Continuous System Model Research Articles

Exploring the dynamic behavior of system model construction with unknown parameters and achieving synchronous control of fuzzy neural networks

This study proposes a method that combines constant terms with state variables to construct the target system model. The three-dimensional system model is used for verification, starting with integer-order and fractional-order continuous system models. Through the integration of information entropy, path entropy, permutation entropy, the SALI algorithm, and complexity methods, the dynamic behavior of the target model is thoroughly analyzed. Finally, by considering the range of values when the constant term is involved in the construction, the study integrates fuzzy neural networks to effectively construct a self-organizing fuzzy neural network with parameters(SFNNP). Using a three-dimensional continuous system as a simulation case, the study successfully realizes the synchronous control of a fuzzy neural network based on fuzzy parameterization.

Inventory Planning of Raw Materials for Furniture Products (Case Study: CV XYZ Furniture)

The burgeoning industrial sector in Indonesia has intensified competition among businesses vying for market share. The furniture industry is a prime example of this dynamic landscape. To expand their market reach, companies must demonstrate their ability to fulfill every consumer demand. Failure to meet these expectations will prompt consumers to seek alternatives. One crucial factor in meeting consumer demands is product availability, which is directly influenced by the availability of raw materials within the company. CV XYZ Furniture, a furniture company based in Padang City, exemplifies this challenge. The company produces a diverse range of furniture, primarily utilizing rattan as its raw material. However, CV XYZ Furniture currently lacks a structured inventory planning method for raw materials, resulting in excess inventory for each period. To address this issue, this research aims to establish an optimized inventory planning strategy for raw materials used in furniture production at CV XYZ Furniture. The continuous review system method serves as the foundation for this endeavor. The research outcomes encompass the determination of optimal demand quantity, reorder point, and safety stock. The implementation of the continuous review system model yielded a significant reduction in total inventory costs, amounting to Rp8,625,594 or 2.03%. It can be proven that the continuous review system model is suitable for calculating raw material inventory at CV XYZ Furniture for raw material planning in the following years.

Machine learning for structural design models of continuous beam systems via influence zones

Abstract This work develops a machine learned structural design model for continuous beam systems from the inverse problem perspective. After demarcating between forward, optimisation and inverse machine learned operators, the investigation proposes a novel methodology based on the recently developed influence zone concept which represents a fundamental shift in approach compared to traditional structural design methods. The aim of this approach is to conceptualise a non-iterative structural design model that predicts cross-section requirements for continuous beam systems of arbitrary system size. After generating a dataset of known solutions, an appropriate neural network architecture is identified, trained, and tested against unseen data. The results show a mean absolute percentage testing error of 1.6% for cross-section property predictions, along with a good ability of the neural network to generalise well to structural systems of variable size. The CBeamXP dataset generated in this work and an associated python-based neural network training script are available at an open-source data repository to allow for the reproducibility of results and to encourage further investigations.

CoDBench: a critical evaluation of data-driven models for continuous dynamical systems

We introduce CoDBench, an exhaustive benchmarking suite comprising 12 state-of-the-art data-driven models for solving differential equations, including 4 distinct categories of models, against 10 widely applicable benchmark datasets encompassing challenges from fluid and solid mechanics.

Analysis of continuous dynamical system models with Hessians derived from optimization methods

Analysis of continuous dynamical system models with Hessians derived from optimization methods

An effective controller design strategy for higher order systems

The recent methods that guarantee the stability of the reduced-order models are Mihailov stability, improved Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization. Further, these methods could overcome the limitations such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. This research emphasizes the design of the proposed compensating algorithm by using an additional open loop zero for the stable reduced-order models of large-scale single-input single-output linear time-invariant continuous time systems. The results of the proposed algorithm are compared with the existing compensating methods and the design is validated and illustrated numerically.

Data-Driven pH Model in Raceway Reactors for Freshwater and Wastewater Cultures

The industrial production of microalgae is a process as sustainable as it is interesting in terms of its diverse applications, especially for wastewater treatment. Its optimization requires an exhaustive knowledge of the system, which is commonly achieved through models that describe its dynamics. Although not widely used in this field, artificial neural networks are presented as an appropriate technique to develop this type of model, having the ability to adapt to complex and nonlinear problems solely from the process data. In this work, neural network models have been developed to characterize the pH dynamics in two different raceway reactors, one with freshwater and the other with wastewater. The models are able to predict pH profiles with a prediction horizon of up to eleven hours and only using available measurable process data, such as medimum level, CO2 injection, and solar radiation. The results demonstrate the potential of artificial neural networks in the modeling of continuous dynamic systems in the field of industry, obtaining accurate, fast-running models that can adapt to different circumstances. Moreover, these models open the field to the design of data-driven model-based control algorithms to account for the nonlinear dynamics of this biological system.

Fuzzy Modeling of non-MCDM Problems Under Indeterminacy

Fuzzy set theory (FST) is a useful approach for modeling the uncertainties of real-life problems. In some cases, uncertainty level of the events may not be determined surely because of some environmental factors. This is named “incomplete information” case and the hesitation level about the uncertainty is represented with the indeterminacy concept. There are various FST extensions in the literature that consider indeterminacy in modeling. These FST extensions consider similar scenarios, and some parts of the theories overlap with some others so the theories and the nature of considered scenarios must be understood well to obtain reliable results. Nevertheless, most of the studies in the literature do not conceptually analyze the nature of the uncertainty and decides an FST extension as a pre-step of the study without expressing an apparent reason. Therefore, the quality of the obtained results becomes questionable. Moreover, these FST extensions have been developed in line with the requirements of Multi-Criteria Decision-Making (MCDM) problem so, assumptions and the limitations of these theories can cause reliability issues for the fuzzy models of non-MCDM problems and continuous systems. In the scope of this study, capabilities, advantages, and disadvantages of well-known FST extensions that consider indeterminacy are conceptually analyzed and compared in line with the needs of modeling of non-MCDM problems and continuous systems. The analysis has also been illustrated on numerical examples to make findings clear. The analysis showed that, some extensions have clear advantages over others in terms of applicability, ease of calculation and scenario comprehensiveness. This study builds a preliminary step for a guiding approach for the selection of the most reliable FST extension in fuzzy modeling. Besides, it is an invitation to fulfill the gap in the field of fuzzy modeling of non-MCDM problems.

Guided identification of nonlinear reduced-order models via the incorporation of von Kármán beam theory

A reduction in the number of Degrees Of Freedom (DOFs) of a nonlinear structural model can significantly decrease the computational time of dynamic analyses, especially in problems where long analyses are required. A Reduced-Order Model (ROM) of a structural system is commonly generated using some combination of dimensionality reduction, such as substitution of a modal basis or static condensation of membrane DOFs. Perhaps the most common and widespread framework for developing low-order models of continuous systems is the Ritz method in conjunction with a smooth modal basis. The Ritz method requires access to the closed form governing differential equations, and it is difficult to implement for problems with complex boundary conditions. In recent decades, an alternative framework that instead constructs a low-order model from an existing Finite Element Model (FEM) has been developed. Such models are typically known as NonLinear Reduced-Order Models (NLROMs). Such NLROMs can be used to handle complex boundary conditions so long as the FEM can do the same, and they allow the analyst to start from an existing finite element package as opposed to directly working with the governing differential equations. The form of the NLROM restoring force function is assumed by the analyst prior to identifying the model, and the parameters of the function are identified to achieve a high-quality fit to the FEM load–displacement data. This research aims to examine the connection between classically derived models using the Ritz method and NLROMs in order to predict the coefficients of NLROMs and to develop simplifying assumptions about their structure. Specifically, the Condensed Von Kármán (CVK) beam equation is used as a basis for the study of nonlinear beam structures. The Ritz method is applied to the CVK beam equation, and the matrix form of the equilibrium equation is determined. The equivalence between the CVK coefficients and the NLROM coefficients is shown, and a simplified, tangent stiffness-based identification procedure is proposed to determine the coefficients of the CVK-based model. An arc-length continuation algorithm is used to predict the static load–displacement response of the models studied and to assess the accuracy of the ROMs. In the case of initially straight, post-buckled beams, the proposed identification procedure is shown to generate a model that generally outperforms a corresponding NLROM identified using a more traditional displacement-based procedure.

Robust estimation of state vector coordinates in the controlled helicopter motion problem

The problem of finding H∞ – a observer of the state vector of a linear continuous non-stationary dynamical system with a semi-infinite time of functioning is considered. It is assumed that a mathematical model of a closed-loop linear continuous deterministic dynamical system with an optimal linear regulator, found as a result of minimization of the quadratic quality criterion, is known. For solving the state observer synthesis problem the reduction of the problem to a min-max optimal control problem is used. In this problem, the minimum of the quality criterion is sought by the observer’s gain matrix, and the maximum – by the external influence, measurement noise, and initial conditions. To solve this problem, the extension principle is applied and sufficient optimality conditions are obtained that requires the choice of auxiliary functions of the Krotov–Bellman type. As a result of the implementation of the procedure for choosing an auxiliary function and using the rules of matrix differentiation, relations for the synthesis of the observer and formulas for finding the best matrix of observer gains, as well as the laws for choosing the worst external influences and noise, were obtained. We find a solution to the problem of state vector coordinates estimation in the presence of limited external influences and disturbances in a linear model of the measuring system. As an example, the equations of motion of the Raptor-type helicopter are used.

Accounting for simulation errors in continuous-discrete Kalman filtering

In continuous-discrete Kalman filter implementations there is a tradeoff between the computational requirements for real time implementation, and errors incurred by selection of step size and method order in the simulation of the continuous time system model between sampling instances. Because the Kalman filter corrects errors in the state vector using output measurements, a systematic approach to account for the effects of simulation errors in the continuous-discrete Kalman filter allows the filter to be designed to deal with simulation errors in addition to conventional process (state) and measurement (output) noise.

Networked control systems with probabilistic time-varying delay based on event-triggered non-fragile [formula omitted] control

The non-fragile H∞ problem for networked control systems with probabilistic time-varying delay, stochastic nonlinear, controller gain fluctuation and adaptive event-triggered mechanism is studied. The random interval delay, nonlinear fluctuation and gain fluctuation of the controller all obey a certain uncorrelated Bernoulli distribution white noise sequence. An improved time continuous delay system model for networked control systems is constructed by using input delay method. A two-sided closed-loop Lyapunov–Krasovskii functional is constructed considering the sawtooth structure of artificial time delay, and the asymptotically stable conditions of closed-loop system with little conservatism are obtained. A non-fragile H∞ control strategy based on adaptive event-triggered is proposed and the co-design method for gain matrix of the non-fragile controller and event-triggered matrix is obtained. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Adaptive symmetry control in secure communication systems

Chaos-based secure communications is a broadly studied field in nonlinear dynamics. Such technique is traditionally based on chaotic synchronization between master and slave systems implemented as the transmitter and receiver. A common way to encode the message is switching the bifurcation parameters of the master system, which leads to perturbation of the dynamics and often breaks the synchronization. The time of the transient process to restore the identity of the trajectories of the master and slave systems can be unacceptably long for practical applications. Therefore, the development of techniques for fast re-synchronization of models of chaotic systems is of interest. In this paper we propose a novel technique for synchronizing finite-difference models of continuous chaotic systems through adaptive control of the so-called symmetry coefficient. We experimentally confirm that the proposed approach can be faster than the traditional control of the bifurcation parameter. In addition, we discovered that changing the symmetry coefficient in semi-implicit models leads only to a slight deformation of the stability regions of the finite-difference scheme and practically does not affect the nonlinear properties of the simulated chaotic system. The applied analysis shows that detecting a transmitted message through the modulation of the symmetry coefficient is difficult compared to the conventional approach.

Research on Fractional-Order Global Fast Terminal Sliding Mode Control of MDF Continuous Hot-Pressing Position Servo System Based on Adaptive RBF Neural Network

In this paper, a novel fractional-order global fast terminal sliding mode control (FGFTSMC) strategy based on an adaptive radial basis function (RBF) neural network is proposed to improve the performance of a medium density fiberboard (MDF) continuous hot-pressing position servo system with parameter perturbation and external load disturbance. Primarily, the mathematical model of the MDF continuous hot-pressing position servo system is constructed based on the dynamic equation of the hydraulic system. Then, a FGFTSMC is designed to speed up the convergence rate of the system, in which an adaptive law is used to estimate the upper bound of the unknown parameters to overcome the existing parameter perturbation of the system. In addition, an RBF neural network is introduced to approximate the external load disturbance of the system. The stability of MDF continuous hot-pressing position servo system based on the control scheme developed in this paper is proven using the Lyapunov theory. Finally, the simulation results show that the presented control scheme can effectively ensure the tracking accuracy of the system and enhance the robustness of the system.

Dinamička analiza posmičnih stijena s čeličnom ispunom

In this paper, the Timoshenko beam model (continuous system model) is originally adapted for dynamic analysis of steel plate shear wall (SPSW) systems. Dynamic characteristics for the first three modes are found by solving differential equation of the equivalent Timoshenko beam model using the differential transformation method. Dynamic characteristics are tabulated for quick and practical calculation. With the help of the dynamic characteristics, the response spectrum analysis of such buildings is performed. The continuous system calculation model has been used in the literature for free vibration analysis of such systems. Using the approach developed in this study, it is possible to calculate not only natural periods, but also the base shear force, maximum storey displacement, and maximum storey drift ratio. The differential transformation method is used in this study for solving the differential equation written according to the continuous system calculation model. To investigate the suitability of the method presented in the study, an example taken from the literature is solved and the results are evaluated. The results show that the method presented can be used in the preliminary design stage.

Optimization of Raw Material Inventory Control CV. Dirga Eggtray Pinrang Using Probabilistic Model with Backorder and Lostsales Condition

This research discusses about the comparison of raw material inventory control CV. Dirga Eggtray Pinrang. It starts with forecasting inventory for the next 12 periods using variations of the time series forecasting method, where the linear regression method provides accurate forecasting results with a Mean Absolute Percentage Error (MAPE) value of 1,9371%. The probabilistic models of inventory control used are the simple probabilistic model, Continuous Review System (CRS) model, and Periodic Review System (PRS) model. The CRS model with backorder condition is a model that provides the minimum cost of Rp. 969.273.706,20 per year compared to another probabilistic model with the largest difference of Rp. 1.291.814,95 per year, with the optimum number of order kg, reorder level kg, and safety stock kg.

Optimization of Inventory Costs Using the Continuous Review System (CRS) Method in Controlling the Need for Raw Materials for the Crimean Industry

Forecasting is an estimate of something that has not happened or will happen in the future. Determination of the policies implemented by the company resulted in more costs for storage costs, resulting in wastage of costs and reduced company profits due to the accumulation of capital in the form of raw materials that had not been produced. This study describes the planning and control of sodium caseinate inventory. Of the many inventory control planning methods, the continuous review system model is used to determine the optimal number of orders and when orders are made. The total cost of inventory based on average usage in 2018 to 2020 is IDR 252,323,882,141.00 per year. The results showed that the continuous review system lost sales inventory control model has a minimum total inventory cost of Rp. 251,641,850,991.00 per year with an optimal number of orders.

An Optimized Efficient Galerkin Averaging-Incremental Harmonic Balance Method for High-Dimensional Spatially Discretized Models of Continuous Systems Based on Parallel Computing

Abstract Modern computers are generally equipped with multicore central processing units (CPUs). There has been a great interest to introduce a parallelized harmonic balance method to make full use of computing resources and improve the efficiency in dealing with nonlinear dynamic analysis of high-dimensional spatially discretized models of continuous systems. In this work, an optimized efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method for solving high-dimensional spatially discretized models of continuous systems based on parallel computing is introduced. Independent sampling and EGA procedures are introduced to achieve generality. Optimized parallel implementation based on tensor contraction is introduced in time-domain series calculations and the quasi-Newton method is used in the iteration procedure, which greatly accelerates computational speeds of both serial and parallel implementations. Especially, the parallel implementation achieves high parallel efficiency when multiple CPU cores are used. Due to its high computational efficiency and good robustness, the proposed method has the potential to be used as a powerful universal solver and analyzer for general types of continuous systems.

The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods

The present paper is concerned with the determination of the frequency equation and sensitivity of the eigenfrequencies of a fixed-free longitudinally vibrating rod and transversally vibrating beam carrying a tip mass by using several methods. First, the exact frequency equations of the such systems are established, and then approximate formulas are given for the fundamental frequency using several methods which contain the equivalent system, Rayleigh quotient, Dunkerley’s formula and continuous system model. The applicability and proximity of these methods versus exact solutions reviewed. The results are compared in a wide range of relevant parameters to give a clear idea about the validity of the proposed formulas. These new derived equations can be very useful for a design engineer who is interested in the eigencharacteristics of similar systems and their sensitivity.

Dynamical system learning using extreme learning machines with safety and stability guarantees

SummaryThis article presents a continuous dynamical system model learning methodology that can be used to generate reference trajectories for the autonomous systems to follow, such that these trajectories are invariant to a given closed set and uniformly ultimately bounded with respect to an equilibrium point inside the closed set. The autonomous system dynamics are approximated using extreme learning machines (ELM), the parameters of which are learned subject to the safety constraints expressed using a reciprocal barrier function, and the stability constraints derived using a Lyapunov analysis in the presence of the ELM reconstruction error. This formulation leads to solving a constrained quadratic program (QP) that includes a finite number of decision variables with an infinite number of constraints. Theorems are developed to relax the QP with infinite number of constraints to a QP with a finite number of constraints which can be practically implemented using a QP solver. In addition, an active sampling methodology is developed that further reduced the number of required constraints for the QP by only evaluating the constraints at a smaller subset of points. The proposed method is validated using a motion reproduction task on a seven degree‐of‐freedom Baxter robot, where the task space position and velocity dynamics are learned using the presented methodology.