A thorough accuracy analysis is performed using spatial rigid-body transformations and relative measurement analyses of photogrammetrically reconstructed surfaces of nondeformable objects. The effects of camera calibration, exposure time, object velocity, and object surface pattern quality on the quality of adjusted 3D coordinates are taken into consideration. While the exposure time does not significantly influence the quality of the static measurements, the results of dynamic experiments demonstrate that not only an insufficient frame rate but also an increased noise level resulting from short exposure times affects 3D coordinate accuracy. Using appropriate configurations to capture dynamic events, the errors in dynamic experiments do not differ significantly from the errors obtained in static measurements. A spatial mapping error of less than 1 In the context of setting up a stereo high-speed camera system for accurate 3D measurements in highly dynamic experiments, the potential of a  Due to their high spatio-temporal resolution, high-speed optical systems are widely used to quantify the behavior of objects in dynamic events. A compilation of structural dynamics applications using photogrammetric techniques can be found in . The benThe result is a continuous full-field formed by surface meshes with spatial coordinates of the generated points. These coordinates are the basis for the evaluation of the structural behavior via different mechanical analyses such as deformation ,3,4,5, cHigh strain rates or impact velocities are applied to different structures to assess the response of the material to the dynamic tests. Because of the applied high strain rate, the time of interest for analyzing the material deformation in these impact experiments is short, and high frequency measurements are needed. In addition, the stepwise relative deformation of the material during this time of interest may lie in the micrometer range for small-scale objects. For this reason, the mechanical properties derived from the optical measurements can lead to false conclusions if the quality of the photogrammetric measurements is insufficient.While capturing short-time dynamic events, image blur is an obvious motion effect that increases the uncertainty of image matching processes. An uncertainty in dynamic conditions is explored in  by compaImage blur can be minimized by decreasing the exposure time in the camera configuration. Reducing the exposure time requires an increase in illumination to ensure an optimal signal-to-noise ratio (SNR) in the images. As explained in , the phoDespite the drawbacks presented above, the field of civil engineering often resorts to these systems to monitor concrete structures loaded with different forces and impact directions. As an example, the impact resistance of existing building materials is analyzed by the Research Training Group GRK 2250 of the German Research Foundation . In the Appropriate configurations of the optical systems for accurate measurements in highly dynamic experiments are needed in order to correctly describe the performance of the tested materials within the research group GRK 2250. As mentioned before, the motion blur resulting from recording moving objects with a long exposure time affects the image matching process for coordinate determination. Moreover, a short exposure time can deteriorate SNR, degrading the image quality and therefore the measurement accuracy.X, Y, or Z axes, is complex to ensure. Furthermore, the same position over the object surface could not be evaluated because the sensors would restrain the camera field of view.As stated before, external devices have been used to quantify the uncertainties coming from photogrammetric measurements. A consistent external validation of optical measurements with other devices such as accelerometers, strain gauges, or pointers is difficult to provide for high frequency spatially resolved experiments. The accuracy of these sensors depends on the frequency; therefore, it varies. The accuracy given by the manufacturer often only applies to lower frequencies than the frequencies used by high-speed camera systems. Furthermore, the sensors are often not able to capture a surface but only discrete points. The measurement direction of these sensors is in most cases uniaxial, and its exact orientation within the orientation of the optical device, either in the Alternatively, the potential of photogrammetric measurements can be assessed using the internal precision statements of the adjusted parameters for camera calibration and coordinate determination. However, these statements needed for an accuracy analysis of the results are not provided by “GOM Aramis”.To overcome these limitations, the accuracy analysis methodology for 3D high frequency testing proposed in this work is based on spatial similarity transformations, together with 3D relative measurements. Both analyses are based on the surface point coordinates determined by “GOM Aramis”. The transformation analysis is limited to object measurements without deformations, because it is not possible to make assumptions from a spatial similarity analysis regarding the deformation behavior. Since there is no deformation in the measurements, the scale factor is fixed for all transformations and set to 1. This special case of 3D similarity transformations is called rigid-body transformation (RBT). The basic idea of the rigid-body motion evaluations is the analysis of the spatial mapping error variations, which reflect the abovementioned degradation effects.The proposed analysis is performed for two event conditions: First, a static object was recorded at different frame rates to analyze the effect of short exposed images on the temporal and geometrical stability of points surfaces without motion. Furthermore, the effect of different exposure times when capturing images for camera calibration on the 3D coordinate determination is also evaluated. Second, a moving object was recorded with the same scheme of exposure times, as was used in the static case. Here, in addition to the geometrical stability of the reconstructed surfaces, the dependency of accuracy on parameters such as camera exposure time and object velocity are analyzed.This work is structured as follows: First, the experimental setup for static and dynamic measurements is presented. Afterward, the methodology for accuracy analysis based on RBT and different quality parameters is presented. The results of the transformations and 3D relative measurements, as well as image performance analyses, are then presented. Finally, the possible reasons for the results are discussed and concluded. The complete experimental data and results are available upon request from the author responsible for the correspondence.“Photron Fastcam SA-X2” cameras. The main technological specifications of this camera are listed in “1kW-LED-4438” lamps in continuous mode, placed on the left and right sides of the camera system. The evaluation of the images in order to obtain the 3D coordinates, and the corresponding camera calibration, were carried out using the software “GOM Aramis”.Systematically generated patterns (SPs)  and randThe evaluated static and dynamic testing configurations are presented in the workflow of The dependency of the accuracy on the dynamic event conditions and camera configurations was evaluated using a single 3D Camera Calibration, as presented in From the presented testing configurations, 770 and 352 experimental configurations (presented in (i)Tested:Pattern quality: Different levels of stochastic information are provided in SPs and RPs.Exposure time: Its effect on image capturing is evaluated in static and dynamic event conditions.Frame rate: It is also included to the extent, as it limits the maximal exposure time.“CP20 90 mm × 72 mm” produced by the software provider. A test field calibration is characterized by the fact that reference points and reference lengths are known [Camera calibration: Test field camera calibrations were performed using the calibration plate re known . In this(ii)Considered:Sensor cleaning: Before testing, the cameras sensors were cleaned to avoid errors coming from dust particles.Lighting: Adequate brightness and contrast before and after recording were verified for all captured images.Facet size and point distance for DIC: The facets are square sections in the right and left images. The point distance describes the distance between the center points of the adjacent facets. For all the experiments, a facet size of 19 px and a point distance of 16 px were set.Slider distance and measuring distance: These denominations are defined by the software, respectively, as the distance between the camera sliders and the distance between the object and the bar on which the cameras are held. This is different from the stereo baseline and the object distance, which are defined in photogrammetry as the distance between the perspective centers of the cameras and the distance between the baseline and the object. For the calibration plate and a camera lens of 75 mm, a slider distance of 105 mm and measuring distance of 620 mm is recommended by the software. These correspond approximately to a baseline of 200 mm and an object distance of 470 mm.(iii)Negligible:The variation of the drop-weight velocity obtained from the same height due to friction problems in the facility.External conditions such as temperature variation and vibrations, since the tests were performed in a controlled lab environment. A lab temperature of 20 To qualify the potential of high frequency optical measurements, the following uncertainty sources were taken into account during testing:The workflow shown in intersection deviation and stereo residual given by “GOM Aramis” are also taken into account to evaluate the coordinate precision given by the software itself. The intersection deviation describes how much the calculated 3D coordinate position deviates from the calculated 3D coordinate of the same point based on the calibration. The stereo residual describes the difference in the gray value distribution of a facet between the left and right camera and is specified in gray values.The internal quality variables Template Matching Correlation Coefficient presented below is used to match the pattern surfaces. Here, the pattern surface (P) with pixel coordinate position I) by locating the resulted pixel position Since these internal quality variables did not provide enough information to explain the quality of the experimental configurations, a performance evaluation of the surface pattern images was carried out to support the results of the RBTs and relative 3D measurements. From the recorded static images, the best performing RP and SP surfaces were cropped using the corners’ pixel positions. To obtain the pattern surface from the dynamic recordings, the pixel accuracy method P) image, as well as the SNR per pattern image pixel (m) rows, (n) columns, and (g) gray values. The t) of the total (T) images captured by the corresponding experimental configuration.The cropping and the matching process are applied to the images captured with the right and left camera of the corresponding experimental configurations. The parameters brightness  coordinates and accuracies, as those are of central relevance in dynamic measurements using stereo high-speed camera systems.As schematized in  Formula . This evThe geometrical stability analysis is performed by evaluating the effect of random errors on constructed geometries within a pattern surface mesh. Temporal length variation  are  are BP, The total apparent displacements Z-axis contributes more to the amplitude of the total apparent displacement, as shown in the range variations in A systematic oscillation in The length variation The total From these findings, it can be concluded that even small variations in light over time can affect the results. This is because the signal detected by the sensor pixels directly affects the quality of the matching process, and thus, the resulting 3D measurements. The matching errors or gray level differences for determining the different surface points vary within the image. This variation in “Fastcam SA-X2”. Analyses of rigid-body transformations and relative coordinate accuracy were carried out on the basis of surface point coordinates and relative measurements computed by the software “GOM Aramis”. With the help of these studies, the accuracy determination of the 3D surface measurements of nondeformable objects was used to evaluate the stability of the stereo camera system.Different experimental configurations, varying camera settings, and motion parameters were systematically tested in order to evaluate the potential of the optical high-speed stereo camera system A large number of high frequency experimental data were obtained to evaluate the influence of the experimental configurations in static and dynamic measurement conditions. For all of the tested experimental configurations, each pattern with a surface area of First, the spatial mapping errors , it may significantly degrade the quality of results of 3D object reconstruction, thus requiring additional effort. Errors introduced by these cyclic displacements can for instance be compensated by using static background targets in a suitable configuration.Since the presented studies are based on spatial mapping analyses, rigid-body transformations can also be used to assess the accuracy of a single camera. In order to obtain the real dimensions of the object surface under study, a scaling factor must be used. The resulting 2D surface coordinates can also be evaluated under dynamic conditions, where the distance between the camera and the object should remain constant. Effects of the experimental setup used, such as the type of illumination, must also be taken into account in the analyses.Rigid-body analyses to test the accuracy potential of a stereo high-speed camera system have the limitation that only a single velocity is considering during the experiment. Material deformations at high dynamic rates propagate at different velocities due to the material response of the structural behavior. This complicates the choice of an appropriate exposure time. However, a generalization of the experimental velocity can be used to set up the optical measurement system.


Sensory information is conveyed by populations of neurons, and coding strategies cannot always be deduced when considering individual neurons. Moreover, information coding depends on the number of neurons available and on the composition of the population when multiple classes with different response properties are available. Here, we study population coding in human tactile afferents by employing a recently developed simulator of mechanoreceptor firing activity. First, we highlight the interplay of afferents within each class. We demonstrate that the optimal afferent density to convey maximal information depends on both the tactile feature under consideration and the afferent class. Second, we find that information is spread across different classes for all tactile features and that each class encodes both redundant and complementary information with respect to the other afferent classes. Specifically, combining information from multiple afferent classes improves information transmission and is often more efficient than increasing the density of afferents from the same class. Finally, we examine the importance of temporal and spatial contributions, respectively, to the joint spatiotemporal code. On average, destroying temporal information is more destructive than removing spatial information, but the importance of either depends on the stimulus feature analyzed. Overall, our results suggest that both optimal afferent innervation densities and the composition of the population depend in complex ways on the tactile features in question, potentially accounting for the variety in which tactile peripheral populations are assembled in different regions across the body. Touching an object elicits neural responses from hundreds or thousands of individual tactile receptors of different classes embedded within our hand. Information about the extent of contact, the strength of the touch, and its temporal profile are carried jointly in this population response to be processed further by the central nervous system. However, studying the nature of the population code is empirically challenging, as electrophysiological recordings are typically obtained from single or a small number of neurons at most. Here, we make use of a computer simulation to recreate the population activity of large numbers of tactile neurons and examine how information is spread across different neurons. We find that tactile information increases with afferent density, but the saturation point depends on both the tactile feature and afferent class. Importantly, information is generally spread across multiple afferent classes, such that a combination of afferents from multiple classes yields higher information than the same number of neurons from a single class. These results will be useful to guide future experiments and theoretical work on the processing of tactile information by the central nervous system. The brain processes information and makes decisions based on the activity of populations of neurons . StudyinTactile interactions are mediated by mechanoreceptive afferents and the glabrous skin of the human hand is innervated by approximately 17,000 fibers . These aA particular source of debate in the tactile literature has been the role of different afferent classes. Traditionally, each afferent class was thought to carry information about different and complementary stimulus features . HoweverHere, we investigate the contribution of large neural populations in tactile stimulus coding and examine the interplay of tactile submodalities in this process. Because the lack of population level data currently precludes empirical study, we used a large-scale computational model, Touchsim , to simu2 were considered for each afferent class. Therefore, we could test the effect of low, medium, and high densities . In contrast, PC afferents did not carry any information about stimulus size at any of the densities considered. This result can be explained by the fact that PC afferents exhibit extremely large receptive fields [For encoding stimulus size, we found that SA1 afferents were most informative, with information increasing and then saturating at a density of 40 afferents/cme fields , certainNext, we considered the encoding of the frequency of stimulation. PC afferents provided the highest frequency information, as predicted by the fact that PC afferents are well known to carry frequency information in vibrotactile stimulation . Given tPC afferents were also the most informative class about the stimulus ramp length, followed by SA1 and RA afferents, which provided similar levels of information, but required higher densities than PCs to reach saturation. Finally, SA1 afferents carried the highest amounts of information about ramp amplitude, with PC afferents not encoding any information. RA afferents again provided higher information than SA1 ones at the lowest density, but adding more fibers did not increase information for this class.The information saturation density, which we defined as the smallest value of density at which the population carried the asymptotic value of information reached for the highest simulated density, was the highest across classes for SA1 afferent for all considered stimulus features. Conversely, the information saturation density was the smallest for PC afferents in all cases . Notably2), RA afferents were more informative than SA1 for all features considered, suggesting that the optimal way to encode a tactile feature might depend on the number of neurons available.Finally, our result shows that the RA class at saturation density always encodes less information than the SA1 and PC populations about any feature considered in this study . HoweverNext, we investigated how tactile stimulus information was encoded in the joint activity of multiple afferent classes. In particular, we asked whether the information about stimulus features carried by an afferent class adds to and complements the information carried by other classes or whether the information carried by different afferent classes is redundant. To answer this question, we computed the information carried about each stimulus feature by the joint activity of populations of two or three afferent classes and compared the resulting values with the single-class information calculated above. Specifically, we used the concept of complementary information : we defiWe first considered whether afferent classes that were not the principal source of information about a stimulus feature added information that was complementary to that of the principally contributing afferent class. To do so, for each feature, we quantified the amount of complementary information that the less informative classes add to the information carried by the most informative class . The amoNext, we investigated which amount of each afferent class’s information contribution was complementary or redundant when considered against the information contribution of the other afferent classes. For each stimulus feature and each individual afferent type, we computed the fraction of the information carried by the considered afferent that is complementary with respect to the information already carried by the other two afferent classes. This fraction is an index of the specific novelty of the information of a given afferent class with respect to all others . In geneFor vibration frequency and ramp length, the two stimulus features for which all three afferent classes encoded considerable information, we found mostly redundant coding, with relatively small fractions of complementary information  to that of other classes. RA afferents carried less information than SA1 afferents, but part of this information (43%) was complementary to that of SA1 afferents. In this case, the encoding appears again to depend on the fraction of afferents that are activated by the stimulus, as was the case for stimulus size. This is a genuine form of population coding that would not be evident from single afferent analyses. PCs again provided negligible information see , and thuHaving established that information about individual stimulus features is carried by multiple, rather than single, afferent classes and that different afferent classes often carry complementary stimulus information, we next asked how the complementarity of information depends on the spatial density of afferents. We were especially interested in whether, given the functional properties of afferents in each class, it would be more efficient to allocate all receptors to the most informative class or spread the receptors across different classes to take advantage of the complementarity of different classes. To address these questions, we systematically analyzed the information carried by individual afferent classes and their combination at different densities . We testA substantial increase in the amount of encoded information was found for all features when increasing the density from the lower limit to realistic densities. Conversely, increasing the densities from the finger values further to the upper limit did not lead to additional increases of encoded information, neither when considering individual classes nor their combination, suggesting that the information in multi-class population coding saturates similarly to single-class coding. The only exception was probe size, for which information content at the upper limit was higher than at the finger density. As shown in Together, these results show the advantages for information encoding at the population level of spreading information across classes of receptors with complementary information rather than simply packing more receptors of a given class into the skin, even if receptors of this class are highly informative about the stimulus.After establishing how much information is encoded by each afferent class and their combinations, we investigated the nature of the population coding in more detail. In particular, we asked two questions relevant to understanding the spatial and temporal organization of the population code. First, how important is the precise temporal structure of the population activity for decoding stimuli from spatiotemporal patterns of neural population activity? Second, how important are differences in spatial neuron-to-neuron response profiles to decode stimulus information from spatiotemporal population activity?The importance of the spatial structure of the afferent population code for information coding, that is, the afferent-to-afferent difference in stimulus tuning properties at different spatial locations, is supported by the finding that natural tactile stimuli elicit specific firing patterns in afferents located in different places , 32. A cFirst, we evaluated whether the distribution of afferents in space, parameterized in the simulation as the distance of the afferent location from the stimulation site, impacts the population coding capabilities. To do so, we kept the NMF spatiotemporal modules computed on the original data and recomputed the NMF activation coefficients on the spiking activity obtained after destroying spatial information by randomly shuffling the neural responses across neurons for all time bins. Then we used the classifier trained on the original data to compute how much information about each stimulus feature could be decoded see . We callNext, to quantify the specific contribution of temporal structure to decoding information from the spatiotemporal population activity, we computed a “time-coding removed” information value from the population responses. To do so, we randomly shifted the spikes with each shift independently drawn from a uniform distribution with range ±2, ±5, and ±10 ms before recomputing the NMF activation coefficients and estimating the information content see . The difmore classes, has scarcely been investigated before. Here, we used a recently developed computational model that allows simulation of tactile neural responses at the population level with high accuracy. Although any putative population-level coding mechanisms derived from modeling would need to be experimentally verified, this approach allows investigating aspects of the neural code that are currently experimentally intractable and can therefore generate ideas for potential downstream decoding mechanisms.This study is based on a simulation paradigm, which provides novel insights on stimulus coding by tactile afferent populations. Much of our current understanding of encoding mechanisms of tactile stimuli derives from electrophysiological studies. However, these are severely limited in the number of afferents that can be recorded at a time. In addition, many previous studies have focused only on those afferents terminating directly at the stimulus contact location. Thus, a biased picture of tactile coding might have emerged. In fact, to our knowledge, population coding of tactile afferents, taken as the spatiotemporal activation of multiple afferents belonging to one or We first investigated how the density of afferents from a single class plays a role in the encoding process. We showed that the information content of both SA1 and RA populations increases asymptotically with afferent density until saturation. This effect was consistent for all features considered, although the specific saturation densities varied between features. This result highlights that tactile information is generally spread across a population of multiple afferents, even for features that are not explicitly spatial. Furthermore, the afferent class most informative about a tactile feature at low innervation densities might be different from the most informative class at high densities. Consequently, judging or predicting the information content of a population from recordings of single afferents only might be misleading and provide a biased picture of how information is represented in full populations.In contrast to SA1 and RA afferents, the information level for PC afferents was essentially constant for all density values considered across all tactile features. While this result might be taken to suggest that the PC population does not contribute information above that of a single afferent, there is evidence to suggest that PC populations might be important in different tactile contexts than the ones explored here: making contact with surfaces causes mechanical waves to spread throughout the hand, activating PC afferents as far away as the palm and their joint population activity carries information about how contact is made and other aspects of the grasp .It should be noted that for all afferent classes, the minimum density needed to recover the maximum information for any tactile feature is lower than the empirical afferent densities estimated for the human hand . We spec2). This result suggests that the way information is spread across afferent classes depends in part on receptor density, and in turn, should affect optimal decoding downstream. Indeed, tactile innervation density changes dramatically across different body areas, both in terms of the absolute number of afferents and relative innervation densities of different classes [Interestingly, we found that the RA class at saturation density tended to encode less information than the SA1 and PC populations, but in contrast, was more informative than SA1s at low densities . QuantiNot all information was complementary however, and we also found considerable degrees of redundancy between afferent classes. Redundancy in neural coding has been extensively debated . AccordOur study focused on the three main classes of tactile afferents that mediate discriminative touch. However, other classes also contribute to tactile coding, such as SA2 afferents, which are thought to primarily signal skin stretch but are consciously perceivable . FurtherAs the findings are based on computer simulations, the veracity of the results will depend on the accuracy with which the spiking responses can be replicated in the computational model. The stimuli we used, namely indentations by a single probe orthogonal to the skin surface with a superimposed vibration, are similar to those on which the original model was fit and fall into the range where it has been validated most extensively . Still, To study the effects of different innervation densities, we considered a simplified setup, distributing the afferents over a single dimension while neglecting some properties affecting the spatial distribution of afferents, for example the complex shape of the human hand. Future studies should take this aspect into account to reveal how the shape of the hand, the different afferent densities, and the composition of the population in different areas of the hand plays a role in stimulus encoding. In the same direction, population coding strategies and afferent distribution might be coupled with natural stimulus statistics in different body areas to deepen the understanding of how the human somatosensory system is optimized to receive and process natural tactile stimuli.Finally, as in other information-theoretic analyses on large-dimensional neural response spaces, our analysis can only provide a lower bound on the true information contained in the population spiking patterns. As direct calculation of the information is prohibitive with respect to the amount of data that would be required, we chose a method that decomposes the high-dimensional responses, with information values subsequently estimated in the lower-dimensional space. An additional benefit of this method is that the initial unsupervised decomposition of the neural responses reflects aspects of neural processing in sensory pathways. However, the resulting information values will be affected by choices regarding this decomposition specifically, and the information calculation more generally, and different choices might yield somewhat different outcomes. To directly test the robustness of our method, we compared our method with a different analysis pipeline. We found qualitatively very similar results, suggesting that our main findings, for example regarding the benefits of integrating across different afferent classes, hold generally, rather than being dependent on the specific analysis method chosen.2 for a total of 16 different populations per afferent type. This range includes the physiological innervation densities estimated for the human hand [To generate the spiking activity of tactile afferents, we used a previously published and validated model called Touchsim . We emplman hand . In someWe designed stimuli with circular shapes, which are indented in the skin following a ramp-and-hold function see . When thInformation calculations from high dimensional data require prohibitively large datasets. A common strategy to address this issue is by first performing unsupervised dimensionality reduction on the data. Here, we used spatiotemporal Non-Negative Matrix Factorization (NMF) to decompose the spatiotemporal matrix of spiking responses across the population.R ∈ RM × TN, where M is the total number of trials, T the number of time bins, and N the number of afferents in the population. NMF decompositions are naturally suited to describe spatiotemporal matrices of spiking responses, because spike trains are non-negative, and because commonly occurring spike patterns may be non-orthogonal and partly overlapping, and NMF does not require assumptions of orthogonality or non-overlap of different activity modules. NMF describes a single trial spike train as a sum of trial-independent non-negative spatiotemporal modules  and trial-dependent non-negative activation coefficients representing the strength of recruitment of each module in the considered trial [H ∈ RM × K contains the non-negative activation coefficients for the K modules in each trial and W ∈ RK × TN contains the non-negative modules. We used the function NMF included in the scikit-learn Python library [Responses were discretized by binning the spike trains into 2-ms intervals and counting the number of spikes falling into each bin. This resulted in a matrix ed trial , 23:R= library  to calcuK as the minimum number of modules capable of explaining a selected level of variance of the original data in R, as follows. First, to consistently select the level of variance explained between populations of the same class but with different densities, we calculated the saturation level of the accounted variance for each population considered (tolerance <1%). We averaged the saturation levels across populations of the same class with different densities and used this value as the new threshold for the explained variance. Finally, we calculated k modules W and activation coefficients H on the same 25-set. Given the W modules from the 25-set, we computed the activation coefficients H on the remaining 75-set. Given the random initialization of the spatiotemporal basis functions with the NMF decomposition, we computed 50 instantiations of the NMF to account for the variability of the method.We performed the NMF decomposition separately for each of the three afferent classes at each density value considered. Beforehand, we randomly separated the whole set of trials into balanced sets with a 25/75 split. We used the 25-set to determine the number of modules H computed with the NMF to a stimulus decoder. We used multinomial logistic regression to decode each stimulus feature separately on a trial-by-trial basis based on the neural activity  to predict the probability of outcome s for trial i such that:Hi is a vector containing the NMF activation coefficients for trial i and βk stores the coefficients associated with outcome s. When generalizing to Sn features, the multinomial logistic regression model consists of Sn − 1 independent logistic regression models regressed against the remaining Sn outcomes. Note that outcomes correspond to the possible values that the stimulus features could take and vary for each feature.After dimensionality reduction, we fed the activation coefficients larly to ). The sclarly to  was usedlbfgs in combination with L2 regularization. We selected the parameter C for the regularization by performing grid search. The scoring of the classifier was the negative log-likelihood, also known as the cross-entropy loss.The 75-set was divided equally and stratified into training and test sets. We trained the classifier on the activation coefficients of the training set and evaluated performance using the activation coefficients of the test set. The training procedure was performed using a stratified 5-fold cross-validation. This process was repeated for each population of afferents (both for single and combined classes) and all afferent densities. The solver used for the fitting procedure was The final fitted model outputs the posterior probability of observing each stimulus feature given the neural activity captured in the NMF activation coefficients . From thS, s and decoding stimulus p(s) and s and Sn is the number of values that the stimulus can take.Next, we computed the mutual information  from theTo assess the complementarity of stimulus information carried by different classes, we computed the information carried about each stimulus feature by the joint activity of populations of two or three afferent classes and compared it to the information carried by a single-class population. We defined the amount of information carried by the pair of afferent classes that is complementary to that of a reference class as the difference between the information carried by all the classes  and the information carried by the reference class. We repeated this process, taking each class as the reference class in turn. As an example, for SA1 afferents as the reference class, the complementary information is computed as:We defined the redundant information between the additional classes and the reference class as the sum of the information carried individually by the reference class and the additional ones minus the information carried by all the classes together, such that :The sum of redundant  and compR. Then, keeping the non-negative modules W obtained with the NMF decomposition on the original, non-shuffled data, we computed the activation coefficients on the spatial-shuffled data. We finally used these activation coefficients to feed the classifier previously trained on the original activation coefficients. To destroy the temporal structure in the data, we randomly shifted the spikes with a uniform distribution of ±2, ±5, and ±10 ms. Then, as for the spatial case, we obtained the activation coefficients on the time-shuffled data and used those to feed the classifier trained on the original data and estimate the residual information content after disrupting the data temporal structure.We assessed the contribution of fine temporal and spatial resolution within the spiking activity to information coding by destroying the temporal and spatial structures in the data. To destroy the spatial structure, we randomly permuted the order of afferents in the spiking matrix Rcount. We then applied the NMF decomposition on Rcount to find spatial modules Wspace capturing which afferents are firing together, such that:M was the same as described above for the spatiotemporal NMF.To test the robustness of the analysis pipeline with respect to the choice of low-dimensional representation, we calculated information values from an alternative NMF decomposition of the data. We first computed the spike count over the whole trial, Ht for each spatial module and time bin producing in total a number of activation coefficients per trial equal to the product of the number of modules M times the number of time bins T, a larger number than the activation coefficients per trial of the spatiotemporal NMF decomposition described above .We computed a single set of spatial modules using the population activity pooled over all time bins. We then calculated a different activation coefficient For the supervised decoding of the activation coefficients in each trial, we used the same GLM decoder described above.S1 Fig(A) stimulus size, (B) frequency, (C) ramp length, and (D) ramp amplitude. Note that we have conditioned on the remaining features for each panel and that the afferent densities chosen in this example correspond to the ones in the finger.Responses are shown for the three afferent classes as a function of (TIF)Click here for additional data file.S2 FigThe analysis presented in (TIF)Click here for additional data file.


Coreless filament winding is an emerging fabrication technology in the field of building construction with the potential to significantly decrease construction material consumption, while being fully automatable. Therefore, this technology could offer a solution to the increasing worldwide demand for building floor space in the next decades by optimizing and reducing the material usage. Current research focuses mainly on the design and engineering aspects while using carbon and glass fibers with epoxy resin; however, in order to move towards more sustainable structures, other fiber and resin material systems should also be assessed. This study integrates a selection of potential alternative fibers into the coreless filament winding process by adapting the fabrication equipment and process. A bio-based epoxy resin was introduced and compared to a conventional petroleum-based one. Generic coreless wound components were created for evaluating the fabrication suitability of selected alternative fibers. Four-point bending tests were performed for assessing the structural performance in relation to the sustainability of twelve alternative fibers and two resins. In this study, embodied energy and global warming potential from the literature were used as life-cycle assessment indexes to compare the material systems. Among the investigated fibers, flax showed the highest potential while bio-based resins are advisable at low fiber volume ratios. Fiber-reinforced composite materials are widely used in aerospace, automotive, energy, and marine applications because of their favorable material properties, such as high mass-specific stiffness and strength ,2,3, corCoreless filament winding (CFW) emerged in the field of construction, enabling an automated  and FE-sCarbon and glass fiber-reinforced plastics (C/GFRPs) with epoxy resins have been utilized almost exclusively in CFW. The design language of CFW is well suited for intricate framework structures, matching the property profile of such high-performance materials, but it is also optimal for lattices ,14 and s2 emissions. Filament winding is one of the less energy-intensive manufacturing processes compared to other composite fabrication techniques [The research efforts to promote CFW in the construction sector are motivated by the increasing worldwide demand for building floor space in the following decades . CFW allchniques ; howeverThere are several alternative fiber materials to carbon and E-glass, including both technical and natural fibers. The usage of natural fibers in the general field of fiber-reinforced plastic manufacturing is increasing to meet the growing industrial demand for more sustainable and structural components. This change is motivated by customer awareness, increasingly including other non-technical or economical parameters, such as ecological or social issues . For exaIn terms of fabrication, the rovings must endure the handling characterized by fast variations in fiber tension during the winding ,26 and sCoupled with the fabrication challenges, the structural engineering of these systems is also unconventional. The geometrical uncertainties and material deviations require the development of structural design methods integrated during the computational design process in a continuous feedback loop ,16. The The potential of these new material systems should be analyzed considering their mechanical performance along with their sustainability aspects. For this assessment, the specific amount of material needed to fulfill a specific strength of stiffness requirement can be compared to sustainability indexes . State-oConsidering that only a limited number of alternative materials have been implemented in CFW in previous studies ,25, the In a first step, a collection of material properties for potential fiber and matrix candidates was extracted from an exhaustive literature review /Table A1There were several criteria for the pre-selection of fiber materials. First, many plant-based fibers were excluded since they are not locally produced in Europe, such as bamboo, banana, and pineapple, keeping logistics minimal to contribute to the sustainability. Another important aspect was that the materials should be producible in quantities relevant for the construction. Further criteria were set based on the mechanical performance parameters. Materials with excessively high elongation at break are unsuitable for CFW, as they cannot withstand the constant fiber tension during winding. This issue affects spider silk, polyester, and palm fiber. Moreover, since stiffness and strength are required simultaneously for structural application, materials with one significantly low value were excluded, as with the case of cotton and coir. Another parameter would be the price per kilogram, which excludes boron fibers. Furthermore, the ratio between the mechanical performance parameters and the sustainability parameters should be in a range that could be superior to other fiber materials. Wool, for example, has a relatively low strength compared to its GWP and loses approx. 20% of its capacity when wet . In addiA conventional epoxy resin was compared to a bio-based epoxy resin. Investigating other types of thermosetting resins was out of the scope of this study for several reasons. Polyester resins are less performative than epoxy resins , especiaBased on this screening, the following materials  were selCarbon and glass acted as a benchmark to evaluate the alternative fibers since the CFW process was developed primarily based on these two materials. All the selected technical fiber products exhibit high consistency in their material parameters; however, plant-based fibers are natural products with significant variations in material parameters between batches and along the fiber bundle. These variations come from defects in the short individual fibers or the production of long yarns, as the fibers need to be held together by stapling them . ViscoseIn addition, the engineered fiber products come with a sizing that ensures good fiber-matrix adhesion to a particular matrix system. In the case of natural-based fiber products, the presence of hydroxyl groups gives a highly hydrophilic nature to the fiber, resulting in low moisture resistance and, consequently, in a weak interfacial fiber-matrix bonding . ChemicaThe production of long fiber bundles is also not as easy as with technical fiber. Twisting is commonly used to avoid the breakage of fibers that are just stapled together, producing better friction between fibers ; howeverCarbon fibers exhibit excellent processability using state-of-the-art CFW equipment. Its high mass-specific mechanical performance parameters, especially stiffness, are in accordance with the CFW design language, allowing the realization of filigree truss structures. It also incorporates a high chemical resistance. As a disadvantage, carbon fibers are obtained from non-renewable petroleum-based raw materials such as polyacrylonitrile (standard) or pitch (high-performance). It is also possible to produce carbon fibers from a renewable material by converting viscose fibers into carbon fibers, although the resulting fibers are less performative. For its production, the carbon concentration in the precursors is gradually increased in an energy-intensive stretching process. This process involves oxidative stabilization and carbonization/graphitization steps under an inert gas atmosphere, using high temperatures. Carbon fibers are relatively expensive and practically non-recyclable .Glass fibers show good mechanical performance at a lower price level than carbon. It is more suitable for high-strength applications than for high-stiffness ones. The processability in the CFW process is slightly worse than that of carbon, but still suitable. Glass fibers are spun from molten silica sand and have high chemical resistance. Several types of glasses with different properties can be created depending on their chemical composition. This study includes E-glass with a market share of about 99%  as a benAramid fibers combine high mass-specific tensile strength at a lower density than glass with high impact resistance. Aramid is spun from petroleum-based raw materials dissolved in sulfuric acid and its production is a very energy-intensive process. The fiber exhibits a low thermal expansion, similar to carbon, but achieves only lesser adhesion to the resin. It absorbs moisture and is sensitive to ultraviolet radiation. Although it is flammable, it features a good-natured behavior in the case of fire.Two basalt fiber products were selected for this study, made from raw material with different chemical compositions. The fibers are spun from a melt of crushed volcanic rock and their absolute stiffness and strength values are slightly higher than glass fibers. In high-temperature applications, the values fall below those of glass fibers .The good mechanical performance of stainless steel (1.4404) fibers is, compared to other technical fibers, relativized by its very high density. As a metal, it offers the possibility of being fully recycled by melting down. The stainless-steel fibers’ high electrical and thermal conductivities are not the primary concern in structural applications; however, if combined with carbon fibers, their high ductility can positively influence the failure behavior of components while maintaining a similar stiffnesses.For flax, two products were also selected, a circular yarn and a flat tape. The tape allows for having parallel fibers, whereas the yarn has 20 tpm (turns per meter). Among the plant-based fibers, flax has the highest stiffness. In contrast to carbon fibers, flax has a lower density since it presents a hollow fiber structure. The flax yarn used had a European origin and received only an alkali washing by the manufacturer While the bio-degradable flax fibers were extracted from the stem of their plant.2 can be saved. Cotton was used as a crochet thread, to bind the individual fibers of the hemp together to a coherent fiber bundle. The density of the hemp card sliver used (0.86 g/cm3) was lower than the literature values for hemp yarns  from the winding head, and allows damage-free collisions by swerving upwards. Sudden increases in the TCP velocity should be avoided to keep the fiber tension low, especially when processing natural fibers. The design of the winding head allows for fiber bundle retraction if the ceramic ring is not installed or does not become loose. The maximum retraction length is given by the distance from the upper ceramic eyelet to the current resin fill level in the system.The objective of the structural testing was to obtain comparative characteristic values for the mechanical performance parameters of the complete selection of materials and to provide a comparative evaluation of them for the subsequent sustainability assessment. In this context, the sample fabrication should exhibit the CFW process characteristics as comprehensively as possible. Due to the wide variation in bundle diameters of the selected fibers, it is not easy to design a setup that keeps the relevant cross-sectional area of the samples constant for all materials. In addition, due to the variability of the mechanical properties of these materials, the failure mechanism and location of tensile and compressive testing commonly used in CFW ,49 are nAs a remedy for this study, a specific sample with some geometrical adjustments  was desiTo maintain CFW fabrication characteristics but obtain comparable geometries, the samples had to be produced in a hybrid CFW process using an aluminum mold . The desThe fiber materials were dried before processing, reducing the influence of moisture. The fibers were placed without crossings during the winding, except for the last layer, while counting the repetitions. After thermal curing of the resin, the bolts were unscrewed, the samples were removed from the mold and PTFE foil, and cut to length. Prior to testing, the sample dimensions as well as the weight were measured, and the average densities were determined. The sample volume can be measured via the outer geometry (cuboid) using a caliper or utilizing the Archimedes’ principle by weighing it in a liquid with a known density and temperature .The fiber bundles needed to fill the cavity spans from 2 for the hemp (H), and up to 300 for the aramid (A). This difference demonstrates the substantial variation in the linear density of the selected fibers. The average variation in sample height was only 6.5% of the one for the sample width. There was no correlation between the number of required bundles and the variation in cross-sectional dimensions, nor between the variation in the sample height and width. For example, the S-glass (G2) exhibited the highest deviations in the cross-sectional between samples, and the stainless steel (S) the lowest. The sample mass ranged from 22 g for the aramid (A) to 41 g for the stainless steel (S). Moreover, while the aramid showed the lowest deviations in mass between samples, the highest deviations were found in the basalt (B2), S-glass (G2), and hemp (H). The last two also entailed the highest deviations in both volume parameters. The average fluctuation in the geometrically determined volume was 16% higher than in the volume by Archimedes’ principle. The latter volume parameters averaged only 86% of the geometric volume ones, which is plausible since the geometric volume overestimated the actual sample value due to curvature on the sample edges.The inner composition of the samples must be determined for structural calculations and for an environmental impact assessment. The reference quantity for structural analyses is the volume or cross-sectional area of the sample, while for material consumption analyses, the relevant one is the mass. The presence of voids is reflected only in the volume-related variables, as such cavities that are filled with air, which is weight-neutral. The results are shown in the following parameters: fiber volume ratio (FVR), resin volume ratio (RVR), void volume ratio (VVR) as well as fiber mass ratio (FMR), and resin mass ratio (RMR). The volume and mass ratios can be converted using the densities of fiber and resin material by neglecting voids (Equations (1)–(4)):d filament/fiber diameter,f number of filaments/fibers per roving/fiber bundle,r number of rovings/fiber bundles,a relevant cross-sectional area of the sample.These conversions highly depend on the reliability of the densities of fiber yrolysis  is not pT linear density of the roving/fiber bundle.If the filament diameter is unknown, it can be measured from microsections or by a micrometer screw, especially for thicker filaments. In case the number of filaments/fibers is missing, it can be calculated by:l sample length,and then to convert it via Equation (1). This method entails the uncertainties of the fiber and resin densities. The linear density can be determined by measuring the length and weighing of the dried roving/fiber bundle. The sample mass can be measured on a scale if the material is equally distributed over the relevant section of the component. There are also alternative methods to get the FMR via the sample volume as:The number of rovings at a certain location in the fiber net can be identified by the winding plan . It can and then converted into the RVR using Equation (3). Fiber and resin consumptions can also be read from the fabrication protocol, which should include the weight of the fiber bobbins and resin containers before and after the winding. This method is only useful if resin leakage can be neglected and fiber cutoffs are absent or logged. The VVR can then be calculated as:This method may be beneficial if the cross-sectional parameters are more complicated to determine than the total sample volume, which can be calculated from geometry By using the FVR calculated via the cross-sectional area (Equation (5)), fewer uncertainties are incorporated. Alternatively, the VRR can also be obtained via the density of the sample as:The theoretical compressed samples density is given by:Applying these equations to the produced four-point bending samples results in the following characteristic values .(area) for the technical fibers C–A was in the range between 38–25%, whereas the value for steel was at 10%. Based on previous experience in CFW on carbon and glass fibers, this value is remarkably low, especially the one for steel. The hybrid winding technique used in this study can be identified as the main contributor to this decreased FVR (area) values. The mold prevented the drainage of resin during the winding and curing stages. For the natural fiber types V–J, the FVR (area) covered a comparatively larger range, between 19–56%. The scatter between samples of the same fiber type was 62% larger on V–J compared to the technical fibers. The natural fibers incorporated higher fluctuation in the material parameters. Interestingly, the highest FVR (area) was achieved in the flax tape, which also had the highest values for the VVR (area&mass). Since the RVR* (mass) was converted via Equation (3), it showed the higher standard deviation of all materials. The FVR (area) of the flax yarn sample was lower than the one of the tape and both were to be expected. The VVR (area&mass) for the aramid was calculated to be −6.2%, which as a negative value is not plausible. It can be assumed that the VVR for the aramid was very low due to the comparatively high number of rovings per sample. For carbon, the petroleum-based resin samples showed higher values in the FVR (area) and the FMR (mass) compared to the respective bio-based sample sets. This ratio was reversed on the flax tape samples.The internal composition of the samples can be given with respect to the sample volume a or mass(mass) ratios and their standard deviations; however, the FMR (mass) values were higher, between 32–93%, which can be explained by the ratio of the densities between fibers and resins. Obviously, very high values such as those for the flax tape should be used with caution. It can be noticed that the outlying value for steel is no longer present in the mass-related analysis. Compared to the technical fibers, the natural fibers V–J showed, on average, a 46% larger standard deviation between samples of the same fiber type.When considering the ratios related to mass b, the sa(vol) strongly underestimates the real value, as the sample geometry is assumed to be a cuboid. The FVR* (den) is used instead since typical CFW geometries cannot be well approximated using cuboids. Compared to the FVR (area), the FVR* (den) underestimated the ratio on average by 49%. The standard deviation on the FVR* (den) ratios was compared to the area-based volume ratios (Both methods using the sample volume as an input (Equation (8)), become useless when applied to the natural fibers c. For the ratios a 4.2 time ratios b 2.3 tim(area&mass) and the VVR (den) ((den) scattered 76% more than the VVR (area&mass) if averaged over all material types.Although the ratios calculated by volume are not reliable, there was a good match for all samples except B2, A, and H when comparing the VVR VR (den) d. The VV(area) should be used and for a calculation referring to mass, the FMR (mass) should be used instead. This differentiation avoids including the uncertainty of the density-related conversion equations. Area- and mass-related methods should be preferred over volume-based methods, especially when applied to natural fibers.In conclusion, for volume-based calculations, the FVR Generic cylindrical components were coreless wound to test the fabrication suitability of the various selected materials using the developed equipment. The winding fixture  for thosThe winding syntax of the samples started with a sine–cosine-shaped edge reinforcement, followed by a fiber bridge connecting both sides, and the repetition of the edge reinforcement sub syntax on the other side. Then, the sub syntax followed that formed the component. Here, after each hooking, the side was changed with the shift between winding pins, and the fixture was rotated in the traveling direction to maintain the working area. At the end of this sub syntax, another edge reinforcement per side was wound connected by a second fiber bridge. The edge reinforcements sub syntaxes could be carried out several times, especially for fibers with a low linear density. After curing the resin, the fixture could be disassembled, and the sample removed.The switch from petroleum-based to bio-based epoxy resin did not impact the winding equipment. Although an increase in resin leakage must be expected with a decrease in viscosity, this was not the case with the bio-based resin. The sample size and the consequential duration of a winding session were not big enough for the pot life to make a difference. The only noticeable impact of using the bio-based resin was that curing could not take place at room temperature. During the curing of the bio-based resin in the oven, its viscosity dropped before the crosslinking process was sufficiently advanced to prevent the resin from flowing down due to gravity. Thus, samples accumulated resin on the side that was facing downwards. The thicker the fiber bundle, the more pronounced this effect became. In extreme cases, resin dripping from the component could also be observed, which increased the FVR of the component locally during curing. The uneven distribution of the resin can be detected by measuring the cross-sectional area of the fiber bundles along the sample. An uneven resin distribution has a negative impact on the structural performance of such a component. Rotating the sample during curing could reduce this effect.For each fiber material processing, the ceramic eyelets and the setting of the ceramic ring in the winding head had to be adjusted. The setting with the lowest deflection possible at sufficient impregnation of the fiber bundle core was selected.Carbon a and glaWith a setting with a lower deflection, the viscose roving e was notDue to the high linear density of hemp h, major In this study, except for the flax fibers, all selected natural fibers showed a significantly higher resin consumption per sample than the benchmark fibers, carbon and E-glass. When scaling up this CFW process with natural fibers to an architectural scale, two further general process characteristics would apply to any fiber material with lower mechanical properties, namely, the free-spanning fiber length and the fiber tension during winding should both be limited. The tension should preferably be actively controlled since tension peaks exceed the ultimate strength of the weaker material quicker. Unanticipated fiber rupture is a safety hazard to personnel, which usually happens at the winding pin or the winding head nozzle. By limiting the distance between the TCP and the last winding pin, sagging at low fiber tension levels can be avoided.As described in Compared to the other investigated materials, the stainless-steel samples showed the most brittle failure behavior. All steel samples (S) exhibited a complete fracture into two or three pieces, triggered by tensile stresses in the lower center of the sample type J—j. CarbonIn contrast to the mentioned technical fibers, the behavior of the natural fibers was mostly ductile with large areas of strain hardening. Only basalt (B1 and B2) and the flax yarn (F2) also presented necking areas before failure. Whereas the flax tape (F1) was dominated by failure type D , the usage of the petroleum-based resin with flax (F1*) changed the dominant failure type to B . The flax yarn (F2) showed more variable failure behaviors with type B combined with C, I, and A. Whereas the jute (J) failed by type B and viscose (V) by type C, the failure type on the hemp samples (H) was not identifiable. The variations in the manufacturing process caused the failure deviations in the same sample type, whereas between the different materials the ratios in the mechanical properties of the fiber and resin were decisive. Carbon and flax tape were investigated with both the bio-based and the petroleum-based resin. A higher ultimate strength could be found for the petroleum-based resin in both cases . This ef(area) was observed in the steel, jute, flax tape, and E-glass. All these materials performed relatively better than their datasheet value would predict. Although the highest VVR (area&mass) was found in the flax tape and basalt, no performance anomalies reducing the stress at failure could be found.(mass) did not equal to good impregnation. Having a similar FVR (area), both versions of the carbon samples (C and C*) and of the flax tape (F1 and F1*) should have similarly or slightly better performed, as the bio-based resin was higher in strength than the petroleum-based resin  and both basalt types (B1 and B2), where the behavior trend was not maintained, and the results showed a significantly lower performance than in the literature. The measured performance of viscose and steel fibers was also outside the expected range but from the upper bound. These results show that it is not reliable to fully trust data sheet information for CFW. In all cases, deviations have to be attributed to fabrication issues. It is remarkable that the interquartile ranges of the boxplots in relation to the length of their whiskers were larger on the technical fibers, showing the difference in uncertainties between both material groups.giving appropriate results for initial assumptions of the bundles’ tensile modulus. This conservative reduction is necessary because the CFW structures entail voids that prevent the bundles from properly bonding, which is one of the necessary assumptions to apply to the ROM. Moreover, deviations in the FVR along the same sample can create deviations in the real stiffness of the specimen. The flexural modulus calculated from the bending test was expected to be slightly lower than the tensile modulus, but it should have shown the same trends. The calculated ROM was based on the datasheet values for the material ((area) ((area) influence (The Voigt estimate or rule of mixtures (ROM) can approximate the longitudinal tensile modulus  . Therefonfluence .(area) and VVR (area&mass) of these samples were remarkably high , the results matched the prediction in this case. The comparison in stiffness between both resin types used, did not show a significant difference; however, a decrease could have been predicted based on the resin material properties . This approximation resulted in two cases. In Case 1, the structural depth was calculated for each sample so that it would fail at the same force level as the average carbon (C) sample. The formal relation describing this is:In Case 2, the structural depth was calculated for each sample so that it exhibited the same spring stiffness as the force over the strain at failure. Which expresses to:The method can be used to understand the relative performance and how these scaling factors could be used for design, as structural depth adjustments are common practice in structural engineering to increase both strength and stiffness.For the sustainability assessment, each sample’s theoretical resin and fiber consumptions in grams were calculated based on the adjusted structural depth , the reaAs the values used for these calculations do not correspond to the actual products but are just taken as a reference from the literature, the graphs’ whiskers in 2. The carbon showed a substantial contribution to both sustainability markers. The glass and basalt presented the lowest embodied energy, while for GWP, the lowest was flax. The resin contribution was more relevant with samples with a higher FMR (mass) or with fibers with low mass-specific markers, as in the case of the jute. It could also be seen that using bio-based resin helped to reduce the environmental impact, especially in terms of the embodied energy requirements. This reduction was recognizable by comparing C and C*. As the flax (F1 and F1*) samples FMR (mass) were high, this effect could hardly be found in those samples. The flax fibers seemed to be the most suitable material among all the investigated fibers, regarding both its mechanical performance and environmental impact. The deployment of bio-based resins can be justified in this comparison if a lower FMR is present.In comparison to its performance, the aramid required the highest amount of energy to produce and generated the most COThree different assessments were used in this study: fabrication suitability, structural performance, and sustainability of the selected materials. It should be noted that other crucial aspects not considered, such as long-term behavior and fire resistance will play an important role for real applications.The structural performance of CFW full-scale structures will highly depend on the consistency of the fabrication; it was essential to reflect the technique uncertainties in the samples to be evaluated. Due to this reason, two types of specimens were designed. One resembled geometry and fiber interaction on a small scale to test the fabrication difficulties of new material systems. The other was a simplified coupon test to compare the structural performance of the materials. For the second sample type, a tensile and compressive axial loading evaluation would have better represented the actual mechanical performance of a CFW structure; however, the four-point bending tests allowed the comparison between the significantly different mechanically performing materials with a common reference parameter, and the structural depth of the sample. Due to the adjustments in sample geometry required by some fiber types, the presented test results of this study may not be directly transferable to other four-point bending results from the literature. Nevertheless, they allowed for obtaining reasonable and comparable results in terms of strength and stiffness, also uncovering possible detriments in the performance resulting from fabrication issues, such as impregnation issues of the fibers or consolidation of the bundles.The sustainability assessment performed was not meant to give final results but to demonstrate the range in which each material scores. Specific information from each material supplier needs to be collected in order to perform a proper sustainability assessment which was outside the scope of this paper. A complete assessment should also be undertaken for all stages of the material’s life cycle. Further important aspects such as respiratory effects, aquatic contaminations, carcinogens, and land occupation should be included. It is also not entirely realistic to only perform the evaluation at a specimen level; large-scale applications could show different results as the scalability effects have not been investigated. In this study, the results rely on values collected from the literature and are limited to only two markers; however, these results reveal several important aspects. Firstly, the potential of some of the materials in terms of sustainability compared to carbon and glass. Secondly, the variability in the sustainable ranges coming from different suppliers and manufacturers, making crucial the detailed investigation of these aspects prior to the material product selection . Thirdly, the lower bound of this range can be frequently associated with developments in the manufacturing processes, namely, towards more sustainable processes. In this context, it is remarkable that the lower range of carbon, especially in terms of embodied energy, matched the upper values of some natural fibers.In future studies, apart from a testing-supported sustainability assessment and fabrication-related issues, more aspects should also be considered, such as resistance to environmental impacts, aging by ultraviolet irradiation and discoloration, nesting of pests, fungi growth, fire behavior, water absorption, scalability, and design requirements. It should also be taken into account that the absolute numbers of the ecological impact are linked to the available energy mix, which may change with time.The novel fabrication technique of CFW produces components with high uncertainties at a macro-structural level coming from fluctuations in the process parameters and the resulting geometry. Substituting the currently used carbon and glass fibers with natural fibers brings additional uncertainties as their properties’ variations translate to an additional inconsistency at the material level. Unpredictable stronger fluctuations translate to higher safety factors and higher material consumption. Since natural fibers generally present a worse mechanical performance compared to the benchmark, it can be expected that significantly increased fiber consumption is needed to achieve the same component structural performance. Higher fiber consumption also translates into a higher resin consumption and this effect could be so dominant that it could affect the design strategies for CFW.In terms of fabrication, a higher material consumption would manifest into large-scale winding setup designs that tend to use external resin supplies. Fiber feeds would also be needed to reduce the traveling of highly resin-saturated fibers, either by deploying pre-tows or by a direct impregnation system. Another effect would be that winding pins would need to be increased in number or size to accommodate the larger amounts of natural fibers. It should also be noticed that more material for the same component would result in a different architectural appearance, which should be considered for its design.The system’s scalability in terms of structural capacity should also be evaluated. The increment of material for less performative fibers is not always linear. Structural behaviors such as low stiffness or high ductility can be exponential and critical when scaling up the material system. Even when increasing the material amount correspondingly, it can be expected that not all the materials can be suitable to substitute carbon and glass fibers at any scale or design strategy, especially in long-span applications. This study does not cover the structural system’s scalability effect, a topic that should be further evaluated in future works.In addition, the adjustments performed in the fabrication domain were designed and proved effective for producing smaller CFW samples; however, some aspects may require further adaptations to transition into a larger architectural scale, such as hairiness, tension limitations, production sessions over several hours, accommodation of the higher material consumption, and different curing methods. Especially for longer winding sessions, fiber fragments generated by natural fibers with pronounced hairiness must be expected to accumulate. Prolonged continuous production may result in a detachment followed by a dislocation of such an accumulation, possibly reducing the diameter of feedthrough in the winding head and thus leading to either reduced resin flow or fibers becoming stuck. This characteristic can be mitigated by reducing the fiber deflection setting, a gentler fiber handling of the dry fibers, providing additional buffer volumes inside the lower impregnation chamber to catch any accumulation, or applying a safety factor to the diameters of the feedthrough. The latter measure is not recommended with natural fibers as the diameters must already be designed relatively large due to the geometrical inconsistencies along the fiber bundle.It should also be considered that the amount of material processed simultaneously will have to be increased in large-scale productions compared to the material consumption in this study. This adjustment will avoid the proportional increment of the duration of winding sessions, which is limited primarily by the pot life of the resin. To achieve a higher material processing rate, multiple impregnation chambers, one per fiber bundle, should be used in parallel instead of a single chamber processing multiple fiber bundles.On a larger scale, it would be preferable to use a continuous dryer instead of an oven to set the humidity content of the natural fibers. This adjustment would also avoid any adverse effects on natural fibers resulting from too long or a repeated drying process step. In order to improve fabrication robustness, it would also be advisable to implement an active tension control to the equipment. During curing, a rotation of the samples to achieve a homogeneous resin distribution on hot-curing resin systems with a noticeable drop in viscosity can be needed. This process can be realized on a large scale by an additional rotational axis in the component, which is already usually attached to increase the reach of the robotic system.Not only the material amount increment and scalability of the system needs to be considered when implementing natural fibers into the CFW process. Further adjustments need to be designed to mitigate the adverse influence of the fibers’ lower mechanical properties.The limitation in winding tension that applies to fibers with lower absolute strength per fiber bundle, as with natural fibers, is even more crucial with large-scale production because of the longer distances to be traveled between the winding pins, requiring a higher fiber tension. The fiber tension can be calculated according to the catenary equations. This issue could only be solved by geometrical adjustments on the component or by reinforcing the fiber bundle. Geometrical adjustments to reduce the traveling distances could include changes in the winding syntax or a different clustering or position of the winding pins. These adjustments would have a considerable impact on the design strategies. On the other hand, a reinforcement of the fiber bundle could happen by introducing small amounts of a higher dry-fiber-strength fiber material as was already completed in a recent application . To implFor materials with lower stiffness, another effect occurs. When spanning the fiber between two points , the sagging on such materials would be comparatively high. The deflection of the fiber could exceed a tolerable threshold when increasing the distance between both points. This issue could be avoided by applying the same measures as for low-strength materials. Another solution could be implementing a passive tension control at each winding pin. As the pins would move to maintain a constant tension, adapters would be needed to connect to other components later.The fiber bundle type, which also influences the dry fiber’s mechanical performance, needs to be taken into account. Tapes would have a better structural performance as they are aligned with the expected axial load but would require more adjustments for winding, as previously explained. Yarns are more suitable for winding, but the twist can bring difficulties in the impregnation and the macroscopic bonding between fiber bundles. In this study, the effect of a missing consolidation was not as prominent as it could be in CFW applications, as the samples were produced in a half-open mold. Therefore, a loss in the structural performance of the flax yarn could be expected in large-scale components, which solely rely on consolidation by curvature and pressure applied by the robot pull when winding. With the fabrication adjustments in this study, the flax tape performed better than the flax yarn. This behavior can be justified by the difference in FMR and the better consolidation of the tape. Adjusting the winding process to include a subsequent complete consolidation step entails several economic disadvantages and design limitations to CFW; however, this step could be a valid option to increase the FMR when adjustments to the equipment fail to achieve it.This study investigated several aspects: the adjustments needed to the fabrication equipment and processes due to the characteristics of natural fibers, the suitability of selected fiber materials for the CFW technology, and the structural performance and sustainability assessment of the selected alternative fibers supported by structural testing. The aim was to determine if such alternative materials could offer a more sustainable option for CFW than carbon and glass fibers with a petroleum-based epoxy resin. The ranking was normalized in sample performance for the four-point bending test. For reference, two sustainability markers were used: the embodied energy and the global warming potential for raw material production, obtained from the literature.It was confirmed in this study that the inconsistencies of natural fibers add to uncertainties in the parameters of CFW components. This variability affects the geomaterial parameters, their inner composition, and as a result, also the structural performance.(area), whereas mass-related calculation should be based on the FMR (mass). Converting between FVR and FMR should be avoided, as this would include further uncertainties. Especially for natural fiber composites, methods based on the sample area and mass should be preferred over volume-based methods, such as cuboidal approximation or applying Archimedes’ principle.For CFW, the void content should not be neglected, and especially not for natural fibers. The volume-based calculation should rely on the FVR The hairiness, tension limitation, worse impregnation characteristics, and water absorption characteristics entailed by naturals fibers can be mitigated by winding equipment adjustments and process adaptations.The inclusion of natural fibers affects large-scale winding setup designs so that they tend to rely on pre-impregnated fibers or a direct impregnation with a resin feed. Adjustments to the size or arrangement of the winding pins or to the winding syntax are needed. Additional elements to help with impregnation and a continuous dryer and tension control, preferably actively controlled, are also needed.The resin contribution could be reduced by decreasing the footprint of the resin or by increasing the FMR. Further fabrication adjustments or a subsequent consolidation of the structure can help to reduce this issue.In materials with a low FMR, the resin contribution is significant, which can justify using resins with a low ecological impact, such as bio-based epoxies; however, its higher mass-specific price also needs to be considered. In addition, the difference in the obtained FVR between petroleum-based resin and bio-based resin, produced by differences in the fiber’s impregnability by these materials, should also be taken into account.The highest lightweight performance is still exhibited by carbon in terms of stiffness, while glass is the better option over carbon for strength because of its economic and ecological benefits. Carbon and glass are not sustainable options if embodied energy and GWP are considered; however, when other architectural or engineering applications such as long-span and low deflection demanding scenarios, the current material choice could still be considered the most viable option.Aramid does not offer a higher mass-specific stiffness than carbon but exhibits significantly higher energy consumption and GWP, making it non-preferable for CFW.Viscose and steel showed a higher GWP than carbon, although a lower embodied energy; however, viscose especially cannot be competitive with other natural fibers and, therefore, it should not be used for CFW. The recycling potential of steel fibers, which can be fully recycled by melting them down, makes them worthy of further investigation, especially in a scenario where the components are recycled multiple times.Based on the approach in this study, flax is found to be the best overall alternative to C/GFRP in CFW as it balances both sustainability markers equally and presents a relatively high mass-specific mechanical performance. Flax also presents an economic advantage over carbon.Other materials, such as jute, basalt and hemp, would become suitable options if the resin contribution would be significantly reduced. Specifically, hemp could show a smaller ecological impact since it is a card sliver and not a finished yarn, which removes production steps and, thus, saves resources.Under economic aspects, the usage of jute fibers would be interesting, as its price range is low compared to flax . The basThe research on the alternative materials suitable for CFW application is just at its initial step. This study has uncovered the potentials of some of these materials and the possible future research directions. The investigation of other possible fibers or material combinations should also be considered. The number of sustainability markers could be increased, more products per material type, or a combination of those into a hybrid system could also be incorporated in the research; however, a deeper study on the design influences and scalability of the system is needed.Replacing virgin with recycled materials could subsequently also be investigated, such as recycled carbon fibers . They coUltimately, each material’s mechanical performance and design requirements should be integrated into the current computational design framework for CFW structures  as param


The rare earth extraction process has significant time delay characteristics, making it challenging to identify the time delay and establish an accurate mathematical model. This paper proposes a multi-delay identification method based on improved time-correlation analysis. Firstly, the data are preprocessed by grey relational analysis, and the time delay sequence and time-correlation data matrix are constructed. The time-correlation analysis matrix is defined, and the  The rare earth extraction process includes dozens or even hundreds of extraction tanks. The mixing speed and time of each group of agitators are different, which affects the reaction and transmission time of materials, leading to multi-delay, so a large amount of data cannot be effectively utilized. Current modeling studies of the rare earth extraction process do not consider time delay or take it as a constant ,2,3, resA series of solutions have been proposed for the problem of time delay identification. The step response method was used in the time delay identification of systems ,5, but tIndustrial processes have become complex with the rapid development of science and technology, resulting in multi-delay, and the abovementioned methods have been unable to meet practical requirements. Xie et al.  improvedThis paper draws on the successful application of the time-correlation analysis method  in the aTime-correlation analysis is a time delay identification method based on the relationship between data sequences, which has the advantage of high efficiency. This paper improves its shortcomings in data preprocessing and selection.Grey relational analysis (GRA) is derived from the grey system theory in system science . Its basCompared with traditional multi-factor analysis methods , this method has lower data requirements and less computational burden. It is suitable for quantitative analysis of the dynamic development process and hence can be used to analyze the correlation between a large amount of process data obtained from a production site and the content of rare earth elements.N work units be T is the sampling period, the delay sequence is ith work unit. The content of n rare earth elements and m process variables is obtained by k times sampling. The element component content jth rare earth element component content. The process variable data lth process variable data.Let the time base of a critical process variable in The original data are normalized to eliminate the influence of different dimensions on the results. Standard processing methods include initialization and averaging. This paper adopts averaging,lth characteristic variable corresponding to the content of the jth rare earth element component, and The correlation coefficient is used to express the degree of closeness between the index values of the comparison and reference sequence in grey relational analysis. The higher the value, the greater the degree of proximity,According to the correlation coefficient, the correlation degree between each process variable and the content of rare earth elements can be obtained asThe correlation degree is sorted from large to small. If ith unit outlet process variables, respectively. The process variable with the highest gray correlation is taken as the key process variable, and its standardized data E describes the degree of correlation between the data corresponding to the time sequences. Multiple time sequences are described by the time-correlation analysis matrix,E, whose standard deviation of column i is The matrix R is a time-correlation analysis matrix, which reflects the correlation degree of multiple groups of sequences under multi-delay. The A maximum value of the According to the extraction production site experience, each unit’s time delay during operation will fluctuate within a fixed range. Based on this, the time-base value range of key process variables can be determined as Equation  can be tIn summary, the steps of the improved method of combining grey correlation analysis with time-correlation analysis are as follows.Step 1: Based on the original data of the rare earth extraction process, the multi-delay sequence Step 2: Grey correlation analysis is used to identify key process variables and construct a time-correlation data matrix according to Equation ;Step 3: According to Equation , the timStep 4: The time delay identification results are obtained using Equation .There are many methods to solve the time delay identification. The discrete state transition algorithm (DSTA) has been successfully applied to typical discrete optimization problems such as Boolean integer programming  and stafDiscrete state transition algorithm is an individual-based optimization algorithm. Its basic idea is to regard the solution of an optimization problem as a state, and the process of updating the solution is called state transition. The standard form of the discrete state transition algorithm can be described asThe four special transformation operators  are as f(1)Swap transformation:(2)Shift transformation:(3)Symmetry transformation:(4)Substitute transformation:The initial solution is given randomly in the discrete state transition algorithm, and the solution significantly affects the convergence performance of the algorithm. DSTA easily falls into local optima in the iterative process. Therefore, an adaptive chaotic discrete state transition algorithm (ACDSTA) is proposed by introducing the opposition-based learning strategy, chaotic perturbation strategy, and adaptive recovery strategy.The initialization method of the discrete state transition algorithm has the problem of uneven distribution, which somewhat affects its optimization efficiency. Therefore, an opposition-based learning strategy (OBL) is introduced to initialize the discrete state transition algorithm. OBL  is a macD-dimensional space. The reverse solution based on OBL is Let Based on the idea of OBL, the best initial solution is selected asChaos comes from nonlinear dynamic systems. Because of its unique randomness, ergodicity, and complexity, it can effectively prevent the algorithm from falling into local optima, and it is widely used in optimization problems . We propThere are many rules to generate chaos, among which logistic mapping is common, but it has the problem of uneven frequency distribution. Zhou et al.  combinedThe chaotic variables generated by Equation  cannot bIn the iterative process of the discrete state transition algorithm, the chaos perturbation strategy is introduced to generate new solutions, which can effectively improve its ability to jump out of local optima. However, the new solution directly enters the next iteration, which will decrease the algorithm’s convergence performance. To only use the greedy criterion can no longer meet the convergence requirements. We propose adaptive recovery, adopting the greedy criterion to ensure the general convergence of the algorithm. The current value is restored to the preserved historical best value with adaptive probability to further improve convergence performance.P, P, The discrete state transition algorithm is in the stage of rapid optimization in the early stages of iteration, which greatly decreases fitness. The recovery probability should be small at this time, so as not to affect the searchability of the algorithm in the early stage of iteration. In the middle and later stages, the searchability decreases, and the optimal historical value should be restored with a large probability. We use a nonlinear adaptive adjustment method ,(17)P=–(12)) in turn;Step 4: According to Equation , judge wStep 5: Determine whether the condition of the chaotic perturbation strategy is satisfied. If so, generate the chaotic variable according to Equation , and theEquation  for the Step 6: Determine whether the iteration termination condition is satisfied. If so, terminate the search and output the final optimization result. Otherwise, return to step 3.Many applications in economics, chemistry, manufacturing, and other fields can be transformed into unconstrained integer optimization problems. To verify the feasibility, superiority, and applicability of ACDSTA, three functions of unconstrained integer optimization problems  are seleThe algorithm was simulated using an Intel Core i5-11300H CPU at 3.10 GHz, with 16.00 GB RAM, Windows 10, and MATLAB R2018a, and compared with particle swarm optimization (PSO), DSTA, and DSTAI , based oThe maximum numbers of iterations of ’s study .The average error, average value, and accuracy of optimization From In summary, ACDSTA was superior to the other algorithms in the test of unconstrained integer optimization problems, especially when the dimension and optimization range were extensive, which can better reflect the advantages of ACDSTA. This demonstrates the feasibility, superiority, and applicability of ACDSTA when solving practical engineering problems.Rare earth extraction is the obtaining of a single rare earth product from rare earth liquid, extractant, and detergent through specific equipment. We use the praseodymium/neodymium (Pr/Nd) extraction and separation process as an example, as shown in The extractant is added from the first stage, and it flows from left to right through the stirrer. The detergent is added from the There are many extraction stages, and it is necessary to control the content distribution of Pr/Nd components in the tank to ensure the stability of product quality. It takes several hours or more to cause changes in the content of the export grade Pr/Nd component due to changes in the flow rate of the feed solution, extractant, and detergent. Therefore, it is necessary to obtain the residence time of materials in each unit group for timely control.To verify the ability of the proposed method to solve the engineering delay problem, the delay identification of the 30-stage Pr/Nd production process in a rare earth extraction plant was carried out. During the Pr/Nd extraction process, the content of Pr/Nd components in different tanks changes with time, which leads to a change in the color of the solution. Therefore, the characteristic color variable of the solution image can be selected as an auxiliary variable to identify the time delay.E was obtained.The sampling period was 5 min, and 220 groups of data of Nd component content and color characteristic variables  were selected in the continuous stable production process. The grey correlation method was used to analyze the correlation between Nd component content and color characteristic variables. The results are shown in E is constructed, and the time delay sequence solution is transformed into the optimization problem by Equations (5) and (6), as shown in Equation  was proposed, using an opposition-based learning strategy to initialize and accelerate the convergence of the algorithm, and an adaptive recovery strategy to improve its convergence performance. A chaotic perturbation strategy can improve the ability of the algorithm to jump out of local optima. An experimental comparison with three unconstrained integer optimization problems showed that ACDSTA can effectively solve such problems, and verified its effectiveness, superiority, and applicability; An improved time delay identification method was proposed to solve the problem that the data are not preprocessed and are randomly selected in the time-correlation analysis method. The method was applied to the time delay identification of a rare earth extraction process. The superiority and effectiveness of the proposed improved time delay identification method were verified by comparing the time-correlation analysis method and the data without the identification method under the same Nd component content. To sum up, the proposed time delay can provide a reference for modeling the rare earth extraction process and has guiding significance for the improvement of the online detection accuracy of component content.