As important sources in fault diagnosis of rotary machinery, vibration signals are usually processed in the time or frequency domain as features to distinguish different classes of faults. However, these kinds of processing methods always ignore the corresponding relations among multiple signals, resulting in information loss. In this paper, a new fault description strategy named vibration image is proposed, based on which three new kinds of features are extracted, containing coupling information between different channels of vibration signals. Additionally, a new feature fusion method called two-layer AdaBoost is designed to train the fault recognition model, which avoids overfitting when the dataset is not large enough. Features based on vibration images combined with two-layer AdaBoost are adopted to diagnose faults of rotary machinery. Taking an active magnetic bearing-rotor system as the experimental platform, a dataset with four classes of faults is collected and our algorithm achieves good performance. Meanwhile, features based on vibration images and two-layer AdaBoost are both proved to be efficient separately. Rotary machinery plays an irreplaceable role in modern industry. Over the past decades, the safety of equipment has received more and more attention and the fault diagnosis of rotary machinery has become a hot research topic. Faults not only include the imbalance of the rotor itself but also may occur at the bearings, gear boxes and couplings, which determines the variation and complexity of faults. Hence, how to describe faults is key to fault diagnosis. Various sources such as vibration , electriAs a kind of time series, vibration signals are generally processed via time or frequency domain analyses, which are the mainstream methods. The tools widely used in the signal processing and communication field are also used to describe faults of rotary machinery. These methods include Fourier transform, statistical moments , autoregDue to the non-stationary and nonlinear characteristics of vibration signals, time–frequency methods are introduced into fault signal analysis. Short time Fourier transform applies a time variable to the traditional Fourier spectrum, and moves a short time window along time to divide a signal into slices, which reflects the time–frequency characteristic of the vibration signal in the short time period ,13. FurtIn recent years, with the advancement of machine learning, fault diagnosis technology has been greatly promoted. Fault signals are projected into the nonlinear space for processing, according to locally linear embedding , sparse Most fault diagnosis algorithms excavate the time–frequency characteristics from vibration signals and describe the faults of rotary machinery. However, vibration signals are collected from different sensors and processed equally. The relationship between vibration signals collected from sensors fixed in different locations is always ignored, although this factor is important to distinguish various faults. For example, as the vibration signals collected from sensors fixed at the same axis line are coupled, when an impulse is added to the location of one sensor, it will also obtain the response from another sensor at the axis line. Hence, there exists a coupling relationship between the vibration signals from different sensors. If these vibration signals are processed separately and the coupling relationship is ignored, it will lead to information loss.Shaft orbit ,22 is onAs a research target, rotating machinery supported by active magnetic bearing (AMB) is introduced and the above algorithm is designed in combination with the characteristics of the active magnetic bearing-rotor system. The corresponding research results can also be extended to the fault diagnosis of other rotary machinery. The main contributions of this paper can be summarized as follows.(1)A new fault description strategy termed vibration image is proposed to describe faults in rotary machinery, to capture the coupling information between different sensors installed in various positions.(2)Three new features based on vibration image are created to describe faults in different views.(3)To overcome the problem of overfitting, a new fusion algorithm called two-layer AdaBoost is employed to fuse multiple features and diagnose faults in rotary machinery.In this manuscript, AMB is introduced in An AMB–rotor system is a typical mechatronics rotary machinery. Compared to mechanical bearings, AMB does not need lubrication. Moreover, it can reduce friction and increase efficiency because it does not contact the rotor. AMB can also reduce the excessive vibration of a high-speed rotor system at the critical speed, which helps the motor run over the critical speed stably. These remarkable advantages enable the application of AMB to many fields, such as high speed motors, centrifugal compressors, high-speed flywheels for storage energy, molecular pumps and turbines ,24,25.An AMB–rotor system is a closed-loop control system consisting of a rotor, displacement sensors, a controller and a power amplifier. The displacement sensor of an AMB–rotor system measures the offset of the rotor from the center position. This can not only be utilized as feedback to ensure the stability of the system but is also viewed as the vibration of the rotor. Therefore, an AMB–rotor system has a natural advantage in fault diagnosis. It is not necessary to add new vibration sensors and the existing displacement sensors can be used for vibration analysis to achieve the target of fault diagnosis. Fault diagnosis is essentially a pattern recognition problem, and feature extraction is the key to pattern recognition. Hence, the method chosen to describe the faults effectively decides the accuracy of the fault diagnosis. The vibration image approach and three features based on it are detailed in the following paragraphs.Multiple vibration signals collected from different sensors are processed separately, and the coupling relationship between them is not considered. As previously mentioned, the correlation exists and the information is useful to distinguish different classes of faults. Inspired by orbit shaft, two channels of vibration signals from different sensors are laid together, and pairs of vibration signals at the same time are viewed as point couples in orthogonal coordinates. All the point couples form a trajectory and two channels represent the vertical and horizontal coordinates, separately. We call this trajectory in the coordinates vibration image and refer to the point couples as vibration points. When the two channels of signals are two orthogonal directions in the same radial plane, the vibration image is equivalent to the orbit shaft. The vibration image method generalizes the concept of orbit shaft, and extends the signals to any two channels, which provides more chances to create new features to explore the relationship between vibration signals. In the traditional shaft orbit method, the two channels of signals should be captured by two orthogonally placed sensors in the same radial plane. When the machine runs in its normal state, the shaft orbit is a circle or an approximate circle. The vibration image approach relaxes the requirements of the positions of the sensors. As long as the relative positions of the two sensors are fixed, the two vibration signals captured by them can construct a vibration image. When the system is in a normal state, the vibration image is a certain shape. When the system is in a fault state, the vibration image seriously deviates from the standard shape. Taking the Y1-Y2 signal combination in When there are more than two channels of signals, the vibration image is constructed by arbitrarily selecting two channels; hence, multiple vibration images can be generated. For example, an AMB–rotor system with five sensors can construct 10 vibration images. Features are extracted from each vibration image. Multiple types of features from vibration images are combined by two-layer AdaBoost. This feature construction mechanism provides plenty of feature combinations for recognizing faults from different views, which was used in the experiments.The basic idea of vibration image is intuitive and simple, and has many advantages. First, vibration image converts one-dimensional (1D) signals into two-dimensional (2D) signal combination. In fact, an image is a 2D signal, and all image processing methods are also considered signal processing methods. Hence, a variety of existing image processing and description algorithms can be used to analyze vibration images. Second, the vibration image reflects the coupling relationship between the two channels of signals. The amplitude and phase of two channels of signals are shown in the vibration image and the coupling relationship between them is also presented in such an intuitive form, which was previously hidden in a separate signal and difficult to express. Third, a vibration image can be constructed by selecting two channels of vibration signals arbitrarily. This feature construction mechanism provides plenty of feature combinations for recognizing faults from different views.Similar to the shaft orbit method, vibration image is an identical description of faults and requires basic features to be described. Based on vibration image, we design three description methods from views of vibration amplitude, vibration phase, and frequency analysis.The amplitude of the vibration signal is an important characteristic of faults. To describe the two channels of vibration signals and the coupling relationship between them simultaneously, a histogram of vibration image (HVI) is designed to achieve this work. HVI can be constructed in the following steps.M is total number of vibration points, the center coordinate First, calculate the vibration image center. Assuming the vibration points as R as the radius, while the points outside the circle are regarded as noise points. Calculate the Euclidian distance R is calculated based on Equation Ai=P. FinallHVI uses the form of a histogram to describe the distribution of vibration amplitude variation in a vibration image. Obviously, it reflects the coupling relationship between the two channels of signals, and it is also invariant to rotation of the vibration image, which means it is more robust. Different from HVI, a histogram of oriented vibration image (HOVI) represents the distribution of vibration points in various directions. HOVI is calculated according to the following procedure.R is the radius of the vibration circle.The first step is similar to that of HVI. Find the vibration center Second, calculate the phase of each point according to Equation . The phaN intervals and find Third, divide the phase space into Equation ). The biEquation ).N is the dimension of HOVI. As N increases, the division of the vibration image plane becomes finer and the description of the vibration image becomes more accurate. HOVI is a description of vibration images used to explore the coupling relationship between two vibration signals. Different from HVI, HOVI focuses on using the phase of vibration points to describe the distribution of points in different directions. In the perspective of time analysis, HVI and HOVI represent the distribution of the vibration amplitude and phase, respectively, and can be used to reveal the coupling relationship of vibration signals. Learning from time–frequency analysis methods, vibration image can also draw more meaningful conclusions in the frequency domain. Fourier analysis is an important frequency analysis tool, and vibration images can be seen as a two-dimensional image signal; hence, 2D fast Fourier transform (2DFFT) is selected to describe the frequency characteristic of the vibration image. The calculation procedure of vibration image 2DFFT is detailed as follows.First, divide the two coordinates of the vibration image into N equal intervals, so that the entire vibration image is partitioned into Second, apply 2D fast Fourier transform to the 2D 1–0 matrix and obtain the frequency amplitude and phase map that have same size as the 2D 1–0 matrix.Third, recognize the amplitude and phase map as 1-D vectors and combine them together as a feature vector. The dimension of the 2DFFT feature is Three types of features based on vibration image describe the vibration signals from different perspectives. Different from HVI and HOVI described above, 2DFFT discovers coupling information of two channels of vibration signals in the frequency domain. 2DFFT includes amplitude and phase of FFT result of vibration image and gives much more discriminative information to distinguish the faults of rotary machinery. Three features based on the vibration images are used to characterize faults. They are viewed, respectively, from the amplitude distribution of vibration points synthesized by two channels of vibration signals, the distribution of vibration points in different directions, and the analysis of vibration points in the frequency domain. The high-level feature description of the vibration image is formed by these three types of features.Essentially, fault diagnosis of rotary machinery is a problem of pattern recognition. Besides feature extraction, classification is another important problem. Many common methods in machine learning field are brought into fault diagnosis. Support Vector Machine (SVM) , K-Nearex is a sample. H represents weak learner and w is the trained weight. F is the result of combining weak learners, the dimension of which is equal to the number of sample classes. Each element of F indicates the probability of the sample x belonging to the corresponding class. D is the sample class which is given as the final decision of classifier .(9)D=aIn fact, the basic idea of AdaBoost is similar to fusion algorithms combining different types of features according to a group of weights. Hence, AdaBoost outperforms most simple classification algorithms.According to Vapnik–Chervonenkis dimension theory (VC dimension theory), the ability of a classification algorithm is related to the dimension of the sample feature and the size of the dataset. As the dimension of features is closer to the number of training samples, the generation ability of the classification algorithm is weaker. VC dimension theory tells us that a high dimension feature or a small dataset is prone to overfitting. In the traditional pattern recognition problem, the dataset usually contains thousands or even millions of samples and overfitting is not considered; hence, the dimension of features can extend to the thousands or larger. However, in rotary machinery, accidents or faults only occur occasionally and it is difficult to obtain a large dataset of fault samples. Most datasets used for research contain fewer than 2000 samples, which forces the algorithms to face the contradiction between a high dimension description and few samples.Multiple features can be used to describe faults comprehensively, but they inevitably face the high dimension problem. Thus, there is a need to design a fusion algorithm that not only fuses more information from features but also overcomes overfitting.There exist three main strategies to fuse multiple types of features.First, combine features directly (CFD) to describe faults. This is a simple strategy; however, it faces overfitting and is only suitable for low dimension features.Second, adopt dimension reduction to shrink the dimensions of features. This method projects the features into another orthogonal space, and loses the residual which may include redundant descriptive information.Third, train classifiers separately by different types of features and combine the classifiers according to a series of weights. Many methods have been developed to identify proper weights for this purpose.jth type of feature and is also a vector with dimension n is the number of feature types and M is total number of samples.In this paper, our two-layer AdaBoost algorithm is derived from the above strategies and it is designed to avoid overfitting as well as make full use of feature information. The proposal contains two layers of AdaBoost. The feature extracted from one sample is defined as Equation ):(10)Xi=n AdaBoost classifiers jth type of feature m-dimension vector, each element of which indicates the probability that the sample m is the number of fault classes. The first layer consists of m-element vector with the dimension equal to the number of classes. Each element in the mapped vector corresponds to a class, and the sample belongs to the corresponding class of the largest value in the mapped vector. Hence, the element value in the mapped vector represents the probability that the sample belongs to the corresponding class. When the difference between the element values in the mapped vector is relatively small, that is, the probabilities that the sample belongs to multiple classes are similar, the method of taking the maximum element value as the result can easily cause misidentification. In the conventional methods, when various types of features pass the first layer of AdaBoost, voting or weighting is performed to combine the maximized results of the mapped vectors and much information contained in the mapped vectors is ignored. To discover more useful information, we introduce the second layer of AdaBoost instead of taking a maximum step after the first layer of AdaBoost directly.As mentioned above, the essence of AdaBoost is to map a high dimension feature vector into an In the second layer, all Equation ):(11)X¯iEquation ):(12)yi=When a new sample In two-layer AdaBoost, the first layer is a dimension reduction step, which in essence shrinks multiple high dimension features into a short feature vector with the dimension of The algorithm procedure can be summarized in the following steps see .(1)Collect the vibration signals under four conditions: normal, unbalance, misalignment, and rub-impact. Each sample consists of five channels of signals, which lay in two planes and axes named X1, Y1, X2, Y2 and Z.(2)Select some combinations from any two of the five channels, and construct vibration images of each sample.(3)Extract three types of features based on the vibration images for each sample.(4)Divide the dataset into two parts, one for training and the other for testing.(5)Via the training dataset, train the two-layer AdaBoost model.(6)Using the two-layer AdaBoost model, test on the testing dataset and obtain the diagnosis results.To verify the performance of our algorithm, series of experiments were performed on a rig of an AMB–rotor system see . The rigFour classes of data including unbalance, misalignment, rub-impact and normal state were collected and the size of dataset was 1445 samples. From each class, 150 samples were randomly selected as training samples and the others were utilized as testing ones see . Each saAll experiments were repeated 20 times by selecting training samples randomly and averaging the results to make them credible.D to represent the dimension number of features to compare them conveniently (see D was from 1 to 12. There existed 10 two-channel combinations and we marked them as C from 1 to 10 (see D, C} kinds of features.Due to the difference of formation principle, we used the mark ntly see . The rano 10 see . In sum,D, C}. Overall, 2DFFT performs best and HVI is relatively weaker. However, these features describe vibration images from three different views. Therefore, the information contained in the features is complementary to each other and needs to be comprehensively used in the fusion algorithm.We used AdaBoost to train the three types of features separately, and found that they could achieve more than 80% accuracy at most. Although they do not satisfy the diagnosing task requirements alone, they are still powerful features. The dimension and channel combination of the features are two factors that affect the classification performance of a single feature. Generally, with the increase of feature dimensions, the accuracy of recognition is higher, but this trend is not very clear, and, in some cases, the recognition accuracy in the case of low dimensionality is higher than that of high dimensionality.Compared with feature dimension, channel combination has more obvious influence on the recognition results. D,C}. SVM and KNN using CFD fusion strategy and two-layer AdaBoost performed best except for a small number kinds of features. With the increase of number of features, two-layer AdaBoost gradually improves and is obviously better. When the dimension os higher, the performance of SVM and KNN are not as good as that with a relatively low number of the dimensions, which shows that both standard algorithms are limited when facing an overfitting phenomenon. Two-layer AdaBoost overcomes the phenomenon of overfitting and improves the accuracy when faced with high-dimensional features.We shrunk the testing samples by 1/2, 1/3, and 1/4 of formal testing dataset size and show the results in To explain the superior effect of two-layer AdaBoost, we compared it with three other methods, as listed in The comparison results of four fusion algorithms are shown in The series of experiments proves the robustness and applicability of the vibration image and two-layer AdaBoost. However, the purpose of our algorithm is not to show our features are better than all traditional features but is to propose a new idea that is different from the traditional signal processing methods, and explore the coupling relationship between sensors at different locations. By vibration image, more advanced methods in the field of image processing and computer vision can be introduced, which are not limited to the three feature extraction methods proposed by us. In practice, faults often need to be described from multiple views. Hence, various methods including vibration image, and basic time or frequency methods can be used for multi-feature fusion, and various features complement each other to achieve a more comprehensive description of the fault.In this manuscript, we propose vibration image to describe faults in rotary machinery. Vibration image combines two channels of vibration signals to discover the coupling relationship between different signals from sensors. Three features, HVI, HOVI, and 2DFFT, are designed based on vibration images in terms of signal amplitude, signal phase and frequency domain, respectively. To make full use of feature information, two-layer AdaBoost is proposed to overcome overfitting and fuse multiple features. Experiments showed that our algorithm is efficient and performs better than traditional methods.In the future, we intend to develop more effective descriptions of vibration images to achieve better accuracy, and apply vibration images to online fault detection and fault prediction. Vibration images will also be researched to extend from 2D plane to high-dimensional space to discover coupling information among multiple channels of signals.


Prolong walking is a notable risk factor for work-related lower-limb disorders (WRLLD) in industries such as agriculture, construction, service profession, healthcare and retail works. It is one of the common causes of lower limb fatigue or muscular exhaustion leading to poor balance and fall. Exoskeleton technology is seen as a modern strategy to assist worker’s in these professions to minimize or eliminate the risk of WRLLDs. Exoskeleton has potentials to benefit workers in prolong walking (amongst others) by augmenting their strength, increasing their endurance, and minimizing high muscular activation, resulting in overall work efficiency and productivity. Controlling exoskeleton to achieve this purpose for able-bodied personnel without impeding their natural movement is, however, challenging. In this study, we propose a control strategy that integrates a Dual Unscented Kalman Filter (DUKF) for trajectory generation/prediction of the spatio-temporal features of human walking  and an impedance cum supervisory controller to enable the exoskeleton to follow this trajectory to synchronize with the human walking. Experiment is conducted with four subjects carrying a load and walking at their normal speed- a typical scenario in industries. EMG signals taken at two muscles: Right Vastus Intermedius (on the thigh) and Right Gastrocnemius  indicated reduction in muscular activation during the experiment. The results also show the ability of the control system to predict spatio-temporal features of the pilots’ walking and to enable the exoskeleton to move in concert with the pilot. Recently, research on powered wearable exoskeleton technology have been directed towards assisting workers in manual handling operations . Manual Global data on work-related injuries due to prolong walking are sparse. Statistics from the EU nations and some Asian countries have however confirmed an increasing awareness of its high prevalence. A study among young workers in the manufacturing sector across 27 EU Member States indicated about 72.9% exposure rate to the risk of musculoskeletal disorder (MSD) due to prolong walking (or standing) . The conExoskeleton technology is a modern solution to assisting workers in manual handling jobs. Exoskeletons can improve workers efficiency, endurance and agility by augmenting the lower limb power, thus minimizing high muscular activation in prolong walking jobs. Deploying exoskeleton technology for human walking assistance, especially for able-bodied persons, is one of the challenging aspect of application of robotics , 8. HumaSeveral exoskeleton control techniques have been proposed for human walking assistance in the recent past. The techniques are often tailored to their intended application . For medical and rehabilitation applications, there have been three popular techniques: the pre-define trajectory-based control technique, the assist-as-needed (AAN) control, and the intention-based control technique. These techniques have been applied to assist disabled  patients and elderly subjects needing physical assistance for walking. For example, the pre-define trajectory based control have beenThe third popular technique which can be refered to as intention-based control technique integrates sensors system (e.g. electromyogram (EMG) sensor, force/torque sensors, etc.) to the control framework to extract human intention for walking assistance or gait re-learning. Human intention based on EMG signal was extracted and used in HAL-3 , 20exoskThese control techniques have been mainly developed for lower-limb disabled subjects with difficulty in walking . With regards to power or strength amplification applications for able-bodied walking assistance , control requirement emphasizes natural (or synchronous) walking assistance since the able-bodied subjects can mainly walk normally on their specific gait. Four popular control techniques that tend to encourage natural walking or user-specific gait adaptation are identifiable from several reported studies. These include the sensitivity amplification control (SAC), the dynamic movement primitive, the adaptive frequency oscillator, and the EMG feedback control technique. For the purpose of this study, we provide some elaboration on these control techniques.The sensitivity amplification control (SAC) was initially adopted for heavy load carrying while enabling the wearer to walk freely , 23. SACDynamic movement primitive is another strategy reported in literatures for walking assistance. DMPs are a set of nonlinear dynamic systems for generating discrete and periodic movement behaviors , 28. TheAdaptive frequency oscillator (AFO) is another powerful technique developed by Righetti, et al.  for reprDuring walking, the muscles in the lower limb activates in a rhythmic pattern which corresponds to the walking pattern. The electrical activity, i.e. the electromyogram (EMG) signal, generated by the muscles therefore provides a basis for understanding or predicting a subject’s walking behavior or gait. This phenomenon has been exploited by a number of researchers to directly control lower-limb exoskeletons for walking assistance. Kawamoto, et al.  applied In this study, we propose a dual unscented Kalman filter (DUKF) to predict and generate human joint trajectories  based on a partial model of the coupled human-exoskeleton, and partial observation from noisy position sensors. We then attract the exoskeleton motion to this trajectory using an impedance controller integrated in a supervisory control architecture. The controller has capability to allow the exoskeleton to follow the human movement to enable synchronous dynamic walking, atypical in manual handling operations. The main motivation of this study is the need to provide lower-limb locomotion  assistance to able-bodied subjects such as the manual-handling industry workers  who are routinely engaged in prolong walking. Exoskeleton technology can benefit these working personnel by reducing their lower-limb muscle activation or the onset of fatigue of the lower-limb , and the risk of WRLLD due to prolong walking. Since exoskeleton assistance for able-bodied personnel needs to be flexible and natural (or synchronous) to facilitate dynamic walking, we propose the control technique based on Kalman filter that can predict/generate the human dynamic walking motion. The Kalman filter is popular in several fields including aerospace , SLAM 4 etc. forThe rest of the paper is organized as follows: Section II presents the modelling and description of the human-exoskeleton dynamic system. Section III introduces the design of the DUKF. Section IV presents the control architecture. Section V discusses the experiment design and result; and Section VI gives the discussion, conclusion, and recommendations.Knowledge of the biomechanics of the human walking is an important requisite for the development of exoskeletons. It is useful in planning appropriate torque and power requirements for exoskeleton drives and actuation systems. A number of literatures have given comprehensive analysis of the biomechanics of human walking , 53. TwoBased on the duration between one heel strike (foot-strike) to the next heel-strike, the human walking is commonly divided into two cycles or phases: the stance and the swing . The staDuring early stance, the hip extensors (hamstring muscle group etc.) contract to stabilize the hip while the quadriceps and tibialis anterior contracts eccentrically to support the heel strike. The ankle also dorsiflexes  eccentrically to control plantar flexion moment while the quads contract to stabilize the knee and counteract the flexion moment. At late stance, the toe flexors, the tibialis posterior, and the hip flexors  contract to propel the advancing limb. For the swing movement, the hip flexors contract concentrically to advance the swinging leg. This is followed by ankle dorsiflexion to ensure foot clearance (at mid-swing). Finally, in late swing, the hamstring muscles decelerate forward motion of the thigh preventing the leg from over-extending. The knowledge of the phases of human walking is extremely useful in developing exoskeleton control algorithms for human walking assistance.The human body can be divided into three planes: sagittal, coronal , and horizontal (transverse) planes . The domThe torque and power profile on the hip, knee, and ankle are also quasi sinusoidal during level walking . The thrThe knee joint also exhibits positive energy phase (for torque generation) and a negative dissipative phase (for energy absorption). The average knee power  is howeThe ankle joint also exhibit positive and negative power transfer phase, however the average torque is almost entirely negative , 57whichThe prototype exoskeleton system  is a lowTo ensure firm coupling between the pilot and the exoskeleton, there is provision of four soft braces attached at the thigh and shank links. These also facilitate compliance in coupled motion. Upper-body rigid support for the exoskeleton is partly provided by a backpack worn around the shoulder of the operator. Embedded in the backpack is a fairly thin aluminum plate attached on one end to a rigid mechanical bar around the hip, which serve as the torso of the exoskeleton.The exoskeleton communication unit (i.e. the interface between the exoskeleton and the PC) is housed in the backpack to allow ease of movement. The communication unit consist of motor drivers, signal conditioning shields for the torque sensors, and a data acquisition system from National Instrument.The dynamic model of the coupled human-exoskeleton system for walking is derived by analyzing the kinematic configuration of the lower limb in each gait cycle. During the swing phase (single support phase), if a single leg model approach is adopted, it is possible to model the swing leg as a 3-DOF serial link mechanism pivoted to the hip joint and supporting only its weight, as adopted in the control of BLEEX . For theWe make some assumptions to obtain the partial model of the coupled system. The thigh, shank, and foot links of the exoskeleton are assumed lumped up firmly with corresponding segments of the human leg such that a new mass, and moment of inertia parameters can be obtained as approximate values. We also assume that their centers of mass are taken from the same references.q = T are the joint angles  is the stiffness torque which is a function of joint angle position. We present the estimation of the friction and stiffness torque parameters by a system identification method in the Result section.To minimize model uncertainties and to ensure an accurate relationship between the actuating torque and motion of the exoskeleton, an appropriate model of joint friction and stiffness torque is required. Our friction and stiffness torque model is given by , 59:τf, the right calf/shank (RC), the right foot (RF), the left thigh (LT), the left calf/shank (LC), and the left foot (LF). The mass, centre of mass, and moment of inertia of these segments influence the dynamics of walking. They are important factors in estimating the joint driving torques and in deriving dynamic models of human walking. Techniques exist for estimating these segment parameters to some degree of accuracy. Based on cadaver averages, the segment masses can be estimated as a fraction of the body mass, while the segment centre of mass can be estimated as a fraction of their length to the proximal or distal end . GeometrThe well-known Kalman filter is an optimal estimator for generating maximum-likelihood estimate of states of a linear, discrete-time, dynamic system . It provAside states estimation, an important extension of the Kalman filter is for supervised learning or parameter identification of a partially known dynamic model given noisy observation. This important feature has motivated several applications in adaptive control involving the dual estimation of states and parameters. The dual estimation method works heuristically by alternating between estimate of states using the model, and estimate of the model using the states . If the The standard Kalman filter is however limited to linear systems. An extension to nonlinear systems necessitated the formulation of the Extended Kalman filter (EKF)  which inWe apply the dual unscented Kalman filter approach in this study for dual estimation of hip and knee joints trajectories and model parameters update using the partial model of the coupled human-exoskeleton.yk represent the noisy position observation from sensors. w stands for the system parameters (e.g. link masses). H is the measurement function. v represents the process noise which is assumed additive with covariance matrix given as Pv, and n denotes the measurement noise, non-additive, with covariance matrix given as Pn. Both the process and measurement noise are assumed white and Gaussian, with zero mean Consider the Exoskeleton dynamics given in Eqs  and 2),,2), if tu = τa + τh − JTF. The hat symbol The non-linear term er Merwe .yk from sensor, at kth sampling time, our goal is to generate optimal estimates of states, xk. The UKF does the estimation, much the same way as the EKF, using the following recursion . An approximate positive P value of 1 , the 4-state hybrid automaton is transited to coordinate and synchronize the motion of the left and right leg. Each state thus enables the trajectories of the hips and knees. Based on the computed In this section, we present the experimental setup and evaluation of the control strategy on the exoskeleton system. Three aspects of the system are evaluated: the capability of the system to minimize subjects’ lower limb muscle activation during walking, the capability to predict subjects’ gait trajectory, and the controller performance for reference tracking.Participants gave their written informed consent to participate in the experimental study. The ethics clearance for the experiment was granted by the University of Malaya Research Ethics Committee (UMREC).Note: the individual in this manuscript  has giveFour subjects with average age of 25 ± 5 years, average height of 169 cm ± 2cm and average weight of 77kg ± 7kg participated in the experiment. Two of the subjects were recruited in September, 2017 from the Centre of Product Design and Manufacturing (CPDM), Department of Mechanical Engineering and the other two subjects were recruited in April, 2018 from the Mechanical Engineering Workshop, Department of Mechanical Engineering. Initially five subjects from the Mechanical Engineering Workshop consented to participate in the experiment, however, three drop-out and only two were available for the experiment. All the subjects who participated have no history of musculoskeletal disorders or neurological diseases. The physiological features of the participants such as height were considered in their selection to ensure fitness with the exoskeleton suite.The participants were guided generally on the functionalities of the wearable exoskeleton suit and how to use the power-down switch to shut-down the system for safety in case of discomfort and emergency. Preliminary tests were also conducted to further acquaint the participants with the operation of the exoskeleton. One EMG sensor from Shimmer Sensing Technology is firmly attached at the location of the Right Vastus Intermedius (Quadriceps muscles on the right thigh) and another one attached at the location of the Right Gastrocnemius  to monitor/record each participants’ muscle activity level during walking. MATLAB software is used for rectification, low pass filtering, and analysis of the recorded EMG signals. The task of the experiment was to carry an object/load weighing 2.0kg while walking on horizontal ground a distance of 10m in three different modes: load carrying without wearing the suite, load carrying with suite in passive mode, and load carrying with suite in active mode.In this mode, the participants are to carry the load of mass to the stated distance, walking freely without wearing the exoskeleton suite. This procedure was repeated three times. The subjects were instructed to walk at their normal speed levels with a 2 minutes rest interval between each trial. The subjects’ EMG signals from the two lower limb muscles were recorded to evaluate subjects’ average muscle activation level during load carrying and walking.The second mode was carried out mainly to compare the lower limb muscle activation level when carrying the same load, walking, fully-dressed, on the exoskeleton suit. The same procedure in the first was also repeated. The exoskeleton is operated in passive mode (unactuated) in this procedure. The driving torque to move exoskeleton thus come from the wearer.In this mode, the participants repeated the same procedure in Mode 2 but with active motor assistance from the exoskeleton. The muscle activity on the two lower limb muscles and the controller performance for trajectory generation, tracking and parameter estimation were evaluated.M is mean, MD is mean difference, SD is standard deviation from the mean, SE is standard error of the mean, and p is the confidence level. The average recorded muscle activity, for all the participant, during the active mode experiment  was found to be significantly less than the average muscle activity recorded during the free walking mode . The highest muscle activity is recorded during the passive mode experiment . The bar chart in The lowpass filtered EMG signals taken from the 1st participant’s Right Vastus Intermedius and the Right Gastrocnemius for the three modes: carrying a load while walking freely (without suite), walking in passive mode with suite, and walking in active mode with suite are shown in MD = 0.024mV, SE = 0.004mV, p<0.05  indicating reduction in muscle activity. Between the free walking mode and the passive mode, the difference is also statistically significant  indicating however a net increase in muscle activation level.Overall, the mean difference in muscle activation between the free walking mode (mode 1) and the active mode (mode 3) for all participants was found to be statistically significant at 95% confidence interval for difference: .05 see, . This shShould have small magnitudeZero mean andNo autocorrelation, except at zero lag.The extensive Monte Carlo simulations , 63 was xk = T; where the first three elements  are taken experimentally from the position sensors on the hip, knee, and ankle in double stance phase, and the last three elements  to account for model inaccuracies and the effect of unknown disturbances on the plant. The higher values of process noise covariance reflect the knowledge that the states are more impacted by modelling errors. We also provided our knowledge  of (sensor) measurement noise covariance as n = diag. The DUKF generated states (simulation results) using recorded hip and knee gait trajectory as sensors’ input to the filter is shown in Prior to validating the robustness of the DUKF for state estimation/generation, we make our initial guess of states and covariance matrices. For both simulation and experiment, our initial states guess is given as xk  is also found to be small and uncorrelated with approximately zero mean, indicating boundedness of the states’ estimation errors. σ uncertainty bounds from the filter error covariance estimate. The σ (sigma) uncertainty bounds indicate the confidence interval around the best estimate. Less than 30% of the errors exceeding the 1-sigma uncertainty bound implies good estimation. The first states estimation (i.e. joint positions) errors for hip and knee exceed the 1-sigma uncertainty bound by approximately 0 percent and 27.81% (less than 30%) respectively of the time steps which indicate good confidence and robustness in the filter performance. The second states estimation (i.e. joint velocities) are slightly higher than 30% (Refer to The error between the estimated states Refer to . Howeveru = −Kp(q − qd) where u is the voltage sent to the actuators, qd is the desired joint angles and Kp is the proportional gain. The stiffness torque parameters are then computed from a regression plot of actuating torques versus static joint positions, after subtracting the effect of static friction torque and gravitational torque, see We estimated the parameters of the friction and stiffness torque experimentally using a combination of static gnal see  and locagnal see . The stiu = −Kp(q − qd). The joint static friction torques are zero in this case since the joints are in motion. The joint kinetic and damping friction torque are computed by a regression analysis of actuating torques versus joint angular velocities (from motor rpm) after subtracting the effect of stiffness and gravitational torques  joint trajectory from joint position sensors serves as the reference trajectory to the controller during the walking experiment. m1, m2, and m3. The parameter m3 (i.e. the mass of thigh) is influenced by the torso mass during the stance phase. More parameter variations are thus noticed for m3 during stance to swing transition. Parameter variations for the other links are somewhat straight.The DUKF online estimated model parameters are shown in The results of the experiment show that the exoskeleton control method can be applied for walking assistance in prolong walking conditions. There is significant reduction in the level of muscle activation recorded at the two muscles (on the right leg) when assisted with the exoskeleton. On the average, 43.4% (Right Vastus intermedius) and 60.4% (Right Gastrocnemius) reductions in muscle activity  was founIn passive mode, the burden of the exoskeleton on the wearer is apparent. More muscle activity was required by the user to walk with the exoskeleton during the swing phase . The intWith regards trajectory generation, the performance of the controller is evident from results in m3 increases significantly during the stance phase which can be ascribed to the loading effect of the torso mass on the thigh  walking speed (1.3m/s) while lifting and carrying a payload of 2.0kg on level ground. This is an applicable speed range for manual handling industry operations. Higher speed levels are possible however our current system has not been rigorously tested for higher speed walking. In comparison, HUALEX system by Huang, et al.  has beenTo the best of the authors knowledge, this study is a novel application of dual unscented Kalman filter (in a supervisory control framework) for trajectory generation (and control) of the dynamic human walking  using a partial model of the coupled human-exoskeleton system and noisy signal from position sensors. Other closely related technique like the traditional adaptive frequency oscillators (AFOs) have been quite useful and popular for gait trajectory generation however they are mainly suitable for generating uniform (or pseudo-uniform) walking trajectory from sensor signal. Dynamic movement primitive (DMPs) on the other hand encompass AFOs to allow dynamic walking generation, but their robustness to dynamic interaction situation may be an issue. Moreover, they require considerable expertise knowledge or experience to derive an appropriate policy or non-linear equation to represent the dynamic human walking. EMG Feedback control are also very useful and popular however the inconsistencies in EMG estimation and the modality of application in feedback control are critical issues to consider.In the study we proposed an exoskeleton control strategy for synchronous walking assistance in manual handling works that involve prolong hours of walking. The strategy of assistance is based on real time trajectory generation of the spatio-temporal features of human walking, i.e. hip and knee joints position, and velocity, and acceleration, for control of the human-exoskeleton system. By this, we adopt the notion to movement primitive which suggests representation of dynamic movement behavior such as walking using kinematic representation. Kinematic representation of movement primitive is thought to offer more flexibility for workspace planning of complex movements than direct motor command. Our proposed strategy is an integration of dual unscented Kalman filter for trajectory generation and an impedance controller for trajectory following. To enable synchronous walking between the human and exoskeleton system we implemented a supervisory hybrid automaton which coordinate the coupled movement based on the detected human intention and walking phase.The effectiveness of the controlled system to reduce lower limb muscle activity has been evaluated on four participants in a mimicked load carrying industrial scenario. There is more than 40% reduction in muscle activity recorded at the Right Vastus Intermedius and Gastrocnemius muscle of the participants during the walking trials. The controller is also able to synchronize the movement of the exoskeleton with that of the participants using the generated walking trajectory from the dual unscented Kalman filter. One potential limitation in the experimental setup however is the response time of the exoskeleton to the control signal which can be adduced to the communication layers from the host model on Simulink to the exoskeleton actuation system. The experimental findings presented in this study have nonetheless indicated that this strategy could be deployed to benefit workers engaged in prolong walking in dynamic working environment where movement behaviour may be non-uniform and complex.S1 DataThe dataset is in .sav format (SPSS) and consist of EMG signal values taken from two muscle groups (of each participant): R. Vastus Intermedius and R. Gastrocnemius, in three walking trials and three mode of exoskeleton assistance.(RAR)Click here for additional data file.


Complete mesocolic excision is gradually becoming an established oncologic surgical principle for right hemicolectomy. However, the procedure is technically demanding and carries the risk of serious complications, especially when performed laparoscopically. A standardized procedure that minimizes technical hazards and facilitates teaching is, therefore, highly desirable.An expert group of surgeons and one anatomist met three times. The initial aim was to achieve consensus about the surgical anatomy before agreeing on a sequence for dissection in laparoscopic CME. This proposal was evaluated and discussed in an anatomy workshop using post-mortem body donors along with videos of process-informed procedures, leading to a definite consensus.In order to provide a clear picture of the surgical anatomy, the “open book” model was developed, consisting of symbolic pages representing the corresponding dissection planes , vascular relations, and radicality criteria. The description of the procedure is based on eight preparative milestones, which all serve as critical views of safety. The chosen sequence of the milestones was designed to maximize control during central vascular dissection. Failure to reach any of the critical views should alert the surgeon to a possible incorrect dissection and to consider converting to an open procedure.Combining the open-book anatomical model with a clearly structured dissection sequence, using critical views as safety checkpoints, may provide a safe and efficient platform for teaching laparoscopic right hemicolectomy with CME.The online version of this article (10.1007/s00464-018-6267-0) contains supplementary material, which is available to authorized users. Precision of oncological resections has an impact on cancer recurrence and survival. In total mesorectal excision (TME) , the keyBefore the CME era, laparoscopic colorectal procedures were viewed as oncological equivalent to open surgery . To meetThe objective of our working group was to establish a standardized procedure for laparoscopic right hemicolectomy that meets all CME criteria, with maximal surgical safety which can also serve as the basis of a training program.An expert group of 13 experienced laparoscopic colorectal surgeons, one anatomist, and one graphic artist (and surgeon in training) met three times. In order to achieve our objective of a safe, teachable, and radical CME, the following requirements were initially defined:Clear definition and depiction of surgical anatomy.Definition of oncologic radicality.Description of hazards.Drafting of a proposal for a laparoscopic standard technique that provides procedural safety and radicality.Inclusion of the critical view concept analogous to that in laparoscopic cholecystectomy  Each of the expert surgeons had a minimum of 13 years of post-certification experience (13–30 years) and had performed at least 750 (750–1800) colorectal resections, including > 500 (500–800) laparoscopic colorectal resections and 90–220 laparoscopic right hemicolectomies.To depict the surgical anatomy, the “open-book” model was further developed from a template published previously . CriteriDuring the first consensus session, videos of laparoscopic CME right hemicolectomies performed by the experts were individually reviewed by the entire group. Essential or potentially difficult steps of the operation were identified, or their relevance acknowledged for further standardization.A consecutive workshop evaluated each of the variants and the key steps of the operation which had been consented previously, including the usefulness of the open book model in four body donors. Under the supervision of the anatomist (TW), the operations were performed simultaneously by four rotating teams using the same dissecting and ultrasound-based sealing devices. Port placement was agreed upon on the basis of the most frequent pattern among the participants and applied in all cases .After each surgical step, the procedures were interrupted and the results discussed. If there were any complications or critical situations, the supervising anatomist called for a time out and the situation was presented to the entire group. This protocol enabled the surgical expertise of all participants on the progression of the procedures to have maximal effect. It also ensured maximal learning for the whole group from any differences between the body donors . All donors presented with a venous gastro-pancreatico-colic trunk (GPCT) collecting a superior right colic vein (SRCV), a right colic vein (RCV), and a right gastroepiploic vein (RGEV). Since evaluation of CME quality was not the objective of the body donor workshop, no tissue samples were histologically analyzed.At the end of the workshop, consensus was reached regarding the type and order of the required procedural steps. Each sequence of the operation resulted in representative anatomical scenes. As a result, eight critical views were unanimously adopted as a means of documenting what constituted an adequate operation according to the standardized procedure.In a third meeting, additional surgical videos were reviewed which documented laparoscopic right hemicolectomies after implementation of the previous consensus. This last step allowed for adjustment and the final definition of the critical views which are described here. Each step and each critical view as well as its sequence within the procedure were discussed until full consensus was reached.Target criteria of CME for oncologic radicality:Preservation of visceral fascia without injuring the mesocolon.Complete removal of the regional lymphatic vessels and lymph nodes.Division of the supplying arteries close to their origin (ileocolic artery (ICA), right colic artery, right branch of the middle colic artery).Complete removal of the lymphatic tissue along the right side of the superior mesenteric vein (SMV) from approximately 3 cm distal to the ileocolic vein (ICV) up to the GPCT with division of all veins running from the mesocolon into the GPCT (SRCV and RCV).Preservation of the GPCT including the pancreatic contributories and the veins that merge into the SMV ).To facilitate the surgical overview, the open book model of the fascial and vascular relations was developed . The SMV can now be followed up to the confluence of the ICV and the SMV. This ensures that the lymphatics at the ileo-mesenteric junctions are completely resected. This approach also increases safety because the control of the SMV is facilitated due to its dorsal mobility. Before division of the ICV, the confluence (SMV/ICV) is completely dissected.An instrument passed behind the ICV ensures unequivocal circular dissection.In this step, the ICA is divided. If the artery runs anterior to the SMV, it is divided close to its origin at the SMA. If the ICA crosses dorsal to the SMV, its division is performed at the level of the right border of the SMV. Using this approach, often the SMA becomes visible dorsal to the SMV so that a complete lymphadenectomy on the right aspect of the SMA can be performed .Further cephalad preparation along the SMV is terminated at the level of the inflow of the GPCT. Then the lesser sac is opened while preserving the gastro-omental arcade.View into the lesser sac on the posterior wall of the stomach  merge with the GPCT. Dissection step 6 results in a sulcus running from the area of the middle colic vessels to the anterior aspect of the duodenum (part II) between the cephalad mesogastrium and the caudally located transverse mesocolon. The GPCT and—further to the left— the pancreatic body, mark the posterior border of the sulcus. In relation to the sulcus, the course of the SRCV is special in the respect that it bridges the gap between the transverse mesocolic and the mesogastric page in the open book model before it merges into the GPCT (Video No. 1). Therefore, dissection of the SRCV needs to avoid inappropriate tension.View from medial to lateral shows the sulcus between the mesogastrium and transverse mesocolon on the pancreatic head crossing over the duodenum. The anterior aspects of the SRCV and the right gastro-omental veins can be identified  to be performed before division of the vessels. This is a clear difference to other techniques of laparoscopic hemicolectomy—including the classical medial approach. For example, when the medial approach is applied, the ileocolic vessels and the SMV are dissected before the mesenteric root and the mesentery of the ascending colon are mobilized. Under these circumstances, injuries to the SMV or the ileocolic vessels are hard to control. The same holds true for the middle colic vessels and the veins joining the GPCT. Control of the GPCT can only be reliably achieved when the space between the mesogastric and the transverse mesocolic page are separated and the SMV has been unmistakably dissected.The operation was divided into well-defined steps in order to facilitate adherence to the suggested sequence. In addition, the concept of the critical view of safety was adopted from laparoscopic cholecystectomy. Because laparoscopic right hemicolectomy is more complex, eight specific critical views were introduced. Failure to achieve the critical views should prompt the surgeon to re-evaluate the anatomy and consider conversion to laparotomy, so that safety and radicality are not compromised. This is analogous to the widely held view that, when Strassberg’s view of safety in laparoscopic cholecystectomy is not achieved, conversion may be indicated.An additional focus of the consensus process was to choose critical views that are independent of surgical devices and dissection techniques. As a result, port placement and patient positioning, choice of sealing devices, or even robot use or the location of the mini laparotomy are not in the scope of standardization. In this respect, our suggestion should be considered as the description of a surgical principle rather than a text-book guidance that can be applied independently of operation room setting and choice of surgical instruments.The strength of our work is that a large group of experienced surgeons together with an anatomist were able to find a consensus about a putative safe way to perform and teach laparoscopic right hemicolectomy with CME.However, our expert opinion alone does not constitute evidence that the standardized proposed procedure is safer in practice than any other approach to laparoscopic right hemicolectomy with CME. Therefore, our group has initiated a multicenter trial (DRKS-ID: DRKS00012369) in which the procedure is evaluated. The first patient was recruited in July 2017.In conclusion, the suggested standardized approach for laparoscopic right hemicolectomy with CME based on the open book model and using the critical views of safety may contribute to a safe implementation of this procedure in routine practice.Below is the link to the electronic supplementary material.Supplementary Video No. 1 (M4V 72322 KB)Supplementary Video No. 2 (M4V 49255 KB)Supplementary Video No. 3 (M4V 46467 KB)Supplementary Video No. 4 (M4V 50871 KB)


In the field of indoor pedestrian positioning, the improved Quasi-Static magnetic Field (iQSF) method has been proposed to estimate gyroscope biases in magnetically perturbed environments. However, this method is only effective when a person walks along straight-line paths. For other curved or more complex path patterns, the iQSF method would fail to detect the quasi-static magnetic field. To address this issue, a novel approach is developed for quasi-static magnetic field detection in foot-mounted Inertial Navigation System. The proposed method detects the quasi-static magnetic field using the rate of change in differences between the magnetically derived heading and the heading derived from gyroscope. In addition, to eliminate the distortions caused by system platforms and shoes, a magnetometer calibration method is developed and the calibration is transformed from three-dimensional to two-dimensional coordinate according to the motion model of a pedestrian. The experimental results demonstrate that the proposed method can provide superior performance in suppressing the heading errors with the comparison to iQSF method. High accuracy and infrastructure-free indoor pedestrian positioning is a highly desired ability for finding and rescuing firefighters or other emergency first responders, or for personal navigation assistance. With the adoption of Global Navigation Satellite System (GNSS), positioning in outdoor environment has witnessed a dramatic success. However, GNSS performs poorly in indoor environment and is not suitable for indoor positioning because of weak signal reception and radio wave multi-path effect. Developers have suggested various indoor positioning technologies such as Ultrasound ,2, RadioA practical solution to indoor positioning is to use inertial sensors such as microelectromechanical systems (MEMS) gyroscopes and accelerometers. Inertial-based positioning systems can track the position of the user with no pre-installed infrastructures or a geographical fingerprint. These systems are generally in the form of wearable devices, which can be worn on the helmet, belt or shoe of a person ,10. AmonIn order to solve this problem, other aiding sensors or information sources are utilized. For example, with magnetometers, the measure of the Earth’s magnetic field can be used to estimate errors associated with gyroscopes. In Reference , the difTo address the aforementioned issues, we propose a novel quasi-static magnetic field detection approach for foot-mounted IMU system. The proposed method detects the quasi-static magnetic field using the rate of change in differences between the magnetically derived heading and the heading derived from gyroscope. The proposed method will not be subject to the straight-line constraint. The quasi-static magnetic field detected by the proposed method can be utilized as the measurement, which can be fed into the ZUPT-aided EKF to estimate the gyroscope biases. Moreover, a calibration method of the magnetometer is proposed to eliminate the hard iron and soft iron distortions caused by system platform and shoes. The calibration of the magnetometer is carried out before it is adopted for positioning.The Earth’s magnetic field can be precisely measured and utilized to estimate heading by magnetometers. The three-dimensional Earth’s magnetic field vector is shown in Here From Equation (1), it can be observed that the magnetic field components should be transformed to navigation frame (defined to be North-East-Down on the ground) so as to find the horizontal component of the Earth’s magnetic field. Let In other words, the three-axis magnetometer can be used as the two-axis magnetometer in horizontal plane coordinate (North-East frame).Similar to inertial sensors such as accelerometers and gyroscopes, magnetometers also suffer from errors due to magnetic deviation which can result in an inaccurate heading measurement . The maiMany calibration algorithms have been proposed. One use measurements collected by a 360° rotation of the levelled magnetometer in the horizontal plane to find the maximum and minimum values to estimate biases of the sensor. The iterative least squares algorithm is utilized to estimate the bias and the combined scale factors for a given data set . This alWhen the foot is stationary on the floor, the platform is only affected by gravity. Then we can calculate the attitude angle of the platform according to Equation (3). Using the attitude angle, we can transform the magnetic field from sensor body coordinate system to navigation coordinate system. In addition, as abovementioned discussion, the orthogonal field component (1)Let the IMU be installed in the heel of the pedestrian’s shoe, then the pedestrian walks around a loop as shown in (2)By using the stored data, the stance phase can be identified according to the Zero-Velocity detection algorithm in Reference .(3)Transform the magnetometer’s measurement from the sensor body coordinate frame to the navigation frame according to Equation (4). Then the average maximum and minimum values for each of the axes can be calculated.(4)Let (1)Find major axe and minor axe of the ellipse by a loop calculation of stored magnetic field database (2)Determine inclination angle of the ellipse by:Then, the rotational matrix can be constructed to align the rotated ellipse with one of the coordinate system axes. The rotational matrix (3)Rotate the ellipse:(4)Scale The coordinates set of the circle is rotated back to initial position using the rotational matrix and inclination angle:Compensation for the soft-iron distortion includes finding mathematical representation of the ellipse that is caused by disturbed magnetic field. The calibration procedure is as follows:Although the Earth’s magnetic field is a good measurement for heading estimation outdoor, it suffers severe perturbations in buildings. These perturbations induce random variations in the magnetic field estimations. As To solve this problem, we use the rate of change in difference between the two headings mentioned above. As the error accumulation of the heading derived from gyroscope is very small during short periods, the heading derived from angular rate can be utilized to assess the stability of the magnetically derived heading. If the rate of change in differences between the magnetically derived heading and the heading derived from angular rate is approximate to zero, then the magnetic field can be considered as quasi-static. Herein, the detection of the quasi-static magnetic field is unrelated to the shape of the paths. In addition, the measurements of total magnetic field magnitude and inclination angle are also adopted. The magnetic field can be detected as quasi-static if both the changing rates of total magnetic field magnitude and inclination angle are equal to zero. The proposed detection approach is elaborated as follows.Let γ is determined fromOwing to the lack of knowledge about the signal Padé approximation of the exponential function is utilized to update orientation [If the magnetic field is detected as quasi-static, the magnetically derived heading will be adopted to estimate the heading errors of the gyroscope based on the ZUPT-aided EKF algorithm. Let entation :(27)Ct=fHere, as the magnetic field is detected as quasi-static, the heading According to the above description, we summarize the procedure of the proposed method and the flowchart is shown in To analyze the performance of the proposed method, experiments have been carried out. As shown in We conducted one test to assess the performance of the proposed magnetometer calibration method. In the test, the proposed method was compared with the CLSEF method. We performed the CLSEF method by rotating the sensor in all possible directions in a constant uniform magnetic field. The sensor measurement of rotation is depicted in The results for heading calibration by the two methods are compared in To use the proposed detector effectively, there are several tuning parameters, denoted in Equation (26), need to be quantified.To evaluate the positioning performance of the proposed method, we conducted two tests in real indoor environments which are very common for pedestrian navigation application: office and shopping mall. In the office test, we walked along the corridors and walls in a typical office at normal speed (approximately 5 km/h) and then kept walking three loops with the same path. The total distance of the path was approximately 1018 m in 786 steps. We conducted the second trajectory test in a shopping mall to evaluate the effectiveness of the proposed method in large-scale scenario. The total distance of this trajectory was approximately 2480 m in 1920 steps and 14 landmarks were set along the path to calculate the positioning errors. During the test, we crossed the 14 landmarks for a total of 42 times and counted the positioning errors of the iQSF method and the proposed method as shown in In this paper, a heading error estimation method for using the quasi-static magnetic field has been developed. The proposed approach is implemented in two sections. Firstly, to eliminate the errors originating from the system platform, floor and shoes, a magnetometer calibration method is proposed. In the proposed calibration method, the three-axis magnetometer calibration is transformed to that of two-axis according to the motion model of the pedestrian, hence the calibration procedure is simplified. Secondly, a novel quasi-static magnetic field detection approach is developed and utilized to suppress the heading drift of the gyroscope. The proposed method detects the quasi-static magnetic field using the change rate of the magnetic field magnitude, the inclination angle and the difference between the magnetically derived heading and the heading derived from gyroscope. The detected quasi-static magnetic field is utilized as the measurement fed into the ZUPT-aided EKF to estimate the heading errors. Selection of two real indoor environments  provided data sets for a detailed analysis of the performance of the proposed method. The experimental results indicate that the proposed method is capable of effectively suppressing the heading errors caused by the drift of gyroscopes, reducing the overall positioning error budget by over 85% in shopping mall environment. No other sensors of any kind are used in the proposed method, except IMUs and magnetometers. The approach developed herein are self-contained and assumed a denied GNSS environment. However, GNSS is partly available in numerous indoor environments and urban canyons. Therefore, we will integrate the two approaches to maximize availability and accuracy in the future.


A multi-scale phase-field approach, which couples the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow, is proposed to study how the crystal growth of semi-crystalline polymers is affected by flows. To make the simulation feasible, we divide the problem into three parts. In the first part, a finitely extensible nonlinear elastic (FENE) dumbbell model is used to simulate the flow induced molecular structure. In the second part, formulas for estimating the density, orientation and aspect ratio of nuclei upon the oriented molecular structure are derived. Finally, in the third part, a massive mathematical model that couples the phase-field, temperature field, flow field and orientation field is established to model the crystal growth with melt flow. Two-dimensional simulations are carried out for predicting the flow effect on the crystal growth of isotactic polystyrene under a plane Poiseuille flow. In solving the model, a semi-analytical method is adopted to avoid the numerical difficult of a “high Weissenberg number problem” in the first part, and an efficient fractional step method is used to reduce the computing complexity in the third part. The simulation results demonstrate that flow strongly affects the morphology of single crystal but does not bring a significant influence on the holistic morphology of bulk crystallization. As is well known, crystallization of polymers is very different from that of the small molecular materials. Generally, the crystallization of polymers is more complex, and no polymer can be fully crystallized. The final morphology and crystallinity of polymers strongly depend on both their interior structures (molecular configuration and chain conformation) and exterior conditions. Because the resulting crystalline structures have significant impacts on material properties and further determine the performance of products in end uses, the research of polymer crystallization has great significance.After extensive study over a long period in the past, the research findings and theories about polymer crystallization in quiescent conditions are on the way to perfection. However, under real processing conditions , polymers always undergo the force  of external fields. In this case, the crystallization behavior of polymers will be greatly changed. It has been known that flow shortens the nucleation time, enhances the nucleation density and accelerates the crystal growth of polymers ,2. MoreoThese years, numerical simulation has been necessary, complementary to the experimental study of polymer crystallization. Plenty of simulations using approaches ranging from simple expressions to multi-scale models have been performed to predict the flow effect on crystal growth of semi-crystalline polymers. Rong et al.  presenteIn morphological research, there have been many simulation approaches available, which include molecular dynamics methods ,11,12,13The phase-field method uses a crystal order parameter to describe phase transition. Evolution of the crystal order parameter can be governed by a group of nonlinear partial differential equations derived from the Ginzburg–Landau theory. So far, this method has gained great success in understanding the dendritic growth of small molecular materials ,32,33,34In fact, much effort has been made on simulating the coexistent system of flow and dendritic growth of metals by the phase-field method ,40. HoweThe rest of this paper is arranged as follows. In The physical problem considered is first putting the hot polymer melt into a fast simple flow for a period of time, and then decreasing the flow to a large extent and cooling the melt to a scheduled crystallization temperature quite rapidly. This process may be divided into three stages, which are molecular stretch and orientation by fast flow, nucleation upon the flow induced structure and crystal growth with slow melt flow. For this reason, our mathematical model includes three parts accordingly. Details for this are showing below.When polymer solution or melt is undergoing the shear or elongation of fast flow, the whole chain or chain segments of a molecule will have the opportunity to be stretched and oriented. The stretched and oriented structures would be completely or partly retained after the weakening or cessation of flow, and then have important effect on the subsequently crystallization. Several computational models have been available for predicting the molecular orientation of polymer undergoing flow, such as the Leonov model , the FENThe FENE-P model is developed from the dumbbell model of polymer molecules. A dumbbell, which consists of two rigid beads connected by a massless spring, is an abstract representation of a polymer molecule. At any given time, the beads are subjected to friction force, Brownian force and spring force. According to Newton’s second law and neglecting the acceleration, the equation for the relative motion of the beads would be obtained asThe substitution of Once the flow velocity Generally, directly solving Equation (3) is rather difficult, so the moment-closure approach is very popular and adopted in this work. The equation for the second moments readsBy inserting Equation (6) into Equation (5) and defining the dimensionless conformation tensor By employing the dimensionless conformation tensor obtained . From thIn addition, the conformation tensor may also be used to quantify the molecular stretch. Generally, the first invariant Based on the above, once It has been well known that flow has great influence on the crystallization of polymer, especially on the nucleation stage. Stable nuclei or precursors with some degree of order can often be generated from polymer melt that has just experienced flow history. Generally, flow affects the nucleation stage of polymer crystallization by providing both extra nucleation sites and oriented templates. The former accelerates kinetics of the crystallization and the latter induces anisotropic crystal growth. The following content in this subsection will focus on seeking mathematical descriptions for the two aspects.Much evidence has shown that the number of activated nuclei formed during solidification from the melt with flow history is usually greater than that without flow history. Based on the experimental observations, the total nuclei may be divided into two parts, which are the general nuclei observed in quiescent condition In quiescent conditions, the following equation, which describes the nucleation density as a function of temperature, is generally used in literature to evaluate ulchiron , the numFor two-dimensional problems, the 3D nucleation density giving in Equation (11) should be converted to a 2D nucleation density. Referring to the work done by Charbon and Swaminarayan , the ste process , the expAs to the oriented templates, the flow induced molecular structure plays a very important role. It is generally accepted that the ordered (stretched and oriented) structures generated by flow is responsible for the oriented nucleus formation and hence the subsequently anisotropic crystal growth. Different crystalline patterns or morphologies may be produced depending on the molecular orientation and stretch prior to the start of crystallization. Because our attention in this work is mainly paid to the crystalline morphology, it is necessary to establish the relationships between the ordered structures and oriented nuclei.In theoretical modeling, the oriented nucleus is usually regarded as possessing a cylindrical appearance for simplicity’s sake . This waCompared to Equations (15) and (20) provides a more intuitive expression. It actually uses the “aspect ratio” of the orientation ellipse to describe the aspect ratio of the nucleus. Moreover, this equation also means that nditions .In this work, we will model the crystal growth of semi-crystalline polymer upon oriented nuclei by using phase-field approach. At present, the studies of crystal growth based on phase-field methods mainly consider the point-like nuclei. However, it is lucky that we have successfully developed the oriented nuclei into phase-field modeling in our recent work . For thiThe formation of morphological features in solidification of semi-crystalline polymers under flow conditions has been investigated over many years. Through experimental observations, many flow induced crystallization patterns that are very different from those obtained from quiescent conditions have been found. However, little has been known about the influence of flow on microstructure development. Generally, when crystal growth is accompanied by slow melt flow, not only does flow influence the crystallization pattern, but the evolving microstructure can also trigger unexpected and complicated flow phenomena. Therefore, it is necessary to develop a flow and crystal growth coupled model to study the complex interaction between melt flow and morphology evolution of polymers.For modeling the coexistent system of crystal growth and melt flow of polymers, the existing relevant studies on small molecule materials may be used as a reference. At present, there are mainly two kinds of methodologies mostly used, which are developed by Anderson et al. ,55,56 anLet ), viz.,F=∫[), viz.,F=∫[By substituting Equations (22)–(25) into Equation (21), one obtains the following phase-field equation for planar crystallizations:Because the melt flow during solidification is usually very slow, migration of crystallized structure by flow may be neglected. Accordingly, we assume that the phase-field variable is not advected by flow, thus the phase-field Equation (26) is unchanged from the stationary diffusive case.To determine the temperature at the growing crystal fronts, a heat conduction equation may be deduced from the conservation law of enthalpy. For simplicity, the liquid and solid are assumed to have the same density n et al. ,57, the For crystal growth and melt flow coexistent system, conservation equations for mass and momentum need to be valid not only in the solid and liquid phases, but also in the diffuse interface region where the solid and liquid phases coexist. During solidification, the phase-field variable Note that Equation (29) is indeed absent in the solid phase. Recall that the solid is assumed to be stationary and rigid, such that a momentum equation for the solid phase is not needed. In order to solve Equation (29), a constitutive equation for calculating the extra stress tensor If the problem considered is a sharp interface one instead of the diffuse interface one, there would be no volume flow at the interface. That is to say, the flow has a no-slip condition between the melt and the solid. The work done by Beckermann et al. realizes this condition via a drag resistivity in the diffuse interface region . In thisSo far, plenty of researches have demonstrated that the crystallization has a dramatic influence on polymer viscosity and this phenomenon must obviously be taken into account . DespiteAs we have stated at the beginning of Simulations are carried out in 2D for the models presented above using rectangular computation domains. The inlet velocity boundary conditions are imposed on the left side boundary and their values are Tc=200°C . In addiFirst, the growth of single crystals with viscoelastic fluid flow is investigated. At this situation, the fast melt flow prior to crystallization is not considered and all the crystals grow from point-like nuclei. r metals . MoreoveIn literature, the dendritic growth of metal crystals in shear flows has been studied for a long time. Newtonian fluid flows were considered in these studies. However, for polymers, the melt usually exhibits elasticity. Thus, it is reasonable to consider viscoelastic fluid flows in simulating the polymer crystallization under flow condition. At present, it is not clear to what extent the viscoelasticity affects the crystallization. Except for the dendritic growth pattern, polymer crystals often exhibit many other growth patterns. Researches about the growth of single crystals have important scientific values in predicting the growth mechanism of grains. However, in fact, there are almost no such single crystal morphologies in real materials. The knowledge getting from the study of single crystals only has guiding significance to the local crystallization behavior. In order to predict the flow effect on the holistic crystallization behavior of semi-crystalline polymers, the simulations should contain all of the three steps, which are: fast flow induced molecular structure, nucleation upon oriented molecular structure, and crystal growth with slow melt flow. Because of the numerical difficult of “high Weissenberg number problem”, the above simulations are limited to the crystal growth under a plane Poiseuille flow of FENE-P fluids. The possible improvements of our tool include extending the simulations to other type of flow, different polymer melt, 3D, etc. For these improvements, the main challenges are the numerical stability and computational cost. To ensure the stability, we can develop a more stable numerical method or use another polymer model. To settle the problem of high computational cost, we can propose a more efficient numerical method and use a faster computing platform. If these improvements are realized, more phenomena would be predicted by our model.In this work, a multi-scale phase-field method has been presented for predicting the viscoelastic flow effect on the crystal growth of semi-crystalline polymers. To simplify the problem, the crystallization is divided into three parts. Firstly, in modeling the flow induced molecular structure, the FENE-P dumbbell model in microscale is coupled with the viscoelastic Navier–Stokes equations in macroscale to calculate the molecular orientation and stretch. Secondly, in modeling the nucleation upon oriented molecular structure, the influences of flow on nucleus shape and nucleus number are both taken into consideration. Concretely, the nucleus shape is related to the flow induced structures and nucleus number is linked to the flow induced stress. Thirdly, in modeling the crystal growth with melt flow, a massive mathematical model is established by coupling the phase-field with the temperature field, flow field and orientation field. The three parts together couple the mesoscopic crystallization with the microscopic orientation of chain segments and macroscopic viscoelastic melt flow. In solving the model, a semi-analytical method is adopted to avoid the numerical difficulty of “high Weissenberg number problem” in the first part, and an efficient fractional step method is used to reduce the computing complexity in the third part. Simulations are carried out for the crystallization of isotactic polystyrene under a plane Poiseuille flow. Results show that the flow effect on the morphology of single crystals is more prominent than on the morphology of bulk crystallizations. Specifically, the growth of single crystals including dendritic pattern, snowflake pattern and seaweed pattern all tilt toward the upstream direction. Meanwhile the growth of side branches gets promoted and inhibited on the upstream and downstream side, respectively. By comparison, the growth on the downstream side is more susceptible to fluid flow. For different growth patterns, the morphology having more branching structure seems less influenced by flow. Importantly, it is ascertained that the influence of viscoelasticity on the crystal morphology is not significant. As to the bulk crystallization in real materials, we find that flow does not have a significant influence on the holistic crystal morphology during the crystal growth stage and flow affects the morphology mainly through affecting the nucleation.