This paper introduces a new method which facilitate the use of smartphones as a handheld low-cost mobile mapping system (MMS). Smartphones are becoming more sophisticated and smarter and are quickly closing the gap between computers and portable tablet devices. The current generation of smartphones are equipped with low-cost GPS receivers, high-resolution digital cameras, and micro-electro mechanical systems (MEMS)-based navigation sensors . These sensors are in fact the essential components for a MMS. However, smartphone navigation sensors suffer from the poor accuracy of global navigation satellite System (GNSS), accumulated drift, and high signal noise. These issues affect the accuracy of the initial Exterior Orientation Parameters (EOPs) that are inputted into the bundle adjustment algorithm, which then produces inaccurate 3D mapping solutions. This paper proposes new methodologies for increasing the accuracy of direct geo-referencing of smartphones using relative orientation and smartphone motion sensor measurements as well as integrating geometric scene constraints into free network bundle adjustment. The new methodologies incorporate fusing the relative orientations of the captured images and their corresponding motion sensor measurements to improve the initial EOPs. Then, the geometric features  visible in each image are extracted and used as constraints in the bundle adjustment procedure which correct the relative position and orientation of the 3D mapping solution. Over the past two decades, mobile mapping systems (MMS) have been a vital source of direct geo-referenced data, which can be used for a variety of applications  data updates). Although land-based MMS is one of the main sources for acquiring direct geo-referenced data, there are many drawbacks to using the current MMS  and GNSS receivers) which have restricted their widespread adoption in the survey and mapping industries. Consequently, the market for land-based MMS is small, and the existing MMS typically are operated by the companies or institutions that built them, which unfortunately means that their more efficient data collection is not available for wider use . The resThe proposed system overcomes the drawbacks of the current MMS  that have restricted their widespread adoption in disciplines which demand meter-level accuracies . The development of such a system will satisfy the demand for a MMS that can compete both in cost and in user-friendliness with current terrestrial photogrammetry. The proposed system does not attempt to replace existing MMS, rather, it offers new low-cost alternative for applications requiring one to five meters accuracy. The GPS receivers used in most of the current smartphones  have poor positioning accuracy. Furthermore, the MEMS sensors, especially gyroscopes, will accumulate position drift over short time because of their high signal-to-noise ratio over time. Furthermore, magnetometers can be easily disturbed by the presence of metallic objects in its vicinity. Although these sensors offer the ability to acquire direct geo-referencing data, their low-level sensor measurements can lead to inaccurate exterior orientation parameters (EOPs) which, in turn, decrease the mapping accuracy of the system. These erroneous EOPs must be corrected before calculating the final 3-D mapping coordinates of the points of interest. Therefore, a relative orientation approach is introduced in this paper to refine the initial EOPs. Then geometric features  are extracted, matched, and used to impose constraints on the object space calculation and adjustment inside the bundle adjustment model. The coplanarity constraint  is a welThe process of integrating geometric constraints into bundle adjustment has generated a lot of interest within the photogrammetric community. McGlone ,10 incorCurrent smartphones integrate on one platform low-cost GPS receivers, barometers, cameras, IMUs, and magnetometers, which are the ideal MMS components and have the key advantages of low cost, small size, and easy availability. A limited number of studies in the literature have investigated the use of smartphones for mapping applications. Al-Hamad and El-Sheimy ,16,17 deFurthermore, the errors of the MEMS sensors, used in smartphones, typically change over time (due to changing temperature) and from turn-on to turn-on of the smartphone ,22. AlsoAn iOS software application was developed to capture and synchronize the images with their corresponding GPS and motion sensors measurements (location and orientation) at the time of exposure. As illustrated in The main objective of this step is to find the relative rotation between each two images based on the absolute 3D rotations, which are directly acquired by smartphone’s motion sensors. These relative rotations are then used to evaluate the accuracy of each absolute rotation when compared with the SfM rotations.The IMU along with magnetometers are used to obtain the direct 3D rotation of the smartphone instantly when the smartphone’s camera captures an image. The accelerometers sensor in the IMU are used to obtain the pitch and roll angles, which are rotation angles around the iPhone x-axis and y-axis respectively. Whereas, the magnetometer is used to derive the heading angle of the iPhone, which is measured w.r.t the iPhone y-axis as illustrated in These Euler angles are used to compute the rotation matrix In photogrammetry, the desired orientation is related to the involved camera frame. Therefore, the Euler angles derived by the IMU (inside the phone) are used to determine the photogrammetric orientation angles  utilizing a boresight matrix as shown in Equation (2), where omega, phi, and kappa are the rotation angles around the camera x-axis, y-axis, and z-axis respectively: i) and mapping frame . j) and mapping frame. i) and image (j). These final absolute rotation angles are used to establish the Global Relative Rotation (GRR) between each two images in the network as expressed by Equation (3). For instance, if we have a network consisting of three images and we have the absolute EOPs acquired by the smartphone motion sensor, the RO between image 1 and image 2 can be calculated using these absolute EOPs: This procedure is repeated for each paired image in the network. These relative rotations then are compared to the relative rotations acquired by SfM algorithm in order to find the most accurate absolute IMU rotation, which finally will be used to rotate the SfM model to the mapping frame.As mentioned earlier, closed form solutions  are much faster and do not require initial approximations of the unknowns compared to the traditional coplanarity conditions. Therefore, SfM is adopted for initial relative EOP estimation. The process of the SfM algorithm begins with the automatic computing of modified coplanarity condition using overlapped image pairs with at least eight or five matched tie points depending on the previous knowledge of the IOPs. The modified coplanarity condition is based on computing the essential matrix, which used to estimate the transformation parameters between each image pair. The initial EOPs of the network w.r.t the first image, are established via successive resections to compute the position and orientation for each image in the network, whereas, the initial 3D coordinates of the tie points are computed using successive intersection. These relative preliminarily EOPs and 3D coordinates of tie points are then refined using Bundle adjustments with adoptive (non-strict) outlier rejection tolerances ,24. The main idea of this process is to compare the GRR derived from IMU with the corresponding RO obtained by SfM model. However, the GRR derived from IMU are computed for each paired image in the network. For example, the third image is considered a reference for the relative coordinate system based on IMU rotations (GRR), hence the GRR of any image is computed w.r.t the third image. However, the RO obtained by SfM are obtained with respect to the first image in the network. Therefore, new workflow is introduced to make each image in the network reference, one at a time, for the SfM model, while the EOPs of other images are computed relatively to the new reference image ith instead of 1st image. Therefore, The workflow begins by rotating each image to the chosen reference image, which is illustrated in As mentioned earlier, the objective of this step is to identify the image that is directly geo-referenced with the most accurate IMU rotation angles, where it can be used to rotate the SfM model to the global frame. Therefore, once the GRR and the SfM’s relative rotation for each paired image in the network are obtained, the difference between each corresponding rotation is calculated using Equation (6) as illustrated in The difference  and (7), the norm value is used to reconstruct a (n by n) matrix that consists of the difference, where n is the number of images in the network. For example, for a network consisting of three images, the norm of the difference matrix  ,25. TherAs shown in The GPS chipset built into most smartphones does not provide raw measurements, such as pseudorange or carrier phase. The user can only log the final position solution with its standard deviation as calculated by the iOS or Android API system . As a reThe mapping scale can be determined using the ratio between two distances. One of which is obtained in the SfM arbitrary coordinate and the other one is calculated in the actual mapping  coordinate as expressed by Equation (9):These distances can be calculated either between two points or two camera locations. Hence, the distance between two images is employed in this method. The mapping scale can be acquired using a traditional technique, which measures the distance between two points using measuring tape or imaging an object with a known length. The two distances are used to derive the scale value as shown in Equation (9). Although this technique is the most accurate one, it requires user interference in the process. Therefore, some pedestrian navigation techniques  are adapted to calculate the scale automatically. Lee et al. developed a robust step detection algorithm against the dynamics of smartphones, which is based on the 3D magnitude of accelerometer measurements. This algorithm begins by filtering the acquired data using a low-pass filter, and then extracting the measurements corresponding to the smartphone’s motion. Then, the extracted motions epochs are classified as peak-valley relationships using adaptive thresholds that are based on step average and step standard deviation. Furthermore, the adaptive time threshold is used to correct the candidate peak and valley. This algorithm shows 98.6% step detection accuracy . As a result, this algorithm is adopted in this method to detect the user steps between two successive captured images as illustrated in The main challenge of validating the proposed scale method over a known reference distance is that it is impossible to start and end exactly over the start and end points of the reference distance. Therefore, image-based technique is introduced as well to determine the possible shift between the reference distance and the start and end distance estimated using the accelerometers. Two color coded targets are placed on ground with a 7.22 m distance between them. The diameter :Several validation tests were conducted to assess the performance of the distances measured by the accelerometers and the result indicated the presence of approximately 7 cm errors between the known truth distance and the proposed method.As mentioned previously, geometric information  that are visible in the captured images can be used as constraints to the bundle adjustment. These constraints are independently determined observations, capable of being added to the system equations in the normal matrix to ensure more reliable and higher quality solutions . Therefoa, ya; the perspective centre ground coordinates are The 3D object reconstruction is conducted using collinearity equations, which defines the mathematical relationship between the image and the ground coordinate system ,25 as exThe study in this paper aimed to develop a stable low-cost direct geo-referencing system that can be operated in any outdoor environment without the need for GCPs whereas, the bundle adjustment requires a fixed reference consisting of seven parameters, which defines the network datum. The datum is traditionally defined by at least three GCPs for indirect geo-referencing or very accurate GPS/IMU systems for direct geo-referencing. To overcome the datum deficiency issue, a free bundle-adjustment procedure was used. This procedure uses the inner constraint matrix (G) to remove the rank defect of the normal matrix ,28,29. TTo test the developed methodologies, an iPhone 6 was used to collect close range images along with their corresponding motion sensors measurements. As shown in The experimental data were collected over a small building located in a harsh environment, for both the GPS and magnetometers, where the building is surrounded by high buildings which could introduce multipath in the GPS signals. Moreover, the building is located close to large parking, whereby, the presence of vehicles causes magnetometers measurements. Such environment is very challenging for all MMS especially those with low-cost sensors.Zero-Order Design (ZOD), which is associated with datum problem.First-Order Design (FOD), which is associated with optimum network configuration.Second-Order Design (SOD), which is associated with optimum number of observations and their corresponding weighting scheme.Third-Order Design (TOD), which is associated with enhancing the network by adding more images, observations, and object points.According to Clive , networkThese precautions were considered in the planning stage of this experiment, more specifically the ZOD, FOD, and SOD, which are discussed in The initial EOPs and OPs were determined using the SfM algorithm, which provided a good shape for the network compared to the ground data collected using Total Station as shown in First the scale was determined using the distance between two successive images; then, the SfM model was rotated using the most accurate IMU data corresponding to one of the images. Finally, the GPS centroid was utilized to translate the network. The results of the transformation process and the corrected initial EOPs are illustrated in Then, the well-known intersection method was conducted to calculate the 3D coordinates of the desired tie points utilizing the image measurements and the corrected initial EOPs of the involved camera stations as illustrated in Although, the initial EOPs were corrected using the proposed relative orientation, they still contained some errors due to the uncertainty of the scale automatic determination and the low-cost sensor errors. Therefore, the corrected initial EOPs and OPs became the input to the free network adjustment; and all the selected OPs were included in the inner constraints matrix to fix the network as illustrated in Each of these lines is defined by two points that were measured manually to ensure the accuracy of extracting the same line in the overlapped images. The solution was obtained using the free network adjustment two times; one with and the other without adding the geometric constraints equations to the normal matrix. The inclusion of the linear constraints provided more accurate results as illustrated in As can be observed from To verify the robustness of the proposed methods, especially the relative accuracy; eight images out of the previously used network are considered as a new network as illustrated in In this section, the ZOD is considered to determine the network datum. Also, the impact of the mean precision (RMS) of the final 3D OPs by changing the standard deviation . First, the relative rotations are calculated w.r.t the first image in the network utilizing the SfM algorithm. Then, this procedure is repeated to make each image in the network a reference for the SfM model, thereby achieving the relative rotation between each two images in the network. However, to evaluate the absolute rotation for each image that are acquired directly by smartphones, these rotations are used to derive the relative rotation between each two images in the IMU domain. Hence, the difference between each corresponding relative rotation obtained in different domains are evaluated to identify the images that have the most accurate relative rotation. Then, based on statistical evaluation, the absolute rotation of one of these images is used to rotate the SfM model established w.r.t this image. Subsequently, this model is scaled using the ratio between two corresponding distances, where one distance is acquired based on a step detection algorithm utilizing accelerometer measurements along with a pedestrian navigation technique, and the other distance is measured from the selected SfM model. The network global absolute centroid is calculated using the acquired GPS solutions for all the captured images, and this centroid is used to translate the centroid of the SFM model to the global coordinate. Finally, the corrected initial EOPs are incorporated with the linear features constraints, and refined using free network bundle adjustment. The proposed methodology was applied to a small building that has well distributed GCPs all around the building facade. The proposed system and methodology showed promising results for applications that require three to five meters absolute accuracy. Although this system provided reasonable accuracy compared to the employed sensors and their uncertainty, future research should include finding a way to extract the scale without the user step length measurement, which can introduce large error in case the user step length is changed while walking between two images.


The brain is a paradigmatic example of a complex system: its functionality emerges as a global property of local mesoscopic and microscopic interactions. Complex network theory allows to elicit the functional architecture of the brain in terms of links (correlations) between nodes (grey matter regions) and to extract information out of the noise. Here we present the analysis of functional magnetic resonance imaging data from forty healthy humans at rest for the investigation of the basal scaffold of the functional brain network organization. We show how brain regions tend to coordinate by forming a highly hierarchical chain-like structure of homogeneously clustered anatomical areas. A maximum spanning tree approach revealed the centrality of the occipital cortex and the peculiar aggregation of cerebellar regions to form a closed core. We also report the hierarchy of network segregation and the level of clusters integration as a function of the connectivity strength between brain regions. Accordingly the functional architecture of the brain has been described in terms of patterns of communication between brain regions, treated as evolving networks, whose dynamics was found to correlate with behavioral outcomes5. Brain networks are characterized by a balance of dense relationships among areas highly engaged in processing roles, as well as sparser relationships between regions belonging to systems with different processing assignments. This segregation facilitates communication among brain areas that may be distributed anatomically but are recruited for processing specific tasks6. Along with that the integrated functional organization of the brain involves each network component executing a discrete cognitive function mostly autonomously or with the support of other components where the computational load in one is not heavily influenced by processing in the others7. In this quest for a constantly improving quantitative description of the brain and of the cardinal features of its functioning complex networks play a cr ucial role11. Specifically, it proved to be able to elicit both the scaffold of the mutual interactions among different areas in healthy brains12 and the local failure of the global functioning in diseased brains15. The use of complex network theory passed progressively from an initial assessment of basic topological properties18 to a more sophisticated description of global features of the brain, as small-worldness19, rich-club organization10 and topology21. However, a clear understanding of the functional advantage of a network organization in the brain, the characterization of its substrate and a description of brain regions aggregation as a function of the level of their interaction are still missing. In this paper, we show, for the first time, the hierarchical participation of brain regions to the whole network as a function of the weights assigned to the links among them, as well as the existence of a linear backbone of the human resting state functional network. Here the weight of a link between two regions represents the strength of correlation between the time-series of spontaneous neural activity within the two regions, as measured by blood oxygen-level-dependent (BOLD) functional MRI (fMRI)22. Specifically we interpret a functional connection between two nodes as the magnitude of the synchrony of their low-frequency oscillations, which is associated with the modulation of activity in one node by another one24 largely constrained by anatomical connectivity26. We used a percolation analysis27 to highlight the progressive engagement of brain regions in the whole network as a function of the connectivity strength. Subsequently, by means of the maximum spanning forest (MSF) and the maximum spanning tree (MST) representations28 we obtained the basal scaffold of the brain network, whose structure is characterized by a linear backbone in which few nodes  play a central role, even progressively increasing the spatial resolution or reducing nodes size.The intrinsic functional architecture of the brain and its changes due to cognitive engagement, ageing and diseases are nodal topics in neuroscience, attracting considerable attention from many disciplines of scientific investigation. Functional neuroimaging and electrophysiological monitoring provide multiscale and multilevel signatures of brain intrinsic functional connectomics, giving access to amount of data previously inconceivable and nowadays tricky to examine. In this framework complex network theoryWe explore the inter-subject variability with several approaches. We compute the standard deviation of pairwise correlation values across the 40 individuals and report it together with the average correlation matrix used for the analysis. Figure As next step, we compute the pairwise cosine similarity between the correlation matrices of subjects. We find high similarity between subjects Fig. , with fe4. Here, to avoid any arbitrary assumption we perform a percolation analysis27 on the whole network.The representative human functional brain network is often analyzed introducing specific thresholds to map the fully-connected correlation matrix in a sparse binary matrixWe rank correlations in increasing order. One at a time we therefore remove from the network the link corresponding to the actual correlation value in the list, then we delete it from the rank. Step by step, we explore the global organization of the network after link removals. Specifically, in Fig. plateau (stable state). The emergence and the number of plateaux shed light on the hierarchical structure of the network, their length unveils the intrinsic stability of certain network configurations after the removal of links. For the human functional brain network a remarkable hierarchy in the disaggregation process emerges from the comparison with a proper null model. The same percolation analysis is performed on the ensemble of 100 randomizations (Methods) of the observed correlation matrix showing a faster disaggregation in disconnected components with plateaux absent or of small length.When by going down in the list of correlation values, the removal of several links does not lead to the increase of the number of components, we have a flat horizontal pattern defined n to n + 1 components and show it in Fig. We compute the distribution of plateaux length looking at the increment of correlation values when the network passes from The percolation analysis highlights the existence of a not trivial functional organization of the human brain network. Here, we investigate it considering a filtered network where for each area all weighted links but the strongest are discarded. This approach gives rise to 36 disconnected components forming a Maximum Spanning Forest (Methods) with a new information on link directionality. It simply indicates that each source points toward its maximally correlated brain area and it is not necessarily reciprocated. Figure 24. All randomized correlation matrices exhibit a star-like organization of components in the MSF, while the number of modules of size 2 is dramatically reduced. Moreover, colors of linked nodes are completely random. In Figure We build the MSF of the 100 randomizations of the real network obtaining a number of components varying in the rangeAs next step, we link together all groups of nodes in Fig. The MST in Fig. The maximum spanning tree approach doesn’t provide any evidence about the internal connectivity of components observed in the MSF, as loops are not allowed. Here we show a number of snapshots of the network associated with specific percolation phases.We proceed in the following way: (i) we consider the correlation values associated with such percolation states as thresholds for the real network; (ii) we discard correlation values below them; (ii) we inspect the network formation process according to the strength of edges.The rationale behind this approach comes from the possibility to explore the level of segregation of brain areas and how they functionally and hierarchically integrate.The appropriate percolation states and related thresholds are chosen among the stable states of the percolation curve Fig.  considerFigures 27 and is characterised by some improvements21 among which it must be recognized the ability to detect newly disconnected modules from secondary components.In this paper we have reported the results of a network theory-based investigation of a large human fMRI dataset, aimed at assessing the basal architecture of the resting state functional connectivity network. We have computed the Maximal Spanning Forest (MSF) and the Maximal Spanning Tree (MST) for our population-wise brain. The former showed a peculiar composition of the basic modules composing the network, by revealing their structure as linear chains. The MSF reveals both intra- and inter-hemispherical modules, and the presence of small modules alongside with larger sub-networks. The MST, on the other hand, enables the classification of connectors and provincial areas. We also used a modified percolation analysis that retains the information on all the connected components of a given network. Such variation of the percolation analysis does not require the application of a threshold to obtain binary connectivity networks. By means of this technique, applicable to experimental correlation matrices, we showed hierarchically the progressive integration of brain regions in the whole organization of the connectivity network, which does not appear in a null model defined by constraining the spectrum of the observed correlation matrix. The percolation analysis here used represents a generalization of the classical one29. Remarkably, our percolation analysis unearthed the existence of a hierarchical organization of areas, clusters of areas and modules within the human functional brain network. The process of network aggregation from isolated components appeared slow - compared to the null-model - with the emergence of significant stable configurations identified by several plateaux in the percolation curve. This outcome suggests a progressive engagement of brain regions according to the local amount of connectivity, namely a network organization in hierarchical modules whose participation to the entire structure is progressively included as the links strength decreases. The sequence of stable network configurations that, from the single areas, leads to the fully connected network, can be achieved by choosing values associated with specific plateaux of the percolation curve. Although this is technically topological modularity it is remarkable that it reflects functional and anatomical features. For instance bilateral correspondence of regions belonging to the same module was obtained without the introduction of symmetry constraints imposed in the analyses, supporting the conclusion that a hallmark of large-scale resting-state networks is their inter-hemispheric symmetry30. Interestingly, descending the hierarchical staircase of the percolation we found that occipital regions as the cuneus, the lingual gyrus, the occipital superior and middle gyrus and the calcarine sulcus tended to form a densely interconnected module. Along with that, frontal, cerebellar and temporal regions resulted involved in different modules characterised by linear chains, which joined the occipital cluster, in a progressive integration process, through a nodal bridge represented by the precuneus. In particular, temporal and occipital lobes resulted connected thanks to the bridging action of the fusiform and the inferior occipital gyrus as expected by considering the local cytoarchitecture31. Thalamus, putamen, pallidus, hippocampus, amygdala and caudate (here refereed to as deep grey matter) was found to form binary bilateral modules that joined the whole structure at the end of the integration process. If on one hand the remarkable connectivity within the occipital lobe can be ascribed to an efficient coupling via the interplay of tangential intracortical and callosal connections32, on the other hand such connectedness could be ascribed to fixational eye movements33. In support to this observation, it must be noticed that in Parkinson’s disease patients, which present with eye movement disturbances that accompany the cardinal motor symptoms, the worse the oculomotor performance is, the more the regional functional connectivity is decreased34.As a complex system, the human brain is intrinsically organized into modules, creating a high degree of flexibility and adaptability of the system without fundamentally altering underlying structure35, is implicated in the elaborate circuitry associated with awareness36 and uniquely  characterized by the presence of Von Economo neurons38. On the other hand the fragmentation of the temporal lobe can follow the mosaic structure of its functional specialization. In fact it includes auditory sensory and association cortices, part of the posterior language cortex, visual and higher order association cortices, primary and association olfactory cortices and enthorinal cortex39. The grouping of other heterogeneous clusters is due both to spatial closeness  and to homofunctional specialization . The MST representation of the functional brain network scaffold was found characterized by a long linear structure, whose skeleton follows the anatomical spatial distribution of lobes , small chains linked alongside and a star-like structure (composed of cerebellar regions) at the end of one side. The main connectors along the main chain included: the cuneus/precuneus, the superior temporal gyrus, the superior occipital gyrus, the inferior parietal lobule, the medial orbitofrontal cortex/gyrus rectus and the VI lobule of the cerebellum. Notably, precuneus, inferior parietal cortex and medial orbitofrontal cortex constitute the Default Mode Network41, which is a crucial module of the whole brain network both for its functioning and as the first target of metabolic alterations both in neurological and psychiatric diseases43. The large connectivity with the Default Mode Network showed by the superior temporal gyrus, which confers to this region a central role in the MST, has been observed in fMRI data44 but never found in FDG-PET data. Since one of the differences between the two techniques is the level of noise produced during the recordings (relatively silent during FDG-PET vs intensively noisy during MRI), the absence of overlap of the patterns of connectivity reported in that region might be explained by the auditory engagement included in the MRI experiments45. The same argument works as far as the central role of the superior occipital cortex, being the visual activity engaged by the fixation during the resting-state fMRI experiment. A final comment must be reserved to the cerebellar module. The understanding of human cerebellar function has undergone a paradigm shift. No longer considered purely devoted to motor control, a wide role for the cerebellum in cognitive and affective functions is supported by anatomical, clinical and functional neuroimaging data47. Recent evidence from functional connectivity studies in humans indicates that the cerebellum participates in functional networks with sensorimotor areas engaged in motor control and with association cortices that are involved in cognitive processes50. The evidence of the cerebellar engagement in higher cognitive functions as well as in sensorimotor processes might explain its central role in the basal scaffold of the whole functional brain network. Specifically, it has been reported that the lobule VI of the cerebellum, here found as a main connector of the network, has been found to be involved in different cognitive tasks, from mental rotation to working memory processing51. In addition, it has been showed that during the first stages of consciousness loss, induced by mild sedation, the pattern of thalamic functional disconnections included regions belonging to the cerebellum52, supporting the evidence of a strong cerebello-thalamic interaction showed by the MST analysis.A second striking result has been obtained from MSF and MST analysis of the whole brain network. For the first time we report a non-trivial and ordered structure for the basal scaffold of the functional network of the brain. Keeping track only of the strongest connection for each region, the network appeared organised in components exhibiting a linear chain-like structure. When the same procedure has been applied to a proper randomisation of the real human brain functional network, the outcome strongly differed: hubs and star-like structure emerged. This result was tested for robustness by improving the number of regions included in the grey matter parcellation. We calculated correlation matrices from two further templates composed of 276 and 531 regions of interest, respectively, each obtained as a sub-parcellation of the AAL template. The chain-like organization has been proved to persist as the topological outcome of the MSF and the MST analyses of the human brain functional network, against the randomised counterpart that showed a star-like organization  was used. Positive and negative correlations, characterized by the same absolute value, refer to the same amount of information in terms of connectivity strength. Since in this study we considered undirected weighted graphs, the phase-shift between time series, which gives rise to the sign of the correlation coefficient, was not significantly informative. Indeed55, and efficient in terms of wiring costs56. In addition the chain-like feature of the basal modules facilitate the wiring and reconnection processes, not asking for a specific region as a hub, but functioning the whole module as a multiple access point for the functional plasticity.In conclusion we have reported that the whole architecture of the brain activity at rest is characterised by chain-like structures organized in a hierarchical modular arrangement. This kind of organization is thought to be stable under large-scale reconnection of substructure57) and the SCID-5 Personality Disorders (SCID-5-PD58). Exclusion criteria included: (1) a history of psychoactive substance dependence or abuse during the last one year period evaluated by the structured interview SCID-5-RV, (2) a history of neurologic illness or brain injury, (3) major medical illnesses, that is, diabetes not stabilized, obstructive pulmonary disease or asthma, hematological/oncological disorders, B12 or folate deficiency as evidenced by blood concentrations below the lower normal limit, pernicious anemia, clinically significant and unstable active gastrointestinal, renal, hepatic, endocrine or cardiovascular system disease, newly treated hypothyroidism, (4) the presence of any brain abnormality and microvascular lesion apparent on conventional FLAIR-scans. The presence, severity and location of vascular lesions was computed using a semi-automated method59, (5) IQ below the normal range according to TIB  (6) global cognitive deterioration according to a Mini-Mental State Examination (MMSE)60 score lower than 26, (7) dementia diagnosis according with DSM-5 criteria61 and (8) non-Italian language native speaker. All participants were right-handed, with normal or corrected-to-normal vision. They gave written informed consent to participate after the procedures had been fully explained. The study was approved and carried out in accordance with the guidelines of the IRCCS Santa Lucia Foundation Ethics Committee.Forty healthy subjects  participated in this study. All subjects were carefully screened for a current or past diagnosis of any DSM-5 Axis I or II disorder using the SCID-5 Research Version edition . Head motion estimation parameters were used to derive the frame-wise displacement (FD): time points with high FD (FD > 0.2 mm) were replaced through a least-squares spectral decomposition as described in ref. http://www.picsl.upenn.edu/ANTS/). Finally data were spatially smoothed . In order to create an average adjacency matrix at the population level, subject-wise matrices were Fisher-transformed, averaged across subjects and back-transformed.FMRI data were collected using gradient-echo echo-planar imaging at 3T (Philips Achieva) using a (T2*)-weighted imaging sequence sensitive to blood oxygen level-dependent (BOLD) . A thirty-two channel receive-only head coil was used. A high-resolution T1-weighted whole-brain structural scan was also acquired (1 × 1 × 1 mm voxels). Subjects were instructed to lay in the scanner at rest with eyes open. For the purposes of accounting for physiological variance in the time-series data, cardiac and respiratory cycles were recorded using the scanner’s built-in photoplethysmograph and a pneumatic chest belt, respectively. The human brain was segmented into 116 macro-regions from the AAL templateWe used a variation of the percolation analysis proposed by ref. wij represents the strongest link for node i, this does not imply that wji represents the strongest link for node j. We ended up with a directed network of exactly N links connecting each source-ROI with its maximally correlated target-ROI.Starting from the initial correlation matrix, corresponding to the fully connected network, we built a subnetwork keeping only links associated with the maximum value of each row. In other words, for each node only the strongest link survives. The relation is not symmetric, indeed if This approach is equivalent to create a network from scratch in three steps: (i) to rank in decreasing order all the pairwise correlation values; (ii) to look at the list from the top and adding a new link if at least one of the two involved nodes has degree zero, otherwise discarding such correlation; (iii) to update the node degrees. The procedure ends when all nodes have at least degree equal to one. In both cases, the resulting network is made up by several components of nodes connected through their strongest links and without forming loops. In other terms, we have a Maximum Spanning Forest (MSF) of the initial correlation network. Furthermore, the first procedure introduced a directionality, simply revealing for each brain area which is its maximally correlated counterpart.N − 1)).As second step, we connected all components of the MSF to form a unique tree-like component, following this procedure: (i) we took the correlation values discarded during the construction of the MSF and ranked them in increasing order; (ii) starting from the top of the list, the link associated to the considered correlation value was added to the network if the two nodes involved did not belong to the same group and the two sets were merged into one; (iii) otherwise the correlation value was discarded. The procedure ended when all the nodes belonged to the same connected component. By construction the resulting subnetwork of the original network is a Maximum Spanning Tree (MST) as it does not contain loops and maximizes the total weight with the minimum number of links  after that all the pre-processing steps were perfomed.The data collected for the study and analysed in this work are available at the following link: Supplementary Material


Researchers have identified trajectories of pain derived using statistical techniques on longitudinal data. These trajectories have potential to be of use clinically but the repeated data collection required is currently impractical for such situations. Our aim was to investigate the validity of a self-report  for pain. Analysis included participants from 2 prospective cohorts of people seeking primary health care for back pain (n = 622). A question was developed asking people to classify their pain experience into one of a number of trajectories using visual and word descriptions. Overall 98% of participants completed the question; criterion validity was established by comparing self-report trajectories and trajectories derived using longitudinal latent class analysis, and construct validity was established by comparing responses to the questionnaire against an existing model of back pain stages. As expected variables such as pain intensity and widespreadness, other symptoms, and psychological distress showed an increasing trend of severity across trajectory categories in line with the hypothesized model. In conclusion, the self-report single-item Visual Trajectories Questionnaire-Pain is acceptable to patients and supported by evidence of face, criterion, and construct validity. Further research is needed to investigate the clinical usefulness of the question.This study provides a new questionnaire  that captures the longitudinal state of a patient's pain experience. The Visual Trajectories Questionnaire-Pain has shown aspects of face, criterion, and construct validity, and has the potential to be clinically useful. Over the past few years, a number of studies have identified trajectories of back pain.One solution is to ask patients themselves which trajectory best represents the course of their back pain, and this has been suggested in a recent review of research on back pain trajectories.There are a number of stages needed to test the validity of such a question. The first element of this is face validity; whether patients can understand the question and assign themselves to a trajectory.The aim of this study was therefore to investigate the validity of a self-report question  asking patients to identify the trajectory that best represents their pain experience.This study was nested in 2 cohorts of people seeking primary health care for their back pain (Back Pain Research in North Staffordshire [BaRNS] Study and Beliefs about Back Pain [BeBack] Study). Study participants were consecutive patients visiting their general practitioner about back pain during 2001 and 2002 (BaRNS) or 2004 through 2006 (BeBack); all were invited to take part in a prospective cohort study using questionnaires and followed for up to a year. Further details are published elsewhere.A draft question asking patients to classify their back pain experience into a trajectory was developed on the basis of trajectories previously derived through statistical modeling. Four trajectories were developed directly from typical individual trajectories identified within previously published work on the basis of regular reporting of back pain intensity.Initial assessments of acceptability and components of face validity were carried out with a small group of patients with experience of musculoskeletal pain—the Research User Group (RUG) at the Research Institute for Primary Care & Health Sciences, Keele University. The RUG has approximately 100 members and many have conditions such as back pain, osteoarthritis, rheumatoid arthritis, ankylosing spondylitis, mental health conditions, and long-term health conditions. The age range is from 33 to 87 years, and there is an even representation from male and female members. RUG members are involved in most aspects of the research process and take part in advisory groups, steering groups, research meetings, coapplicants, and implementation meetings. The group involved in the VTQ-Pain development consisted of 8 members, all with musculoskeletal problems . These RUG members were sent the VTQ-Pain in advance and then invited to a meeting, and asked whether they understood the question, and whether they could suggest any improvements.After amendments on the basis of RUG feedback (see Results section), the VTQ-Pain was included in the baseline and 12-month second study period questionnaires for the BaRNS and BeBack Study cohorts. The 7-item version was included in the baseline questionnaire, referring to the period since the start of the study (7 years or 5 years previously); the 8-item version  was included in the 12-month follow-up questionnaires referring to the previous year. Components of face validity were tested by the views of the RUG feedback, as detailed previously, and also determining the proportion of patients who were able to answer the question in the baseline second study period questionnaires using response/completion rates as an indicator.Criterion validity was explored by comparing self-report trajectory responses in the 12-month follow-up questionnaire with statistically derived trajectories. These trajectories were derived using longitudinal latent class analysis (LLCA) in both cohorts, using the first 6 months of data from the second study period phase. Monthly reported back pain intensity scores were used to derive trajectories using LLCA; each participant was allocated to a trajectory on the basis of their largest probability. Briefly, pain intensity was measured on a monthly basis using the mean of three 0 to 10 numerical rating scales. These values were trichotomized into no pain (scoring <1), mild-moderate pain, and high pain (score of ≥5) for each month. LLCA was then used to group participants into clusters on the basis of these pain measurements over 6 months. Derived posterior probabilities indicated the probability of a participant belonging to each cluster, and participants were allocated to the cluster for which they had the largest probability of belonging . Cluster-specific probabilities of having each level of pain for each month, considering the membership of that cluster, allowed descriptions of the pain pathways for each cluster. The derived clusters have been shown to have a good fit to the observed patterns.Construct validity was tested by comparing responses to the VTQ-Pain in the baseline questionnaire of the second study period against constructs supported by the stages of pain model .2) by the VTQ-Pain and by the LLCA trajectories for each of the construct validity variables.Pain in the back was represented by pain intensity at baseline using the mean of three 0 to 10 numerical rating scales.The patients in the RUG group reported that the VTQ-Pain was easy to understand, they did not report any difficulty in understanding the axes, there was no mention of additional trajectories, and they would be able to complete it. They suggested a minor amendment to the formatting of the trajectory pictures that they believed would make them more easily understood . The final VTQ-Pain is presented in In the second study period baseline questionnaires, 98% of respondents were able to answer and complete the VTQ-Pain (202 of 208 in BaRNS and 420 of 429 in BeBack). Similar response frequencies were found in the 12-month follow-up. Frequencies of response to the individual trajectories at baseline are shown in The self-reported visual trajectory responses given in the 12-month questionnaire from the second study period of the studies were compared with trajectories derived using LLCA for the 2 cohorts (n = 373) in All variables showed an increasing trend of severity across trajectory categories from: a (single episode) to e (persistent severe back pain), meaning that patients with less frequent and less severe pain have better health than patients with more frequent and severe pain see , Table 4We have shown that a new single-item VTQ-Pain, which asks people to categorize themselves into trajectories of pain, is supported by evidence of face, criterion, and construct validity in 2 independent cohorts of primary care back pain consulters. The question is acceptable to patients, and people selecting different response categories are also different in other ways including their statistically derived trajectories of pain, pain radiation and spread, and amplification to other symptoms and psychological distress.There is support for concordance between the reported trajectories and the LLCA clusters. Most respondents who described their trajectory as having no back pain, improving back pain, or only having a single episode fell within the no or occasional mild pain LLCA trajectory (and none were found in the fluctuating or severe pain LLCA trajectories), whereas those who chose severe pain all the time, pain that goes up and down with severe episodes, or back pain that has gradually worsened, were predominantly in the persistent severe pain LLCA trajectory. An assignment of variables broadly in line with the stages of pain model was shown, but there was not always a clear distinction between the stages and “gray” areas will exist using such categorizations. For example, there were gradually increasing mean levels of anxiety as the visual trajectory severity increased, rather than a sudden leap of scores from the other trajectories to the trajectory representing severe pain all or nearly all of the time. Evidence from previous work also shows that rather than a set of stages through which people progress over time,This study has the strength of testing the VTQ-Pain in 2 independent cohorts of primary care back pain consulters. However, because of the nature of identification and retention of participants included in this study, we cannot give estimates of the prevalence of the visual trajectories. There may be different proportions of people identifying with the response categories in different studies and settings, and this remains to be tested. Testing criterion validity against the reference standard of statistically derived trajectories is a strength. However, agreement between self-report and statistically derived trajectories was limited, possibly reflecting bias in recall of trajectories, compared with trajectories derived using longitudinal data. There were also limited numbers for the analysis with LLCA-derived trajectories, and although previous work has shown that people providing data for longitudinal analyses are broadly similar to the whole sample,LLCA did not identify systematically increasing or decreasing trajectories of change. Only 6% of the population self-reported such patterns . This may be a reflection of this population (people with long-term back pain). Inspection of the baseline levels of pain intensity for these groups show high pain levels for group f (>7) and low levels for group g (<2) and this may reflect the relative stability of pain within this cohort (2 long-term back pain cohorts) with little room to reflect change in the 12-month period. It may be that the relative frequency of the trajectory groups, including those that capture change over time, may well be different for different populations . Kongsted et alThe VTQ-Pain has potential clinical usefulness, because it is simple for patients to answer, and provides relevant information about other characteristics of the patient. In addition, it allows the measurement of trajectories over time without the need to collect data longitudinally. Although there are, as yet, no treatments designed to be matched to different pain trajectories, the characteristics of the patients in the different trajectories do present potential targets for intervention. For example, patients who are mostly pain free may benefit from simple advice and reassurance, whereas patients with mild pain most of the time may require more management of pain elsewhere and other symptoms, and people with constant higher levels of pain may require interventions targeting psychological aspects of their health as well as their pain and other symptoms. Future research may provide more information about which treatments could be best matched to patients in the different trajectory groups. Furthermore, the visual trajectories question may have the potential to be used as an outcome measure, for example, to illustrate change in course after an intervention, however, further research would be needed to test such a measure within this context .We have developed an acceptable single-item question on visual trajectories of pain, with evidence of validity, and potential usefulness in research and clinical practice.


Artificial intelligence (AI) techniques, which can effectively analyze massive amounts of fault data and automatically provide accurate diagnosis results, have been widely applied to fault diagnosis of rotating machinery. Conventional AI methods are applied using features selected by a human operator, which are manually extracted based on diagnostic techniques and field expertise. However, developing robust features for each diagnostic purpose is often labour-intensive and time-consuming, and the features extracted for one specific task may be unsuitable for others. In this paper, a novel AI method based on a deep belief network (DBN) is proposed for the unsupervised fault diagnosis of a gear transmission chain, and the genetic algorithm is used to optimize the structural parameters of the network. Compared to the conventional AI methods, the proposed method can adaptively exploit robust features related to the faults by unsupervised feature learning, thus requires less prior knowledge about signal processing techniques and diagnostic expertise. Besides, it is more powerful at modelling complex structured data. The effectiveness of the proposed method is validated using datasets from rolling bearings and gearbox. To show the superiority of the proposed method, its performance is compared with two well-known classifiers, i.e., back propagation neural network (BPNN) and support vector machine (SVM). The fault classification accuracies are 99.26% for rolling bearings and 100% for gearbox when using the proposed method, which are much higher than that of the other two methods.  Abnormal operations induced by gear or bearing failures should be detected as early as possible to avoid serious and even fatal accidents. A variety of methods have been applied for the diagnosis of rotating machinery based on vibration and acoustic signals ,2, thermThroughout the previous researches, we find that ANNs are one of the most commonly used classifiers in intelligent fault diagnosis, among which back propagation neural network (BPNN) is the representative one based on supervised learning . It consDeep learning ,27,28,29This paper proposes a novel AI method based on a DBN to achieve unsupervised feature learning and automatic fault diagnosis of a gear transmission chain. In this method, the DBN is first pre-trained layer by layer in an unsupervised manner and then fine-tuned with a back propagation (BP) algorithm under supervision. The unsupervised process aims to obtain representative features characterizing the health conditions of machinery from the raw data directly, and the supervised process is implemented to discover the discriminative information from these features. Besides, the genetic algorithm is used to optimize the structural parameters of the network. Compared to the conventional AI methods, the proposed method can adaptively exploit robust features related to the faults from the unlabelled time domain data, which little field expertise is needed. Besides, the proposed deep network has superiorities to model complex structured data, thus can discover the discriminative information of these data and achieve accurate classification. To illustrate the application of the proposed method, the rest of this paper is organized as follows: In this section, a DBN-based AI method is proposed to achieve unsupervised feature learning and automatic classification. DBN is an unsupervised feature learning model with deep architecture. Each layer of the DBN is a restricted Boltzmann machine (RBM) ,35,45, wFor given visible and hidden units, the energy function is defined as:Several RBMs can be stacked to produce a DBN, the output of a lower-layer RBM is the input to a higher-layer RBM. The DBN classifier model is trained according to two main steps: (1) pre-training of each individual RBM layer by layer with unsupervised learning and (2) further fine-tuning of the DBN with a back propagation (BP) algorithm for classification.k iterations of Gibbs sampling (often k = 1) is usually used to train the RBM [In the first step, each RBM can be trained by performing a stochastic gradient descent on the negative log-likelihood probability of the training data. The gradient of the negative logarithmic probability of the visible layer with respect to parameter  the RBM ,47. WhenTherefore, the update rule of the parameter The parameters After the DBN is pre-trained, fine-tuning process is utilized in the next step of the DBN training. The fine-tuning process further reduces the training error and improves the classification accuracy of the DBN-based classifier model. As for classification tasks, the output of the DBN calculated from the input sample Based on the DBN, this paper proposes a new AI fault diagnosis method that can learn representative features from the raw signals of a gear transmission chain, instead of using features selected by a human operator, to automatically provide accurate classification results. The basic procedures of the proposed method are briefly illustrated in N evenly spaced points, where N is the next integer power of two from the length of the raw data. The whole process requires neither conversion between the time and frequency domains nor any other signal processing techniques, thus avoiding some potential problems associated with different signal processing techniques. Finally, these intercepted time domain data form the sample set mth sample, First, the measured signals must be arranged to fulfil the constraints on the DBN. Conventional AI methods use human-selected features to form the sample set. Here, the measured signals are directly segmented to form the sample sets. The segmentation process has two main steps: (1) determine the axis crossing corresponding to one revolution of the shaft through the measured tachometer signal; and (2) interpolate the time domain data between each of these axis crossings using cubic spline interpolation. The main reason for interpolating the time domain data is that the raw data points between each of these axis crossings may be different because of unstable speed or other complex operating conditions. Each set of time domain data is integrated over the shaft cycle, with durations containing the same number of points to guarantee the capture of all the useful information during each shaft cycle and to correlate the phase features. Following standard practice, the data is interpolated at exactly 2N hidden layers based on genetic algorithm and pre-train layer by layer in an unsupervised manner. It should be noted that the number of RBMs refers to the number of hidden layers because each RBM only contains one hidden layer. Specifically, the input samples are first given to the visible layer of the first RBM. Then the parameters of this RBM are continuously optimized based on the updated rule. While the training epoch reaches its maximum number and the training of the first RBM is accomplished, the hidden layer of this RBM becomes the visible layer of the second RBM. Then the training process is continued for the second RBM. Finally, by training N individual RBMs, all of the hidden layers of the DBN are pre-trained.Second, set up a DBN with Third, determine the dimension of the output layer based on the number of health conditions. Then the BP algorithm is utilized to fine-tune all of the parameters of the DBN by minimizing the error between the output calculated from the input samples and the corresponding labels. Unlike the unsupervised pre-training process, in which each RBM is trained independently, the supervised fine-tuning is applied to all layers simultaneously. Finally, the completely trained DBN is utilized to fault classification of a gear transmission chain.Besides, it should be noted that some parameters could greatly affect the performance of the DBN. Some researchers have proposed several guidance on how to determine the parameters ,47. HoweThrough the proposed method, unlabelled time domain data, which are easy to obtain and do not require diagnostic expertise, are utilized and the features are learned from the data instead of being selected by a human operator. Meanwhile, the complex relationship between input data and health conditions can be established to achieve accurate classification. Therefore, the proposed method is capable of the fault diagnosis of a gear transmission chain.Signals originating from the gear transmission chain are complicated because of the system’s complexity and its operating conditions . This seAll bearings used in this work are SKF 6004-2RSH deep groove ball bearing. Some parameters of the bearing are listed as follows: inside diameter: 20 mm; outside diameter: 42 mm; ball diameter: 6.4 mm; pitch diameter: 31 mm; ball number: 9.Various faults are introduced to the test bearing using the WEDM method. These faulty bearings are shown in k-fold cross-validation method, where k is chosen as four. Therefore, four subsets are generated where one subset containing 20,000 samples is used as the testing set and the other three subsets containing 60,000 samples are used as the training set. Eleven features in the time domain and four features in the frequency domain, which are listed in In this work, we utilize the statistical features to characterize the bearing health conditions and employ the BPNN for fault classification. To reduce feature dimensionality and improve classification accuracy, feature selection is critical to the subsequent classification. Several researchers have proposed effective methods of feature selection. Because of its simplicity and reliability, the distance evaluation technique (DET) is widely used to feature selection . This meThe results show the poor accuracies when only four or five features are used. Meanwhile, when the number of features is larger than five, the average accuracies improve slightly but are still unsatisfactory under several engineering applications. The performances of different feature subsets have not improved when increasing the number of features, which implies that the original feature set contains irrelevant or redundant information. In addition, the performances for each feature subset vary greatly over the four trials. For instance, when seven features are included in the feature subset, the highest and the lowest accuracies are respectively to be 94.86% and 84.79%. These results indicate that the BPNN-based method offers poor stability and unacceptable robustness.The performances of different feature types are also evaluated in this work. Ten feature subsets, each containing seven features, are selected from the original feature set, and the features in each subset are not necessarily the same. The features in the first subset are selected based on DET, whereas the others are selected randomly. The results of this analysis are shown in From the above analysis, it is clear that learning representative features for each task is crucial for classification. In this work, 15 statistical features in the time domain and frequency domain are extracted from the raw signals and the DET is used to select the sensitive features. It is feasible that by employing other appropriate data analysis algorithms, better classification accuracy may be obtained. However, this process largely depends on prior knowledge of signal processing techniques and diagnostic expertise. In addition, the signal processing techniques adopted to solve one specific issue may not be suitable for others. Because of these problems, unsupervised feature learning is expected to be more effective against the challenges facing fault diagnosis of gear transmission chains.Rolling bearings and gears are the key components in rotating machinery. Faults occurring in these components must be detected as early as possible to avoid fatal breakdowns of machines. In this section, two experiments of rolling bearings and gearbox are used to validate the proposed method.k-fold cross-validation method, where k is chosen as four. Therefore, four subsets are generated where one subset containing 20,000 samples is used as the testing set and the other three subsets containing 60,000 samples are used as the training set. Each sample contains the time domain data from duration of three shaft cycles, with 2048 data points. The DBN has 2048 input units, equal to the dimension of the samples, and eight output units, equal to the number of health conditions. There is one hidden layer with 1000 hidden units, which is determined through the genetic algorithm. In the process of unsupervised pre-training, the maximum training epoch is 25, the learning rate is 0.005, the momentum is 0.5 and the biases are initialized to zero. In the process of supervised fine-tuning, the weights are initialized randomly and the maximum training epoch is 10.In this subsection, the fault signals collected from the experimental system described in For comparison, the BPNN and SVM are trained using the same data for fault diagnosis as well. The BPNN has the same architecture as the DBN and is trained by the same parameters. The SVM uses RBF kernel function as the basic function and the kernel width is set to be two. The classification results are shown in Besides, the training errors (MSE) of DBN and BPNN in one trial are shown in As mentioned above, in the proposed method, the unsupervised process aims to adaptively exploit representative features characterizing the health conditions of machinery from the unlabelled time domain data instead of relying on diagnosticians. Besides, when designing the architecture of the DBN, in general the unit number of the next layer is smaller than that of the previous layer so that the data can be compressed layer by layer. Therefore, the unsupervised process in the DBN can correspond to the feature extraction and feature selection in the conventional AI method. These features are considered as the input of the output layer of the DBN. The output layer of the DBN can be treated as a classifier to achieve fault classification after supervised fine-tuning. In this case, the DBN has one hidden layer with 1000 hidden units. Therefore, 1000 features are exploited from each sample through unsupervised feature learning and then are used to fault classification. To verify the ability of these 1000 features in characterizing the health conditions of rolling bearing, we set these features as the input of two well-known classifiers, i.e., BPNN and SVM, to achieve fault classification. The average accuracy using the unsupervised feature learning and BPNN is 98.94%, with a standard deviation of 0.04%. The average accuracy using the unsupervised feature learning and SVM is 98.49%, with a standard deviation of 0.11%. Compared to the results listed in The architecture selection is an important process for most neural network models. Certain architecture parameters, such as the number of hidden layers and the number of hidden units per layer, are critical to the performance of the neural network model . In the To further evaluate the performance of the proposed method, we change the number of hidden units, and the results are shown in Moreover, It can be seen from #Gear 1 has 32 teeth, #Gear 2 has 96 teeth, #Gear 3 has 48 teeth, and #Gear 4 has 80 teeth. The two-stage gearbox vibration data used in this subsection are provided by the 2009 Prognostics and Health Management Data Challenge ,50,51. F#Gear 2, #Bearing 4, #Bearing 5, and #Bearing 6, are in health condition. In comparison with the experiment in the previous section, more fault categories and different fault locations in the gearbox are investigated in this experiment. An accelerometer mounted on the input side of gearbox is used to acquire vibration signals, and a tachometer mounted on the input shaft is used to acquire the real-time input shaft speed. The data are collected under the no-load and the maximum load (10 in-lbs.) conditions with a sampling frequency of 66.67 kHz. The motor speed is 3000 rpm. Eight experiments are conducted under different health conditions. These conditions involve multiple fault categories for the gear, bearing, and shaft components, as described in k-fold cross-validation method, where k is chosen as four. Therefore, four subsets are generated where one subset containing 440 samples is used as the testing set and three subsets containing 1320 samples are used as the training set. Each sample contains the time domain data from duration of three shaft cycles, with 4096 data points. The data collected under different loads are not separated, so that the same health condition under different loads is treated as one class.In this study, 220 samples can be obtained for each health condition. These samples are randomly partitioned into a training set and a testing set by using Similarly, three methods are used to process the dataset and the classification results are shown in In this experiment, as the hidden layer of the DBN has 1000 hidden units, 1000 features are exploited from each sample through unsupervised feature learning and then are used to fault classification. Similarly, we set these features as the input of BPNN and SVM to achieve fault classification, and the average accuracies are 100% when using both methods. Compared to the results listed in The analysis in Feature extraction and feature selection are crucial steps in fault diagnosis because the relevance of the extracted features directly affects the classification accuracy. In this work, we present the results of the BPNN-based method applied to raw data and different time domain features, and it is found that the classification accuracies vary dramatically at unsatisfactory levels. To overcome these limitations, developing robust features that capture the relevant information for each issue may improve the classification accuracy. However, this process is time-consuming and largely depends on diagnostic expertise. In contrast, the proposed method uses unsupervised feature learning to obtain representative features from the raw data and achieve accurate classification. This offers the advantage of using raw data instead of extracting features based on the expertise of a human operator. The whole process requires neither conversion between the time and frequency domains nor other signal processing techniques, thus avoiding some potential problems associated with different signal processing techniques. To verify the ability of the proposed method in adaptively exploiting fault features, we set the features exploited through unsupervised feature learning as the input of BPNN and SVM to achieve fault classification. In the first experiment, the average accuracy is 98.94% when using the unsupervised feature learning and BPNN, and 98.49% when using the unsupervised feature learning and SVM. In the second experiment, the average accuracies even reach 100%. Compared to the results list in The architecture selection is an important process for most neural network models. In this paper, the DBN contains one hidden layer with 1000 hidden units, which is determined through the genetic algorithm. To further evaluate the proposed method, we changed the number of hidden units and calculated the classification accuracy. This analysis showed that the limited variation of some architecture parameters has little effect on the performance of the DBN.The influence caused by different sample sizes has also been considered. In N data points are captured per cycle of rotation. In this way, we can directly train the DBN using raw data in the time domain without any pre-processing.In this paper, the unlabelled time domain data of integrated shaft cycles are utilized for classification. The only pre-processing step is to apply the tachometer signal to determine the shaft cycle duration. Beyond that, no other signal processing technique is required. Currently, some data acquisition systems can adjust the data sample rate based on a tachometer signal so that 2This paper proposes a DBN-based AI method for the fault diagnosis of a gear transmission chain. In this method, the DBN based classifier is first pre-trained layer by layer in an unsupervised manner and then fine-tuned with a BP algorithm under supervision. Besides, the genetic algorithm is used to optimize the structural parameters of the network. In contrast to the supervised neural network, the proposed method takes full advantage of unsupervised feature learning to extract features from the unlabelled time domain data instead of relying on a human operator to extract features. Therefore, the proposed method depends less on field expertise or prior knowledge of diagnostic techniques. Moreover, the proposed method has superiorities to model complex structured data, thus can discover the discriminative information of these data and achieve accurate classification.Two experiments, i.e., rolling bearing faults and gearbox faults, are conducted to verify the performances of the proposed method. Various fault categories, fault locations and fault severities under different loading conditions are considered in the experiments. The fault classification accuracies are 99.26% for rolling bearings and 100% for gearbox when using the proposed method. Besides, the confusion matrix shows that the accuracy of each health condition retains at high level with strong robustness. In contrast, the performance of the BPNN-based method and the SVM-based method in both experiments are comparatively poor. The above results show that the proposed method performs better in the classification of gear transmission chain faults compared to the conventional AI methods. Besides, the vibration data utilized here is obtained from only one sensor, our future work will focus on a more comprehensive fault diagnosis of rotating machinery based on the multi-sensor data fusion and deep learning methods.


Experimental tests and constructive assessments are presented for a simple bamboo framed structure with innovative low-cost and low technology joints, specifically conceived for small buildings in developing countries. Two full scale one-storey bamboo frames have been designed by using the simplest joints solution among three different tested typologies. The entire building process is based on low-technology and natural materials: bamboo canes, wooden cylinders, plywood plates and canapé rods. The first full scale specimen (Unit A) is a one-storey single deck truss structure subjected to monotonic collapse test; the second full scale specimen (Unit B) is a one-storey double deck truss structure used to evaluate the construction time throughout assembling tests. The first full scale specimen showed ductility in collapse and ease in strengthening; the second one showed remarkable ease and speed in assembling structural elements. Finally several constructive solutions are suggested for the design of simple one-storey buildings; they are addressed to four purposes  by the composition of the proposed full scale bamboo frames. Ease of use and maintenance with a low level of technology contribute to application in developing countries although not exclusively. Bamboo is a low-cost building material, widely available in the world; it is lightweight, durable, flexible, and easily cultivated and processed. The use of bamboo as a structural material is well-known in constructive traditions and in recent innovations. Its mechanical properties have been studied from several points of view: e.g., in ,2 the miExamples of bamboo usage, as a composite material joined with other structures or organized throughout fibers, demonstrate its full potential as a structural and environmental friendly material. The research into the reduction of environmental impact and/or the use of cheap or recycled materials  represenThe reduced ductility of bamboo elements is a critical aspect from structural point of view: bamboo is characterized by brittle behavior, mainly for tension forces, and the collapse is, in most cases, caused by longitudinal cracks along the weakest lines. Another negative aspect for traditional bamboo frames is the relative weakness of the joint between the canes. Often the nodes are built, in vernacular contexts, throughout tied ropes or by incisions of the canes, simple to realize but not suitable to transmit the entire bearing capacity of the bamboo elements. By contrast, modern technologies allow joints with high structural features, but complicated technologies or materials are not easy to supply or disseminate in developing countries ,31,32,33The first full scale specimen (Unit A) tested in the present paper is a single deck trussed structure, made with a couple of frames with a wooden roof, loaded up to collapse with monotonic vertical loads. The second full scale specimen (Unit B) is a symmetrical double deck frame, with Polanceau beam and coupled columns, subjected to assembling tests. The collapse test showed the global ductility behavior of the bamboo frame in the presence of vertical loads. The failure mechanism, involving only wooden pins in a joint with large inelastic deformations, prevented brittle collapse of the other elements such as bamboo canes. It therefore determines a safe structural behavior avoiding any brittle collapse and also permitted an economical repair with the simple substitution of the pins. Analytical evaluations confirm the ductile behavior attained by the third joint solution, by comparing expected performances with experimental results. In addition, the assemblage tests, held by a group of un-skilled workers, showed the ease and the speed of the constructive phases.Finally several buildings plans with Units A and B in modular schemes are presented for typical one-storey buildings such as housing, schools, small churches and health centers; the aim of this is to contribute to proposals for self-construction activities and encourage their dissemination among building workers in developing countries.shear-bending failure of wooden pins (weak pins);hole deformation in plywood plate (weak plywood plate);tensile tearing-out of bamboo canes ;longitudinal cracks in bamboo canes between the holes (weak bamboo canes by shear).In this section a series of static tensile tests on three types of joints for bamboo structures are discussed. From a structural point of view, the main collapse mechanisms that can be expected during the tensile tests have been the following:s = 5 mm). The joint is reinforced by means of a wooden cylinder and connected to 10 mm thick metal plate ;the wooden pins are deformed by bending moment inducing relative displacements between plywood and bamboo (slipping phase);the wooden pins are affected by inelastic large deformations with consequent wide relative displacements up to maximum force (plastic phase); softening stress-strain curve is caused by the progressive failure of the wooden pins (starting from the extremity pins), partially constrained by the canapé wires (softening phase).The mechanical behavior of the connection can therefore be expressed in four phases:The design of the 3rd type of joints is meant to favor the first mechanism  with net area A and ultimate stress kf is:G is a load factor between 1.0 and 1.5, D is a reliability factor in execution (mainly 0.5) and γm the bamboo safety factor (2.25). In the considered example, given A equal to 13.7 cm2 and kf of 18 MPa, the maximum tensile load The observed ductility factor of node By substituting ud = 7.97 mm, it would be possible to deduce an estimation of the work done during the cyclic deformations, by evaluating the area under the diagram of Considering the average value of the ultimate displacement Another aspect related to the 3rd type of joint consists in the fact that the single rod test is representative even of the mechanical behavior of multiple rod joints. It is important to emphasize that the collapse of wooden pins is independent from the number of rods converging on the node.Moreover, the entire constructive system is able to favor a precast activity. A unique shape of plywood plates can be used for several spans of frames, due to the homotheticity of the truss nodes. Last but not least, the entire set being eco-friendly materials is a remarkable value in favor of this last type of joint.The full scale specimen named unit A  is forme(a).composition of each beam truss to work site;(b).connection of each beam truss with two pairs of bamboo columns;(c).erection of each single bamboo frame (truss/columns), inserting each base column into a precast concrete pot with pressed sand;(d).execution of bamboo bracing to absorb out-of-plane loads on the frames;(e).construction of the roof made by wooden purlins (6 cm × 6 cm) and tables (thickness 22 mm).The assembly phases have been the following :(a).com2. The load steps and the axial force in the rods of the truss are shown in D1, vD2) are shown in E = 3000 MPa. Higher values of the displacements were detected in the frame 1 (32 mm) with respect to frame 2 (15 mm). This is due to more significant damages on nodes and imperfections on bamboo canes of frame 1. A visible crack during the 6th load step was observed on the pins at node B of the rod BC. The other nodes did not reveal visible damages. All the relative displacements histories in B are reported in The static vertical loads were applied throughout a series of cement bags of 25 daN weight, CE certified with a tolerance less than 1%. The loading program was divided into eight steps at 100 daN each with the sequence displayed in The maximum value of the testing loads was progressively decreased in four steps (2.0 KN each). The vertical displacements of the node D of both frames are displayed in It can be observed that the bamboo structure has been protected from risks of brittle collapses and from failures with complicated repair; this is due to the role of the wooden pins. Also the occurrence of a failure in a node at the 6th stepdid not prevent the structure from taking additional load steps up to the 8th, demonstrating the remarkable inelastic behavior of the entire frame after a local collapse. That is of primary importance to ensure people's safety and also the safety of the related investment.After the full scale experiment, it was sufficient to renovate the failed wooden pins and to apply a new set of canapé rods in the collapsed node. The repairing activity was performed easily and in a short time (less than one hour). The loading program was then repeated without any inconvenience. It can also be noticed that the tests have been conducted in the absence of horizontal forces. However, the shear and bending moment on the columns, due to transversal forces simulating seismic or wind action, did not induce further stresses on the trussed roofs, if a hinged joint between truss and columns is adopted. Moreover, the increment of axial force on the truss elements, given by horizontal forces on the roof can be easily evaluated by numerical analysis: the lightweight of the roof anyway imply not relevant seismic effects. Further tests can be carried out to experimentally investigate this aspect.The third joint type was adopted in another full scale model (Unit B) described in The assembling tests were conducted by unqualified workers, to demonstrate the simplicity of the constructive phases and the ease of the dissemination phase to unskilled personnel. Each Polanceau beam of span L = 7.50 m has a self-weight of about 40 daN, allowing them to be handled without elevator devices. The entire frame was assembled in about 120 min by three volunteers in both conditions, using only a drill, a saw and a hammer.It is relevant to point out that the mechanical behaviour of several nodes a is coveThe structural solutions here tested through full scale frames can be easily implemented in different types of buildings, which are common in a large number of states like India, Latin America, East Asia or Sub-Saharan Africa ,41,42,43The three proposed types of joint provide different solutions in terms of technology. From the first to the third type, an increasing ductility was detected, together with an increasing simplicity in execution. The increasing ductility has been obtained throughout a progressive weakening of joints. In the first joint the collapse strength was higher but brittle. The use of bolts, internal reinforcement and glue induced a brittle collapse of the bamboo cane. In the second joint the collapse caused wide deformation of the holes in the plywood plate. In the third joint the collapse was associated with the bending moment and shear in wooden pins showing large deformations. This has been made possible by removing the internal reinforcement (due to wooden cylinder in the first joint and bamboo sticks in the second joint) and coupling the bamboo canes to symmetrically connect them to the plywood plates. Tensile stress with a low number of cycles has always characterized all tests. Further experiments should be programmed to explore the mechanical behavior of the joints in presence of high number of cycles.The third type of joint is easy in execution, in maintenance and in repair. It is also simple to design, taking into account that the diameter and number of the wooden pins can be easily evaluated throughout ISO/DIS 22156 Equations (1) and (2). The concern that weakening the joint (from 1st to 3rd solution) could be dangerous for bamboo constructions disappears, considering that the deformation of the wooden pins permits adaptive displacements of the structure, as shown in the full scale collapse test. Any brittle collapse is thus avoided. Moreover, the weakening of the bamboo canes by holes is common to many solutions presented in technical codes  or in liIn this work the full collapse test has been limited to monotonic vertical loads. Moreover, as convenient strategy in case of on-site tests, the experimental apparatus has been intentionally limited, ensuring sufficient accuracy in the measurements of the displacements (tolerance 1/100 mm) .Further experiments should be conducted to test the bamboo frame under horizontal and cyclic time history loads. Regardless, in this case, due to the structural scheme with hinged joints between the bamboo truss and the columns, the horizontal loads induce bending moments and shear loads only in the columns. To emphasize the dissipating properties, the connections of the columns to the ground can be designed to perform seismic base-dissipation taking into account the “biaxiality effect” induced by the restraints at the base .The constructive technique proposed here is easy to disseminate especially in earthquake prone areas: the significant difference in the loss of life caused by earthquakes in developing countries can be mitigated by spreading construction practices characterized by simplicity, together with the setting up of tutorials and international networks to promote collaboration and information sharing . In thisetc.Finally the set of plan schemes from the presented frames is an attempt to transfer the results to practical applications, offering suggestions for possible destinations. Obviously, the structural aspect is not the only one to investigate: other properties should be analyzed, such as vertical walls type, finishing, covering, In this work three different types of bamboo joints are proposed. From the first to the third type, an increasing ductility was detected, together with an improvement of simplicity in execution. The third type of joint provides easy construction and simple repair procedures, a reduction of the level of technology providing environmental friendly materials, and satisfactory structural performances. The strategy of the “weak pins” leads joints to ductile collapses protecting bamboo from brittle failures and the nodes from complicated repairs. The cyclic tests show the hysteretic behavior of the structure.Two different full scale one-storey trusses show the structural efficiency and the feasibility of the system for construction and repair. The proposed bamboo joints can also be applied for a wide range of span trusses, allowing for a precast structural system. The ease of execution and assembly is a relevant feature of the proposed frames, permitting dissemination and maintenance in low-technology areas and promoting self-construction or self-enterprise for local communities, together with the subsequent maintenance activity.The application of the proposed technique is not exclusive for developing countries. It can be also adopted in all the areas with environmental and technological features for the use of bamboo constructions, in view of its eco-friendly characteristics. Moreover the structural system involves only natural materials  with strong reduction of environmental impact in those areas where the natural materials are available.Further investigations should be conducted to protect the façade walls (here not considered) from the risk of rocking falls from the movements of the roof, as in ,48, due