Currently, braking control systems used in regional railways are open-loop systems, such as metro and tramways. Given that the performance of braking can be influenced by issues such as wheel sliding or the properties of the friction components present in brake systems, our study puts forward a novel closed-loop mechanism to autonomously stabilize braking performance. It is able to keep train deceleration close to the target values required by the braking control unit (BCU), especially in terms of the electrical–pneumatic braking transform process. This method fully considers the friction efficiency characteristics of brake pads and encompasses running tests using rolling stock. The test results show that the technique is able to stabilize the actual deceleration at a closer rate to the target deceleration than before and avoid wheel sliding protection (WSP) action, especially during low-speed periods. Urban rail train transit is extensively utilized, and advancements in train braking technology have led to the need for improved control performance in order to enhance the efficiency of urban rail train braking systems. Ensuring accurate parking during operations entails fulfilling more stringent criteria for braking distances and precision. This task becomes especially demanding during peak operation periods, characterized by limited departure intervals and a high volume of passengers. Insufficient control precision in braking directly affects train deceleration and position control accuracy, thereby reducing the overall door-to-door precision throughout the braking process. The graphical representation of this requirement is depicted in Currently, urban rail train vehicles employ two primary braking methods: electric braking and pneumatic braking. Electric braking is accomplished via the traction system of the train regulating the traction motor to produce reverse torque. In contrast, pneumatic braking employs compressed air, which is transformed into friction via the braking actuator. In the braking procedure, especially during rapid and emergency braking, the objective is to sustain a uniform braking pressure among all wheel sets, taking into account the load conditions of each unit. In theory, this uniform pressure ensures a constant deceleration since the applied braking force remains constant. However, real-world operating conditions prevent the vehicle from achieving ideal circumstances. Even with sufficient adhesion, the actual deceleration deviates from the theoretical value primarily due to variations in the friction coefficient between the brake pad and brake disc friction pair within the brake unit. The variation in the friction coefficient is primarily influenced by the temperature fluctuations experienced by the brake disc before the onset of braking. The energy input, responsible for determining the temperature of the brake disc, is influenced by factors such as the vehicle’s initial braking speed, as well as external conditions, including temperature and humidity. Additionally, running on inclines, curves, tunnels, and other sections of the track generates additional running resistance. The uncertainty associated with the friction braking torque and running resistance contributes to the uncertainty in the overall braking force of the train.In railway braking systems, the currently used open-loop control system lacks automatic correction based on output during the braking process. Within this system, the brake command functions as the input, whereas the change in train speed serves as the output. Consequently, the accuracy of deceleration control in the braking system is inadequate. Researchers have started investigating closed-loop control techniques for the train braking process to tackle this issue. In the closed-loop control mode, the braking control system employs the braking deceleration as feedback. It adjusts the braking force based on the difference between the target deceleration and the actual deceleration. This approach is known as deceleration closed-loop control.In 2002, Nankyo proposed the feedback control of deceleration which involved adjusting the braking force of the entire train through the train information management system (TIMS) ,2. CloseTo summarize, the main challenge lies in achieving precise control with a multi-parameter controller under limited conditions, particularly when dealing with hysteresis control involving the friction coefficient of the brake disc and the adhesion coefficient of the wheel/rail. In order to tackle this issue, a simplified control system is proposed, which employs a dynamic parameter set of disc coefficients. By effectively handling the complex and variable uncertainties, the system is able to primarily concentrate on the feedback control of the adhesion coefficient between the wheel and rail. This significantly reduces the computational requirements of the system.The implementation of feedback control for deceleration involves addressing two key issues. First, it requires obtaining accurate real-time information on the train’s deceleration. Second, a suitable brake cylinder pressure correction factor must be determined. Furthermore, the system needs to consider coordinating conditions such as actuator response time and compatibility with other control links within the train to achieve an advanced solution. This involves employing a series of acceleration sensors to accurately measure the overall train deceleration, especially the difference between the front and rear cars during braking and the impact of rampways on deceleration. Furthermore, a set of brake cylinder pressure-modified factors, derived from the characteristics of the brake pads, is employed. It is apparent that the main source of deceleration instability lies in the properties of the brake pads, as their dynamic temperature influences friction efficiency and, consequently, deceleration stability. To tackle this problem, a closed-loop control system is proposed, which utilizes deceleration feedback to stabilize braking performance. This approach functions as a tracking control mechanism. Once the braking demand is determined, the controller selects the appropriate braking deceleration based on the current train speed and allocates it to electric and pneumatic braking. The distribution of braking force is adjusted in real-time if the braking efficiency of the brake pads fluctuates. This technology modifies the pneumatic brake based on the dynamic friction efficiency characteristics of the brake pads. In essence, this technology relies on deceleration feedback to correct the braking effect (deceleration or brake cylinder pressure), aiming to achieve more accurate train stopping and prevent discomfort resulting from deceleration oscillation.In general, the braking control unit oversees the overall braking operation based on the braking command issued by the driver or the automatic train operation system (ATO). This includes managing the distribution and application of braking forces. Two types of braking forces are employed: the electric braking force and the pneumatic braking force. The electric braking force is generated by the traction system and is applied solely to the motor car. The remaining braking force requirements are fulfilled by the pneumatic braking force, which ensures a balanced distribution of braking forces across the entire train, with each unit receiving an appropriate share. The prevailing braking force management mode used in modern urban rail trains is typically marshalling control, which operates at the train level and adheres to the principle of lagging friction braking. In this mode, the electric braking force of motor cars is prioritized, with friction braking utilized as a supplement when the electric braking force is insufficient. As a result, the allocation of braking forces among vehicles is uneven when operating in the multiple-vehicle control mode. Currently, urban rail trains employ electric multiple units (EMU), consisting of two interconnected units, often joined together using close-coupled semi-automatic couplers.The characteristics of electric braking force result in its minimal contribution at low speeds, with the entirety of braking force being primarily provided by the pneumatic braking force during such instances. During emergency braking scenarios, the pneumatic braking force becomes solely responsible for deceleration. Brake commands typically encompass seven levels, each corresponding to distinct deceleration targets. However, existing brake control systems are structured as open-loop systems, with the brake command serving as the input and train deceleration as the output. Nonetheless, these current brake control systems, as seen in The BCU has undergone improvements to achieve and sustain target deceleration until the completion of the braking process, as depicted in 2, which is essential for accurate control. Unlike the calculation of deceleration based on speed, the use of deceleration sensors eliminates the need for additional calculations, thereby saving data processing time. Furthermore, the deceleration data acquired from these sensors can directly assist in determining the vehicle’s entry and exit points when encountering rampways.One significant advantage of the new system structure is the incorporation of deceleration sensors, also known as a MEMS-based inertial sensor. It has a limited range but offers high accuracy and resolution. It can achieve highly precise measurements, up to 0.1 m/sThe controller equipped with the deceleration sensor is installed on the train, but the operational vibrations introduced noise into the deceleration signal. To address this, a Kalman filter was employed for filtering. The discrete variable form of the filter offers a simple structure, requires minimal calculations, and facilitates real-time operation in the train controller. It is crucial to address the issue of the deceleration sensor’s sensitivity, as it is able to detect speed fluctuations even during non-braking situations.During motion, the deceleration sensor is sensitive not only to external acceleration but also to the force of the gravity that it measures. Consequently, the signal from the deceleration sensor represents the combined effect of gravity and external acceleration. Hence, a challenge arises in mitigating the impact of gravitational acceleration during ramp sections. Two potential approaches are discussed in this context. One approach involves treating the gravity component as a measurement error and directly filtering it out during the design of the Kalman filter. The other approach involves determining the train’s state and treating straight sections and rampways separately. The choice between these methods depends on the specific conditions of the railway line. The first method is more suitable for occasional ramps that are not lengthy, as it simplifies the decision-making process for the entire system. However, the second option must be chosen if there is a prolonged ramp state or even parking on a ramp. This is because ramp information will persist for an extended period during the braking decision-making process, and the influence of gravity cannot be disregarded.A crucial component of orientation estimation using an inertial sensor is the determination of external acceleration. This is achieved by subtracting the gravitational acceleration from the deceleration sensor signal. It is important to highlight that this subtraction only necessitates attitude information and does not require the complete 3D orientation ,8,9. TheIn railway design standards, the slope of a rampway typically ranges from 20‰ to 30‰. When the ramp is sufficiently long, the train’s attitude can be determined by observing the effect of gravity on the acceleration of the front and rear cars, as shown in Theoretically, railway tracks do not have continuous ramps; instead, they resemble the presence of steps, especially when the ramp length is shorter than the train’s length. In such operating conditions, the gravity component is treated as noise and is processed by the filter.The well-known Kalman filter is one of the fundamental mathematical tools employed for stochastic estimation from noisy sensor measurements. The Kalman filter is a mathematical tool that employs a series of equations to implement a predictor–corrector estimation approach, which is considered optimal under specific assumptions. Its objective is to minimize the error covariance of the estimate. Since its inception, the Kalman filter has found widespread application in the field of navigation, particularly in sensor attitude recognition and precise positioning.However, when dealing with dynamic systems, time domain signals, such as train acceleration signals, often exhibit nonlinearity. The basic Kalman filter can introduce errors during its operation. In the course of its development, alternatives like the fuzzy adaptive Kalman filter and the nonlinear extended Kalman filter (EKF) have been considered. Ultimately, the nonlinear EKF was chosen due to its computational process and accuracy.To approximate the estimation around the current estimate, a technique resembling a Taylor series expansion is utilized. For this purpose, partial derivatives obtained from the process and measurement functions are commonly employed.It is important to note that the distributions of the different random variables no longer adhere to Gaussian distributions once they undergo nonlinear transformations. This demonstrates a fundamental limitation of the EKF. However, through linearization, the EKF can still approximate the optimality of Bayes’ rule ,11.The dynamic process is currently governed by a nonlinear stochastic difference equation, as shown in Equation (2):With a measurement One cannot know the individual values of the noise To estimate the process of Equations (6) and (7), which exhibit nonlinear relationships between differences and measurements, additional governing equations are introduced to linearize the estimation of Equations (4) and (5).the random variables and ,,, and It should be noted that, for simplicity in the notation, the time step subscript Now a new notation for the prediction error can be defined asSince Then, the estimate of Equation (14) called Given these approximations and letting the predicted value of By substituting Equation (17) back into Equation (16) and making use of Equation (13),Now, Equation (18) can be used for the measurement update in the extended Kalman filter, with The subscript k − 1) to the current time step (k).The time update equation enables the projection of state and covariance estimates from the previous time step  is introduced to this paper to capture the variation in friction force between the brake disc and brake pad.To obtain the disc temperature increase Utilizing existing data as an adjustment factor to correct the brake cylinder pressure presents challenges. To alleviate the computational burden on the BCU, a preset adjustment coefficient set is necessary for the BCU’s calculator. This coefficient set should cover all potential speed categories of the train. To accomplish this, machine learning techniques are employed to forecast the performance of various speed grades. However, the utilization of data prediction methods to supplement untested data presents challenges in this approach, greatly affecting the reliability of the coefficient set. Among the models considered, LSTM is favored for predicting the optimal set of friction coefficients due to its ability to process and forecast important events with long intervals and time delays in time series data. It should be noted that other models, such as moving average, linear regression, AutoARIMA, and prophet, were explored during the method selection process. However, many algorithms encounter challenges in accurately capturing the correlation between the friction coefficient and speed level, especially when it comes to fitting the braking duration.Long short-term memory (LSTM) is a type of artificial neural network employed in the fields of artificial intelligence and deep learning. Unlike conventional feed-forward neural networks, LSTM incorporates feedback connections . The namIn conventional RNNs, node outputs are exclusively determined by weights, biases, and activation functions. Additionally, each time step utilizes the same parameters within a sequential structure. LSTM introduces a gate mechanism that governs the flow and retention of information, addressing the long-term dependency issue encountered in RNNs .In the initial stage, marked in red, the determination of which information to discard from the cell state is performed by a layer referred to as the forget gate. This gate reads tanh layer, where The input gate, marked in blue, consists of two parts, LSTM generates new states by performing addition operations instead of multiplication. The result The output gate layer, marked in green, is calculated through input information By arranging multiple LSTM cells, it becomes possible to process sequential data inputs. These LSTM cells are typically organized in layers, where the output of each cell serves as the input for subsequent cells. The incorporation of a layered structure enhances the capacity of the network and allows for the capture of more complex dependencies within the data.Having grasped the operating principle of LSTM for data forecasting, the friction coefficient data from existing speed categories are utilized as the training set, with the missing data predicted at 10 km/h intervals. To economize computational resources, the dataset is selectively sampled at suitable time intervals, with the selection of this interval being guided by the response time of the pneumatic components within the braking system.Therefore, the obtained results As shown in The target deceleration is determined by the brake control unit based on the braking class and train speed provided by the controller. The brake control unit determines the required brake cylinder pressure Broadly speaking, the brake execution unit is composed of two segments: the pneumatic control group and the fundamental brake group.The charging and exhausting process of the brake cylinder pressure by the rail vehicle pneumatic brake system can be given in a simplified version as a first-order inertial link and its transfer function In Equation (33), Upon comparing Equations (24) and (32), it becomes apparent that the discrepancy between the desired and actual braking force arises from the variance between the average friction coefficient and the actual friction coefficient.As depicted in It is essential to recognize that this system operates as an additional element beyond the standard braking control. There are several reasons for not opting to incorporate this functionality into the core control of the BCU. Firstly, it is imperative to ensure that the fundamental braking function remains unaffected by the computation, thereby guaranteeing the promptness of braking. Secondly, in the case of anti-skid and emergency braking commands, their priority overrides the necessity for precise parking. When conflicting demands arise, the emphasis is placed on braking requirements, which results in the disengagement of the deceleration closed-loop control chain. In essence, the BCU computes the braking demand based on a fixed friction coefficient and then optimizes it through a dynamic friction coefficient. However, the optimization process can be bypassed, a decision taken from a system security viewpoint.The initiation of the entire deceleration feedback control module is governed by the ratio of actual to target deceleration. Upon the commencement of braking, should the ratio between the two fail to fall within the range of 90–110% for a duration exceeding 0.5 s, the deceleration closed-loop control will be engaged. The brake cylinder pressure will be adjusted proportionally, and the coefficient In cases when the deceleration still cannot meet the requirements after correction, then During the determination of a vehicle’s slope position via the acceleration signal, it is imperative to remove the component of gravity for an accurate assessment of the actual deceleration. This task can generally be accomplished in two ways. When the deceleration signals from the front and rear cars encounter an incline, a temporary disparity is observed. Additionally, while on the slope, a consistent difference will persist between the measured deceleration signal and the deceleration calculated by differentiating the speed signal.Upon receiving a braking command for either rapid or emergency braking, the deceleration feedback control remains inactive. When the wheel slide protection function is activated, the deceleration closed-loop control module is deactivated. At this point, it becomes necessary to assess the modification factor. If the modification process amplifies the brake cylinder pressure and the deceleration closed-loop control is subsequently released, the state preceding the modification is not restored. In contrast, the adjusted brake cylinder pressure is preserved to prevent an excessive braking force when braking is re-engaged.Serving as an auxiliary measure, the deceleration closed-loop control system does not impact the primary control functionality of braking from a safety standpoint. Primarily, this control system is designated for the pneumatic aspect of traditional and accelerated braking. While emergency braking is also a facet of pneumatic braking, the maximum braking efficiency is given priority, thus excluding the involvement of the deceleration closed-loop control system. When the wheel slide protection feature is triggered, the deceleration closed-loop control is deactivated and the deceleration is reduced. If the deceleration does not meet the error tolerance after the activation of the deceleration closed-loop control system, the closed-loop control will be disabled.A specially designed test train was employed to validate the efficacy of the deceleration closed-loop control system. The total weight of the train simulates the operational conditions under full load. The train operates on a route punctuated by extended slopes. The comprehensive validation procedure comprised the arrangement of the deceleration sensors, a brake disc examination, the projection of the corresponding friction coefficient set, and a track test.To meet the ramp judgment criteria outlined earlier, two uniaxial deceleration sensors were mounted on the front and rear vehicles, with their respective parameters provided in The positioning of the deceleration sensor is illustrated in Collecting the performance data of the brake disc prior to the line test is crucial. To achieve this objective, a specialized testing apparatus is utilized to investigate the evolving pattern of brake disc temperature and friction coefficient during the braking procedure across different speed categories. The results of this test are depicted in Due to the time constraints of the test, only commonly used speed classes, namely 50, 80, 120, 160, and 180 km/h, were selected as the initial speeds for the simulated braking test. Using the temperature of the braking disc as a reference, the friction coefficient at different speed classes can be determined and are illustrated in By utilizing the friction coefficient from the test as the training set, LSTM is employed to predict the braking duration and the friction coefficient of the brake pad at various other braking speed classes, as shown in Given that the response delay of pneumatic components is approximately 50 ms, a time interval of 100 ms was selected. Moreover, a speed class interval of 10 km/h was selected, and the subsequent test results validated that this data scale meets the requirements of the braking system. The calculation workload is not excessively high, ensuring that it does not impact the braking response time, and the data intervals are not too sparse to compromise accuracy.The test was conducted on a specific three-kilometer route that includes ramps and has a maximum gradient of 5‰, with a speed of 100 km/h. Different braking conditions were examined. The test vehicle was set up to mimic the typical operating load of AW2.The signals collected by the deceleration sensor indicate that the application of Kalman filtering and digital signal processing techniques successfully mitigated noise and the acceleration–deceleration oscillations resulting from uneven speed during vehicle operation, as depicted in 2 between the deceleration sensor signal and the signal derived from the speed differential solution. This suggests a nominal rampway angle of approximately 5‰.Since the test route does not include any curves, it was not possible to assess the road conditions related to curves using acceleration information. However, Furthermore, upon comparing the deceleration signals of the first and last carriage, it can be observed that the deceleration of the entire train is consistent, as depicted in 2. This demonstrates the effectiveness of adjusting the brake cylinder pressure using the dynamic friction curve.The brake cylinder pressure and deceleration during the braking process were analyzed for the selected speed classes, with a focus on a lower speed of 60 km/h for safety purposes. The aforementioned prototype of the deceleration feedback braking control technology demonstrates the achievement of smooth deceleration through experimental validation. However, there are several areas that offer the potential for improvement:The weight distribution among different carriages during actual operation may not be as optimal as in the test train due to elastic connections. This can lead to inconsistent deceleration among the carriages and the entire train. To improve precise deceleration control, the sensor arrangement can be further optimized, for instance by using sensors for each trailerIn the future, there may be faster and more efficient methods to obtain the required set of friction coefficients. Currently, testing dedicated coefficient sets for different brake pads is labor-intensive. Furthermore, a universal coefficient set has not yet been identified, as the temperature rise curve and friction coefficient are significantly influenced by the materials and thermal conductivity of different brake pads.While the current approach effectively addresses the instability caused by the friction coefficient, it simplifies the adhesion on the track surface. Significant changes in track conditions, such as slippery surfaces, can render the parameter set collected under ideal working conditions ineffective. To address this, separate considerations of dry and wet rail conditions and the further optimization of the coefficient set based on working conditions are being explored.The application of this technology currently assumes that wheel and rail wear is not severe in the short term. Nevertheless, with the accumulation of operating mileage, the efficiency of braking can be affected by wheel and rail wear, causing changes in the proportional relationship between the original brake cylinder pressure and deceleration. The design team has considered employing a dynamic simulation algorithm that automatically updates to adapt the coefficient set to the degradation process. However, distinguishing long-term decay from short-term deterioration caused by humidity is challenging within short time frames.This research introduces a deceleration feedback-based braking system with a closed-loop control function. The system aims to tackle challenges associated with the fluctuating friction coefficient between the brake disc and pad when braking. By automatically adapting the brake cylinder pressure, the system maintains a stable actual deceleration at the target value, thus achieving the desired braking distance. To ensure accuracy in monitoring train deceleration, a specialized deceleration sensor is applied. Machine learning techniques are utilized to determine the friction coefficient based on braking time, temperature, and different speed classes, using data from brake disc and pad tests. This approach effectively mitigates oscillation caused by fluctuations in the friction coefficient during braking. Experimental tests are conducted on a test line to evaluate the system’s performance. The test results demonstrated that the technique was effective in achieving a more precise alignment between the actual deceleration and the target deceleration, while also preventing wheel sliding protection (WSP) activation, particularly during low-speed periods. Furthermore, the implementation of this technique did not cause any delays or disruptions to the braking time or the BCU operation.In the future, this work aims to integrate deceleration feedback information from all trains on the same line and develop an automated platform for updating the dynamic friction coefficient set. The revised friction coefficient set will consider factors such as the wheel–rail adhesion coefficient and environmental humidity.


Musculoskeletal models, like all theoretical models of physical processes, depend on the assumptions needed to construct the model. For musculoskeletal models, these assumptions include, among other things, the kinematic data, the kinetic data and the muscle parameters. The former (dynamic) data can be acquired relatively easily from living subjects, but the latter are usually based on limited information, frequently determined from cadaver studies performed on elderly individuals. Previously, we determined the sensitivity of forces to dynamic differences among 10 humans walking on a straight path. Here, we assess the sensitivity of the muscle and joint reaction forces developed in human walking to variable muscle parameters obtained from 10 living adults, whose data were recently reported, and compared the results with the values from a standard model that depends on cadaveric data. We found that, while the force patterns across the stance cycle were similar among muscle parameter models, differences of as much as 15% in the force magnitude were produced. Whether or not the variation between the standard model and other muscle parameters is important depends on why the forces are required. Social media summary: Typical human variation in muscle architecture changes internal forces by 15% in a musculoskeletal model of walkingThe nature of the biomechanical requirements and consequences of bipedalism, from its inception in the hominin lineage to its manifestation in modern humans, remains a puzzle that motivates the research of many biological anthropologists, anatomists and functional morphologists. Bipedalism is rare among mammals, but ubiquitous within hominins for at least 4 million years  is to assume how the body allocates muscle force or, in other words, how the body determines the degree of active contraction to produce in each muscle at any given point. This physical system is difficult to study empirically, so modern musculoskeletal models use muscle strength  to determine activation level via an allocation or cost algorithm. This allocation algorithm is the critical assumption for determining the force produced by a particular muscle because muscles in a functional group are all capable of producing forces that produce similar joint moments. Given that our goal is to use muscle forces to interpret bone morphology, the force that a particular muscle produces is critical because some muscles in a functional group originate or insert on different bones than other muscles in the same functional group. For example, soleus connects the tibia to the calcaneus across the ankle and subtalar joints, but medial and lateral gastrocnemius and plantaris originate on the femur, crossing subtalar, ankle and knee joints. Even though the primary action of all the muscles of the triceps surae complex is to cause the ankle to plantarflex, for examining femoral evolution, the distribution of force among the muscles is important because soleus does not directly interact with the femur.Our musculoskeletal model produces muscular forces that are consistent among steps, trials and individuals for functional muscle groups , the hamstring muscles  and the quadriceps . Changing muscle parameters within a model does not change the external kinematic and kinetic conditions, so joint moments do not change. However, because muscle parameters determine muscle strength and the cost algorithm distributes force to muscles based on their strength, the distribution of force among the various muscles in a muscle functional group or among groups could change and this could change joint reaction forces. Consequently, although our approach is predominantly data exploration, we hypothesise that:Ten healthy participants  were recruited from the student population at the University of Washington. Exclusion criteria included gait abnormalities and a recent history of injury. Biometric data were collected from each participant, including stature, mass, limb segment length and limb segment circumference. The University of Washington's Institutional Review Board approved all aspects of this study (IRB no. STUDY00001125). The experimental protocol for the kinematic data collection process has been described in detail elsewhere  while the motions of 30 infrared-reflective markers placed on anatomical landmarks were measured with a 10 camera motion capture system  in the Amplifying Movement and Performance Laboratory at the University of Washington. Each participant completed five trials, but the data from two trials for two participants were unusable, resulting in 46 total dynamic cases with two consecutive stance periods .The baseline model used to calculate lower limb joint reaction and muscle forces in this study was the MoCap model included as part of the commercially available AnyBody Modelling System  and hosted on the AnyBody musculoskeletal model repository (AnyBody Managed Model Repository AMMR v. 2.3.0). This is a validated, multi-trial, full-body, motion-capture-driven human gait model with head, trunk, and left and right lower limb components , ankle (plantarflexion/dorsiflexion) and subtalar (inversion/eversion) joints. The pelvis (relative to the ground) has six degrees of freedom, three translational and three rotational. Thirty-seven anatomical muscles are represented by 169 muscle elements (force actuators) in each lower limb (e.g. gluteus medius is composed of 12 separate muscle element actuators).As detailed in our previous reports using these dynamic cases , a similar process was undertaken using stature: the stature of the KH model was divided by the stature of the Charles et al. subject and multiplied by the optimal fibre length values provided in Charles et al. , to gain insight into how the muscle force allocation algorithm influences the joint reaction and muscle forces.Our first hypothesis is that muscle parameter models, i.e. the CS models and KH, would all exhibit similar shapes of their joint reaction and muscle functional group force curves. r2 = 0.91, p < 0.001). In the hamstring muscles, CS and KHP3 also follow a strong trend . In the quadriceps muscles, CS and KHP3 demonstrate the same trend . The effect of the exponent on the ankle is minimal . An exponent of 2 produces lower triceps and hamstring muscle forces, but higher quadriceps forces . An expoOur ultimate goal is to produce a generic set of joint reaction and muscle forces that can be used to interrogate the effect of variation in bone morphology that is seen in the fossil record. We had previously found consistency within and among individuals in the forces exerted by the propulsive and stability-focused muscle functional groups when we used the same muscle parameters  and, therefore, is allocated more force, the soleus's somewhat shorter moment arm requires a higher muscle force, which increases joint reaction forces of the ankle .The muscle forces in the quadriceps group in the KHP3 model are similar to, or somewhat higher than, the CS muscle model parameter models in the earlier parts of the stance phase, but smaller in the later portion of stance. The hamstring group demonstrates a more complex picture that depends on the portion of stance and the particular CS muscle parameter model. The knee joint forces also depend on the muscle parameter model to some degree with the KH model producing lower and higher forces than the CS model in some dynamic cases. As with all models, assumptions are necessary and whether or not the differences in magnitudes that we found are important depends on the question of interest. To demonstrate this point we offer two possible analyses that might utilise these data.Australopithecus on femoral neck strain, during bipedal walking. Each muscle insertion or origin and the joint contact surfaces of the bone actively load the bone across the stance phase. Each boundary condition constitutes a non-trivial exercise in pre- and post-processing the finite element model. Our initial focus is the hominin femur; our goal, therefore, is to identify those points in the stance phase likely to produce the highest strains in the femur. Consequently, we aim to reduce the number of conditions to an envelope that contains as few conditions as possible to produce the maximum strains in the femur. We specifically seek to identify the points in the stance cycle when hip, knee or patellar joint reaction or femoral muscle forces are maximum within and among people given inherent kinematic, kinetic and muscular variability. While the creation of this envelope is beyond the scope of this paper, it is clear that conditions in early (~20% of stance phase) and late (~80%) stance are needed due to the peaks in the hip and knee joint contact and muscle forces that occur during those gait phases and that conditions near midstance might be less useful. Most biomechanical analyses of the evolution of the morphological features associated with bipedalism have focused on a single stance  is consistent when the muscle parameters  are varied, which is consistent with our previous work examining kinematic and kinetic variation  into the muscle forces, but this seemingly straightforward relationship is variably reflected in multiarticular muscles. While the relationship between relative maximum force and strength exhibits the shape expected from the algorithm for the triceps surae and hamstring functional groups , that ofA principal limitation of these analyses is that the kinematic and kinetic data derived from different individuals than the muscle parameter model data. Consequently, we do not know if the movements of the dynamic individuals could be achieved by each individual whose data were used to create the muscle parameter models. Most musculoskeletal model simulations use generic muscle parameter models, typically derived from elderly cadavers (e.g. Klein Horsman et al.,


The online monitoring of a multi-jet electrospinning process is critical to the achievement of stable mass electrospinning for industrial applications. In this study, the construction of an ejection state recognition system of a multi-jet electrospinning process based on image processing is reported. The ejection behaviors regarding multi-nozzle electrospinning were recorded by CMOS industrial cameras in real time. The characteristic information regarding the multi-jet cone tip was obtained by processing the images regarding Roberts operator edge detection, Hough transform line detection, and mask histogram analysis. The jet anomalies of the hanging droplets in the nozzle outlet area could be obtained and identified by the vision. The identification accuracy towards the target hanging droplets was more than 85%. This work reports the intelligent control of large-scale multi-nozzle electrospinning equipment. Electrospinning is one of the main methods of preparing ultrafine nanofibrous materials, which have broad applicational prospects in the fields of air filtration , polluteElectrospinning utilizes a high-voltage electric field to induce a charged jet and thus produces nanofibers from a polymer solution, and typsof this technique include single-nozzle or multi-nozzle electrospinning and needleless electrospinning. At present, stable multi-nozzle spinnerets are available; for example, Jiang  et al. dIn this paper, aiming to develop a convenient detection and identification method for state recognition applied to multi-nozzle electrospinning, an online multi-jet state identification system was established based on Python and Open-cv, which can identify the jet anomalies of the nozzle outlet area and display warning signs. If there is a hanging drop instead of a cone jet at the nozzle outlet, it is judged as abnormal ejection. This work promotes the development ofan intelligent control technology towards the realization of mass electrospinning for the efficient production of nanofilms.ωM = 3 × 105 g·mol−1, Changchun Dadi Fine Chemical Co., Ltd., Changchun, China) was selected as the analyzed material. The solvent was deionized water/ethanol (v:v = 3:1) mixed solvent. The mass concentration of PEO solution is 10 ωt%. Polyethylene  of the images were established, and the hanging drops of the cone tips were recognized. The processing flow of the multi-jet electrospinning imagesis shown in There was little difference in the grey values between the target objects and the background. In order to obtain more accurate and reliable results, the initial images needed to be initially adjusted. The preprocessing stage and its results are shown in Automatic color enhancement (ACE) is based on the theory of the Retinex algorithm ,23, and The ACE algorithm consists of two steps: (1) the adjustment of the color and space of the image to complete the correction of color difference; (2) the dynamic expansion of the corrected image . Its calω is the weight coefficient, g is the relative contrast adjustment parameter g(x) = max , −1.0), and a is the control parameter.In this formula, In this paper, the ACE algorithm was used to process the initial image. The maximum inter-class variance method proposed by the Japanese scholar Nobuyuki Otsu (OTSU) was used to select a threshold at which to divide the image into foreground and background parts  and thenIn this formula, The three-channel image processed by the ACE algorithm was grayed to convert it into a single-channel image, as shown in The Roberts operator is a gradient algorithm based on cross difference, which detects edge lines by local difference calculation. The algorithm has a remarkable effect on image edge enhancement of ±45°. In this paper, the Roberts operator was used to detect the edge of the spinneret cone wall, and the result is shown in On this basis, the contour information was obtained via Hough transform, which was widely used for curve detection in image processing. In addition, in this paper, the cumulative probability Hough transform was adopted. Its basic principle is to transform the pixels of an image from the Cartesian coordinate system to the polar Hough space system, and then accumulate and randomly extract the fitting points until the number of fitting lines reaches the threshold. The polar transformation formula of the Hough transform is as follows:r is the distance from the origin to the nearest point on a straight line, and x axis and the straight line.In the formula, Before initiating line detection, in order to improve the system’s recognition accuracy, binarization processing and morphological operation were used to remove marginal fine noise. Then, the target line segments were selected according to the vertical slope and an appropriate range of length to exclude the interfering curves. The detection results are shown by the red lines in In the nozzle outlet areas of the images, the hanging drops at the spinneret cone tips could be found. Due to the refraction and scattering of light, there are obvious pixel changes in this area, which have an approximately waveform-like shape. The mask histogram analysis of the ROI is shown in In this paper, two methods for the detection of hanging drops at the nozzle outlet area were adopted. Firstly, the mean square deviation threshold was set to screen and identify the hanging droplets. The mean square deviation can accurately describe the distribution of a histogram. The larger the mean square deviation, the more scattered the pixel distribution of the histogram. Secondly, the coordinate distribution range of the cone tip was compared with the pixel fluctuation range of the ROI. If the pixel fluctuation range in the ROI is greater than the distribution range of the cone tip coordinate, it was surmised that there was a hanging droplet. Combining the results of the two detection methods, the warning indications were defined. Multiple groups of video-framing outputs were selected to verify the results. The accurate identification rate of hanging droplets at the multi-jet cone tip reached 85%. The specific verification data are shown in Based on Python and Open-cv, an online multi-jet state identification system was built, which realized the monitoring of the multi-jet ejection state and the recognition of hanging droplets in the nozzle outlet area. CMOS industrial cameras were used to obtain the original images. The ACE algorithm and OTSU threshold processing effectively solved the problem wherein the overall background of the original image was dim and the difference in the grey values between the target pixel and the background pixel was small. After image preprocessing, the Roberts operator edge detection and Hough transform line detection adaptively obtained the endpoint coordinates of the multi-jet cone tips and established the ROI area. According to the regional pixel fluctuation of the hanging drops in the ROI, histogram analysis and pixel fluctuation detection were carried out to effectively identify the jet anomalies of hanging droplets in the nozzle outlet area. The feedback recognition results of image processing were consistent with the actual situation, which was conducive to achieving the intelligent control of large multi-nozzle electrospinning equipment.


Precision machining fields often require worktables with different stroke sizes. To address the need for scalability and facilitate manufacturing, this study proposes a novel infinite expansion magnetically levitated planar motor (MLPM) based on PCB stator coils. Different from existing magnetic levitation systems that use PCB coils, the design presented in this paper utilizes smaller coil units, with each coil being independent of one another. The coils are structured in a spiral pattern on a 16-layer PCB, comprising 15 layers of coils, while the last layer is dedicated to wiring and other circuits. Magnetic field modeling is conducted for both the stator coil and the 2D Halbach array structure employed in the system. A simple table lookup method is employed to accurately account for the prevalent end effects observed during system motion. Additionally, the decoupling effect of magnetic force and torque is evaluated by solving for the current vector at different points along a specific trajectory. To verify the accuracy of the proposed system’s modeling, a prototype is developed and tested. Experimental results demonstrate that compared to traditional harmonic model methods, the proposed approach improves the calculation accuracy of magnetic force by 50.31% and torque by 70.65%. This study presents a new MLPM system with vast potential applications in precision manufacturing and robotics. The innovative design and improved performance characteristics make it a promising technology for enhancing the capabilities of worktables in precision machining fields. Magnetic levitation technology has garnered significant interest in various applications, including chip manufacturing ,2,3,4, mThe utilization of printed circuit boards (PCBs) in magnetic levitation technology offers potential benefits such as reduced volume and higher current density, resulting in enhanced levitation and propulsion capabilities. A direct drive 6-DOF moving magnet levitation planar motor is proposed in . The motThis paper introduces a novel infinite expansion magnetically levitated planar motor (MPLM) with moving magnets. The coils are strategically arranged in a spiral pattern on a 16-layer PCB, as shown in For the magnetic levitation system structure designed above, this article first conducts magnetic field modeling. The MLPM given in MLPM possesses unique inherent advantages for high-precision manufacturing and processing applications. Its desirable features, including an isolation environment, multiple degrees of freedom, and strong carrying capacity, render it applicable in specialized high-precision equipment such as extreme ultraviolet lithography machines. With the advancement of MLPM technology, there is a growing demand for higher working stroke capabilities. To address this need, an innovative MLPM system with infinite expansion capability is proposed in this article. In pursuit of a simpler structure and extended working stroke, the design of the proposed structure is delineated in The key components of the MLPM proposed in this article are the stator and translator, responsible for generating the magnetic force. The stator comprises spliceable PCBs that integrate both hall sensors and coils. The coil design employed in this system resembles a hollow square shape, featuring a hollow side length denoted as Two coordinate systems have been established to analyze the force and torque between coil and magnets given in Based on the arrangement principle of the Halbach array and the position of the coordinate origin, the magnetic flux density at any point Equation . The calIn order to accommodate the restrictions imposed by the operational speed of the controller, it becomes imperative to simplify the force and torque model of the coil. In this particular model, the current area of the square is divided into four individual segments, as illustrated in I in Ampere-turns, the expressions for force and torque integrals, calculated using the local coordinate system, are presented as follows.The Lorentz integral is employed to determine the magnetic force and torque acting on the translator. The coil is divided into four individual segments, for which the integral region is the summation of these segments. The mass center point of the coil is assumed as The final calculation results of forces and moments can be expressed asThe aforementioned calculations are based on conventional harmonic models, which yield satisfactory magnetic fitting outcomes within the center region of the translator. However, considerable discrepancies arise when the coil is positioned at the edge region of the translator. In this system, a multitude of coils are situated at the periphery of the magnetic field at every translator position, thereby rendering the end effects an indispensable factor. Hence, it becomes imperative to account for the end effects in the proposed model.In order to facilitate a more comprehensive analysis of the end effects, the 2D Halbach array employed in the system has been partitioned into three distinct regions: the center region, side region, and corner region, as illustrated in 1.Along the 2.Along the According to the findings of end-effects research on a 2D Halbach array presented in , the magThe observed phenomenon can be attributed to the calculation of the magnetic field expression , which ipression  represeneference  proposesDifferent from the side regions, the components in the By utilizing a six-axis force sensor, the magnetic force in the corresponding coordinates can be measured, allowing for the determination of the coefficients eference , resultiAccording to , the conn) below the magnet array are energized. By utilizing the magnetic force and torque models developed in the previous section, the force and torque exerted on the translator by a single active coil at various positions can be determined in a local coordinate system. These results can then be converted from the local coordinate system to the corresponding values in the global coordinate system, resulting in the derivation of the current–wrench transformation matrix represented in the global coordinate system. The current–wrench transformation matrix can be expressed as follows: To achieve precise and efficient motion control, only a subset of coils ..S, each 3.The current–wrench transformation matrix is derived, allowing the determination of the current vector using the method described in Equation . This enBy following these three steps, an accurate model of the entire MLPM system can be established, and effective control can be achieved. The utilization of pre-stored position information and the current–wrench transformation matrix significantly reduces the computational burden. Moreover, the careful consideration of magnetic field interactions guarantees high-fidelity performance. Overall, this proposed method enables efficient and effective control of the magnetically levitated planar motor, delivering high precision with minimal power consumption.To validate the accuracy of the proposed model and magnetic decoupling, a principle prototype is constructed for experimental purposes, as depicted in In the proposed system, the coils are arranged in a spiral pattern on a 16-layer PCB, as depicted in In the implemented prototype, a 2D Halbach array is integrated into an aluminum plate, serving as a translator as illustrated in By constructing a prototype of the principle, the magnitude of the magnetic force acting on the rotor when the coil is located in the edge region can be measured, and the coefficient of the magnetic field can be calculated. It can also measure the electromagnetic force acting on the translator when a coil or multiple coils are energized with a specified current. In addition, the boundary element simulation software Radia is used for simulation experiments under the same conditions. The proposed model is compared to the commonly used harmonic model, Radia and measurement results. This comparison enables the quantification of the accuracy improvement achieved by utilizing the proposed model, which incorporates the non-linear effects existing in the system.Through this verification process, the proposed model has been proven to have superior accuracy and fidelity compared to traditional harmonic models. This validation provides confidence in the proposed model’s ability to accurately predict the behavior of the planar motor, enabling effective design and control strategies.x, y and z directions, as well as rotation around the z-axis within the To validate the accuracy of the proposed model, an experimental setup, depicted in y = 6 mm, while the coil traverses the three designated regions in sequence. The corresponding results are depicted in During force measurement experiments, the protocol involves initially supplying 1A of current to a single coil using the DC power source. The four-degree-of-freedom moving stage is then controlled to transport the translator at a predetermined height, allowing the energized coil to sequentially pass through side region 2, the center region, and side region 4, as illustrated in In the global coordinate system, the This behavior can be attributed to the fact that as the air gap widens, the coil moves farther away from the magnetic field region generated by the magnet array, thereby resulting in a decrease in the interaction force between the coil and the translator. Additionally, it is evident that at the initial and final stages of the translator’s motion, when the coil is positioned near the edge of the magnetic field, the force acting on the translator no longer follows a sinusoidal pattern but approaches zero. These outcomes align as expected based on the underlying principles of the system.Based on the results depicted in k values, additional experiments are conducted. In these experiments, the three coefficients obtained are used to calculate the force and torque experienced by the translator at three different air gaps when y = 70 mm. While maintaining this specific Once these coefficients are determined for a specific air gap, the force and torque acting on the translator at any point at that suspension height can be obtained. To validate the feasibility of this approach and the accuracy of the obtained Through a comprehensive comparison between the experimental results obtained from the proposed model and the actual values, a high level of consistency was observed. Furthermore, the simulation results obtained using the commercial software, Radia, further substantiate the accuracy of the proposed model. In the majority of cases, the proposed model exhibits closer proximity to the actual values compared to the simulation results. Therefore, the proposed model can be used instead of commercial software for calculation in practical applications. Notably, our proposed model exhibited significantly superior accuracy when compared to traditional harmonic models, particularly in capturing the intricate dynamics associated with end effects. The experimental findings convincingly demonstrate that our proposed approach outperforms traditional harmonic model methods, yielding an impressive enhancement in the calculation accuracy of magnetic force by 50.31% and torque by 70.65%.Collectively, these experiments serve as compelling evidence to validate the effectiveness of our proposed model and the end-effects fitting technique. The confirmation obtained from this validation process instills confidence in the predictive capabilities of our model while substantiating its capacity to faithfully represent the intricate behavior of the planar motor across diverse operating conditions. These outcomes reinforce the significance and practical utility of the proposed model, which can be employed as a valuable tool in accurately predicting and analyzing the force and torque characteristics of planar motors.z-axis and no torque applied. These sampling points are located on a specific trajectory in the 81 mm × 81 mm range as depicted in To evaluate the decoupling effect of magnetic force and torque, a wrench vector Equation .The results are presented in In order to further validate the accuracy of the computed current values, a series of experiments are conducted. The measurement results are then compared to the corresponding desired results, as depicted in This paper proposes a novel infinite expansion magnetically levitated planar motor that is based on printed circuit board (PCB) stator coils. In contrast to conventional magnetic levitation systems that utilize PCB coils, this design features smaller coil units, with each coil operating independently. The higher current density characteristic of the proposed design enables it to generate sufficient magnetic force, allowing for the realization of infinite expansion of the entire system. Furthermore, magnetic field modeling is conducted for both the stator coil and the 2D Halbach array structure utilized in the system. To accurately account for end effects during system motion, a simpler table lookup method is employed. A prototype of the testing principle is built, and experimental results are compared with traditional harmonic models, simulation results and measurement results, demonstrating excellent agreement.Through the decoupling of force and torque, the current of each coil can be obtained. The experimental outcomes validate the feasibility and effectiveness of the proposed approach, which is more suitable for magnetically levitated planar motors with infinite expansion capability. The proposed model represents a valuable tool for accurately predicting and analyzing the force and torque characteristics of the system under different operating conditions.


This paper introduces a robust algorithm that efficiently generates high-quality unstructured triangular meshes to model complex two-dimensional crack growth problems within the framework of linear elastic fracture mechanics (LEFM). The proposed Visual Fortran code aims to address key challenges in mesh generation including geometric complexity, required simulation accuracy, and computational resource constraints. The algorithm incorporates adaptive refinement and updates to the mesh structure near the crack tip, resulting in the formation of rosette elements that provide accurate approximations of stress intensity factors (SIFs). By utilizing the maximum circumferential stress theory, the algorithm predicts the new crack path based on these SIFs. Throughout the simulation of crack propagation, a node splitting approach was employed to represent the progression of the crack, while the crack growth path is determined by successive linear extensions for each crack growth increment. To compute stress intensity factors (SIFs) for each increment of crack extension, a displacement extrapolation method was used. The experimental and numerical results demonstrated the algorithm’s effectiveness in accurately predicting crack growth and facilitating reliable stress analysis for complex crack growth problems in two dimensions. The obtained results for the SIF were found to be consistent with other analytical solutions for standard geometries. The computational design of structural materials with existing cracks necessitates a crucial step: reliably assessing their remaining service life. In order to predict phenomena such as fatigue life, simulating crack growth becomes essential, typically involving a LEFM problem at each load step. The study of fracture behavior involves a combination of laboratory experiments, analytical investigations, and numerical simulations. While experiments are necessary to some degree, they tend to be expensive and time consuming . AnalytiWith reference to The Airy stress function approach is a powerful mathematical tool used in solid mechanics to obtain analytical solutions for stress components Using the Airy stress function, the stress components can be expressed asIn solid mechanics, the compatibility equation is a crucial requirement that must be met by the strain field in a solid to ensure that it represents a physically realistic deformation. This equation is particularly important in stress formulations, where it relates the normal and shear strains in a solid to each other and to the deformation of the solid as a whole. In the context of stress formulations in solid mechanics, it is necessary to ensure that the strain field in a solid satisfies a compatibility equation asTypically, a linear elasticity problem involving plane extension can be solved by identifying a stress function that meets the requirements of Equation (4). Additionally, it is necessary to verify that the boundary conditions of the problem are satisfied by the stresses calculated using Equation (2).r represents the radial distance from the crack tip, X and Y directions, XY direction, IK and IIK correspond to the modes of SIF. The primary objective of LEFM simulations for crack propagation is typically to investigate the combined influence of mode I and mode II. Therefore, researchers are interested in studying how cracks behave under different combinations of tensile and shear stress. There are multiple intricate versions of the Airy stress function that can be employed to address crack problems. In the context of in-plane cracks, Irwin  extensivν denotes the Poisson’s ratio; IK and IIK are the first and second mode of stress intensity factor, respectively; θ denotes the crack growth angle; and Subsequently, this solution has gained significant recognition as a fundamental tool in fracture mechanics research. It has empowered scientists to gain valuable insights into the behavior of cracks in diverse materials and structures. The stress distribution is depicted in Isoparametric quadratic triangular shape functions find common usage in the analysis of structures and other physical systems that demand accurate modelling. This technique involves using the same set of coordinates to describe both the geometry of the element and the variation of the field variable within the element. The accuracy and efficiency of a given element type in finite element analysis depends on the capability of its shape functions to accurately represent the true displacement field. The isoparametric family of elements is a group of elements that employ shape functions for both defining the geometry and the displacement field. In the current study, a quadratic triangle element with quadratic shape functions was utilized as a higher-order element to achieve a more accurate representation of the displacement field within the element. This element type requires six nodes, with three nodes located at the corners of the triangle and three additional nodes located at the midpoints of each side. The additional nodes enable the element to accurately capture the curvature of the displacement field within the element. The shape functions for each node are given by the following equation:i. Likewise, the calculation of displacements can be performed using relevant equations such asThe coordinate values The evaluation of the Jacobian matrix, which will be needed later, is performed as follows:The expression for the inverse of the Jacobian matrix is as follows:The expression for the discretized elemental volume is provided as follows:The value of The relationships between strain and displacement are mathematically expressed asThe strain displacement matrix provided in The values of i ranging from 1 to 3. On the other hand, The intensity of the distributed loading at any point along the loaded edge is expressed asx and y components of the force acting on an incremental length of the loaded edge are as follows:The calculations for the To perform integration along the element edge using the curvilinear variable Solving these equations provides the expressions for the equivalent nodal forces asThe process of mesh generation is intricate and prone to errors, particularly when dealing with practical scientific and engineering computations that involve complex geometries of varying complexity. Zienkiewicz and Phillips  initiateNode generation: In the first step, nodes are generated along the boundary edges to create a discretized boundary for the domain.Element and node generation: Once the boundary is discretized, the next step is to generate elements and nodes within the boundary.Element shape enhancement: In the final step, the quality of the mesh is improved by enhancing the shape of the elements. Element shape refinement techniques involve adjusting the position of the nodes to improve the shape and quality of the elements, such as reducing element distortion or improving element aspect ratios.Furthermore, the method can be employed to generate both structured and unstructured meshes, depending on the simulation requirements. The mesh generation procedure typically encompasses three primary steps, as outlined by Zienkiewicz and Taylor :Node genTo prepare for the generation of triangular elements, a generation front is created using the discretized boundary edges of the domain. This front is composed of closed loops of boundary sides, and if the domain contains multiple connected regions with different material properties, separate initial fronts are formed for each region. The generation front consists of sides defined by their two endpoints and is arranged in a sequence that ensures the regions to be meshed are always situated to the left of the front. In As the front advances, new triangles are generated by connecting adjacent nodes in the front. Each triangle is formed by connecting three nodes in a counterclockwise order. The connectivity of the triangles is based on the specific method used for advancing the front. In their work, Zienkiewicz and Taylor  providedMesh smoothing is a post-processing technique employed to enhance the quality of a generated mesh. It involves modifying the positions of nodes and elements to reduce distortions and irregularities present in the mesh. The objective of mesh smoothing is to enhance the accuracy and efficiency of numerical simulations that utilize the mesh. Typically, mesh smoothing entails adjusting the positions of interior nodes while preserving the topological structure of the mesh. This means that the nodal connections of elements remain unaltered, but the interior nodes are repositioned to generate more regular and well-shaped elements. Laplacian smoothing is a well-established and computationally efficient mesh smoothing algorithm, initially introduced by Cavendish . This mei through Laplacian smoothing is given byN denotes the number of nodes associated to node i.The equation utilized to determine the updated position of an internal node h-type adaptive mesh refinement, where the mesh is refined based on the distribution of the stresses. The choice of smoothing technique and its impact on the accuracy and efficiency of the numerical simulations must be carefully considered. If the sampling points overlap with the mid-side points of isoparametric six-noded elements in finite element analysis, only the stresses at the other three nodes of the element need to be smoothed. To obtain smoothed stresses, the mid-side point stresses can be extrapolated to the other nodes using techniques such as polynomial fitting or averaging. However, it is important to note that the accuracy of the smoothed stresses is contingent upon the quality of the mid-side point stresses.In finite element analysis, stresses are typically evaluated at discrete sampling points within the computational domain. To produce a more visually appealing and physically meaningful representation of the stress field, these discrete stresses must be “smoothed” to create a continuous distribution of stresses that can be plotted using contour plots or other visualization techniques. The resulting smoothed stresses are important in the error estimation process, particularly in h-type adaptive mesh refinement, the objective is to determine the relative stress norm error, which represents the ratio of the element norm stress error to the average norm stress error across the computational domain. This ratio serves as a guide to predict the necessary mesh refinement size for the subsequent iteration. The element norm stress error quantifies the discrepancy between the computed stress value and the true stress value within a specific element, while the average norm stress error is the mean of the element norm stress errors across the entire domain. The refinement process entails increasing the mesh density in regions where the element norm stress error is relatively high compared to the average norm stress error. This approach can yield significant computational savings by reducing the number of elements required to achieve a desired level of accuracy. The adaptive remeshing method employed in this study is extensively explained in [h-type adaptive mesh procedure allows for the definition of the mesh size for each element based on the required level of refinement in a particular region of the problem domain. The following expression is utilized to determine the mesh size of each element:eA represents the area of the triangular element.In ained in ,42,43,44L along the r direction, and the crack tip is positioned at r = 0.0 (or node 1). The distance of node 2 from the crack tip is adjusted by a factor of α. In finite element analysis, a singular element is an element that has a zero or near-zero area or volume, resulting in singularities that can cause numerical instabilities or inaccuracies in the solution. The triangle singular element is a type of triangular element that is designed to handle singularities in two-dimensional problems. Consider a six-noded quadratic triangle element (T6) in Cartesian space, as depicted in u at any point within the T6 element, the nodal displacements N as follows:To determine the displacement b,c,d and e are the nodes around the crack tip. The diagram presented in Here, d Tracey , are useAfter the mesh is prepared, boundary conditions and loadings are applied to simulate the real-world scenario. Shape functions are then calculated, and the stiffness matrix is computed to determine the mechanical response of the structure. Using this information, the displacement, stresses, strains, error estimators, and stress intensity factors are calculated. At this stage, a remesh iteration may be performed to refine the mesh and improve accuracy. This iteration helps to capture the evolving crack geometry more effectively. Finally, based on the calculated results and considering factors such as stress intensity factors, crack growth direction is determined.The process of releasing nodes based on their mechanical properties, commonly referred to as the “relaxation of split nodes”, is employed to simulate crack growth. In order to accurately represent crack openings when the conditions for crack propagation are met, it is crucial to have two distinct nodes at the crack tip. To visualize the deformation, the displacements need to be appropriately adjusted using the coordinates of the boundary nodes. A comprehensive description of the node splitting and relaxation procedure can be found in a previous study . The strIn this section, a variety of meshes produced by the developed mesh generator are presented as examples. These meshes are intended to showcase the versatility and effectiveness of the mesh generator in handling diverse geometries and boundary conditions. Through these examples, readers can gain a deeper understanding of the capabilities of the mesh generator and its potential applications in various fields, including structural mechanics.E = 70 GPa, Poisson ratio ν = 0.33, and fracture toughness ICK = 26 MPa mm0.5.The first example was a compact tension specimen, which is a standardized test specimen used in materials testing to measure the fracture toughness of a material. It is primarily used in the field of fracture mechanics to evaluate the resistance of a material to crack propagation. P denotes the applied load, a is the crack length, W represents the width, and B represents the thickness of the geometry.The analytical first mode of stress intensity factor for this particular geometry can be determined by utilizing the equation provided by Anderson , which cTo assess the accuracy of the predicted results for the first mode of stress intensity factor, obtained from four different types of generated mesh, a comparison was made with the analytical solution presented in Equation (25). This analysis aimed to evaluate how well the predicted values aligned with the analytical solution across varying mesh densities, highlighting the reliability and precision of the results. During the comparisons, a consistent applied load of 8 kN was utilized, along with a geometry thickness of 8.3 mm. These specific values were adopted from the experimental work conducted by Parnas and Bilir , who useTo validate the accuracy of the program’s crack growth path prediction, a comparison was made between two predicted paths using coarse and intermediate mesh densities, as well as an experimental crack growth path obtained by Mourad et al. . The comIt can be observed that the crack growth direction strictly adheres to pure mode I loading. This implies that the crack propagates along a straight path with an angle of zero degrees. Additionally, the values of the second mode of stress intensity factors are nearly negligible. This provides further evidence of the dominance of mode I stress and the straight-line path of crack progression.The following a”, the span length by “S”, and the width by “W”. The material properties are modulus of elasticity E = 70 GPa, Poisson ratio ν = 0.33, and fracture toughness ICK = 26 MPa mm0.5.The dimensions of the three-point bend geometry are depicted in P denotes the applied load and B represents the specimen thickness.Broek  providesB = 1 cm, S = 32 cm, and W = 8 cm, with an initial crack length of a = 4 cm, subjected to an applied load of P = 9.8 kN. These specific values were adopted from the experimental study reported by Wei and Zhao [The problem was explored using three distinct mesh configurations, each characterized by varying densities. In all instances, the mesh was adaptively refined to enhance accuracy near the crack and load position. Notably, the final mesh employed a significantly higher density compared to the preceding two meshes, as clearly illustrated in and Zhao . The strThe crack growth path depicted in the figure demonstrates a pure mode I crack growth, indicating the dominance of mode I fracture behavior.E) of 2.8 GPa and a Poisson’s ratio (ν) of 0.3. A vertical crack was positioned along the bottom edge of the structure, with its length denoted as “a 1 cm”. To assess the precision of the current algorithm in simulating crack growth scenarios, a three-point bending test was modelled, and the resulting path of crack growth was juxtaposed with the experimental outcomes cited in . The geoThe geometry of the double-edge cracked plate with two holes under the assumption of plane stress is illustrated in This paper introduced a robust algorithm implemented in Visual Fortran that efficiently generates high-quality unstructured triangular meshes for modelling complex two-dimensional crack growth problems. The algorithm successfully addresses the challenges associated with geometric complexity, simulation accuracy requirements, and computational resource constraints. The proposed algorithm successfully incorporates adaptive refinement to predict crack paths with high precision. Moreover, the consistency of the obtained stress intensity factor results with established analytical solutions for standard geometries further validates the algorithm’s accuracy and reliability. The comprehensive details and step-by-step development of the proposed algorithm in the present form provide a valuable tool for researchers to delve deeper into the field of fracture mechanics. By providing a solid foundation, the proposed algorithm stimulates innovation and encourages the advancement of knowledge in this specialized domain.


This paper considers the task of appearance-based localization: visual place recognition from omnidirectional images obtained from catadioptric cameras. The focus is on designing an efficient neural network architecture that accurately and reliably recognizes indoor scenes on distorted images from a catadioptric camera, even in self-similar environments with few discernible features. As the target application is the global localization of a low-cost service mobile robot, the proposed solutions are optimized toward being small-footprint models that provide real-time inference on edge devices, such as Nvidia Jetson. We compare several design choices for the neural network-based architecture of the localization system and then demonstrate that the best results are achieved with embeddings  yielded by exploiting transfer learning and fine tuning on a limited number of catadioptric images. We test our solutions on two small-scale datasets collected using different catadioptric cameras in the same office building. Next, we compare the performance of our system to state-of-the-art visual place recognition systems on the publicly available COLD Freiburg and Saarbrücken datasets that contain images collected under different lighting conditions. Our system compares favourably to the competitors both in terms of the accuracy of place recognition and the inference time, providing a cost- and energy-efficient means of appearance-based localization for an indoor service robot. The rapid development of robotics and artificial intelligence applications is leading to the proliferation of mobile service robots ,2. TechnAlso, the growing need for eldercare robots has become increasingly evident as the global population ages. These robots can provide valuable assistance and companionship to older adults, monitoring their health and enhancing their overall well-being . HoweverA common requirement in these service robots is to be able to localize within their workspace, which is usually a man-made indoor environment . AlthougTherefore, we propose a solution to the problem of global localization in a known  environment using a passive catadioptric camera and the principle of recognizing places previously visited by the robot . The appExperimental analysis of neural network architectures in search of an architecture for an image-based place recognition system suitable for implementation on an embedded computer of an intelligent vision sensor with limited power and resources.Experimental verification of the possibility of using catadioptric camera images in the appearance-based localization task without developing them into panoramic form significantly reduces the computational load.Analysis of the strategy for creating training sets in a place recognition task, assuming that the obtained solution should be generalized to different image acquisition conditions, mainly depending on illumination.Although appearance-based localization does not provide an accurate metric position of the robot in a global reference system, the ability to tell if the robot is close to one of the known locations is often sufficient for indoor navigation . If a maA novel, simple-yet-efficient CNN-based architecture of the appearance-based localization system that leverages a lightweight CNN backbone trained to apply transfer learning to produce the embeddings and the K-nearest neighbours method for quickly finding an embedding matching the current perception.A thorough experimental investigation of this architecture, considering several backbone network candidates and omnidirectional or panoramic images used to produce the embeddings. The experiments were conducted on three different datasets: two collected with variants of our bioinspired sensor and one publicly available.An investigation of the strategies for creating the training set and the reference map for the localization system conducted on the COLD Freiburg dataset. This part of our research allowed us to test how our neural network model generalizes to images acquired under different lighting/weather conditions. It resulted in the recommendation of using data balanced concerning their acquisition parameters, improving generalization.We propose a novel approach that adopts a convolutional neural network (CNN) architecture to directly process the omnidirectional images for real-time place recognition to meet these objectives. CNNs are specialized for processing grid-like data, particularly images, using convolutional layers and parameter sharing to capture spatial patterns effectively. The proposed system leverages the concept of global image descriptors, which are already proven to be efficient in place recognition . We emplThe remainder of this article is structured as follows. Most important related works are reviewed in Appearance-based localization from omnidirectional images has garnered significant attention in computer vision and robotics. Researchers have developed various techniques to address the challenges posed by the distortion and wide field of view of omnidirectional cameras. This section reviews the most relevant works that have contributed to the state of the art in this area.The application of passive vision sensors for localization was extensively researched in robotics, resulting in several visual Simultaneous Localization and Mapping (SLAM) algorithms . HoweverTherefore, the appearance-based recognition of locations becomes an exciting addition to visual SLAM for closing the loops and relocalizing a lost robot . This apIn the appearance-based methods, each image is described by descriptors of salient features contained in this image, or is directly described by a whole-image descriptor. Although SURF features were used directly in appearance-based localization performing image retrieval in a hierarchical approach , the dirGlobal image descriptors have proven effective for capturing the overall appearance of omnidirectional images . EarlierMachine learning methods have gained popularity in place recognition, also from omnidirectional images . WorkingAs the construction of invariant feature descriptors for omnidirectional images is problematic, Masci et al.  proposedIn the proposed localization system, the robot figures out its current location by determining the similarity between the currently captured image (query image) and images stored in a database (map) describing the environment. This task refers to efficient, real-time image retrieval . The locThe proposed localization system uses a CNN to determine the set of natural features for a given location, and the K-nearest neighbours (KNN) ,45 algorCNN and KNN are both machine learning techniques, but differ in their approach and application. CNN learns hierarchical representations of data through multiple convolutional layers, pooling, and fully connected layers. In contrast, KNN is a simple and intuitive algorithm for classification and regression tasks. It makes predictions based on the similarity of new data points to the existing labelled data points in the feature space. One can use CNN to extract features from images and then apply KNN to those extracted features for classification. This hybrid approach leverages the strengths of both algorithms, with CNN capturing intricate patterns and KNN using the extracted features for classification . This idThe preparation of the CNN model is based on training the network to correctly recognize places, with the specific aim of training the higher layers of the network to extract feature maps specific to each location properly. Because the CNN used as the backbone of our system is pretrained on images unrelated to the target domain  that describe the global characteristic features of each image in the database, i.e., each unique place visited by the robot. In this way, a global map of all locations based on reference images is created. Not all convolutional network architectures from the literature can be used on a robotic onboard computer with fewer computational and memory resources.This research uses backbone networks from the MobileNet  and EffiThe EfficientNet model, which we have selected for our final architecture, can be seen as a further step towards efficiency compared to the MobileNet model. EfficientNet uses a complex model scaling technique based on a set of specified coefficients. Instead of randomly scaling width, depth, or resolution, compound scaling uniformly scales each dimension using some fixed scaling coefficient set. Such scaling only increases the predictive ability of the network by replicating the underlying convolutional operations and structure of the network. EfficientNet uses the MBConv blocks as in the MobileNet V2 network, but with a squeeze-and-excitation (SE—) block bThe backbone CNN extracts from the image features that uniquely describe different locations and builds embedding vectors that serve as global image descriptors in our system. In the next step, the algorithm creates an index from the global map, which is used for efficient similarity search. The original images collected by the robot are no longer needed for localization and the obtained global map has a compact form. All operations to produce the global map are performed offline.Then, to localize the robot, we need to query the global map (database of embeddings) with the descriptor/embedding produced from the current perception of the agent, which boils down to a similarity search task. Similarity search is a typical issue in machine learning solutions using embedding vectors, and becomes increasingly difficult as the vectors’ dimensions and/or size increase. Classic methods for finding similarity between vector-described elements in an extensive database include linear search and search in K-D-trees . K-D-treEach node in the tree represents a K-dimensional point. Each nonleaf node in the tree acts as a hyperplane, dividing the space into two parts. Using a K-D tree for nearest neighbour search involves finding the point in the tree that is closest to a given query point. For this purpose, the algorithm traverses the tree and compares the distance between the query point and points in each leaf node. Starting from the root node, it recursively moves down the tree until it reaches the leaf node, following the same procedure as when inserting a node. Many implementations of the nearest neighbour search using K-D-trees are known in Python, including the very popular SciKit-Learn library. However, for this project, we selected the Facebook AI Similarity Search (Faiss) library , writtenPlace recognition begins by loading the learned CNN model and index of images (map) into memory, and then the captured images (queries) are compared with the previously created image database using the KNN algorithm in the space of embedding vectors. The embeddings are compared using L2 (Euclidean) distance, which has been shown to be more computationally efficient than feature binarization followed by the comparison applying Hamming distance ,54.i-th query image; i-th query image; i-th query image; i-th query image.Once the similarity between the query image and the map is determined, the results are presented in the form of the image retrieval accuracy and the position error between the query image and the map image determined as the most similar one. As we assume that ground truth positions for all map images and query images are known, as in the COLD dataset , we simpThe architecture of the localization system shown in its general form in To confirm the proposed solution’s effectiveness and determine the best-performing CNN architecture, experiments were carried out at the Mechatronics Centre of Poznań University of Technology using two catadioptric cameras with different parameters. Then, experiments with the publicly available COLD database were carried out to demonstrate the performance of our approach with respect to selected state-of-the-art solutions in appearance-based localization on this dataset.A Labbot robot a with ann in size, which is a global map based on n reference images (n = 484 in the experiment). The robot’s main localization task uses the integrated sensor’s Jetson platform in real time. The configuration of the localization system in this experiment was the following:Raw catadioptric images were used cf.  without The neural network used to produce the embeddings was EfficientNet, which was selected upon literature-based analysis.The considered dataset contains 606 images a,b, whicThe EfficientNet architecture has gained prominence as an effective solution for image processing on edge devices due to its remarkable balance between accuracy and efficiency. By leveraging techniques like compound scaling, which uniformly scales the network width, depth, and resolution, EfficientNet optimizes the model’s architecture to maximize accuracy while minimizing the number of parameters and computations. This enables real-time inference and efficient utilization of resources on edge devices, ensuring faster and more responsive image processing capabilities even with limited computing power . MoreoveThe used EfficientNet B5 has 577 layers and the input image size is . This network has high accuracy with a relatively small number of model parameters, which positively affects the processing speed of the embedded system. The network was fine-tuned before use because EfficientNet B5 was pretrained on images from the ImageNet dataset. This process was implemented using a dataset of about 10,000 augmented omnidirectional images produced from the previously collected database of 606 original images. Only standard augmentation methods available in the TensorFlow environment were applied to the images.A practical problem in the scenario considered in Experiment 1 was the high similarity of the indoor environment in the Mechatronics Centre building. Images were obtained approximately every 0.5 m along the robot’s path, and adjacent images in the database are very similar and often indistinguishable, even by a human. Therefore, the entire dataset was manually divided into 17 different sections, each describing a topologically different location  accuracy are presented for all experiments. For experiments no. 2 and no. 3, we also present quantitative results in terms of the metric localization accuracy, as the datasets used in these experiments provide ground truth for positions of the place images in a global reference system. Moreover, we discuss qualitative localization results, pointing out the most common sources of localization errors and providing recommendations for training strategies of the deep neural networks that make the resulting models robust to changes in the environment.As defined in f 0.9796 .On the test dataset containing 122 query images, the average accuracy of place recognition was 98%, with very few misclassified queries, as shown by the confusion matrix in This experiment allowed us to conclude that the proposed approach to appearance-based localization with embeddings produced by a lightweight CNN suits the target application in terms of both image retrieval accuracy and real-time performance. However, the used sensor, having rather a small field of view and mechanical structure prone to decalibration and defocusing (causing blurred images), did not allow us to extend these investigations to a larger dataset with ground truth positions of images.The conclusions drawn from Experiment 1 were taken into account while designing the next experiment involving the use of a different catadioptric sensor and a more extended and diversified dataset of indoor images with ground truth positions.In Experiment 2, the convolutional neural networks EfficientNet B7, EfficientNet V2L, and MobileNet V2 were compared for Configurations A, B, and C. The quantitative results presented in the graphs show the percentage of Cartesian locations found in the given distance intervals expressed in meters, and the average Euclidean distance measurement error: for Configuration A—A mismatch of the neighbouring places occurs only when the images overlap significantly (note that the catadioptric camera used in Experiment 2 has a much larger field of view that the previously used one) and are very similar to each other due to the self-similar nature of the environment. No significant difference was noticed between the results obtained for omnidirectional and panoramic images, which indicates that for appearance-based localization with our approach, it is unnecessary to convert the omnidirectional images to panoramic images. Hence, we can avoid the time-consuming conversion and rectification procedure , withoutAs a follow-up of Experiment 2, a comparison of localization results was performed between the NetVLAD approach with VGG-16 and VLAD layer, and our approach with two variants of the EfficientNet backbone. This comparison was performed for all three configurations of the reference map  and both the omnidirectional and converted panoramic images.Quantitative results of the average Euclidean distance measurement error for all configurations considered in this test are shown in From Experiment 2, we conclude that the CNN architecture performing best in our system is EfficientNet V2L, a model from a recently introduced family of convolutional networks that achieve faster training and better parameter efficiency than older network models . This moConclusions about the limited generalization ability of the proposed localization system drawn from Experiment 2 were one of the main motivations behind the concept of Experiment 3, which applies the publicly available COLD Freiburg dataset and compares side-by-side to the results obtained on the same dataset and published recently in .In , the besFollowing the methodology of replicating the selected experiments from  with resDuring the analysis of the results, it was noticed that the images recorded on sunny days and nights have different acquisition spots (positions) than those acquired for cloudy days, and some of them are farther than 20 cm from the acquisition spots for cloudy days, e.g., for the room labelled CR-A, the farthest acquisition spot on sunny days was 0.5 m away from the farthest acquisition spot on a cloudy day. For this reason, an extension of the training set no. 1 was made, only with images taken at the missing acquisition spots for sunny days and for nighttime . Note thBased on the data from r nights e. Also, r nights f. Based In order to explore the generalizability of the proposed system to other environments, we also demonstrate localization results for the Saarbrücken sequence from the COLD dataset. This is a sequence of images collected in a different location within a building having different characteristics than the one used for the Freiburg sequence . Both FrThe hierarchical localization of the mobile robot in  is dividThe appearance-based localization methods studied in  include The results shown in The results of the tests of the place recognition software for catadioptric cameras and the edge computing platform allow us to conclude that the proposed neural network architecture and parallel processing make it possible to obtain a real-time localization system that works with raw catadioptric images, despite their distorted nature.The extensive study of the algorithm of appearance-based localization and comparison of results with similar solutions known from the literature demonstrate that the proposed approach makes it possible to obtain highly descriptive embeddings of the observed locations, and consequently, efficient appearance-based localization.The most important conclusions, summarizing the remarks discussed in However, a limitation of the proposed appearance-only approach to global localization is the limited accuracy of the obtained metric position of the robot. This accuracy depends on the density of the global map, because the obtained position of the robot is defined by the known location of the most similar image. If the images were collected close to each other, then the position of the robot can be determined more accurately, but if the distances between the points where the images were captured are large, the accuracy is decreased. This limitation will be addressed in our further research by implementing a neural network that will regress the position of the robot with respect to the reference image retrieved from the map. Further research on this system will also concern the implementation of triplet loss with hard negative mining, as this training scheme turned out to be very effective in a number of localization systems. This training strategy should allow the network to develop more specific features, thus making the localization system more effective in highly repetitive indoor environments.