon visual stimulus using the TReaction app simultaneously with a high-speed camera. Accuracy of the measure was verified using a computer simulator programmed to discharge visual stimuli and obtain the response time. Pearson correlation, Student P=.56) was found between both systems. The methods presented a very strong correlation (r=0.993). The magnitude of differences was trivial (g<0.25), and TEM was 1.4%. These findings indicate a high accuracy between the computer screen and the mobile app measures to determine the beginning of the task and the response time.No significant difference (Our findings suggest that the TReaction app is a valid tool to evaluate the response time in combat sports athletes. The success of combat sports is often determined by fast motor actions in response to a given stimulus -3. RespoTo measure response time from a given visual or audible stimulus, different systems have been proposed to determine the time to perform a specific task or motor action. Most systems use cameras with high sampling frequency ,13 or acDespite the quick results provided by those systems in which computer keyboards are used, they lack specificity  and ecological validity, as combat sports actions are not performed during the task. In addition, systems involving kinematics  or accelerometry to measure response time usually require more time to prepare, collect, and analyze the data. Moreover, these systems are expensive and often have low applicability to athlete training routines.To minimize the aforementioned limitations, the use of a specific mobile phone app  has been proposed to determine the response time of different motor actions (strikes) with a low-cost, highly applicable, and ecologically valid solution. The TReaction app measures the motor response time between the flash fire and sound waves produced from contact with the target through the mobile phone microphone. However, as far as we know, the response time measurement validity obtained by the TReaction app has not been tested. In fact, the use of mobile apps has been growing exponentially in fitness, health, and sports science, which raises the need for scientific evidence . TherefoData collection for this study was performed in 2 sessions. In the first session, a response time test was performed using the TReaction app simultaneously with a high-speed camera . In the second session, the TReaction app measurement reliability was validated with a repeated measures design using a simulator. This simulator was programmed to verify the accuracy of the visual stimuli and the response time with previously programmed fixed intervals.The 2 subjects of this study were selected intentionally. These individuals were male black belt athletes with significant experience in regional and national taekwondo competitions. Furthermore, each selected subject had to have at least 10 years of experience in a modality of combat sport. Before participating in the study, all participants were informed and provided written consent about the specific aims and methods of the study along with possible study risks. The local research ethics committee approved this study (protocol number 145.882). All procedures were performed in accordance with the Declaration of Helsinki.The TReaction app was used to determine the motor response time and the accuracy of the measurement was validated through a repeated measures design that examined motor gesture accuracy during contact with an impact pad. The measurements of values obtained by the mobile app (TReaction app) were compared with those obtained using a digital high-speed camera, which is considered the gold standard method.The response time obtained from the TReaction app is provided as shown in Number 1 represents the mobile phone;Number 2 represents a play button via touchscreen technology present in the mobile app interface and that activates the mobile phone camera flash through an algorithm software developed in Java programming language using integrated development environment Android Studio  and that allows to acquire and process data;Number 3 represents the mobile phone camera flash, emitting the visual stimulus and indicates the beginning of the response time to perform a gesture or task to reach a contact target ;Number 4 represents when contact with the target occurs and a sound wave is generated and processed through the software developed to accurately identify and point response time test results obtained;Number 5 represents the mobile microphone to audio capture.To accurately identify the strike response time , we performed a simultaneous motion analysis using a high-speed digital camera  with a sampling frequency of 1000 Hz and compared it with repeated measures. The response time was determined using a software analysis , capturing the first frame when the flashlight appeared and the moment of the material restitution caused by the contact of the foot with the contact pad.Both athletes performed a total of 59 strikes using the roundhouse kick technique at the height of the trunk. To calculate the response time, 2 different mobile phone devices were used . The tests were conducted as shown in To verify the accuracy of the measurement over repeated measures, a software running with an algorithm developed in Java language, simulating the strike sound and simultaneous change in the computer monitor screen color , was used. The monitor screen was alternating between black and white with the following epochs previously fixed at 3014, 3004, 3014, and 3002 ms. This configuration was chosed to test the consistency of the changes in the monitor screen. First, the TReaction app was set up in the consecutive audio capture mode to verify response time reliability via audio acquisition. Then it was set up in the flash drive mode repeatedly for each auditory stimulus emitted by the computer, with following epochs previously fixed at 3014, 3004, 3014, and 3002 ms. At this moment, the high-speed camera was used to simultaneously record repeated responses of the mobile phone camera flash and the color change of the monitor screen.t test was used to test differences between both methods. The magnitude of the differences was verified from the effect size (g), and it was then scaled for trivial (0.25), small (0.25 to 0.50), moderate (0.50 to 1.0), or large (1.0) effects [P<.05.Descriptive statistics (mean [SD]) were used to present the results, and normality was verified using the Shapiro-Wilk test. Pearson linear correlation was used to verify the relationship between response time obtained by the TReaction app and high-speed camera. A paired Student  effects . The typ effects . The Bla effects  analysesFor mean response time values between the high-speed camera and the TReaction app, there was no difference, and the magnitude of the differences obtained was classified as trivial. The methods to determine the response time presented a strong correlation, and the TEM pointed to the confidence in the measurement obtained from the TReaction app in relation to the high-speed camera.The Bland and Altman plots describing the agreement of response time measurements obtained with a high-speed camera and the TReaction app is presented in This study aimed to verify the validity of the TReaction app, which was designed to evaluate the motor response time of combat sports athletes. In addition, this study aimed to verify if the setup used by the TReaction app to determine the beginning of the task (flashlight stimulus) and the time of contact with the target (time to perform the task) would reach acceptable levels of accuracy. To the best of our knowledge, this is the first study to investigate the validity of the TReaction app. The main results showed no differences between the mean response time of all strikes evaluated using the TReaction app and those obtained by the high-speed camera, which is supported by the effect size observed . The response time results showed a strong correlation between both TReaction app and high-speed camera (gold standard) methods. Besides, the TEM in our study (9.2 ms) is lower than the value (30 ms) observed previously with single-beam photocells across short-sprint studies .When using the TReaction app, considerations must be given to the values of differences by the inference and the degrees of agreement of the Bland and Altman plot. Our results show an average difference of 13 ms for response time between TReaction app and high-speed camera. Response time presented a bias of 13.05 ms, and the 95% limit of agreement for the differences between the high-speed camera and TReaction app was 27.06 ms with 3 individual samples slightly outside the limit of agreement. Although the response time observed in our study presented bias higher than the value (0.35 ms) detected by , the varThis study demonstrated that the difference between the TReaction app and high-speed camera observed is associated with the distinct method that the TReaction app uses to calculate the time between the visual stimulus (flash fire) to perform the task and the moment to determine the motor response time. The TReaction app calculates response time based on the sound wave generated by the impact with the target object. This measure presented a high ICC and no differences between the audio output and the previously programmed computer software.The kinematics is among the most accurate systems used to measure motor gestures associated with performance such as vertical jump ,25, espeOne limitation of the TReaction app may be associated with the small variability observed in the firing time of the flash over repeated measures, which increases the probability of incorrectly identifying the moment of the initial stimulus to perform the task. However, in this study, a high-speed camera (1000 Hz) was used to establish the response time with maximum accuracy, and no differences were observed when compared with the response time values obtained by TReaction app. Another aspect to consider when interpreting our findings is regarding the limited sample size, as a higher variability can be expected from international and national level athletes  in response time when repeated measures of kicks are performed , which mFinally, the reliability observed for computer screen color change time, previously programmed to occur simultaneously to the auditory stimulus at predefined times, was also verified. Results observed allow the use of the screen color change as an alternative to be used as a visual stimulus to initiate a motor task. Therefore, we suggest that the TReaction app can accurately measure response time during different techniques used in combat sports. This is relevant because response time is an important variable for combat sports ,10,15,26The results of this study suggest that TReaction app is a valid and reliable tool for measuring response time in combat sports. However, the TEM and observed interference of agreement should be considered when comparing the response time values obtained by TReaction app with other kinematic measurements.The TReaction app provides an easily executable test that provides relevant sport-specific data regarding motor response time. Outcomes from the TReaction app suggest that athletes and coaches involved in combat sports can obtain reliable continuous motivational feedback leading to accurate diagnostic and performance criteria. The TReaction app can achieve and better control training-induced adaptations as well as help choose interventions that will help achieve maximum combat sports success. In addition, the TReaction app showed to be a valid tool that is both cost-effective and highly applicable to combat sports practitioners.


In Global navigation satellite system (GNSS) data processing, integer ambiguity acceptance test is considered as a challenging problem. A number of ambiguity acceptance tests have been proposed from different perspective and then unified into the integer aperture estimation (IA) framework. Among all the IA estimators, the optimal integer aperture (OIA) achieves the highest success rate with the fixed failure rate tolerance. However, the OIA is of less practical appealing due to its high computation complexity. On the other hand, the popular discrimination tests employ only two integer candidates, which are the essential reason for their sub-optimality. In this study, a generalized difference test (GDT) is proposed to exploit the benefit of including three or more integer candidates to improve their performance from theoretical perspective. The simulation results indicate that the third best integer candidates contribute to more than 70% success rate improvement for integer bootstrapping success rate higher than 0.8 case. Therefore, the GDT with three integer candidates (GDT3) achieves a good trade-off between the performance and computation burden. The threshold function is also applied for rapid determination of the fixed failure rate (FF)-threshold for GDT3. The performance improvement of GDT3 is validated with real GNSS data set. The numerical results indicate that GDT3 achieves higher empirical success rate while the empirical failure rate remains comparable. In a 20 km baseline test, the success rate GDT3 increase 7% with almost the same empirical failure rate. In the global navigation satellite system (GNSS) data processing and GNSS based remote sensing applications, integer ambiguity resolution is an important and challenging research problem. The mathematical model for carrier phase based GNSS positioning model can be expressed as :(1)E(y)=Estimating Mapping the real-valued ambiguity to integer with the integer estimator. The integer estimation procedure can be described asPerforming ambiguity acceptance test. The fixed integer Updating real-valued parameters by The mixed integer model can be solved by a four-step procedure : EstimatThe ambiguity acceptance test problem can be solved by either an integer aperture estimator or a hypothesis test. A typical hypothesis test problem involves three aspects: probability basis, a threshold determination approach and a test statistic. The integer aperture estimation for ambiguity acceptance test is based on the ambiguity residual distribution, which considers the stochastic property of the fixed integer candidate, thus provides a sound probability basis. The ambiguity residual is defined as ,4:(3)ε⌣=The probability density function (PDF) of the ambiguity residual fined as :(4)fε⌣(xted with:fa^(x)=1|operator , which cInteger aperture (IA) estimation is a class of ambiguity estimator, which can map the real ambiguity into either integer or float solution. IA estimators allow for presence of gaps between the adjacent acceptance regions, so the integer estimation is only a special case of IA estimation ,8. Accorapproach . The empapproach ,12 and tapproach ,14. The third aspect of the hypothesis test is about the test statistics of the ambiguity acceptance test, which has been the major focus of ambiguity acceptance test research. In early stages, many ambiguity acceptance tests have been derived from different perspective, such as the F-ratio test ,16, the In this study, we propose the generalized difference test (GDT), which improves the performance of the difference test by employing more than two integer candidates. The relationship between the difference test and the OIA and the GDT is also analyzed.Currently, the most popular methods for the ambiguity acceptance tests include the ratio test and the difference test. Both employ two squared Mahalanobis distances for construction of test statistics with the difference in their test statistics formation. According to a previous comparison between the ratio test and the difference, the difference test is theoretically better than the ratio test ,27, so wThe difference test is defined as :(7)‖a^−aSimilarly, the second-best candidate has the second shortest squared Mahalanobis distance. The acceptance region of the difference test can be explicitly expressed and the difference test is a member of IA estimator, which is known as the difference test integer aperture (DTIA). Comparing to the OIA, DTIA only employs two integer vectors in the test statistics construction, while OIA involves infinite number of integer candidates.The probability basis of the DTIA can be derived from the PDF of the float solution. It is noticed that the PDF of the multivariate normal distribution presents the exponential relationship with the squared Mahalanobis distance. Hence, the ratio of the two PDFs subject to the best and the second-best integers can be expressed as: The equation shows that the difference test statistics lies in the ratio of the two PDFs; taken the log form of the equation, then we have:The equation shows that the difference test is actually equivalent to the ratio of two PDFs.Then substituting Equation (7) into Equation (9), we get another form of the difference test:The equation shows that the threshold of the test can be derived from Applying the ’z-translational invariant‘ property, the acceptance region of the difference test integer aperture (DTIA) estimator can also be expressed as:The optimal integer aperture (OIA) estimator is derived from a constrained optimization problem. It is optimal in sense of the maximum success rate with given failure rate constraint. In the ambiguity acceptance test problem, the success rate and the failure rate are both positively correlated to the acceptance region size. For a particular IA estimator, more optimistic threshold always means higher success rate and higher failure rate at the same time, In other word, it is impossible to pursue the highest success rate without increasing its failure risk. As a trade-off, one can strive for the highest success rate with certain failure rate constraint. The objective function of the constrained optimization problem in ambiguity acceptance test can be expressed as :(14)maxΩThe Neyman-Pearson lemma gives a solution to this constrained maximization problem . The NeyThe problem solved by the Neyman-Pearson lemma is defined on given as ,25: (17)More specifically, the two integrable functions Considering the definition of the PDF of the ambiguity residuals, Equation (18) can be rewritten as:There are two challenges in OIA implementation: (1) determining the threshold The first challenge comes from the implicit relationship between the threshold  studies ,29. The The second challenge is solved by an approximation method. As the float solution follows multivariate normal distribution, corresponding squared Mahalanobis distance follows e fε⌣(x) ,30,31. TThe radius parameter It is noticed that both the DTIA and the OIA can be expressed as the ratio of PDFs, while the difference is the denominator. Comparing Equation (13) and (20), it is realized the sub-optimality of the difference test is actually the result of only taking the PDF contribution of Above analysis indicates that the discrepancy between the DTIA and the OIA is caused by neglecting the probability contribution of Current discrimination tests, such as the ratio test, the difference test, the projector test and a few other ambiguity acceptance tests, such as the model separability based ambiguity acceptance test approach  all emplThe PDF of the ambiguity residuals can be expanded as:Substituting Equations (10) into Equation (24), then the PDF ratio can be expressed by the difference test statistics, which is given as:m integer candidates is denoted as GDTm. For example, the generalized difference test with three integer candidate case is defined as:The equation allows for incorporating more than two integer candidates into the test statistics construction and each term has the difference test statistics form, which is denoted as the generalized difference test (GDT). The number of integer candidates depends on the underlying model strength. In order to discriminate the test statistics term number, the GDT with In the equation, the second-best integer and the third best integer depends on the value of The equation shows that the difference test is only a special case of the generalized difference test, which can be denoted as GDT2, the threshold of However, this relationship only holds for GDT2. Another extreme case of the generalized difference test is the OIA, which can be denoted as GDTThe generalized form of the difference test is also an integer aperture estimator. Its acceptance region is defined as: m sets of integer candidates first. In order to optimally determine the practical GDT term number, the impact of the integer candidate number on the success rate with fixed failure rate is examined by comparing the success rates between the OIA and the difference test, GDT3, GDT4 and GDT5. The simulation results are presented in According to the previous analysis, optimal determination of the term number of GDT is meaningful to achieve good balance between the performance and the computation burden. Considering the computation burden, it makes good sense to select fewer integer sets that play the most important role in The fixed failure rate (FF-) approach is theoretically rigorous and applicable to all IA estimators but it is computation exhaustive. Due to the extensive computation in the Monte-Carlo procedure, the FF-approach is difficult to be applied in real-time application. In order to improve the computation efficiency, the lookup table method ,12 and tAccording to the definition, the GDT is an extended form of the difference test, so we attempt to use the similar threshold determination method to improve its computation efficiency. The threshold function method has shown to work well for the difference test, so it is also worth to try in the GDT threshold determination. In order to applying a similar rational function as the difference test, the logarithm form of the GDT threshold is used. The relationship between fixed failure rate threshold of GDT3 and IB success rate can be given as:th Qa^a^ ,35:(30)Pess rate . The decess rate .The relationship between the logarithm GDT3 threshold and the IB success rate is illustrated in m integer candidates. The optimal integer estimator, the integer least-squares, can intermediately give an arbitrary number of best integer candidate sets. Hence, getting m best sets of integer candidates is just a sorting procedure.Finding the best Constructing the test statistics of GDT. For example, the test statistics of GDT3 can be computed as:Computing IB success rate with Equation (26), then determining the threshold Performing ambiguity acceptance test. If After the term number and the threshold function are determined, the procedure for how to apply GDT in practice may be outlined. Recalling the four-step procedure to solve the mixed integer linear problem, the second and the third step should be redefined. The procedure of applying GDT can be summarized as follows:The performance of GDT can be evaluated in terms of success rate and percentage identical to OIA. The success rate acts as an important performance indicator for the IA estimation performance, the IA estimator achieves higher success rate subject to the given failure rate tolerance is preferred. The percentage identical to OIA is used to assess the optimality of the IA estimator.Since the success rate of the GDT is difficult to compute analytically, the Monte Carlo approach is adopted. The description of success rate computation method using Monte Carlo method can be found in Reference . About 4The comparison results are presented in The percentage identical to OIA is used to evaluate the optimality of the GDT estimators. The simulation results are presented in the right panel of Comparing the two panels, it is noticed that the percentage identical to OIA improvement is more significant than the success rate improvement. This is because the percentage identical to OIA is used to measure the similarity of the GDT acceptance region to OIA acceptance region, rather than the success rate, while the acceptance region of OIA gives a good separation on failure probability and the success probability. ftp://geodesy.noaa.gov). As shown in The performance of the GDT is validated by epoch-by-epoch RTK processing of GNSSdata from the NGS CORS network, which is publicly accessible by the FTP server  approach for GNSS ambiguity acceptance test has been investigated in this study. Current discrimination tests, such as the ratio test, the difference test, only consider two integer candidates in the construction of test statistics. In this work, we examined the role of the third, fourth and fifth best integer candidates in ambiguity acceptance test and their contribution to the ambiguity residual PDF is analyzed. It concludes that considering two integer candidates may underestimate the failure risk, especially for a weak underlying model. In order to improve the performance of the difference test, a generalized difference test (GDT) employing an arbitrary number of integer candidates is proposed. The simulation results have indicated that considering more sets of integer candidates in test statistics construction can improve the success rate and the percentage identical to OIA. Comparing to other GDTs, GDT3 contributes to more than 70% of the success rate gain with only considering one extra integer candidates. Therefore, GDT3 is considered as a first choice to balance between the performance and computation complexity when the integer bootstrapping success rate higher than 80% cases. However, more sets of integer candidates may be involved for even weaker underlying models to achieve higher performance. Similar to the difference test the rational function is constructed to rapidly determine the fixed failure rate threshold for the GDT3, which helps circumvent the time-consuming Monte-Carlo procedure and significantly improves the computation efficiency of GDT3. The performance of GDT3 is validated with real GNSS datasets processed in single epoch RTK mode. The test results indicate that the GDT3 achieves higher empirical success rate while the empirical failure rate remains comparable as the difference test in all tested baselines. The improvement provided by the GDT3 is more significant for the longer baseline case. For the 20km baseline, the empirical success rate of GDT3 gains 7% if the difference test and the GDT3 failure rate remains comparable.


Aim or Purpose: To describe the effect of varying scleral stiffness on the biomechanical deformation response of the cornea under air-puff loading via a finite-element (FE) model.Methods: A two-dimensional axisymmetric stationary FE model of the whole human eye was used to examine the effects varying scleral stiffness and intraocular pressure (IOP) on the maximum apical displacement of the cornea. The model was comprised of the cornea, sclera, vitreous, and surrounding air region. The velocity and pressure profiles of an air-puff from a dynamic Scheimpflug analyzer were replicated in the FE model, and the resultant profile was applied to deform the cornea in a multiphysics study . IOP was simulated as a uniform pressure on the globe interior. The simulation results were compared to data from ex vivo scleral stiffening experiments with human donor globes.Results: The FE model predicted decreased maximum apical displacement with increased IOP and increased ratio of scleral-to-corneal Young's moduli. These predictions were in good agreement (within one standard deviation) with findings from ex vivo scleral stiffening experiments using human donor eyes. These findings demonstrate the importance of scleral material properties on the biomechanical deformation response of the cornea in air-puff induced deformation.Conclusion: The results of an air-puff induced deformation are often considered to be solely due to IOP and corneal properties. The current study showed that the stiffer the sclera, the greater will be the limitation on corneal deformation, separately from IOP. This may have important clinical implications to interpreting the response of the cornea under air-puff loading in pathologic conditions. AdditioA simplified axisymmetric FE model of the human eye was developed in COMSOL Multiphysics 5.2a  based on average dimensions Figure , Table 1The geometry was meshed using the built-in meshing capabilities of COMSOL. The central air region and ocular tunic were meshed with mapped 12,837 quadrilateral elements, with 3 elements through the thickness of the cornea and sclera. The remaining air region domains were meshed with 7,453 free triangular elements. The globe interior was meshed using free triangular elements and boundary layers to create a highly refined mesh at the interface of the ocular tunic and the vitreous body and more accurately model corneal deformation response. A convergence study was undertaken to identify the mesh density required to ensure that the solution was nearly independent of meshing parameters ; therefore the unloaded or stress-free state of the eye was first estimated  approaches 0, this aligns with the maximum apical displacement as measured by the CorVis ST. We therefore assumed, as a first approximation, the cornea is in a quasi-static equilibrium such that a static model will capture this particular aspect of the air-puff-induced deformation.In the The CorVis ST was used to acquire data on the biomechanical deformation response of the corneas of 12 pairs of human donor eyes . The donor eye study is considered exempt from review by the university. In each pair, one eye was randomly selected to have its sclera stiffened by crosslinking treatment with glutaraldehyde, while the fellow eye served as a control. The globe was immersed for 30 min in 4% glutaraldehyde in Dulbecco's phosphate-buffered saline (DPBS)  just below the level of the limbus, leaving a visible gap such that the cornea remained untreated. Glutaraldehyde visibly stains ocular tissues yellow after a short period of time. The ocular tissues were visually inspected to ensure that the cornea remained unaffected by the glutaraldehyde treatment.The CorVis ST was used to load the eye and quantify the resulting corneal deformation response Figure . Each eyThe CorVis ST air-puff velocity profile and corresponding pressure profile were simulated in COMSOL 5.2a Figure  along thThe simulated pressure profile was applied as the boundary load on the anterior boundary of the eye. The resulting stress magnitudes were highest at the posterior surface of the corneal apex, which experiences the greatest total deformation and strain Figure . The strex vivo experiments  models have been explored as a way to evaluate in vivo properties and response (Elsheikh, Scleral stiffness significantly influenced corneal apical displacement in both simulations and ex vivo experiments. Several aspects of this result give insights which can be used to inform other models. Several models of air puff-induced deformation are comprised of only the cornea, with a variety of scleral boundary conditions applied at the limbus (Elsheikh et al., This FE model, while simple, achieved qualitative agreement with ex vivo human donor eyes, in an experimental setup that was replicated closely in the FE model.The present model accurately replicated the velocity and pressure profiles of the CorVis ST air-puff. Similar to the work done by Elsheikh et al. the model also estimated the stress-free state of the eye and generated the residually-stressed state before deformation to more accurately describe the stresses in the cornea and sclera and the resultant biomechanical response (Elsheikh et al., ex vivo experiments on human donor tissues. Future iterations of the model will include the dynamic response of the cornea to an air-puff.One limitation of this model is that it does not account for the dynamic time-dependent response of the cornea to the air-puff. The cornea is a soft biological tissue and therefore exhibits viscoelasticity in its biomechanical response. To account for the non-linear behavior of the tissue, we chose to consider the ocular tissues as hyperelastic, resulting in a non-linear response to increasing IOP. The use of an incompressible neo-Hookean constitutive model is a simplification: the cornea and sclera are complex structures with significant anisotropy Nguyen, . In thisThe finite-element model presented in this paper demonstrates that scleral material properties have an important impact on the biomechanical deformation response of the cornea in air-puff induced deformation. Namely, the stiffer the sclera, the greater the limitation on corneal deformation. This may have important clinical implications. Often in the clinic, the observed biomechanical deformation response of the cornea is attributed solely to the material properties of the cornea, as well as IOP. However, it is clear from these simulations and experiments that the deformation response of the same cornea varies significantly with varying scleral properties. This suggests that when looking at air-puff induced deformation, that the observed biomechanical response is a result of the combination of both corneal and scleral material properties, in addition to IOP.The datasets analyzed for the current study are available from the corresponding author on reasonable request.BN, MR, and CR contributed to this study. BN and CR conceived the study design and all authors contributed to the development of the model. All authors contributed to manuscript revision, read and approved the submitted version.CR is a consultant for Oculus Optikgeräte GmbH. The remaining 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.


Wideband microwave imaging is of interest wherever optical opaque scenarios need to be analyzed, as these waves can penetrate biological tissues, many building materials, or industrial materials. One of the challenges of microwave imaging is the computation of the image from the measurement data because of the need to solve extensive inverse scattering problems due to the sometimes complicated wave propagation. The inversion problem simplifies if only spatially limited objects—point objects, in the simplest case—with temporally variable scattering properties are of interest. Differential imaging uses this time variance by observing the scenario under test over a certain time interval. Such problems exist in medical diagnostics, in the search for surviving earthquake victims, monitoring of the vitality of persons, detection of wood pests, control of industrial processes, and much more. This paper gives an overview of imaging methods for point-like targets and discusses the impact of target variations onto the radar data. Because the target variations are very weak in many applications, a major issue of differential imaging concerns the suppression of random effects by appropriate data processing and concepts of radar hardware. The paper introduces related methods and approaches, and some applications illustrate their performance. Microwave imaging may be considered as a method to reconstruct the spatial distribution of matter  based on the electromagnetic sounding of an observation space of interest. Obviously, by referring to (1)b_1b_⋮b_K=[S_1volution . The solFurthermore, one should note that the material parameters The image resolution  depends basically on a spatial parameter of the sounding wave , and the solid angle under which the objects are illuminated and observed . The lasthe sidelobes of the point-spread function of the imaging system, which are a matter of the antenna array structure, the number of antennas, and the bandwidth of the received signals ,5;multipath signals caused by scattering at dominant objects overpowering the reflections of weak bodies;device internal clutter, caused by imperfections of the measurement equipment ;time extension of the sounding waves due to the limited decay rate of the antenna impulse response; andreceiver noise, propagation loss, and others.A further important feature of image quality is the contrast that represents the ratio between the “brightest” and “darkest” image pixels. Bright points are linked to strong reflections caused by extended boundaries  with large gradients of permittivity or permeability. Dark image pixels correspond to weak scattering objects, which are typically small and/or have low permittivity/permeability contrast with respect to their environment. The achievable contrast depends on many factors:This basically prevents the detection or analysis of weak scattering objects by microwave sensing if they are embedded in a strong, multipath environment.temporal fluctuations inherently connected with the test scenario  or on rIn what follows, a simplified signal model to describe the scattering scenario will be introduced with emphasis on the most important aspects of differential imaging. Based on this consideration the most important parameters of UWB devices for differential imaging will be considered. Several examples and measurements are shown for illustration.By restricting ourselves to small objects of interest, which are sufficiently far from the antennas, the set of differential equations  describing the scenario may be approximated by a simple transmission model. It will be finally based on the Friis transmission formula and the radar equation, which we extend to time-domain conditions here. In order to make that approximation already valid for short distances, the involved antennas should be quite small.In what follows, we first introduce this transmission model for the simple case of free space propagation and summarize some methods of localizing/imaging of small, invariant objects without the need of an inversion of Maxwell’s equations. We then discuss variant objects under free space conditions and some methods are introduced to detect them under noisy conditions. For the sake of brevity, we will only refer in this connection to the time variance of those objects. But, this approach will also include the “targeted object modification”  and the “difference between two scenarios”-method, if we regard the related measurements as sequentially done in (observation) time The generic situation is depicted in Herein, the left term of Following (2), the response matrix )∼d2dt2⋯ . The sigFor the reconstruction of the target locations  from the measurements Method 1: The volume to be observed is subdivided into a grid of voxels. In order to get the intensity value If the voxel position coincides with the target position ee e.g., ,13,14,15Finally, the routine Equation (6) superimposes a set of cross-correlation functions—also assigned as delay-multiply-and-sum—determined from the captured response signals ,18,19,20Method 2: Instead of superimposing the measured signals as demonstrated in Equations (4)–(6), one may also try to numerically solve the problem of target localization. If we consider a single measurement  compare  or even In what follows, the localization of a single target shall be illustrated. For the sake of demonstration, we restrict ourselves to mono-static measurements refer to . CorrespHere, This type of solution is optimal if the measurement errors of the involved quantities are Gaussian distributed. The squaring of In order to avoid the bias, a maximum likelihood approach can be applied, which aims to maximize the probability density function (PDF) in Equation (10) with respect to the target position Here again, one subdivides the volume to be observed in voxels assigned by their position  objects ,22. FurtMethod 3: The last imaging approach, at least that we will mention here, exploits the reciprocity of the transmission paths characterized by the multi-static response matrix erred to ,25,26,27approach  with theRestricting ourselves only to the multi-static transmission matrix, its components may be expressed as follows in the case of a time-variant scenario ):Here, In order to capture the time variance of the scenario, it is measured in typically regular time intervals es refer C. As a cBy removing the range influence from the radar data via Equation (13) below, one actually may observe the variability of the backscattering while walking C.(13)b⌢In order to image the target motion in space, one can follow one of the approaches discussed in In many applications, the targets are small, weakly reflecting and moving only a little. This issue, we will address below. A small-sized target leads to Rayleigh-scattering, which provokes a twofold differentiation of the incident field. Hence, in the case of a time variance, such a target may only vary the strength of the backscattering caused by variations of its permittivity, permeability, or volume. This, we will express by:Here, To shorten the notation, we include the delay term in the argument of the largest modulation is provided by the sample located at the steepest part of the received signal;the modulations at rising and falling edges are inverted; andthe modulation at the signal peaks has double frequency (due to the squaring) and is quite weak.As seen from Equation (16), the radar response For motionless targets, where only its reflectivity In the case of properly designed measurement receivers, which are typically based on sub-sampling, the receiver noise . Here, Because in the case of weak targets, the modulation effects will also be quite weak, the major challenge will be to detect the time-variable targets under noise conditions. Many methods are investigated with that goal ,35,36,37In case 1, the selected time sample is located within a flat part of the receiving signal, so we get only noise , its expected value and variance result in the following:In the case of a perfect match between modulation and reference function As seen from Equation (22), the detection performance can be arbitrarily increased by extending the integration time relation .In the simplest case of sinusoidal modulation, the correlation function (20) is implemented by a Fourier-transform in observation time direction . One possible option is to illuminate the target from a second antenna at a slightly different position. The resulting radar data is Because the antennas observe the same object, the modulation function Assuming the target modulation at both signals is largest at the sampling points Because the optimum sampling positions The maximum position of that matrix gives the roundtrip times from both antennas. The idea behind the cross-energy is the noise independency of the merged signals, so with increasing integration time, the noise will mutually cancel out. Such noise independency, we also observe in single antenna measurements as long as the signals are not joined with themselves .Singular value decomposition is also often proposed for noise reduction purposes. It will, however, not help if the signal to be detected is already buried beneath noise.The experimental situation is roughly illustrated in We first restrict ourselves to a stable propagation environment, as depicted in Here, we neither respect any angular dependency of the impulse response function nor the range influence  of the signal magnitude or the polarization of the electric fields. Without loss in general, we only involve one static and one time-variable target. The different symbols stand for antenna impulse responses Before we do that, the noise term in Equation (29) must be accounted for more seriously, because this will be important for the estimation of the clutter reduction. As already mentioned in Equation (17), the randomness of the measurement is caused by amplitude noise (additive noise) The propagation delay is omitted in the signal components for the sake of a shorter notation. Due to the ergodicity of the additive noise, the randomness of the sampling procedure does not influence its statistical properties, where the jitter In order to suppress the static paths, one needs to know Equation (31) assumes that the variable target parts are canceled out due to a sufficiently long integration. Furthermore, it shows that the time shape of the static signal is slightly modified by “a low pass filter” whose IRF is given by the PDF By subtracting The second line in Equation (32) comes from a Taylor series expansion of Equation (30) and the assumption of a not significantly large jitter, so higher terms of the series may be neglected. Further on, the third line ignores the jitter-affected time-variant signals, because they are of very low magnitude, and As we can observe from Equation (32), we get after background removal the wanted signal Then, we still have the additive noise The strength of the background is often 2–3 orders of magnitude larger than the target reflections and with increasing bandwidth of the radar, the signal derivation leads to an additional emphasis of their influence. Hence, jitter may seriously affect the detection performance of a time-variable target under strong multipath conditions , which exploits singular value decomposition (SVD) .χ(T) A. Due tomponents C. Becausmponents D.This section will summarize the requirements for the most important parameters of UWB devices for differential imaging. Basically, there are several approaches possible to implement UWB devices . They diThe basic structure of pulse and M-sequence are depicted in ing) see . The peaIn the case of the M-sequence radar the sounding signal is generated by a fast linear feedback shift register (LFSR) of length However, the received signal ocessing  in orderThe bandwidth of the sounding signal determines the range resolution performance of the radar. Hence, it should be as large as possible. The bandwidth is fixed by the width of the sounding pulse or the chip width of the M-sequence, respectively. The upper-band limits are, however, often restricted by the frequency-dependent propagation losses of the test scenario. Because these losses grow with the increasing target distance, the range resolution will worsen the deeper a target is located in a lossy material.The measurement rate In the UWB case, The sounding signals, pulse, or M-sequence, are periodically repeated with the interval The total net data throughput While an M-sequence radar has to collect the data over the full period Finally, it should be noted that in case of a large unambiguity range , the expected value is a bias-free estimation of the wanted correlation function, and the total noise depends on the strength of the received signal due to the jitter. Unlike the pulse radar, the noise level is not focused on signal edges but is evenly distributed throughout the signal ). Additionally, the noise level decays with increasing length In order to stay in the digital domain, we characterize the overall sensitivity of the receiver  by its effective number of bits This is an important design rule for M-sequence devices in order to balance between resolution, technical effort, and data rate. Assuming an operational frequency band ion (see ). The tiion . The radargram example refers to 6 mg of magnetite and a modulation strength of Another approach is based on nanoparticles, which can be modulated by an external magnetic field ,58,59,60The imaging concept is finally depicted in In order to select an appropriate modulation frequency for the nanoparticles, the intrinsic time variance of a female breast was investigated see . For thaWhile in the first demonstration example, the modulation rate may be appropriately selected to avoid overlap with other motions, this degree of freedom is not given in the second one. Here, the goal is to detect, for example, the motion of the carotid artery. The final example refers to a situation where the time variations of the scenario are not predictable. In the shown case see , the tasMicrowave imaging is advantageous if the internal structure of optically opaque test scenarios must be investigated. However, in the case of strong multipath scenarios and weak scattering targets, microwave imaging creates challenges for the imaging algorithms and the measurement precision of the scattered field. In order to get reasonable precision, extensive calibrations typically have to be performed with the aim of reducing the systematic errors of the measurement arrangement. However, not infrequently, these calibrations have only limited success because precise calibration standards  are missing and/or the reproducibility of the measurements is insufficient.The situation relaxes if one is interested only in a low number of spatially limited targets, which show some inherently or externally induced time variations of their scattering behavior. One can find or implement such conditions in many tasks of medical microwave imaging, non-destructive testing, law enforcement, and so forth. Due to the time variance of the targets, the perturbing, strong multipath signals and the device clutter may be largely suppressed by respecting only time-variable signal components. Furthermore, the limited spatial extension of the targets reduces the imaging problem to a localization task. Nevertheless, the localization may also be challenging, because multipath components involving the object of interest may appear to be a time-varying target. Such signal components must be excluded prior to target localization.Microwave localization or imaging requires the observation of the scene from several antenna positions. Due to the time variance of the scenario, the measurements have to be done in parallel with a sufficiently high measurement rate in order to be able to follow the temporal variations of the scenario under testing conditions. This requires UWB devices with many synchronously operating measurement channels and high measurement speed. From the perspective of system cost and measurement speed, the preferable device concepts should be based on sounding signals using sub-nanosecond pulses or wideband pseudo-noise signals, such as M-sequences.In many practical cases, the targets of interest only weakly scatter the sounding waves. Hence, the noise behavior of the measuring devices becomes a major issue. In the case of UWB devices, two types of randomness are important. These are the randomness of the voltage capturing usually assigned as additive noise  and the randomness of the sampling, also called jitter. While the influence of the additive noise onto the measurement signal may be counteracted by increasing the power of the sounding signal, the impact of jitter does not depend on the signal strength. Jitter provokes additional randomness at steep signal edges. Hence, if there are strong scatterers in the SUT, they will increase the noise level proportional to the level of the sounding signal. Consequently, the detection performance of weak targets will be much worse. Because additive noise and jitter are mainly caused by internal imperfections of the measurement device, one should prefer a device concept that suppresses these random effects as much as possible. As shown in the paper, the pseudo-noise approach outperforms the impulse radar with regard to these aspects. Firstly, the time-extended sounding signal  provides high signal power for additive noise suppression, even if the signal voltage remains low. Secondly, properly designed M-sequence devices are rigidly synchronized so that any jitter generation may be largely reduced. Finally, the impulse compression  spreads the noise provoked by the remaining jitter over the whole impulse response function. Hence, there will no noise elevation at signal edges so that strong static scatterer will not influence the detection of weak time-variable targets.


Silicon retinas, also known as Dynamic Vision Sensors (DVS) or event-based visual sensors, have shown great advantages in terms of low power consumption, low bandwidth, wide dynamic range and very high temporal resolution. Owing to such advantages as compared to conventional vision sensors, DVS devices are gaining more and more attention in various applications such as drone surveillance, robotics, high-speed motion photography, etc. The output of such sensors is a sequence of events rather than a series of frames as for classical cameras. Estimating the data rate of the stream of events associated with such sensors is needed for the appropriate design of transmission systems involving such sensors. In this work, we propose to consider information about the scene content and sensor speed to support such estimation, and we identify suitable metrics to quantify the complexity of the scene for this purpose. According to the results of this study, the event rate shows an exponential relationship with the metric associated with the complexity of the scene and linear relationships with the speed of the sensor. Based on these results, we propose a two-parameter model for the dependency of the event rate on scene complexity and sensor speed. The model achieves a prediction accuracy of approximately 88.4% for the outdoor environment along with the overall prediction performance of approximately 84%. RMSE Root Mean Squared Error SSESum of Squares due to error DAVISDynamic and Active-pixel Vision Sensor IMU Inertial Measurement Unit CDF Cumulative Distribution Function DVS Dynamic Vision Sensor AER Address Event Representation MLE Maximum Likelihood EstimationConventional video cameras capture video, via temporal sampling, in a series of separate frames or images, whose raw pixel values are then processed. In the conventional video sensing approach, the frames are typically acquired with a fixed frame rate, regardless of the scene content and complexity. This approach generates a substantial load in terms of energy consumption, data management and the transmission system. Furthermore, due to technological and resource limitations, temporal resolution is limited, and this may cause critical data loss between the captured frames. For instance, in a highly dynamic scene like an explosion, the fast-moving sections in the scene cause motion blur due to the frame rate and processing power restrictions. Therefore, frame-based video sensing does not appear as the best solution in terms of energy and efficiency for next-generation Internet of Things surveillance, autonomous driving/drone technology and robotics. The most efficient visual computing system is based on biological vision and perception in mammals, which is not based on pixels and frame-based sampling. The mammalian brain only receives new information from the eyes when something in a scene changes. This significantly reduces the amount of information delivered to the biological brain, but is sufficient to identify the surrounding changes and conditions.The rest of this section discusses the Dynamic Vision Sensor (DVS) principle, the relevant literature of scene complexity metrics and the motivation of this study, followed by the contribution provided in this paper.Based on the principle of biological sensing, silicon retina devices capture only changes in scene reflectance, i.e., they report only the on/off triggering of brightness in the observed scene . The firA team led by Tobi Delbruck enhanced the neuromorphic silicon retina sensor based on the adaptive photoreceptor circuits concept . Pixels x and y are the coordinates of the pixel that has undergone a brightness change, t is the timestamp and p is the polarity of the event. The polarity of the event represents either a positive, increase, or negative, decrease, sign of the grey-level intensity change. It is important to note that events are triggered whenever there is a movement of the neuromorphic vision sensor or motion in the scene or both. In other words, no data are transmitted for stationary vision sensors and static scenes. These unique properties enable neuromorphic vision sensors to achieve low-bandwidth, low-latency and low-power requirements. p, rendered as frames. The “green” colour represents events with positive change in brightness, whereas events with negative change in brightness are represented by the “red” colour.Neuromorphic vision sensors are data driven, i.e., they asynchronously transmit events that are pixel-level relative intensity (brightness) changes. These events are produced with micro-second time resolution. The neuromorphic silicon technology utilizes the Address Event Representation (AER) protocol for exchanging data. The protocol, proposed by , is usedIn order to compare the bandwidth of the neuromorphic and conventional vision sensors, let us consider the data rate requirements of the “diving ” sequence with a spatial resolution of In computer vision research, scene complexity information is useful in many applications, i.e., it can be used to determine the bandwidth requirement, as well as the amount of compression that can be tolerated. Furthermore, it can also support image clustering and classification. The definition of image complexity is widely varied, ranging from subjective complexity measures  to diverEmerging applications of the DVS can be found in robotics ,20, autoThe main aim of this work is to estimate the data rate resulting from DVS sensors. Since we expect the data rate will depend on the content of the scene, as anticipated in , one of In order to select the most appropriate one for the estimation of the data rate, the correlation of different scene complexity metrics with the neuromorphic event rate has to be investigated. According to the best of the authors’ knowledge, there has been no study done on the relationship between scene complexity metrics and neuromorphic event rate; hence, this represents the first novel contribution. The second important contribution is the identification of the relationship between the date rate and motion speed of the sensor. These two important contributions form the basis for the design of our proposed bandwidth model for neuromorphic vision sensors.Which of the available scene complexity metrics shows the best correlation with the event rate?Can we define a novel scene complexity metric showing better correlation with the event rate?How can we model the relationship between the event rate and the scene complexity metric?How can we model the relationship between the event rate and the motion speed of the sensor?Finally, how can we model the neuromorphic data rate as a function of both the scene complexity metric and the motion speed of the sensor?This work aims at answering the following research questions:The remainder of this paper is structured as follows. In order to model the event rate of neuromorphic vision sensors for different types of scenes, we utilized a publicly-available well-calibrated event-camera dataset . The avaThe asynchronous neuromorphic event stream in the form of the aforementioned tuple, i.e., The frame-based output, in the form of intensity images, at approximately 24 frames per second. Each intensity image is precisely time stamped, which enables the recording of the number of neuromorphic events between any two intensity images.w.r.t. the three-dimensional velocity.Inertial measurements in the form of a three-dimensional acceleration and velocity reported at a 1-ms interval. This information makes it possible to study the asynchronous event rate The dataset contains the following important information:Shapes scene is very low as compared to the Box and Poster scenes. This is mainly due to the fact that the variability among pixels’ absolute intensity levels is low in Shapes as compared to the Box and Poster scenes. In other words, the majority of the pixels of the Shapes scene have the same brightness levels; therefore, the motion of the camera triggers less brightness changes. On the other hand, the variability in the brightness levels of the Poster and Box scenes is very high, which translates into a higher neuromorphic event rate, as shown in The aforementioned dataset allows us to study the relationship between the neuromorphic event rate and the type of scene. It is important to note that the neuromorphic bandwidth depends on the relative brightness change per-pixel, which depends on the pixels’ absolute intensity values. In other words, information on the distribution of pixels’ static light intensity, or brightness levels, in an image can be useful in determining the total number of the generated neuromorphic spike events. For instance, consider the three different types of scenes in In order to study and compare the correlation performance of different scene complexity metrics on the event rate, we considered similar motion speed of the vision sensor for every type of scene so that the event rate only depended on the scene complexity. The adopted methodology is summarized in the following steps, with Selection of data portions with similar speed of the capturing sensor: According to the analysis of the IMU dataset, the majority of the scene types comprised a magnitude of mean velocity of 1 m/s. Therefore, for every scene, we extracted the data (event rate and intensity images) such that the magnitude of mean velocity was 1 m/s. According to Event rate computation: We computed the total number of neuromorphic events generated, Scene complexity metric computation: The neuromorphic event stream and intensity images were produced concurrently by the DAVIS camera. In the dataset, intensity images were precisely timestamped; therefore, we computed the scene complexity metric by utilizing the intensity images between w.r.t the neuromorphic event rate.Best model fit between scene complexity and event rate: Next, we found the best model , for the relationship between scene complexity metric and event rate. Best model fit between motion and event rate: Our study of the correlation between scene complexity and event rate initially assumed the same mean sensor speed for the different scenes. On the other hand, in order to analyse the correlation performance between motion speed and event rate, the value assumed by the scene complexity metric must remain constant so that the event rate varies as a function of the sensor motion speed only. In the final step, we propose a model for the neuromorphic event rate by utilizing the scene complexity metric and information on the motion of the camera see .The operation of dynamic vision sensors is based on the generation of spike events at local relative changes in brightness. Therefore, identifying and computing abrupt changes in pixel intensity in a scene becomes relevant for our study. In order to locate sharp discontinuities in an intensity image and study its impact on the neuromorphic event rate, the proposed scene complexity metrics range from gradient approximation to texture computation of an intensity image. In this section, we study the impact of such scene complexity metrics on the event rate. The details of these metrics, including their correlation performance with the neuromorphic event rate, are reported in the following subsections.The gradient of an image specifies the directional change in the intensity of an image. Furthermore, it also highlights the magnitude of significant transition in intensity. The main step in computing the gradient approximation of an image is to convolve the intensity image with a small finite filter known as the kernel. The filter is convolved with the intensity image in the horizontal and vertical directions. The three well-known methods to calculate such gradient are Sobel , PrewittI denote an intensity image and The Sobel filtering process consists of convolving an intensity image with an integer valued filter. Let The convolution is simply a linear combination of the kernel and the image. Each convolution operation results in a single gradient pixel output. Let The Prewitt operator  is similThe convolution process of pixel-by-pixel multiplication is the same as that of the Sobel filter, as given by Equation . The majThe Roberts operator  uses 2×2The convolution operation is performed by using the The convolution process between the horizontal kernel and G. These metrics were computed across all the pixels of the image. Let M and N be the number of rows and columns, respectively. The metrics are mathematically expressed as:I.The computation process for the magnitude of the gradient is summarized in Algorithm 1. The first order derivative is computed for the centred pixel in the Algorithm 1 Computation process for the magnitude of the gradient of an intensity image.Input: Intensity image fordoifthen   Use symmetric padding of the border pixel to create else p  Construct a end if p in the horizontal direction according to , but with different average sensor speed. The bar graphs in Walking and Running dataset. The text arrow above the bar graph shows the scene content in terms of Sobel-based mean gradient. The mean gradient varied widely within each dataset; however, the mean gradient for the 33.4-second walking sequence  resulted in lower prediction accuracy as compared to variable multi-direction motion data.In order to analyse the prediction accuracy of the model on unseen data, we extracted an evaluation dataset from , shown iThe model only considers the magnitude of the mean velocity and does not consider the direction of motion. We expected that this would increase the prediction accuracy at the expense of a considerable increase in the model complexity. However, the model still achieved an overall average prediction accuracy of 84% with a simple two-parameter single-term exponential model. Another important factor contributing to the prediction error is the noise, which generally originates from the bias settings of the sensor.Urban sequences was approximately 20%, where the velocity of the sensor was 0.65 m/s. This is mainly because of the proportion of events produced by the object movement. On the other hand, the increase in sensor speed decreased the percentage error. The outdoor Walking and Running sequences, where the sensor moves at a higher speed, resulted in a better prediction accuracy, mainly because the proportion of events produced by the sensor motion prevailed over the events produced due to the object movement. Therefore, the model was capable of achieving better prediction accuracy in scenarios where the velocity of the sensor was higher. The prediction accuracy of the model can be improved for low sensor speed scenarios by considering in the model the motion of objects in the scene.The outdoor sequences in the evaluation dataset, reported in Sensor network devices have limited resources in terms of memory and processing power. Visual sensors with a low data rate consume less power in the device. Therefore, the source data rate becomes extremely important for resource-constrained sensor network devices. In this section, we compare the data rate of neuromorphic and conventional vision sensors by utilizing the evaluation dataset in the previous section. devices .On the other hand, the DVS requires only a fraction of the bandwidth mainly because these sensors capture the dynamics of a scene, thus filtering out redundant information. For applications where a higher frame rate is not desired, the time-stamp information in the neuromorphic data can be filtered out to achieve a lower data rate. Such a filtering policy requires only a spatial location histogram map and location histogram counts . The filEvent-based cameras are very promising sensors for high-speed mobile robots, self-driving cars and drones and many other applications ranging from next-generation Internet of Things to low-latency access to visual medical information. The data rate output by the event-based vision sensors depends on the type of scene and motion speed. In this work, we proposed a bandwidth prediction model by considering the scene content and motion speed. According to the study, the neuromorphic event rate varied exponentially with the scene complexity, with Sobel- and Prewitt-based mean gradient approximation showing the best goodness of fit. In addition, we studied the relationship between the sensor speed and the event rate, which we found to be linear. Based on these analyses, we proposed a two-parameter exponential model for the dependency of the event rate on scene complexity and sensor speed. According to the results, Sobel- and Prewitt-based models showed prediction accuracy of approximately 88.4% for the outdoor dataset along with the overall prediction performance of approximately 84%.


Sensor fault detection and diagnosis (FDD) has great significance for ensuring the energy saving and normal operation of the air conditioning system. Chiller systems serving as an important part of central air conditioning systems are the major energy consumer in commercial and industrial buildings. In order to ensure the normal operation of the chiller system, virtual sensors have been proposed to detect and diagnose sensor faults. However, the performance of virtual sensors could be easily impacted by abnormal data. To solve this problem, virtual sensors combined with the maximal information coefficient (MIC) and a long short-term memory (LSTM) network is proposed for chiller sensor fault diagnosis. Firstly, MIC, which has the ability to quantify the degree of relevance in a data set, is applied to examine all potentially interesting relationships between sensors. Subsequently, sensors with high correlation are divided into several groups by the grouping thresholds. Two virtual sensors, which are constructed in each group by LSTM with different input sensors and corresponding to the same physical sensor, could have the ability to predict the value of physical sensors. High correlation sensors in each group improve the fitting effect of virtual sensors. Finally, sensor faults can be diagnosed by the absolute deviation which is generated by comparing the virtual sensors’ output with the actual value measured from the air-cooled chiller. The performance of the proposed method is evaluated by using a real data set. Experimental results indicate that virtual sensors can be well constructed and the proposed method achieves a significant performance along with a low false alarm rate. Poorly maintained and improperly controlled equipment wastes an estimated 15% to 30% of energy used in commercial buildings . As an iFDD provides a cornerstone for the condition-based maintenance of engineered systems and has been an active area of research and development in the aerospace, process controls, automotive, manufacturing, nuclear, and national defense fields ,5,6,7,8.With the rapid development of the computer’s calculation ability, data driven methods have been widely developed in recent years. Han et al. present a novel FDD strategy, which combines the principle component analysis (PCA) feature extraction technology and the multiclass support vector machine (SVM) classification algorithm for vapor-compression refrigeration systems . In ordeIn another respect, hardware redundancy was first developed to diagnose faults. It has high reliability and can directly isolate faults . Regrettuildings . Howeveruildings .In this paper, a novel chiller sensor fault diagnosis method based on a virtual sensor technique and a data driven method is proposed. Firstly, a large amount of sensor data can be stored when the chiller system is operating. According to the data collected from the chiller system, sensors can be divided into several groups by the maximal information coefficient (MIC) and the sensor grouping threshold. MIC is used to explore relationships among different sensors, which can better describe the nonlinear relationship in data set than traditional methods such as Pearson correlation. Sensors in each group have high correlation which is helpful for improving the performance of the virtual sensors. Subsequently, virtual sensors are constructed by a long short-term memory network (LSTM) in each group. Deep learning models are capable of automatic and deep mining feature information, which have made achievements in many fields ,29,30. AIn order to ensure the performance of virtual sensors, MIC is used to examine potentially interesting relationships between sensors. Chiller sensors with high MIC scores are divided into the same groups. This could dramatically improve the fitting effect of virtual sensors by constructing them in the same group.The performance of virtual sensors could be easily impacted by the input sensors. In order to reduce the false alarm rate, two virtual sensors that have different input sensors are constructed for the same physical sensor. When the two deviations between the corresponding physical sensor and the two virtual sensors both exceed the thresholds, the physical sensor is considered as a fault state.The LSTM model, which can better extract discriminating features from the sensor data, is used to construct the virtual sensors. It could further improve the fitting effect of virtual sensors.The contributions of the paper are as follows:The rest of this paper is organized as follows: The heat is transferred from the low-temperature heat source to the high-temperature heat source via refrigerant circulation loop. In the circulation loop of the refrigerant, the energy conservation can be written asThe refrigerant circulates via the compressor, condenser, expansion valve and evaporator while performing energy transfer with the chilled water. The pressure, enthalpy and other parameters of the refrigerant in the condenser can be affected by the output parameters of the compressor, the outlet refrigerant enthalpy, the mass flow rate, and so forth. Conversely, the compressor power and the refrigerant mass flow can be changed by the compressor input parameters such as the condenser condensing pressure. The parameters, such as the electronic expansion valve mass flow and the outlet enthalpy, can be affected by the output parameters of the condenser, the condensing pressure, the outlet refrigerant enthalpy, and so forth. The condensing pressure can also be affected by the electronic expansion valve mass flow. The electronic expansion valve output parameters and the enthalpy affect the evaporation pressure, the outlet enthalpy and other parameters. The evaporation pressure as the expansion valve input can also affect the electronic expansion valve mass flow. There is also a coupling relationship between the compressor and the evaporator through the evaporation pressure and the mass flow of the compressor. Thus, there is a complicated coupling relationship between the various equipment of the chiller system.X and Y can be defined asX and Y, Due to the complex coupling characteristic of the air-cooled chiller system, MIC which has the ability to examine all potentially interesting relationships is used to explore relationships among different sensors. The calculation of MIC is based on mutual information (MI). MI tells us how much knowing one variable reduces our uncertainty about the other . And theB is a function of sample size n, usually D. Variables X and Y are independent of each other when MIC is equal to 0. And some kinds of functional relationship are existed between X and Y variables when MIC is equal to 1.In order to get the MIC score, MI is first achieved by exploring all the grids by using different partition schemes, then the MIC is normalized between 0 and 1 by dividing lated as (3)M(D)=Raw operating data, which include eleven sensors, compressor frequency The maximum mutual information is calculated between any sensors in The LSTM model is used to construct the virtual sensors for eleven physical sensors. It can better extract feature information among different sensors in the chiller system. As shown in The Formulas –6) are  are 6) aHerein, the input of the LSTM model includes the sensor historical data in same group, compressor frequency and electron expansion valve. And the output of the LSTM model constructs corresponding virtual sensors. Two virtual sensors, which contain different input sensors and correspond to the same physical sensor, are constructed in the same group. The maximum correlation ensures the performance of the two virtual sensors with different input physical sensors. For instance, if the grouping threshold takes 0.3 in l-th sensor is calculated asIn the actual implementation, the fault can be diagnosed by the absolute deviation between the virtual sensors and the physical sensors. A fault diagnosis threshold is calculated to automatically diagnose sensor fault. The fault diagnosis threshold of the Step 1: A physical sensor is selected from eleven sensors. Two virtual sensors, which have been constructed in the training period, are used to predict the value of this physical sensor.Step 2: Deviations between virtual and physical sensors are calculated and compared with the fault diagnosis threshold.Step 3: Obviously, the physical sensor is not considered as a fault state when no deviations exceed the threshold. On the contrary, a sensor fault occurs when the deviations both exceed the fault diagnosis threshold. Input sensors are considered as a fault state if only one absolute deviation exceeds the threshold, because two virtual sensors have different input sensors. Under this situation, another physical sensor from input sensors is selected and step 2 will be repeated to predict the value of another physical sensor.The experimental data are acquired from the device in the Honeywell Home and Building Control Laboratory in Tianjin University, China. During the normal operation of the device, the chiller system can store thirteen kinds of measurement data such as different sensor values and electronic expansion valve opening degree which are highly correlated with the sensor reading. The experimental data, which obtain 45,000 sets of time series, are collected at 2 min intervals and divided into training sets, fault diagnosis threshold determination sets and test sets.Before the experiment began, the raw data need to be standardized and filter out samples with poor quality, such as those during chiller start up and shutdown time periods. Based on the measurement accuracy of temperatures and pressure sensors, eleven sensor faults are introduced by adding the fixed bias in this paper. Various magnitudes of biases, which are determined by the reading range of each sensor, have been added to each sensor in To verify the low false alarm rate and fault diagnosis performance of this method, We assume that only one sensor is considered as a fault state. Input sensors To further verify the performance of this method, the false alarm rate of all chiller sensors is listed in As a deep learning model, the LSTM model, which is developed to address sequential data with its ability to encode temporal information, has a better performance than the linear regression and nonlinear regression models such as the artificial neural network model. Linear regression is a linear approach to modeling the relationship among different sensors. The artificial neural network model, which has great nonlinear curve fitting capability, can achieve a better performance than the linear regression model. Due to the high correlation between sensors in the same group and the strong feature extract ability of the LSTM model, either of the two sensors can achieve a better performance on fault diagnosis. Virtual sensors are used to diagnose faults in this paper, which are constructed by the linear regression (LR) model, the artificial neural network (ANN) model and the LSTM model. The performance of virtual sensors can be verified by the different grouping thresholds. In As shown in N represents sampling steps, To further verify the performance of another virtual sensor during training and testing, the mean absolute error (MAE) is used in this paper. MAE is frequently used to measure the differences between values predicted by a model and the values observed. The MAE between the physical sensor and virtual sensor is defined asp-values between the traditional methods and the proposed method were calculated. The t test can easily be adapted to testing the following hypotheses at a specified level of significance p-values between the traditional methods and the proposed method are always smaller than 0.05. This means that LSTM-based virtual sensors are significantly different to the two other methods.As shown in In addition to In order to verify the performance of different physical sensors, fault diagnosis ratios of all physical sensors with minimum biases are listed in The operating efficiency of an air-cooled chiller system is critical for building energy performance. In this paper, a novel chiller sensor fault diagnosis method was proposed. Chiller sensors were divided into different groups by MIC score and the grouping threshold. Highly correlated sensors can significantly improve the accuracy of virtual sensors. Under the same model, experimental results also show that virtual sensors have a better performance by grouping with the MIC score. Virtual sensors constructed by LSTM model were compared with the linear regression and the artificial neural network model, which reduces the cost of hardware redundancy. In order to reduce the false alarm rate and directly diagnose sensor faults, two virtual sensors corresponding to the same physical sensor were constructed. Comparing the method in this paper with using only one virtual sensor, the method in this paper has the lower false alarm rate. The proposed method with higher accuracy has also been well presented and experimentally validated.The following work needs to be done in the future: firstly, fault diagnosis threshold determination is an indispensable part of the chiller sensor fault diagnosis based on deviation. Threshold will directly impact the performance of fault diagnosis. An excellent method for fault diagnosis threshold should be further researched; secondly, the proposed method will be applied to other refrigeration air conditioning systems to further verify generalization.