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In order to improve the computation efficiency of the four-point rainflow algorithm, a new fast four-point rainflow cycle counting algorithm (FFRA) using a novel loop iteration mode is proposed.

In this new algorithm, the loop iteration mode is simplified by reducing the number of iterations, tests and deletions. The high efficiency of the new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.

The extensive simulation results show that the extracted cycles by the new FFRA are the same as those by the four-point rainflow cycle counting algorithm (FRA) and the three-point rainflow cycle counting algorithm (TRA). Especially, the simulation results indicate that the computation efficiency of the FFRA has improved an average of 12.4 times compared to the FRA and an average of 8.9 times compared to the TRA. Moreover, the equivalence of cycle extraction results between the FFRA and the FRA is proved mathematically by utilizing some fundamental properties of the rainflow algorithm. Theoretical proof of the efficiency improvement of the FFRA in comparison to the FRA is also given.

This merit makes the FFRA preferable in online monitoring systems of structures where fatigue life estimation needs to be accomplished online based on massive measured data. It is noticeable that the high efficiency of the FFRA attributed to the simple loop iteration, which provides beneficial guidance to improve the efficiency of existing algorithms.

This paper sets out to solve a common and crucial fundamental theoretical problem of gray incidence cluster analysis: to [X]={X|ρ(X,Y)≥1−ε0} constitute an approximate classification, it must first be proven that [X]={X|ρ(X,Y)=1} constitutes a rigorous classification.

This paper does not study the concrete expressions of various incidence degrees but rather the perfect correlation essence of such incidence degrees, that is, sufficient and necessary conditions.

For any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree, it is proven that the perfect correlation relation is an equivalence relation. The set composed of all sequences Y that are equivalent to sequences X is studied, that is, the equivalence class of X. The structure and mutual relations of these equivalence classes are discussed, and the topological homeomorphism concept of incidence degree is introduced. The conclusion is obtained that the equivalence classes of the two incidence degrees must be the same when the topological homeomorphism is obtained.

In this paper, only the perfect correlation relation of any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree are studied as equivalent relations.

Not only are the research results of several incidence degrees involved in this paper original but also many other effective incidence degrees have not done this basic research, so this paper opens up a research direction with theoretical significance.

This article aims to identify and describe the research outcomes of studies that have employed the theoretical framework of lesson study (LS) in initial science teacher preparation programs. The focus is on the impact of LS on preservice teachers’ (PST) pedagogical and content knowledge, beliefs, routines and norms for professional learning and instructional practices.

A systematic approach was employed to compile pertinent literature by initially searching scholarly databases using specific keywords and phrases related to prospective science teacher preparation. Seventeen studies, encompassing both qualitative research and mixed-methods research, met the inclusion criteria and significantly contributed to the study’s findings. The authors independently conducted a coding process, applying a predefined code scheme based on Lewis et al.'s (2019) theoretical framework. The outcomes of the coding process were compared, and reliability tests were conducted to ensure the consistency of the coding.

In preservice science teacher (PSST) education, LS proves transformative, enriching pedagogical and content knowledge, shaping beliefs, fostering collaboration and influencing instructional practices. Its collaborative, reflective and iterative nature significantly contributes to the professional growth of preservice science teachers, preparing them for effective, student-centered teaching practices. Further investigation is warranted in the realm of LS, particularly concerning preservice science teachers and their beliefs.

This literature review on science PSTs is one of the pioneering efforts to employ the professional development framework crafted by Lewis et al. (2019).

This study aims to identify significant factors, analyse them using the consistent fuzzy preference relations (CFPR) method and forecast the probability of successful deployment of the internet of things (IoT) and cloud computing (CC) in Gujarat, India’s building sector.

From the previous studies, 25 significant factors were identified, and a questionnaire survey with personal interviews obtained 120 responses from building experts in Gujarat, India. The questionnaire survey data’s validity, reliability and descriptive statistics were also assessed. Building experts’ opinions are inputted into the CFPR method, and priority weights and ratings for probable outcomes are obtained to forecast success and failure.

The findings demonstrate that the most important factors are affordable system and ease of use and battery life and size of sensors, whereas less important ones include poor collaboration between IoT and cloud developer community and building sector and suitable location. The forecasting values demonstrate that the factor suitable location has a high probability of success; however, factors such as loss of jobs and data governance have a high probability of failure. Based on the forecasted values, the probability of success (0.6420) is almost twice that of failure (0.3580). It shows that deploying IoT and CC in the building sector of Gujarat, India, is very much feasible.

Previous studies analysed IoT and CC factors using different multi-criteria decision-making (MCDM) methods to merely prioritise ranking in the building sector, but forecasting success/failure makes this study unique. This research is generally applicable, and its findings may be utilised for decision-making and deployment of IoT and CC in the building sector anywhere globally.

This paper focuses on prospective teachers’ (PTs) participation in a lesson study (LS) that prompted them to research their own practice. We seek to describe the dimensions of PTs’ knowledge of student learning developed during the process and the LS features fostering it.

The participants were two PTs, a teacher educator, a cooperating teacher and a researcher. The LS was integrated into a Portuguese initial elementary teacher education program. Following a qualitative approach, we used participant observation.

The PTs developed their knowledge of students’ learning of the concept of area in four dimensions: theories; students’ interests and expectations; ways students interact with the content and students’ strengths and weaknesses in learning the concept. To support this development, the LS design considered follow-up sessions and emphasised collaborative work.

This study focuses on PTs researching their practice and disseminating the results, which has been overlooked in previous research of LS with PTs. The results highlight the potential of LS to motivate PTs to research their practice and emphasise the importance of involving them in disseminating LS results.

To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

The step effect and support structure generated by the manufacturing process of fused deposition molding parts increase the consumables cost and decrease the printing quality. Multiorientation printing helps improve the surface quality of parts and reduce support, but path interference exists between the printing layer and the layers printed. The purpose of this study is to design printing paths between different submodels to avoid interference when build orientation changed.

Considering support constraint, build orientation sequence is designed for submodels decomposed by model topology. The minimum printing angle between printing layers is analyzed. Initial path through the oriented bounding box is planned and slice interference relationship is then detected according to the projection topology mapping. Based on the relationship matrix of multiorientation slice, feasible path is calculated by directed graph (DG). Final printing path is determined under support constraint and checked by minimum printing angle. The simulation model of the robotic arm is established to verify the accessibility of printing path under the constraint of support and slice.

The proposed method can reduce support structure, decrease volume error and effectively solve the interference problem of the printing path for multiorientation slice.

The method based on projection topology mapping greatly improves the efficiency of interference detection. A feasible path calculated through DGs ensures the effectiveness of the printing path with the constraint of support and slice.

Every business company deals with the dilemma of how much to invest in long-term (LT) versus short-term (ST) problem (LTvST problem). LT operations increase the reputation of the company, and revenue is rewarded in the future. In contrast, ST operations result in immediate rewards. Thus, every organization faces the dilemma of how much to invest in LT versus ST activities. The former deals with the “what” or effectiveness, and the latter deals with the “how” or efficiency. The role of managers is to solve this dilemma; however, they often fail to do so, mainly because of a lack of knowledge. This study aims to propose a dynamic optimal control model that formulates and solves the LTvST problem.

This study proposes a dynamic optimal control model that formulates and solves the dilemma whether to invest in short- or LT operations.

This model is illustrated as an example of an academic institute that wants to maximize its reputation. Investing in effectiveness in the academy translates into investing in research, whereas investing in efficiency translates into investing in teaching. Universities and colleges with a good reputation attract stronger candidates and benefit from higher tuition fees. Steady-state conditions and insightful observations were obtained by studying the optimal solution and performing a sensitivity analysis.

To the best of the authors’ knowledge, this paper is the first one to explore the optimal strategy when trying to maximize the short and LT activities of a company and solve the LTvST problem. Furthermore, it is applied on universities where teaching is the ST activity and research the LT activity. The insights gleaned from the application are relevant to many different fields. The authors believe that the paper makes a significant contribution to academic literature and to business managers.

This article introduces the special issue of Learning and Development in Highly-Dynamic VUCA Contexts. The issue reviews the concept of VUCA (volatility, uncertainty, complexity and ambiguity), highlights its implications for the learning and development function and argues that learning and development play a critical role in helping organisations, people and the societal context in which they operate to work within and navigate VUCA contexts.

The contributions to this special issue propose a novel learning and development framework that will inform L&D as the provision of training, learning and development activities in organisations within highly dynamic VUCA contexts and ensuring a strong external focus including organisational, people, community, economic and societal sustainability.

We, the authors, propose seven features of a strategic sustainability L&D function and L&D professional role that are a fit with highly dynamic VUCA contexts.

The proposed framework has important implications for the way in which L&D is structured, its key priorities and plans and the competencies of L&D professionals to add value to all stakeholders. We also emphasise that the work on the L&D function in highly dynamic VUCA contexts needs to be broader and move beyond a performance orientation.

The proposed strategic sustainability role for the L&D function expands theoretically our understanding of how L&D can have impacts at the nexus of the organisation and highly dynamic VUCA contexts, in addition to broadening the constellation of stakeholders that it potentially enhances.

Fractional Fokker-Planck equation (FFPE) and time fractional coupled Boussinesq-Burger equations (TFCBBEs) play important roles in the fields of solute transport, fluid dynamics, respectively. Although there are many methods for solving the approximate solution, simple and effective methods are more preferred. This paper aims to utilize Laplace Adomian decomposition method (LADM) to construct approximate solutions for these two types of equations and gives some examples of numerical calculations, which can prove the validity of LADM by comparing the error between the calculated results and the exact solution.

This paper analyzes and investigates the time-space fractional partial differential equations based on the LADM method in the sense of Caputo fractional derivative, which is a combination of the Laplace transform and the Adomian decomposition method. LADM method was first proposed by Khuri in 2001. Many partial differential equations which can describe the physical phenomena are solved by applying LADM and it has been used extensively to solve approximate solutions of partial differential and fractional partial differential equations.

This paper obtained an approximate solution to the FFPE and TFCBBEs by using the LADM. A number of numerical examples and graphs are used to compare the errors between the results and the exact solutions. The results show that LADM is a simple and effective mathematical technique to construct the approximate solutions of nonlinear time-space fractional equations in this work.

This paper verifies the effectiveness of this method by using the LADM to solve the FFPE and TFCBBEs. In addition, these two equations are very meaningful, and this paper will be helpful in the study of atmospheric diffusion, shallow water waves and other areas. And this paper also generalizes the drift and diffusion terms of the FFPE equation to the general form, which provides a great convenience for our future studies.