Vehicle handling and stability performance and ride comfort is normally assessed through standard field test procedures, which are time consuming and expensive. However, the rapid development of digital technologies in the automotive industry have enabled to properly model and simulate the full-vehicle dynamics, thus drastically reducing design and manufacturing times and costs while enhancing the performance, safety, and longevity of vehicle systems. This paper focus on a computationally efficient multi-objective optimization framework for developing an optimal design of a vehicle steering system, which is carried out by coupling certain computer-aided design tools (CAD) and computer-aided engineering (CAE) software. The 3D CAD model of the steering system is made using SolidWorks, the Finite Element Analysis (FEA) is modelled using Ansys Workbench, while the multibody kinematic and dynamic is analysed using Adams/Car. They are embedded in a multidisciplinary optimization design framework (modeFrontier) with the aim of determining the optimal hardpoint locations of the suspension and steering systems. This is achieved by minimizing the Ackermann error and toe angle deviations, together with the volume, mass, and maximum stresses of the rack-and-pinion steering mechanism. This enhances the vehicle stability, safety, manoeuvrability, and passengers’ comfort, extends the vehicle systems reliability and fatigue life, while reducing the tire wear. The method has been successfully applied to different driving scenarios and vehicle maneuvers to find the optimal Pareto front and analyse the performance and behaviour of the steering system. Results show that the design of the steering system can be significantly improved using this approach. Moreover, manufacturers are struggling to meet these challenges in the context of a highly competitive and rapidly changing marketplace. In this sense, the smart manufacturing in the automotive industry by means of CAE software has matured rapidly in recent years with the aim to assess the full-vehicle dynamic behaviour during the design, development, and prototype stages5. Compared to traditional experimental procedures, this allows to reduce costs and design and production times while maximizing vehicle performance, comfort, environmentally friendly features, quality, and safety6.The automotive industry is undergoing a period of change because of the digital transformation, the circular economy, and the sustainable development goals7. This is because they are conflicting goals, in which the achievement of one objective is hindered by others. Therefore, there is a trade-off between vehicle handling and ride comfort. In this sense, a superior handling quality implies that the vehicle attains the state of motion required by the driver more quickly and accurately, while a superior stability means that the vehicle is capable of rapidly restoring the original state of motion under external forces and moments. Therefore, an appropriate understanding and design of the crucial parameters associated with the two systems is indispensable.The suspension and steering systems play a major role to achieve a good compromise between the vehicle handling, stability, safety, and ride comfort15). They encompass approaches in which well-known vehicle system dynamics simulation packages or analytical equations are used to simulate, optimize, or perform sensitivity analysis for the estimation of parameters that affect vehicle dynamics behaviour. Moreover, some authors have also coupled either analytical equations that model the dynamic behaviour of vehicle systems or CAE tools with optimization methods, such as evolutionary or genetic algorithms for the same purpose (e.g.19).Several efforts have been made to come up with the best solutions. In this sense, the literature has addressed the design of the suspension and steering systems using several methods , ECS (Electronic Control Suspension system), 4WD (4-Wheel Drive)24. Other authors have also optimized the front suspension and steering parameters of an off-road vehicle using Adams/Car simulation23. An analysis of the kinematics and compliance of a passive suspension system using Adams/Car was presented by22. The vehicle cornering performance evaluation and enhancement based on CAE and experimental analyses was investigated by5. A multi-objective optimization framework for designing a vehicle suspension system together with a comparison of the results using different algorithms was carried out in6.For instance, the Adams/Car  software was used to simulate the kinematics and compliance testing of a virtual suspension system prior to conducting prototype experiments25, while several equations were proposed for relating parameter measurements with the optimized Ackermann steering geometry26. Attempts to relate the inside and outside steered wheels of a vehicle were made to correct the theoretical equation for the Ackermann steering angle based on experimental results27. The effects of the steering geometry and compliance, together with the steering linkage friction and tire static friction torque on the steering effort was also examined28. Moreover, a methodology was proposed for fine tuning the design and dimensions of the steering linkages with the aim to minimize the steering effort while satisfying the imposed restrictions on the hardpoint locations. The repercussion of dynamic load changes on the vehicle steering geometry and the resulting non-uniform tire wear of the front steered wheels was also investigated29. The optimal kinematic design of a multi-link steering system for a bus independent suspension was achieved by means of the application of Response Surface Methodology (RSM)30. The optimum suspension hardpoint locations for attaining steering returnability in vehicle, while an improved design of steering system by reducing the steering ratio were introduced, respectively, by32.Additionally, several analytical approaches based on Ackermann theory were used to analyse and control critical suspension propertiesTo sum up the literature has proven that the employment of CAD/CAE software leads to key benefits in the design, development, and prototype stages of a vehicle. This paper goes a step further in the current literature by coupling powerful CAD/CAE tools that are integrated within an optimization framework for an efficient design of vehicle systems. It poses a multi-objective optimization problem that considers the geometrical features and material properties of vehicle systems, the full-vehicle kinematics and dynamics behaviour, and an analysis of the structural integrity of the key components of the steering system. It takes into account a broad-spectrum of design variables, objectives, and restraints that has been successfully applied to different driving scenarios and vehicle maneuvers. Furthermore, the framework compares different optimization strategies, which comprise heuristics optimizers, evolutionary algorithms, multistrategy optimizers, and gradient-based algorithms. The rest of the paper is organized as follows. First, a brief description of the steering and suspension systems and their key parameters influencing the vehicle dynamics are presented. Subsequently, the methodology and the optimization framework are described. Then, the methodology is successfully applied to different driving manoeuvres, in which the optimization framework finds a suitable compromise between the design variables. Finally, the findings and recommendations are discussed.33, on the steering mechanism in35, while on the vehicle dynamics problems and its corresponding handling, stability and ride comfort in (e.g.36). These systems play a major role in the vehicle handling and ride comfort. In fact, the main factors affecting the ride comfort are the stiffness of the suspension components , the suspension geometry, vehicle mass and weight distribution. Ride comfort prevents passengers from certain harmful effects on body because of vehicle vibrations and is subject to specific regulations. They cover conditions such as back pain, osteoarthritis, hyperventilation, disc slippage, etc.37. The regulations states that ride comfort is dependent on the root mean square (RMS) values of the sprung mass acceleration and the frequency of the body's vibrating. These frequencies can be divided into two categories: those that are unpleasant or dizzying (0.5–80 Hz) and those that are healthy and relaxing. (0.1–0.5 Hz). Road holding, on the other hand, refers to a vehicle tire's capacity to maintain contact with the road surface.An in-depth review of the theoretical foundations with regard to vehicle suspension systems can be found inThey also influence the vehicle handling , which refers to how a vehicle performs specially during cornering, acceleration, and braking as well as on the vehicle's directional stability when moving in steady state condition. The vehicle stability is commonly supported by computerized technology, which allows detecting and reducing loss of traction . The purpose of these vehicle systems, their elements and key design parameters that influence vehicle dynamics are subsequently explained.The suspension system connects the wheels to the vehicle chassis and is made up of several mechanical linkages, springs, and dampers. It transmits the forces and moments between the sprung and unsprung mass, which allow absorbing and damping the impacts and vibrations induced by surface irregularities and dynamic loads while preserving passengers’ ride comfort and vehicle handling and stability. It is also responsible for keeping the wheels in contact with the ground, while minimizing the loss of traction, lateral movement because of centrifugal forces, and tire wear. A high-performance suspension system must consider a wide range of factors. It should allow a movement of a wheel to be independent from the other wheel of the axle and provide structural efficiency by properly transferring the mechanical loads from the suspension system to the vehicle chassis. It should lead to a satisfactory isolation of road irregularities to improve passengers’ comfort, for which a fine tuning of the stiffness and damping coefficients of springs and shock absorbers is required. The suspension system is intended to mitigate the anti-dive phenomenon in which the front of the vehicle dips and the tail rises and the anti-squat (opposite response) in order to increase passengers’ comfort. They occur in the breaking and acceleration events, respectively. The geometry of the suspension system affects the vehicle body roll motion and its lateral behaviour during cornering manoeuvres so that it should be optimized.The steering system allows a directional control of the vehicle in accordance with the driver’s preference by controlling and directing the steering wheel, which rotation is converted into a linear motion by the rack and pinion and eventually transmitted into the wheels by the tie roads and steering arms connected to the uprights by ball joints that can bear harsh road conditions. Additionally, both vehicle systems should be designed with low weight by using optimal geometry and lightweight materials to reduce the transmitted shocks to the chassis, long fatigue life and low cost.Toe angle is the angle between the longitudinal axis of the vehicle and the line of intersection of the wheel plane and the vehicle's XY plane. It is positive if the wheel front is rotated in towards the vehicle body. It has a great impact on the vehicle performance, e.g., on straight line stability, steering and acceleration. It is of vital importance to minimize toe angle variation during wheel travel to avoid bump steer. This occurs when the wheel steers itself without input from the steering wheel. By optimizing the hardpoint locations the bump steer can be minimized. Additionally, toe angle is used to compensate for understeer or oversteer. Common values of the toe angles are between − 1/4 inch plus or minus 1/8 inch.Ackermann angle is the angle whose tangent is the wheelbase divided by the turn radius. Ackermann angle is positive for right turns. Ackermann steering refers to the geometric configuration mainly designed as a trapezoidal linkage, due to its simplicity and ease of manufacturing, whose purpose is to avoid tyre sliding by compensating the effect that the outer and inner wheels travel circumferences of different radii when cornering.Ackermann error is the difference between the steer angle and the ideal steer angle, which gives an Ackermann steer geometry or 100% Ackermann. Since ADAM/Car uses the inside wheel to calculate the turn centre, the Ackermann error for the inside wheel is zero. A positive Ackerman error means that the actual steer angle is greater than the ideal steer angle or the actual is steered more to the right. Ideal steer angle  means the linkage extensions are cut in the centre of the rear axle. If the percentage is greater than 100, they will be cut in front of the rear axle; and behind if it is lower. Then percent Ackermann is the ratio between the actual and the ideal Ackermann expressed as a percentage. In other words, in an Ackermann steer geometry the wheel-centre axes for all four wheels pass through the turn centre. A pure Ackermann steering system is not used in modern vehicles. On the contrary, anti-Ackermann steering is designed for high-speed cornering, where cornering forces are high, in order to improve the steering response by reducing slip and providing more grip to the outside tire during larger radius turning corners. As Ackermann increases, more forces and inertia are held in the steering linkages, which can enhance the steering system ability to self-return. In theory, this should increase returnability.Steering systems inner and outer tierods: they transmit force from the steering wheel to the front wheels, allowing the driver to change directions. They are attached to the steering rack and connect the steering gear to the steering knuckle. They are an essential component of the vehicle steering system that, if they become worn or loose, could lead to tire wear and handling problems.Suspension and steering systems depend on a wide set of parameters that affect the orientation of the wheel regarding the ground and the performance of the vehicle while braking, acceleration and cornering. These wheel alignment settings cover among others the camber, caster and toe angles, scrub radius, track width, and kingpin inclination angle. They can be modified by changing the hardpoint locations and angles of the fixations of the mechanical linkages on the chassis and the uprights. The suspension system, which rotates to permit wheel motion, is what connects the wheel to the chassis. Therefore, maintaining ideal parameter values within the preferred limits becomes more difficult the longer the travel of the wheels because of the road irregularities and forces applied. Consequently, it is of vital importance to carry out an optimization of these parameters to keep them within the limits established and improving vehicle handling and driving stability. The design variables optimized in the multi-objective optimization procedure and their most correlated parameters that affect vehicle dynamics are subsequently presented Figs.  and 2:ToEnables an automated simulation by coupling powerful engineering tools from a single workflow and evaluates thousands of designs.Considers the full-vehicle kinematics and dynamics behaviour, together with the structural integrity analysis of main mechanical components.Deals with a wide range of explanatory and response variables.Takes into account the geometric characteristics and material properties of the steering and suspension systems.Includes different driving scenarios entailing diverse vehicle dynamics manoeuvres.Allows conducting testing procedures, monitoring, and maintenance of vehicle systems.Integrates advanced data analysis to derive the Pareto optimal front and balance conflicting objectives in order to gain deeper insight into design alternatives and make informed decisions.Easily extendable to the design of other vehicle components.Maximizes efficiency and reduces operating costs.The design of a vehicle system demands the use of complex optimization-simulation techniques that allows estimating the crucial parameters and their impact on the vehicle dynamic behaviour. The methodology presents an efficient design and representation of a real-world vehicle steering and suspension systems by posing a multi-objective optimization framework to come up with a good compromise between the design variables and including a wide range of advantages beyond traditional engineering methods:3. In this way the methodology allows the steering system to support the existing loads, while reducing vibrations and increasing its fatigue life.Figure Then the multi-objective optimization procedure minimizes the Ackermann error and toe angle deviations, together with the volume, mass, and maximum stresses achieved in the rack-and-pinion steering mechanism based on the full vehicle dynamics. The methodology relies on an initial set of parameters that are updated during the optimization procedure, which cover the hardpoint locations as well as the stiffness of the spring, bushing, and damping characteristics of the suspension system. Hardpoints are locations that connects the steering and suspension systems to the vehicle body. They play an essential role in the vehicle dynamics characteristics, since they determine certain parameters such as the described wheel angles, the longitudinal and lateral forces and moments on the wheel and load transfer. Therefore, the optimization of the hardpoint locations is justified with the aim of enhancing the vehicle handling stability and ride comfort, finding a suitable compromise between them, and analysing the corresponding trade-offs. The optimal set of parameters also allows to design mechanical components with higher vehicle systems reliability and fatigue life while reducing the tire wear.Note that apart from the optimized parameters, which cover the Ackermann error and toe angle deviations, there are other key parameters that influence the steering and wheel alignment. The selection of these parameters is because they play a major role in the dynamics of the vehicle. The other parameters comprise the camber angle, caster angle, Kingpin inclination, steering angle, slip angle and the wheel instantaneous roll centre. For the sake of conciseness, only the parameters that are optimized have been explained in the previous section, while a deep understanding of the other parameters and their effect on the vehicle dynamics can be found, for instance, in the documentation associated with the Adams/Car. Furthermore, the use of more parameters in the objective function would lead to an overparameterized optimization problem.29. In addition, since the methodology entails the design of 3D mechanical components, full vehicle kinematics and dynamics and the calculation of stresses and deformations of mechanical components using the finite element method (FEM), the reader is referred to the specialized literature and software user documentation for a detailed explanation of the underlying multiphysics processes, theory and modeling aspects of the embedded engineering tools. For the sake of conciseness, note that detailed explanation of such equations is unapproachable and beyond the scope of this scientific article. It is worth mentioning that although the modeFrontier platform offers many advantages for the implementation of a multi-objective optimization problem, the reader should be aware that advanced modelling knowledge of both the platform and the embedded engineering tools and a certain degree of expertise on the underlaying physical processes are required to successfully implement an optimization problem using this platform.The multi-objective optimization framework in modeFrontier allows to perform the optimization using either local (commonly gradient based), global (commonly non-gradient based or evolutionary) algorithms or a combination of or a combination of both depending on each problem. Furthermore, different approaches can also be applied, which cover heuristics optimizers, multistrategy optimizers, evolutionary algorithms, and gradient-based algorithms. An in-depth explanation of such approaches can be found in5.The methodology has been successfully applied to different case studies that cover full-vehicle driving scenarios, that include a wide range of manoeuvres for a complete analysis of the dynamic behaviour of the vehicle. Moreover, this allows the optimization procedure to find a suitable compromise between the design variables for these possible manoeuvres of the vehicle. In this sense, it provides a reduction in the vehicle systems development in terms of time and costs, while enhancing ride comfort and vehicle performance. The case studies are based on the multibody modelling and simulation environment Adams/Car software package. The first full-vehicle virtual test analysis covers a driving scenario that entails a cornering-event, i.e., a braking in turn event S1); the second driving scenario involve a constant radius cornering (S2); the third deals with a straight-line braking event (S3); and the fourth tackles a roll stability event, specifically, a ramp (corkscrew) (S4). The parameters adopted in such events are displayed in Table ; the secOn the one hand, a rack-and-pinion steering system, which convert rotation motion into linear motion, is selected because it provides a simple, compact, and robust control over the vehicle with lower cost with high mechanical efficiency. The most adverse disadvantage is due to the inherent friction, which leads to a constant wear of the mechanical components. On the other hand, a non-parallel double wishbone independent suspension system based on a four-bar guiding mechanism is chosen because its simplicity, ground clearance, impact protection, versatility in providing a wide range of motion, accuracy, and durability. Moreover, it also provides the best cornering performance, an increased negative camber gain while rolling, a vertically independently movement of each wheel on the same axle and an optimum compromise between vehicle handling and ride comfort. On the negative side, it is sensitivity to misalignment, which can affect their accuracy and performance and more expensive to design and manufacture than some other types of linkages.A linear relationship in the front suspension system between the spring force and the displacement has been considered, which varies between ± 12,000 N and ± 100 mm, respectively. With regard to the damper force and the velocity a polynomial relationship has been defined within the interval of  N and ± 1250 mm/s, respectively.A set of restraints are applied to the multi-objective optimization problem, which entail variation intervals for the tierod diameter, its mass, and hardpoint locations (hpl). In fact, the initial guess of the parameter set, which are presented in Table It is important to mention that the optimization problem was carried out to withstand the maximum mechanical loads determined by Adams/Car, and that the four objectives are given equal weights in the penalty function. A Design of Experiments (DOE) has been defined using the modeFrontier platform to do a preliminary exploration of the design space, and a variety of optimization strategies are implemented by employing the given DOE sequence. A total of 500 simulations are obtained for each optimization approach and driving scenario.Figure For each driving scenario and optimization method, five hundred simulation runs were performed. On average 98% of feasible simulations were achieved. The methodology allows obtaining a Pareto-optimal front that comprise a set of non-dominated solutions. This set optimizes the four objectives in the multi-objective optimization problem, which encompasses the Ackermann error, the toe angle deviations, together with the mass and maximum von-Mises equivalent stresses of tierod of the rack-and-pinion steering mechanism.Figure A comparison between the non-optimized and optimized parameters of the vehicle systems has been carried out for the different driving scenarios Table . It presThe simulation findings display that the real vehicle dynamics behavior has been accurately modeled. The methodology aims to achieve a balance between the computational cost, the level of detail of the model, and the quality and precision of the results. This helps to prevent overparameterization issues caused by parameter uncertainty.The input and output variables are related to each other. This relationship can be analyzed and understood. By examining the input and output variables, we can determine how they affect each other. Understanding this relationship is important for making predictions and improving processes.The linear relationship between the variables is measured by means of the Pearson correlation coefficient. Because of the defined geometry and uniform density of the tierod, a perfect correlation between its volume, diameter and mass is achieved. This leads to a reduction of these design variables for the identical set of parameters. Additionally, it should be highlighted that a high Pearson correlation of 0.733 is observed between minimum values of the Ackermann error and the toe angle. A moderate correlation of the outer tierod hardpoint locations between 0.5 an 0.675 is presented for the minimum values of the Ackermann error and the toe angle. The Y coordinate of outer hardpoint location of the lower control arm exhibits a correlation of 0.485 with the toe angle deviations and 0.426 with the Ackermann error. For the rest of the variables a low correlation is observed. For instance, between the tierod mass and the Ackermann error the correlation is 0.011, while between the von-Mises equivalent stress and the tierod mass is 0.042.Figure RSM uses Machine Learning algorithms to obtain a rapid and effective meta-model based on a dataset. This enables the validation of the model accuracy and to perform a reliable RSM-based optimization. Consequently, the use of a RSM as a surrogate model makes possible to explore the design space by means of an adequate Design Of Experiments (DOE) and to carry out the optimization procedure faster with a limited quantity of designs. In addition, a comparison of different algorithms and optimization strategies is presented.6.Furthermore, it enables precise results in identifying the Pareto-optimal front, while avoiding potential downsides of each optimization technique. The optimization strategies can be divided into two groups: local (often based on gradients) and global . The study examines the outcomes of a wide range of optimization techniques, including gradient-based optimizers, multi-strategy algorithms, evolutionary algorithms, and heuristic optimizers30. As a result, this work performs the comparison in accordance with the advice given in the literature. The PilOpt method produced the best outcomes for the multi-objective optimization problem, as shown in Table 39.However, it is important to note the difficulties in evaluating the effectiveness of several optimization techniquesIt modifies the ratio between real and virtual RSM-based design evaluations to boost the performance in the process to attain the Pareto-optimal front. Since it only depends on one parameter, complex parametrization is also avoided. The values presented in Table Table A framework for optimizing the design of the vehicle suspension and steering systems has been developed, which enables an automated simulation by coupling powerful engineering tools from a single workflow and evaluates thousands of designs. The multiobjective optimization framework integrates well-proven simulation tools and considers a broad-spectrum of design variables, objectives, and restraints, which encompasses the geometrical features and material properties of vehicle systems, the full-vehicle kinematics and dynamics behavior, and an analysis of the structural integrity of the key components of the steering system. The methodology allows conducting testing procedures, monitoring, and maintenance of vehicle systems. Furthermore, it integrates advanced data analysis to derive the Pareto optimal front and balance conflicting objectives in order to gain deeper insight into design alternatives and make informed decisions.The methodology has been successfully applied to different driving scenarios entailing a wide range of vehicle maneuvers. These case studies examine the performance of the full-vehicle dynamics by optimizing key parameters of the suspension and steering systems. Moreover, a comprehensive set of optimization strategies has been compared to accurately find the Pareto-optimal front of the multi-objective problem. Results have shown that the efficient optimization approach reduces vehicle systems design time and manufacturing costs while enhancing the vehicle performance . In addition, the fatigue life of the mechanical components is expanded. All optimization approaches obtained a great convergence, diversity of solutions, and percentage of feasible solutions, allowing for finding the Pareto-optimal front. This set of non-dominated solutions efficiently assesses vehicle systems performance and analyzes trade-offs between design parameters. It has been proved that different combinations of these factors can produce quite varied outcomes in terms of a vehicle handling, stability, and ride comfort. This demonstrates the worth of the methodology for significantly enhancing vehicle systems design, especially when compared with conventional simulation engineering approaches for vehicle development.The proposed optimization methodology can be used as a decision support system for designers in determining the set of parameters of the suspension and steering systems to provide the requested vehicle dynamic behavior. This is because different set of parameters lead to opposing vehicle dynamics effects, so it is needed to find a suitable comprise between such parameters. Moreover, the methodology offers flexibility in the selection of trade-offs between design alternatives. As a result, it maximizes efficiency and reduces operating costs.As part of future research, it might be possible to carry out a sensitivity analysis of the impact of additional parameters on the dynamics of the vehicle, and additional vehicle maneuvers and driving tests since they require the assessment of diverse dynamic characteristics. Additionally, the methodology can be applied to other vehicle systems such as transmission or braking systems. Moreover, it can be extended to designing any mechanical system. The only challenge lies in correctly modeling with CAD/CAE tools its geometric and material properties, the kinematics and dynamics of the mechanism, as well as the boundary conditions of each specific problem.


Dynamic objects bring about a large number of error accumulations in pose estimation of mobile robots in dynamic scenes, and result in the failure to build a map that is consistent with the surrounding environment. Along these lines, this paper presents a robust semi-direct 3D simultaneous localization and mapping (SLAM) algorithm for mobile robots based on dense optical flow. First, a preliminary estimation of the robot’s pose is conducted using the sparse direct method and the homography matrix is utilized to compensate for the current frame image to reduce the image deformation caused by rotation during the robot’s motion. Then, by calculating the dense optical flow field of two adjacent frames and segmenting the dynamic region in the scene based on the dynamic threshold, the local map points projected within the dynamic regions are eliminated. On this basis, the robot’s pose is optimized by minimizing the reprojection error. Moreover, a high-performance keyframe selection strategy is developed, and keyframes are inserted when the robot’s pose is successfully tracked. Meanwhile, feature points are extracted and matched to the keyframes for subsequent optimization and mapping. Considering that the direct method is subject to tracking failure in practical application scenarios, the feature points and map points of keyframes are employed in robot relocation. Finally, all keyframes and map points are used as optimization variables for global bundle adjustment (BA) optimization, so as to construct a globally consistent 3D dense octree map. A series of simulations and experiments demonstrate the superior performance of the proposed algorithm. Simultaneous localization and mapping (SLAM) has gradually become a frontier research hotspot in the field of intelligent robots. SLAM enables the robot to use the environmental information perceived by its sensors to estimate its pose in real time and incrementally construct an environment map. In recent years, with the widespread application of depth cameras, it has been possible to simultaneously obtain both the color and depth information of the environment, i.e., RGB-D information, which provides richer environmental perception for the SLAM system of mobile robots. Thus, visual SLAM (VSLAM) using RGB-D information has rapidly developed ,2,3,4.The solutions of VSLAM mainly include feature-based and direct methods. Specifically, the feature-based method relies heavily on the feature points extracted from the image and is sensitive to image quality. In order to improve the robustness of the algorithm in cases of missing features or blurred images, the direct method has emerged to solve the camera’s motion by directly comparing the pixel colors of the images; it avoids feature point extraction and fully utilizes all the information in the image. A typical case is the large-scale direct monocular (LSD) SLAM based on grayscale images, known as LSD-SLAM , which cIt is noticed that most of the existing SLAM algorithms are designed mainly for static scenes. Unfortunately, in practical applications, dynamic environmental conditions present significant challenges to robot perception and decision-making behavior. If the feature points of dynamic objects are included in robot pose estimation, it will result in erroneous feature matching, leading to severe trajectory drift and the inability to construct consistent and accurate environmental maps. Although outlier removal algorithms such as random sample consensus (RANSAC)  can elimIn summary, to meet the application requirements of mobile robots in dynamic scenes, this paper proposes a robust semi-direct 3D SLAM algorithm based on dense optical flow. Compared with the feature-based method, we adopt the semi-direct method in the front-end to quickly obtain the initial pose of the camera and use dense optical flow to detect the dynamic areas in the images, which ensures the real-time performance of the algorithm. Meanwhile, dense optical flow is employed to detect the dynamic regions of the image and eliminate map points in the dynamic regions. It should be noted that the dynamic objects in the scene can be accurately detected using the dense optical flow, which in turn obtains the static map points with high confidence and is utilized in the back-end of the system for the optimization of the camera pose, effectively suppressing the interference of the moving objects and improving the robustness of the system while ensuring the accuracy. Then, high-quality keyframes are selected and ORB feature points are extracted from them for mapping and optimization in the back-end. Considering the tracking failures that occur in dynamic scenes, ORB feature points are extracted from the current frame to recover the robot pose by matching them with keyframes and map points. Finally, global optimization is applied to the mobile robot pose and sparse map points, and a 3D dense octree map that can be used for robot navigation and obstacle avoidance is constructed.The main contributions of this work are as follows:(1) A high-precision dynamic object detection method based on dense optical flow is proposed, which can accurately determine the dynamic region of the image.(2) A high-performance keyframe selection strategy is proposed, reducing the influence of dynamic objects on the quality of keyframes and improving the accuracy of the algorithm.(3) Aiming at the problem that it is difficult to relocate after the direct method tracking loss, an effective relocation method is developed by introducing feature point extraction and matching, hence improving the success rate of relocation and the robustness of the algorithm.The overall structure of this paper is as follows: To reduce the impact of dynamic objects in the scene on the robot’s pose estimation, it is necessary to detect the dynamic objects in the visual odometry at the front-end and remove their corresponding 3D points generated by these objects. So far, the dynamic detection schemes used in the front-end of SLAM can be roughly divided into three categories: optical flow-based, geometric-based, and deep learning-based methods.As a method for estimating the motion of image pixels, the optical flow-based method has been widely used in dynamic object segmentation. Derome et al. ,9 used tThe geometry-based method distinguishes dynamic features from static features mainly by means of epipolar geometry constraints. Li et al.  proposedMost recently, deep learning-based dynamic detection methods have shown high accuracy. The DS-SLAM proposed by Yu et al.  employedThe overall framework of our scheme is shown in For the back-end, the keyframe’s pose and map points continue to be optimized by local bundle adjustment (BA). If the robot poses tracking fails, relocation is performed using the feature point method, where ORB feature points are extracted in the current frame and matched with the previous keyframes or map points in the map to recover the pose. In this way, all keyframes and map points are then employed as optimization variables for global BA optimization, resulting in a globally consistent robot trajectory and 3D dense map. Finally, the 3D navigation map is generated by coupling with the octree map.kI, kI−1 is as follows:T is the robot pose, u is the position of the pixel point in the previous frame, and π is the projection function. In our work, after obtaining an RGB-D image with the depth camera, the sparse direct method is used to preliminarily estimate the robot’s pose, and the initial pose of the robot is computed by minimizing the photometric error between the corresponding pixel points of the same 3D point in adjacent frames. When the previous frame is successfully tracked, the constant velocity motion model is exploited to predict the pose of the current frame, and the 3D points tracked in the previous frame are projected to the current frame by the estimated pose. Based on the assumption of photometric constancy, the photometric error of the pixel points corresponding to the same 3D point between the adjacent frames α and β to perform inter-frame photometric compensation on the previous frame image, i.e.,α is the photometric gain coefficient, and β is the offset of photometric.However, in practical applications, there may be a photometric difference between two adjacent frames caused by factors such as illumination, shadow, exposure, etc. Therefore, to reduce the photometric difference between adjacent frames, this paper introduces two photometric compensation variables kTk−1, from the previous frame to the current frame can be obtained as follows:iu is the ith pixel in the previous frame, R is the whole image.By minimizing the photometric error between adjacent frames, the rough pose estimate For a general case, only using adjacent frames to calculate the robot’s pose is prone to cumulative drift, so it is necessary to search for local maps to obtain more map points that need to be tracked and optimized. Specifically, the local map is first tracked to obtain the covisibility keyframes and covisibility map points of the current frame, and then the covisibility map points are projected to the current frame using the poses obtained in the previous step. For each successfully projected map point, the correspondence between the pixel points and map points of the current frame is optimized by minimizing the photometric error of the corresponding pixel points.i′u and iu denote the position of the pixel point in the current frame and the covisibility keyframe, respectively.As shown in iA T are the pixel point coordinates, and [w yw zwx] are the 3D points in space. According to Equation (29), the coordinates of the real point cloud can be obtained as follows:xc, yc, xf, yf denote the camera internal parameters. In our work, to enable the map to be used for robot navigation and autonomous obstacle avoidance, we capitalize on the RGB image information, depth value, and keyframes’ pose to build a 3D dense point cloud map of the scene, and then combine the octree map to further generate a 3D navigation dense map. Typically, 2D points can be converted into 3D point clouds by using the RGB information and depth value of the keyframes, and the conversion relationship is as follows:When constructing a dense map, it is susceptible to the influence of point clouds generated by dynamic objects. If the map contains information about dynamic objects, the robot cannot determine whether the object exists during navigation or autonomous obstacle avoidance. Hence, in our case, the dynamic points are judged based on the optical flow amplitude of each pixel in the image. During the process of map building, once a keyframe is inserted, each pixel in the keyframe needs to be traversed. First, these pixels with abnormal depth values are eliminated, and then the magnitude of the optical flow amplitude of the pixel point is determined. If its optical flow amplitude is greater than the threshold, the point is determined as a dynamic point and removed from the dense point cloud. After eliminating the dynamic point cloud, the static point cloud is compensated by keyframes from different perspectives to construct a complete static dense point cloud map. Due to the existence of certain redundant information between adjacent keyframes, a large number of repeated point clouds will be generated in the process of constructing a dense map, resulting in an increase in required storage space. Therefore, voxel filtering is employed to down-sample point clouds, which not merely maintains the shape features of the point cloud, but removes certain noise, smooths the interval between point clouds, and finally adopts statistical filtering to filter out outliers again. The process of 3D dense map construction is shown in l is the logarithm of probability, and p is the probability of 0~1. When a node is continuously observed to be occupied, l will continue to increase; when the node is unoccupied, l will continue to decrease. Assuming that n denotes a node and the observed value is z, the probability logarithm of the node from the beginning to time t is L(n|zt1:), then, at time t + 1, the probability logarithm is established as follows: Although the dense point cloud map can intuitively represent each object in the scene, the point cloud map occupies a large amount of storage space and cannot be used for robot navigation and obstacle avoidance. Therefore, this paper further constructs an octree map based on the dense point cloud map. The leaf nodes of the octree map represent the occupancy state of each voxel in the form of probability. If a leaf node is observed as being occupied, the probability is constantly approaching 1. If the leaf node is observed as unoccupied, the probability is constantly approaching 0. To ensure that the probability does not exceed the interval, the logit function is usually used instead of the probability description, i.e.,Apparently, adopting this form can make map updates more flexible and convenient.To verify the effectiveness of the proposed algorithm, a series of simulations and experiments were conducted on the TUM public dataset and real scenes, respectively. The experimental platform was as follows: Intel Core i5-7300HQ, 2.4 GHz CPU, with 16 G RAM, no GPU acceleration, running under the Ubuntu 18.04 operating system.In this work, the “walking” and “sitting” dynamic sequences from the TUM RGB-D datasets  were selTo validate the capability of dynamic point culling in the front-end of the proposed algorithm, experiments were conducted on two scenarios: the camera, relative to the background, being stationary and moving. To evaluate the error performance of the algorithm in dynamic scenes, a series of simulations were conducted on the highly dynamic “walking” sequence and slightly dynamic “sitting” sequence of the TUM datasets, and then absolute trajectory error (ATE) and relative pose error (RPE) were employed as indicators for system accuracy. Herein, ATE was used to evaluate the accuracy of SLAM systems, which directly calculates the error between the actual and estimated poses of the system, reflecting the global positioning accuracy of the system; RPE calculates the difference between the actual and estimated pose changes in the same time interval to evaluate the drift of the SLAM system, including relative translation error (RTE) and relative rotation error (RRE). In this study, to fully demonstrate the effectiveness of the proposed algorithm in dynamic scenes, in addition to comparing with ORB-SLAM2 , the othThe RMSE comparisons of RTE and RRE between our algorithm and other methods under different image sequences are respectively reported in Generally, the mean tracking time of tracking threads and mean sampling frequency could reflect the real-time performance and running efficiency of SLAM systems. In our work, the front-end of the system achieves fast tracking through the semi-direct method. Although the method exploited dense optical flow to complete dynamic detection, the computational complexity of optical flow was reduced by performing down-sampling on the image, so the whole system still has high running efficiency. The comparison results of running efficiency for our algorithm, ORB-SLAM2, DS-SLAM, and the algorithm proposed in  under thIn dynamic scenes, after the interference of dynamic feature points, there are often situations where the number of matching points is too small and there are a large number of mismatches in the matching points, which leads to pose tracking failure and is not conducive to the long-term autonomous navigation of mobile robots. To verify the robustness of the algorithm in dynamic scenes, the proposed algorithm and ORB-SLAM2 were run five times under highly dynamic sequences walking_xyz, walking_half and walking_rpy and their tracking loss count and successful recovery pose count were calculated. From To verify the feasibility and effectiveness of the proposed algorithm in real dynamic scenes, a case study was conducted in an indoor dynamic scene utilizing a mobile robot equipped with an ASUS Xtion depth camera. The depth camera was composed of three main components: an RGB camera, an infrared structured light emitter, and a receiver. Its parameters are listed in To evaluate the capability of eliminating dynamic points in the front-end of our algorithm, a comparative experiment was conducted between the proposed algorithm and ORB-SLAM2 in a real dynamic scene. During the experiment, the mobile robot moved forward at a constant speed along the reference trajectory, and a pedestrian walked in front of the robot to simulate the dynamic object. To further verify the effectiveness of the proposed relocation method and the global localization accuracy in real dynamic scenes, comparison experiments were conducted between our algorithm and ORB-SLAM2 in a laboratory environment and manually interrupted for relocation. This paper proposed a robust semi-direct 3D SLAM algorithm for mobile robots based on dense optical flow in dynamic scenes. The front-end of the algorithm adopted the semi-direct method to calculate the robot’s pose, compensated the image through the homography matrix, and combined with the dynamic threshold to separate the dynamic region in the scene. On this basis, the feature points falling in the dynamic region were eliminated, and the static feature points were used to estimate the robot’s motion, which improved the accuracy and robustness of the algorithm in the dynamic scene. Meanwhile, considering the importance of keyframes to system optimization and mapping, a high- performance keyframe selection strategy was constructed by combining the pose transformation and the dynamic degree of the scene, which improves the quality of keyframes and reduces the complexity of back-end optimization. Furthermore, we also developed a relocation method that combines keyframes and map points, solving the problem of difficulty in retrieving the robot pose after direct tracking failure. Specifically, feature extraction was performed on the current frame that had failed tracking, and the number of candidate keyframes was used to determine whether to use image matching or map matching to restore pose, thereby improving the success rate of relocation. Finally, the effectiveness of the algorithm was verified through a series of simulations and experiments.Considering the dense optical flow has a large calculation error in the case of light changes or noise interference, it will lead to inaccurate tracking and detection of dynamic objects. In future work, we plan to employ a more stable optical flow network to calculate dense optical flow, which can more accurately distinguish the dynamic objects and static backgrounds, thereby reducing false positives and missed detections. Another perspective of this research is to combine a lightweight segmentation network or object detection network to constrain the calculation of optical flow, so as to more accurately detect and track dynamic objects. Indeed, the method further reduces the impact of dynamic objects on pose estimation, while ensuring the real-time performance of the algorithm. As our algorithm only considers the photometric error of the image during the initial estimation stage of the robot pose, the depth image obtained by the RGB-D camera can provide accurate distance information of the scene. Therefore, we also plan to introduce the depth error of pixel points into pose estimation to more accurately estimate the robot’s pose. In addition, there are often different lighting transformations in actual scenes, which have a significant impact on semi-direct methods and dense optical flow calculations. Although inter-frame brightness compensation can reduce the impact of some lighting changes, the algorithm still performs poorly in some extreme cases. As part of future work, we intend to introduce the photometric imaging model into the semi-direct method, reduce the impact of lighting changes on the algorithm by performing photometric correction on the image, and consider combining other types of sensors with the RGB-D camera for data fusion, thereby further improving the robustness of the algorithm and expanding its application scenes.


Woven fabrics are widely used for thermal protection due to their porosity, which provides thermal insulation and breathability. This research focuses on investigating the influential parameters in the thermal protective properties of layer interchanging double cloth, including the woven structure and varying yarn fineness. The properties affecting the protective properties and comfort of multilayered woven fabrics include the fabric thickness, fabric porosity, and air permeability. Darcy’s law is applicable for determining the effective air permeability of woven fabrics. By understanding and controlling fabric porosity, it becomes possible to develop thermal protective clothing that combines improved comfort, cost-efficiency, and effectiveness. This study represents a novel approach for the clarification of airflow permeability behavior in complex structures of elastic multilayer woven fabrics using Darcy’s law. This innovative approach expands the understanding of permeability in fabrics beyond single-layer fabrics with vertical pores or 3D fabrics used in resin injection processes. Woven fabrics are highly porous textile materials made by interlacing warp and weft yarns in a certain pattern. This structure makes the fabric a very heterogeneous planar material in which the volume units of air between the warp and weft yarns make the material porous. The porosity of the fabric indicates the share of pores in the fabric.When describing the properties and behavior of woven fabric, it can be viewed as a two-dimensional or three-dimensional material. Accordingly, there are two types of pores in woven fabric: vertical (open) and volume pores. Porosity is the ratio of the total amount of empty space in the material to the largest volume (domain) occupied by the material. This property is essential for the thermal insulation properties of woven fabrics for technical protective purposes such as firefighting. Air trapped in the pockets of woven fabric pores, as a good heat insulator, will increase heat protection, and a porous structure will increase the breathability of the fabric. Porosity is directly related to the permeability of fluids, air, and light through the woven fabric, which is influenced by the thickness of the fabric, the shape and size of the pores, and the distribution of the space between the yarns. The problem with calculating the woven fabric permeability is the non-uniformity in the distribution of the pores, the spacing between the yarns, as well as their irregular undefined shapes, and the non-uniform thickness of the woven fabric.During the work process, in emergency interventions, the human body is exposed to various dangers. The choice of raw materials in the design process of protective woven fabrics has to contribute to the most effective protection and at the same time ensure comfort . TechnolProtective clothing for firefighters is necessary when extinguishing fires and engaging in similar activities that involve the danger of direct flames and high levels of thermal stress . Such clThe development of fabrics that can efficiently protect the body requires careful attention being paid to functionality and effectiveness. This could be achieved by designing complex woven fabrics known as layer interchanging double cloth, which use fibers of different raw material compositions with integrated protection properties. Such woven fabrics offer multi-functionality, meeting mechanical, thermal, and thermo-physiological requirements in a single process that is cost-efficient and environmentally friendly. However, layer interchanging double cloth is a complex structure and requires extensive knowledge for woven fabric development, production, and application. This woven fabric is created by interlacing two layers of fabric on one loom, using warp or weft threads. The interlacing threads may differ from other threads in terms of raw material, fineness, and production technology. It is essential to coordinate the weave of the upper and lower layer to ensure that the interlacing threads are not visible on either side. Layer interchanging double cloth has the potential to be a game-changer in the development of protective clothing due to its multi-functional properties, but it is not as widely used as conventional single-layer woven fabrics.This research aims to investigate the influential parameters on the multifunctional properties of thermal protective layer interchanging double cloth, such as the woven structure and varying yarn fineness. Compared to current multi-layer protective clothing, layer interchanging double cloth is more cost-efficient and eco-friendly, making it a promising material for the development of effective thermal protective clothing with increased comfort at a lower cost.Multilayered woven fabrics consist of at least two yarn systems in one direction and one yarn system perpendicular to it. Their characteristic is an increased thickness compared to simple structures and better thermal insulation properties. By using complex structures, it is possible to design a woven fabric with different expected properties on the front and back, with the domination of one fiber composition on the front and the other on the back. In two weft systems, the upper weft is on the front side, and the lower weft is on the back side . By changing the weave, various effects can be achieved, such as stripes, squares, etc. By carefully designing the structure of multi-layered woven fabrics, it is possible to obtain optimal protection and comfort properties of the fabric by finding the optimal ratio of the thickness and porosity parameters .Fabric thickness has an important role when it comes to the comfort, thermal insulation properties, behavior, and end-use of textiles. It is the largest distance between the highest peaks on the front and the back of the woven fabric and is measured in millimeters. The change in fabric thickness depends on the individual preparatory stages of the weaving process. In addition, it depends on various factors that affect the shaping of the fabric during the weaving process and during the finishing processes . Fabric The porosity between the fibers;The porosity between the yarns;The effective porosity of the airflow, which is described as the function of fiber porosity and the porosity of the yarn itself.Fabric porosity is directly related to the permeability of fluid and air (gas) through the fabric, which is affected by the fabric thickness, the shape and size of the pores, as well as the distribution of the space between the yarns. Fabric porosity can be observed on several levels :The poroFabric porosity is an important parameter in evaluating the comfort of clothing and the physical characteristics of technical textiles . The fabIn general, all spaces that are filled with air can be considered pores in a woven fabric. However, it only indicates how much air is contained in the fabric and does not say anything about the shape of the pores, their size, or distribution. These characteristics are very important in terms of fabric air permeability .It should be noted that the yarn diameter value is used in numerous models that describe fabric porosity. The cross-sectional shape of the yarn is variable along its length. The spatial geometry of the fabric is generally influenced by the type of weaving, yarn composition and yarn fineness, the structural parameters, and the type and adjustment of the loom. The problem of determining the yarn diameter can be further complicated because of the yarn’s hairiness and high unevenness.There are two types of woven fabric porosity—vertical and volume porosity.Vertical porosity denotes the percentage of the surface area of macro-pores in a unit area of fabric. It is calculated based on the cover factor of the woven fabric. To describe the vertical porosity, one can consider the elliptical vertical pore model, which is also a two-dimensional porosity model, but it is a projection of the fabric onto the vertical plane. Since warp density is usually greater than weft density, an elliptical pore cross-sectional shape is used to represent the situation. The following parameters are commonly used to compare porosity fabrics: pore cross-sectional area, pore surface distribution, pore density, equivalent pore diameter, maximum and minimum pore diameter, pore length, pore volume and open area fraction, pore volume fraction, etc. .Y is the volume of yarn, and VF is the volume of fabric (domain), and it is expanded:m is the fabric mass per unit area (g/m2), L is the thickness of the woven fabric (mm), and ρ is the fiber density (g/cm3).Volume porosity denotes the percentage of the sum of the pores’ volume in the total volume of the fabric (Equation (1)). Volume porosity takes place when the woven fabrics are viewed as a three-dimensional formation. Void spaces (pores) can be found in fibers, between the fibers in the yarn, and between the warp and weft threads in the fabric. As textile materials, woven fabrics have, compared to knitted fabrics or non-woven textiles, the most precisely determined internal geometric model of the porous structure in the form of a tubular system, where each macro-pore has a cylindrical shape with a permanent cross-section of their entire length .(1)ε=VYAir permeability is one of the most important properties of textile materials. It is generally expressed as the ability of an air-permeable fabric to transmit air under certain conditions. When it comes to clothing materials, permeability is an important aspect of comfort. In the case of technical textiles, permeability can even be a property essential to the function of the fabric . The air permeability of woven fabrics is the main property of the internal textile material structure. A very small change in the fabric structure causes a change in its permeability. The size of pores in textiles, as well as their arrangement and distribution of shapes, are crucial characteristics of the fabric from the point of view of air permeability.There is an assumption that if the pores between the yarns are large enough and the air has enough space for free passage, it will flow mostly that way. Therefore, in terms of air permeability assessment, the porosity within the yarn is usually neglected .Henry Darcy published his findings of an experiment he conducted to examine the movement of water through a sand bed, in 1856. This experiment led to the development of a mathematical principle that explains how fluids behave in such porous materials. According to Darcy’s Law, the potential energy gradient inside a fluid is proportional to the rate of flow through a porous media ,11. DarcFrom then until today, his theory has been developed in the above-mentioned areas. In the mid-20th century, there was a growing interest in utilizing Darcy’s law to study nonhomogeneous materials characterized by nonuniform and rapidly changing airflow velocities. The generalized law is then used to solve a few cases of flow near the boundaries of porous media .In its most basic form, Darcy’s law says that the discharge rate q is proportional to the gradient in the hydraulic head and the hydraulic conductivity:Different authors have taken Darcy’s law into account in their research in the field of textiles. Darcy’s law is commonly used in the textile industry, especially for nonwoven textiles with diverse pore structures. Early research  showed tIn the literature, there are numerous studies focusing on the air permeability of fabrics, with most of them concentrating on single-layer fabrics with dominant vertical porosity where laminar flow laws can be applied. Kulichenko and Langenhove  establisWhile Poiseuille’s law needs precise knowledge about the flow geometry, such as the tube’s radius, Darcy’s law just needs the hydraulic conductivity, an empirical constant. As long as the flow is laminar, Darcy’s law can be applied to almost any porous medium. Considering the complexity of the structure of multilayer interchanging double cloth, in this paper, Darcy’s theory was used to determine the effective permeability of the material and assess the state of the structure.Some assumptions need to be considered when using Darcy’s law. Firstly, the saturating air must be inert and not interact with the porous medium—the woven fabric. Secondly, the flow through the sample must be laminar. Thirdly, the airflow should be single-phase and completely saturate the porous medium. Lastly, the permeability of the medium should be constant and not vary with the nature of the fluid, flow rate, or pressure.sat which involves measuring the volumetric flow rate, which can be used with Darcy’s law to determine Ksat , k—coefficient of permeability [m2], A—cross-sectional area of woven fabric exposed to airflow [m2], p1—initial pressure [Pa], p2—final pressure [Pa], μ—air viscosity 1.6 × 10−5 [kg/(m·s)], and L—fabric thickness [m].In its simplest form, the mathematical expression of Darcy’s law is as follows :(4)Q=-kA3/s] is a volumetric flow rate, that is, the volume of air [m3] that passed through the surface of the fabric in 1 s.Q [m1–p2.Specific discharge (Darcy flux) is often referred to as the Darcy flux and it is not the velocity that the fluid traveling through the pores is experiencing :(5)q=-KμThe fluid velocity (v) is related to the Darcy flux (q) by the porosity (ε). The flux is divided by porosity to account for the fact that only a fraction of the total formation volume is available for flow :(6)v=qεThe concept of effective porosity is employed to describe the portion of pores in a complex woven structure that is made unavailable for flow. The Darcy velocity, also known as specific discharge, is obtained by dividing the volumetric flux density (Q) by the bulk cross-sectional area (A) of the material. This measurement indicates the velocity of air passing through the woven fabric’s accessible pores.The actual air velocity varies throughout the porous space , due to In order to increase thermal protection and comfort, a woven structure of the layer interchanging double cloth was developed.In the woven fabric cross-section b it is vThe choice of raw materials for the weft—aramid and modacrylic yarns—and their controlled change resulted in a complete aramid surface on the front of the fabric, while the reverse side is dominated by modacrylic yarns that ensure comfort on the back (next to the skin). This construction ensures satisfactory thermal protective properties  and highConsidering the very complex structure of this material, it is not possible to describe the morphological characteristics of the pores in a simple way, especially considering the fact that the pore system is expectedly very heterogeneous, and their mutual connection is difficult to define. In the research of Badrov et al. , breathaTo establish the specific discharge (air permeability) and the structural stability of the porous layer interchanging double cloth, it is possible to apply the fluid theory, i.e., fluid flow through porous materials. The structure of the layer interchanging double cloth can be described as the system of porous zones of low and high flow velocities and areas where flow does not occur. Cross-section porosity, pressure drop, and superficial velocity have been identified as important values for characterizing flow/porous material air breathability.To achieve specific protective properties in the woven fabrics, a careful selection of fibers was made. Aramid fibers, a mixture of meta and para-aramid fibers, were chosen because of their excellent mechanical properties, fire resistance, and thermal stability. Meta-aramid fibers are particularly successful in fireproof clothing as they do not ignite, melt, or drip and they maintain their mechanical properties at high temperatures. By combining them with para-aramid fibers, their breaking strength increases. For achieving better comfort and softness, a blend of flame-retardant modacrylic and cotton fibers was used. Modacrylic fibers can be blended with natural fibers. Because of their ability to remove oxygen from non-flame-retardant fibers, they can protect both themselves and the other fibers in the blend from burning and overheating. Cotton fibers were added for their comfort qualities. Properties like fabric thickness, mass, vapor permeability, and thermal insulation are affected by the fabric weave and yarn fineness. The woven fabric samples used in this study are layer interchanging double cloth, which has a complex structure and is known for its vapor permeability and thermal insulation properties. For this study eight fabrics were woven, on the laboratory weaving machine DW598 , using the same weave and same yarn types as mentioned in The sample peg plan and the fabric cross-section are shown in The woven fabric samples were tested for their air permeability using an air permeability testing device, Mesdan Air tronic plus. The air permeability  was testTesting area: 100 cm²Air volume: 10 LPressure drop: 5, 10, 15, 20, and 25 PaThe fabric samples were tested from the front side (aramid weft) and the back side (modacrylic weft) under the following conditions:The result of the testing process is the specific discharge, q, measured in cm/s, at each of the mentioned pressure levels.The basic parameters of the woven fabric samples were tested according to the standards: fabric density—ISO 7211-5:2020; fabric thickness—ISO 5084:1997 (under a load of 1 kPa); and fabric mass per unit area—ISO 3801:1977.The basic parameters of the tested woven fabrics are shown in The volume porosity of the woven fabric samples was calculated using the fabric’s mass and thickness and the average fiber density in the fabric structure (Equation (2)).From the graphical representation in In From the graphical representation in Taking into account that the woven fabric samples are two-layered composites, with airflow passing through two textile barriers and being retained within a voluminous pore that extends across the entire width of the fabric, the nonlinearity of air permeability can occur. From the results, it is evident that more pronounced nonlinearity occurs in samples with larger differences in yarn fineness between the upper and lower fabric layers. This is due to the varying capacity of each layer to allow for air passage and the limited volume between these layers. When the airflow passes through such a complex textile composite with voluminous pores of irregular shapes and different dimensions within the structure, the laminar airflow no longer moves in a straight line but takes on different speeds depending on the pore shapes. Although, according to fluid theory, it is still considered laminar flow (Reynolds number < 2000), air permeability is no longer linear and can be described at each pressure drop as the current air permeability, or permeability at a specific pressure drop, as the slope of the tangent to the approximated curve through the points on the q∆p graph .Turbulence is difficult to achieve in a porous medium. Velocity fluctuations dissipate through viscous interactions with the prevalent pore walls.Samples exhibiting nonlinear air permeability behavior have been identified. From the graphs in With the application of Darcy’s law, i.e., finding a Darcy’s constant implies a constant fabric architecture, however, woven fabrics have a certain compressive flexibility that depends on the yarn density and the weave and porosity. With increasing air pressures on the woven fabric surface, there is an evident non-linear decrease in thickness . This maIn The ε/K graph  exhibitsThe nonlinearity of air permeability in woven fabrics used for protective clothing can be attributed to the deformation of volume pores and changes in pore size and shape under pressure. As air pressure increases, the fabric experiences compression, which could cause the deformation of the pores within the fabric structure. This deformation affects the size and shape of the pores, resulting in nonlinear changes in air permeability. Furthermore, the relationship between fabric thickness and air pressure is also nonlinear. As the air pressure increases, the fabric thickness decreases in a nonlinear manner. This behavior indicates the compressive flexibility of the woven fabric, as it can undergo changes in thickness in response to applied pressure. The non-linear decrease in thickness suggests that the fabric structure allows for inter-structural displacements and adjustments, leading to changes in the fabric’s overall thickness under pressure. Regarding the yarn fineness, fabrics with a coarser fineness of the aramid weft exhibit more stable air permeability compared to those with a finer aramid weft. Coarser aramid weft yarns provide a more robust and consistent structure within the fabric, contributing to a more stable airflow and permeability.Overall, the nonlinearity of air permeability in complex structured woven fabrics used for protective clothing is influenced by the deformation of volume pores, changes in pore size and shape under pressure, the compressive flexibility of the woven fabric, the yarn fineness, and the presence of ineffective porosity. Understanding these factors and their impact on air permeability can help in the design and development of more effective and reliable protective fabrics with controlled permeability properties. The application of Darcy’s law in assessing the breathability of woven fabrics used for thermal protection is significant, due to thermal comfort which is a property that is often neglected.The study suggests that the application of Darcy’s law in complex fabric structures can be extended to all elastic woven fabrics with highly complex structures for various non-engineering purposes. This indicates the potential for further development and broader applications of Darcy’s law in analyzing the permeability of fabrics in diverse fields.


Vessels frequently encounter challenging marine conditions that expose the propeller-hull to corrosive water and marine fouling. These challenges necessitate innovative approaches to optimize propeller-hull performance. This study aims to assess a method for predicting propeller-hull degradation. The proposed solution revolves around an innovative Key Performance Indicator (KPI) based on Artificial Neural Networks (ANNs). Our objective is to validate the findings; thus, a thorough comparison is conducted between the proposed method and the baseline solution derived from the ISO-19030. Emphasis is placed on determining the optimal parameters for computing the KPI, which involves applying various features, filters, and pre-processing techniques. The proposed method is tested on real data collected by an Internet of Things (IoT) system installed in different types of vessels. Four distinct experiments with ANNs are conducted. Results demonstrate that the ANN-based indicator offers greater accuracy in predicting propeller-hull degradation compared to the baseline method. Additionally, it is demonstrated that selecting a diverse set of features and implementing consistent filtering and preprocessing techniques enhance the performance of the traditional indicator. The utilization of Deep Learning (DL) in the maritime industry is of great significance, as it enables a comprehensive and dynamic assessment of predictive maintenance of the propeller-hull. The DL index method holds potential for diverse maintenance applications, providing a holistic platform with anticipated environmental and financial benefits. This corrosion leads to long-term damage in vessels, reducing the mechanical properties of the propeller-hull. Recent studies have highlighted another challenge in the form of marine fouling, caused by the abundance of microorganisms in the water. This fouling increases the surface roughness of the vessel ,2. Both mosphere ,5,6. By mosphere . To achimosphere ,9.The utilization of traditional techniques in the maritime industry is founded on the ISO-19030, a collection of standards developed by the International Organization for Standardization. The ISO-19030 serves as a means for the maritime industry to reduce its environmental impact and enhance operational efficiency by providing a standard for estimating propeller-hull performance. The fundamental concept of the ISO-19030 involves the computation of a performance indicator over a specific time frame, which is defined as the percentage difference between the anticipated value of the ship’s speed and the measured value at the same shaft power. In the study conducted by Papageorgiou et al. , the ISOIn the context of the fourth industrial revolution, Deep Learning (DL) has emerged as a transformative force that leverages the collected sensor data. To estimate the corrosion and coating defect of coal handling and preparation plants, Yu et al.  proposedRecent advancements in ship energy efficiency measurement techniques have introduced novel approaches that utilize Machine Learning and DL algorithms . For insPrevious research conducted by Theodoropoulos et al.  and SpanThe novelty of this study in predicting propeller-hull degradation is significant for the maritime industry and forms an integral component of a broader predictive maintenance solution. To the best of our knowledge, no other proposed methods forecast propeller-hull degradation based on KPIs. The remainder of the paper is organized as follows: The proposed prognostic methodology involves projecting the regression line of a novel KPI derived from propeller-hull performance data using ANNs. Prior to the application of ANNs, data preprocessing is a crucial step in the proposed methodology. This section provides a comprehensive overview of all the fundamental components of the proposed approach.The measurements undergo preprocessing through the data-preprocessing pipeline depicted in Considering the outliers removal technique, the extreme values that deviate from the other observations in the dataset are identified and removed. More specifically, a parameter that coincides with the main feature is initially selected, and a data point is considered an outlier if the following condition is met:n samples of the window. Mathematically, the SMA is defined as:Furthermore, the measurements pass through the Simple Moving Average (SMA) algorithm. The SMA aims to compute the unweighted average of the last p-value of each feature is computed. If a feature’s p-value exceeds the significance level, it is removed from the dataset.Considering the feature selection technique, the goal is to identify the most important features. Each feature undergoes an evaluation process for its relevance to the chosen target feature using a Random Forest regressor. In order to accomplish this, a level of significance is selected, and once the regressor is trained, the thi layer, respectively [ANNs aim to model complex relationships and patterns within data by simulating the structure of the human brain, and they comprise input neurons/nodes that correspond to the input data, hidden layers with nodes, and output nodes. Each hidden layer connects its nodes with the nodes of other hidden layers, while the output may consist of one or several nodes, depending on the task of the ANN. In this case, ANNs are utilized in a regression task, and therefore the number of output nodes is equal to one. Weights are assigned to every node of the ANN indicating its impact to other nodes. ectively ,26,27. Tus study . Moreoveus study  selectedThe estimation of the hull-propeller condition is accomplished through the utilization of an innovative KPI known as m-K3. The DL indicator (m-K3), which was introduced by Theodoropoulos et al. , is regaIn the present study, our objective is to advance the investigation by prognosticating the condition of a vessel’s hull-propeller. This prognostication is accomplished by employing a linear regression model to the KPI values over a designated period, referred to as the hindcast period. The linear regression model can be extrapolated into the future, beyond a specified time point to ascertain the future values of the indicator, which is known as the forecast period. We have opted to employ a simple regression model as it can serve as an effective baseline model. Our prior research has demonstrated that simple regression is a valuable tool for diagnosing the degradation of a vessel’s hull-propeller.The proposed method is implemented on a large dataset obtained from a LAROS system as presented in detail in . In shorThe measurements are obtained at a sampling rate of 1 min and are synchronized using common time stamps. The present dataset comprises measurements pertaining to the operation of a bulk carrier, which were collected over a period of approximately 18 months, spanning from 6 November 2021 to 29 March 2023. Notably, the vessel was new at the onset of the investigation period, which holds significant implications for the proposed methodology. Furthermore, two maintenance actions were carried out on 22 March and 22 August 2022, respectively, namely a propeller and a hull cleaning. This section provides a detailed account of the outcomes obtained through the utilization of the proposed DL technique for the prognosis of the propeller-hull condition. The efficacy of the proposed method is assessed through the implementation of diverse experiments.The initial dataset utilized for the various experiments consists of the measurements outlined in The method presented in this study was evaluated through the implementation of four experiments using ANNs, which will be referred to as ANNs #1–#4 in the following paragraphs. These experiments varied in terms of the selected features, as well as the filters and preprocessing techniques applied to the original dataset. In accordance with the preprocessing methods outlined in In contrast to outlier removal and smoothing techniques, feature selection is exclusively implemented on the training and prediction sets of ANN #2, ANN #3, and ANN #4. Following the application of the Random Forest regressor for feature selection, the parameter pertaining to the commander rudder angle is eliminated from both the training and prediction sets.The training datasets previously presented were utilized to train the ANNs. After conducting a thorough investigation into the optimal hyperparameters in our previous studies, we decided to select the same model architecture for the ANNs. Our aim was to examine the impact of different preprocessing techniques on the accuracy of the ANNs with the same architecture. This subsection provides a detailed analysis of the forecasting accuracy of the innovative KPI derived from the use of ANNs. Initially, the trained ANN models utilize various prediction sets to make predictions. Subsequently, four KPIs are calculated based on these predictions, with each experiment having its own KPI. In order to assess the predictive capabilities of the proposed methodology, a subset of the available prediction dataset is designated as the hindcast period, while the remaining portion is allocated for the forecast period. In This section initially presents the baseline method considering propeller-hull degradation, which is based on the ISO-19030. Then, the section compares the prognostic capabilities of the baseline and the proposed method.This subsection elaborates on the details for calculating the baseline KPI, and The computation of the reference power is based on sea trials conducted at specific speeds and load conditions, as depicted in Additionally, the filters that are listed in This subsection presents the results of a comparison between the indicators obtained from four ANNs and the ISO-19030 standard. This paper investigates the implementation of predictive maintenance in ships as a means to mitigate the adverse effects of corrosion and marine fouling, thereby enhancing the efficiency, cost-effectiveness, and sustainability of maritime operations. The primary focus of this study is on predicting the degradation of propeller-hull performance, which poses a significant challenge. The main contributions of this research are twofold: firstly, most existing studies primarily utilize ANNs for diagnosis rather than forecasting propeller-hull degradation, and secondly, a comprehensive comparison is conducted between the DL index and the ISO-19030 KPI using various pre-processing techniques and different types of vessels.The proposed prognosis method involves initially calculating the DL indicator using ANNs. The prognosis is then achieved by fitting a regression line to the values of the innovative KPI. The DL index demonstrates superior performance, offering valuable insights for future maintenance. It is concluded that selecting a wide range of features and applying consistent filtering and pre-processing techniques enhances the overall performance of the indicator. Conversely, utilizing datasets with fewer features or implementing fewer filters during pre-processing may yield unreliable results. The DL index method can be applied to various maintenance applications beyond the propeller-hull, such as main engines and diesel generators, creating a comprehensive maintenance platform. The utilization of this platform is expected to yield environmental and financial benefits.The proposed method can be seen as the initial step towards the development of a versatile predictive maintenance system that can diagnose and forecast the degradation of the propeller-hull in various types of vessels. This system would employ transfer learning techniques to extend its applicability across different vessel types, leveraging the knowledge gained from one type to improve performance in another. It is crucial to explore the integration of real-time continuous data streams into the system, and conducting a comprehensive cost-benefit analysis to evaluate the economic advantages of implementing the predictive maintenance system is also recommended. Demonstrating the potential cost savings and reduced downtime associated with predictive maintenance can provide a competitive advantage for the system.In terms of future research directions, it is recommended that additional pre-processing techniques are explored that can be applied to the measurements in order to obtain the KPIs. Furthermore, it is suggested that the accuracy of advanced regression techniques such as Ridge, Lasso, and Robust regression are investigated. Additionally, the use of hybrid models that combine DL and traditional techniques should be considered to achieve more accurate results.