Mathematics

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21 pages, 5992 KiB

Open AccessArticle

An Efficient Micro Grid Optimization Theory

by Sooyoung Jung, Yong Tae Yoon and Jun-Ho Huh

Mathematics 2020, 8(4), 560; https://doi.org/10.3390/math8040560 - 10 Apr 2020

Cited by 13 | Viewed by 3352

A Micro Grid is an aggregate of many small-scale distributed energy resources (DERs); loads and can be operated independently or together with the existing power grid as a local power grid. The operator of such a grid takes charge of the energy supply [...] Read more.

A Micro Grid is an aggregate of many small-scale distributed energy resources (DERs); loads and can be operated independently or together with the existing power grid as a local power grid. The operator of such a grid takes charge of the energy supply and consumption of these resources and loads available in the grid. Meanwhile, the system operator of the grid considers the entire Micro Grid system to be a single load or a generator and assigns the responsibility of its internal management to the operator. The power production from a passive production resource is largely influenced by external environmental factors such as weather conditions, rather than operating conditions. Thus, this study conducted simulations for the cases where four kinds of conditional expressions had not been applied at all or one of them had been applied to compare and evaluate the effectiveness of each expression. As a result, the conditional equations were found to be effective when attempting to optimize the Micro Grids efficiently. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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18 pages, 3389 KiB

Open AccessArticle

Mathematical Models for Stress–Strain Behavior of Nano Magnesia-Cement-Reinforced Seashore Soft Soil

by Wei Wang, Yong Fu, Chen Zhang, Na Li and Aizhao Zhou

Mathematics 2020, 8(3), 456; https://doi.org/10.3390/math8030456 - 23 Mar 2020

Cited by 11 | Viewed by 4450

Abstract

The stress–strain behavior of nano magnesia-cement-reinforced seashore soft soil (Nmcs) under different circumstances exhibits various characteristics, e.g., strain-hardening behavior, falling behavior, S-type falling behavior, and strong softening behavior. This study therefore proposes a REP (reinforced exponential and power function)-based mathematical model to simulate [...] Read more.

The stress–strain behavior of nano magnesia-cement-reinforced seashore soft soil (Nmcs) under different circumstances exhibits various characteristics, e.g., strain-hardening behavior, falling behavior, S-type falling behavior, and strong softening behavior. This study therefore proposes a REP (reinforced exponential and power function)-based mathematical model to simulate the various stress–strain behaviors of Nmcs under varying conditions. Firstly, the mathematical characteristics of different constitutive behaviors of Nmcs are explicitly discussed. Secondly, the conventional mathematical models and their applicability for modeling stress–strain behavior of cemented soil are examined. Based on the mathematical characteristics of different stress–strain curves and the features of different conventional models, a simple mathematical REP model for simulating the hardening behavior, modified falling behavior and strong softening behavior is proposed. Moreover, a CEL (coupled exponential and linear) model improved from the REP model is also put forth for simulating the S-type stress–strain behavior of Nmcs. Comparisons between conventional models and the proposed REP-based models are made which verify the feasibility of the proposed models. The proposed REP-based models may facilitate researchers in the assessment and estimation of stress–strain constitutive behaviors of Nmcs subjected to different scenarios. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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38 pages, 1408 KiB

Open AccessFeature PaperArticle

Responsive Economic Model Predictive Control for Next-Generation Manufacturing

by Helen Durand

Mathematics 2020, 8(2), 259; https://doi.org/10.3390/math8020259 - 16 Feb 2020

Cited by 5 | Viewed by 3011

Abstract

There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance [...] Read more.

There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types would advance the move toward artificial intelligence properties for this controller beyond those which it has today and would provide new thoughts on interpretability and verification for the controller. This work provides theoretical studies which relate nonlinear systems considerations for EMPC to these higher-level concepts using two ideas for EMPC formulations motivated by specific situations related to self-modification of a control design after human perceptions of the process response are received and to controller handling of anomalies. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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22 pages, 1084 KiB

Open AccessArticle

Parameter and State Estimation of One-Dimensional Infiltration Processes: A Simultaneous Approach

by Song Bo, Soumya R. Sahoo, Xunyuan Yin, Jinfeng Liu and Sirish L. Shah

Mathematics 2020, 8(1), 134; https://doi.org/10.3390/math8010134 - 16 Jan 2020

Cited by 17 | Viewed by 2970

Abstract

The Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (hydraulic conductivity, saturated and residual [...] Read more.

The Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (hydraulic conductivity, saturated and residual soil moistures and van Genuchten-Mualem parameters) are essential for the accuracy of mathematical modeling, yet difficult to obtain experimentally. In this work, an estimation approach is developed to estimate the parameters and states of Richards equation simultaneously. In the proposed approach, parameter identifiability and sensitivity analysis are used to determine the most important parameters for estimation purpose. Three common estimation schemes (extended Kalman filter, ensemble Kalman filter and moving horizon estimation) are investigated. The estimation performance is compared and analyzed based on extensive simulations. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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21 pages, 681 KiB

Open AccessArticle

A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

by Jing Zhu, Yaxin Xu and Xiang Han

Mathematics 2019, 7(12), 1199; https://doi.org/10.3390/math7121199 - 6 Dec 2019

Cited by 9 | Viewed by 2803

Abstract

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. [...] Read more.

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches

10^{- 6}

from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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14 pages, 302 KiB

Open AccessArticle

Inframarginal Model Analysis of the Evolution of Agricultural Division of Labor

by Xueping Jiang, Jen-Mei Chang and Hui Sun

Mathematics 2019, 7(12), 1152; https://doi.org/10.3390/math7121152 - 1 Dec 2019

Cited by 3 | Viewed by 2514

Abstract

Division of labor plays a critical role in many parts of agriculture. For example, a specialized division of labor can lead to the improvement of labor productivity, the reduction of production costs, and the innovation of production technology and organization. At the heart [...] Read more.

Division of labor plays a critical role in many parts of agriculture. For example, a specialized division of labor can lead to the improvement of labor productivity, the reduction of production costs, and the innovation of production technology and organization. At the heart of agricultural management is how the comparative advantages of farmers impact their production decision-making behavior, and, consequently, influence the division of labor structure. In this paper, we apply an infra-marginal model to interpret the selection logic of heterogeneous farmers’ specialized production with exogenous comparative technical advantages and transaction costs. Solving the nonlinear programming problem of the utility function within each respective labor structure leads to a corner equilibrium. Under reasonable assumptions of the model, we reduced the number of possible production–consumption decision modes from the maximum of 64 to an optimal of 3. Through this analysis, we discovered the ranges for transaction efficiency coefficients and preference parameter under which each structure can achieve general equilibrium. Our theoretical model thereby explains the structural evolution of agricultural division of labor. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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21 pages, 1113 KiB

Open AccessArticle

Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload

by María-Eusebia Guerrero-Sánchez, Omar Hernández-González, Rogelio Lozano, Carlos-D. García-Beltrán, Guillermo Valencia-Palomo and Francisco-R. López-Estrada

Mathematics 2019, 7(11), 1090; https://doi.org/10.3390/math7111090 - 11 Nov 2019

Cited by 26 | Viewed by 4099

Abstract

This paper presents the control of a quadrotor with a cable-suspended payload. The proposed control structure is a hierarchical scheme consisting of an energy-based control (EBC) to stabilize the vehicle translational dynamics and to attenuate the payload oscillation, together with a nonlinear state [...] Read more.

This paper presents the control of a quadrotor with a cable-suspended payload. The proposed control structure is a hierarchical scheme consisting of an energy-based control (EBC) to stabilize the vehicle translational dynamics and to attenuate the payload oscillation, together with a nonlinear state feedback controller based on an linear matrix inequality (LMI) to control the quadrotor rotational dynamics. The payload swing control is based on an energy approach and the passivity properties of the system’s translational dynamics. The main advantage of the proposed EBC strategy is that it does not require excessive computations and complex partial differential equations (PDEs) for implementing the control algorithm. We present a new methodology for using an LMI to synthesize the controller gains for Lipschitz nonlinear systems with larger Lipschitz constants than other classical techniques based on LMIs. This theoretical approach is applied to the quadrotor rotational dynamics. Stability proofs based on the Lyapunov theory for the controller design are presented. The designed control scheme allows for the stabilization of the system in all its states for the three-dimensional case. Numerical simulations demonstrating the effectiveness of the controller are provided. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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25 pages, 906 KiB

Open AccessEditor’s ChoiceArticle

Real-Time Optimization and Control of Nonlinear Processes Using Machine Learning

by Zhihao Zhang, Zhe Wu, David Rincon and Panagiotis D. Christofides

Mathematics 2019, 7(10), 890; https://doi.org/10.3390/math7100890 - 24 Sep 2019

Cited by 54 | Viewed by 8198

Abstract

Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) [...] Read more.

Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) and demonstrates the application to two chemical process examples. First, the proposed methodology that integrates a neural network model and a first-principles model in the optimization problems of RTO and MPC is discussed. Then, two chemical process examples are presented. In the first example, a continuous stirred tank reactor (CSTR) with a reversible exothermic reaction is studied. A feed-forward neural network model is used to approximate the nonlinear reaction rate and is combined with a first-principles model in RTO and MPC. An RTO is designed to find the optimal reactor operating condition balancing energy cost and reactant conversion, and an MPC is designed to drive the process to the optimal operating condition. A variation in energy price is introduced to demonstrate that the developed RTO scheme is able to minimize operation cost and yields a closed-loop performance that is very close to the one attained by RTO/MPC using the first-principles model. In the second example, a distillation column is used to demonstrate an industrial application of the use of machine learning to model nonlinearities in RTO. A feed-forward neural network is first built to obtain the phase equilibrium properties and then combined with a first-principles model in RTO, which is designed to maximize the operation profit and calculate optimal set-points for the controllers. A variation in feed concentration is introduced to demonstrate that the developed RTO scheme can increase operation profit for all considered conditions. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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16 pages, 2276 KiB

Open AccessArticle

A Theoretical Rigid Body Model of Vibrating Screen for Spring Failure Diagnosis

by Yue Liu, Shuangfu Suo, Guoying Meng, Deyong Shang, Long Bai and Jianwen Shi

Mathematics 2019, 7(3), 246; https://doi.org/10.3390/math7030246 - 9 Mar 2019

Cited by 12 | Viewed by 4278

Abstract

Springs are critical components in mining vibrating screen elastic supports. However, long-term alternating loads are likely to lead to spring failures, likely resulting in structural damages to the vibrating screen and resulting in a lower separation efficiency. Proper dynamic models provide a basis [...] Read more.

Springs are critical components in mining vibrating screen elastic supports. However, long-term alternating loads are likely to lead to spring failures, likely resulting in structural damages to the vibrating screen and resulting in a lower separation efficiency. Proper dynamic models provide a basis for spring failure diagnosis. In this paper, a six-degree-of-freedom theoretical rigid body model of a mining vibrating screen is proposed, and a dynamic equation is established in order to explore the dynamic characteristics. Numerical simulations, based on the Newmark-β algorithm, are carried out, and the results indicate that the model proposed is suitable for revealing the dynamic characteristics of the mining vibrating screen. Meanwhile, the mining vibrating screen amplitudes change with the spring failures. Therefore, six types of spring failure are selected for simulations, and the results indicate that the spring failures lead to an amplitude change for the four elastic support points in the x, y, and z directions, where the changes depend on certain spring failures. Hence, the key to spring failure diagnosis lies in obtaining the amplitude change rules, which can reveal particular spring failures. The conclusions provide a theoretical basis for further study and experiments in spring failure diagnosis for a mining vibrating screen. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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15 pages, 313 KiB

Open AccessArticle

Weighted Block Golub-Kahan-Lanczos Algorithms for Linear Response Eigenvalue Problem

by Hongxiu Zhong, Zhongming Teng and Guoliang Chen

Mathematics 2019, 7(1), 53; https://doi.org/10.3390/math7010053 - 7 Jan 2019

Cited by 2 | Viewed by 2924

Abstract

In order to solve all or some eigenvalues lied in a cluster, we propose a weighted block Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem. Error bounds of the approximations to an eigenvalue cluster, as well as their corresponding eigenspace, are established and [...] Read more.

In order to solve all or some eigenvalues lied in a cluster, we propose a weighted block Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem. Error bounds of the approximations to an eigenvalue cluster, as well as their corresponding eigenspace, are established and show the advantages. A practical thick-restart strategy is applied to the block algorithm to eliminate the increasing computational and memory costs, and the numerical instability. Numerical examples illustrate the effectiveness of our new algorithms. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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16 pages, 3678 KiB

Open AccessArticle

Target Fusion Detection of LiDAR and Camera Based on the Improved YOLO Algorithm

by Jian Han, Yaping Liao, Junyou Zhang, Shufeng Wang and Sixian Li

Mathematics 2018, 6(10), 213; https://doi.org/10.3390/math6100213 - 19 Oct 2018

Cited by 39 | Viewed by 7972

Abstract

Target detection plays a key role in the safe driving of autonomous vehicles. At present, most studies use single sensor to collect obstacle information, but single sensor cannot deal with the complex urban road environment, and the rate of missed detection is high. [...] Read more.

Target detection plays a key role in the safe driving of autonomous vehicles. At present, most studies use single sensor to collect obstacle information, but single sensor cannot deal with the complex urban road environment, and the rate of missed detection is high. Therefore, this paper presents a detection fusion system with integrating LiDAR and color camera. Based on the original You Only Look Once (YOLO) algorithm, the second detection scheme is proposed to improve the YOLO algorithm for dim targets such as non-motorized vehicles and pedestrians. Many image samples are used to train the YOLO algorithm to obtain the relevant parameters and establish the target detection model. Then, the decision level fusion of sensors is introduced to fuse the color image and the depth image to improve the accuracy of the target detection. Finally, the test samples are used to verify the decision level fusion. The results show that the improved YOLO algorithm and decision level fusion have high accuracy of target detection, can meet the need of real-time, and can reduce the rate of missed detection of dim targets such as non-motor vehicles and pedestrians. Thus, the method in this paper, under the premise of considering accuracy and real-time, has better performance and larger application prospect. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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14 pages, 2291 KiB

Open AccessArticle

The Opening Capability for Security against Privacy Infringements in the Smart Grid Environment

by Sungwook Eom and Jun-Ho Huh

Mathematics 2018, 6(10), 202; https://doi.org/10.3390/math6100202 - 14 Oct 2018

Cited by 10 | Viewed by 3526

Abstract

It is now known that more information can be leaked into the smart grid environment than into the existing environment. In particular, specific information such as energy consumption data can be exposed via smart devices. Such a phenomenon can incur considerable risks due [...] Read more.

It is now known that more information can be leaked into the smart grid environment than into the existing environment. In particular, specific information such as energy consumption data can be exposed via smart devices. Such a phenomenon can incur considerable risks due to the fact that both the amount and the concreteness of information increase when more types of information are combined. As such, this study aimed to develop an anonymous signature technique along with a signature authentication technique to prevent infringements of privacy in the smart grid environment, and they were tested and verified at the testbed used in a previous study. To reinforce the security of the smart grid, a password and anonymous authentication algorithm which can be applied not only to extendable test sites but also to power plants, including nuclear power stations, was developed. The group signature scheme is an anonymous signature schemes where the authenticator verifies the group signature to determine whether the signer is a member of a certain group but he/she would not know which member actually signed in. However, in this scheme, the identity of the signer can be revealed through an “opener” in special circumstances involving accidents, incidents, or disputes. Since the opener can always identify the signer without his/her consent in such cases, the signer would be concerned about letting the opener find out his/her anonymous activities. Thus, an anonymous signature scheme where the signer issues a token when entering his/her signature to allow the opener to confirm his/her identity only from that token is proposed in this study. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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13 pages, 293 KiB

Open AccessArticle

Green’s Classifications and Evolutions of Fixed-Order Networks

by Allen D. Parks

Mathematics 2018, 6(10), 174; https://doi.org/10.3390/math6100174 - 25 Sep 2018

Cited by 1 | Viewed by 2606

Abstract

It is shown that the set of all networks of fixed order

n

form a semigroup that is isomorphic to the semigroup

B_{X}

of binary relations on a set

X

of cardinality

n

. Consequently,

B_{X}

provides for Green’s [...] Read more.

It is shown that the set of all networks of fixed order

n

form a semigroup that is isomorphic to the semigroup

B_{X}

of binary relations on a set

X

of cardinality

n

. Consequently,

B_{X}

provides for Green’s

L, R, H,

and

D

equivalence classifications of all networks of fixed order

n

. These classifications reveal that a fixed-order network which evolves within a Green’s equivalence class maintains certain structural invariants during its evolution. The “Green’s symmetry problem” is introduced and is defined as the determination of all symmetries (i.e., transformations) that produce an evolution between an initial and final network within an

L

or an

R

class such that each symmetry preserves the required structural invariants. Such symmetries are shown to be solutions to special Boolean equations specific to each class. The satisfiability and computational complexity of the “Green’s symmetry problem” are discussed and it is demonstrated that such symmetries encode information about which node neighborhoods in the initial network can be joined to form node neighborhoods in the final network such that the structural invariants required by the evolution are preserved, i.e., the internal dynamics of the evolution. The notion of “propensity” is also introduced. It is a measure of the tendency of node neighborhoods to join to form new neighborhoods during a network evolution and is used to define “energy”, which quantifies the complexity of the internal dynamics of a network evolution. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

22 pages, 635 KiB

Open AccessArticle

Detecting and Handling Cyber-Attacks in Model Predictive Control of Chemical Processes

by Zhe Wu, Fahad Albalawi, Junfeng Zhang, Zhihao Zhang, Helen Durand and Panagiotis D. Christofides

Mathematics 2018, 6(10), 173; https://doi.org/10.3390/math6100173 - 25 Sep 2018

Cited by 49 | Viewed by 5932

Abstract

Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and [...] Read more.

Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and the increasing use of wireless communication, control systems are becoming increasingly vulnerable to cyber-attacks, which may spread rapidly and may cause severe industrial incidents. To mitigate the impact of cyber-attacks in chemical processes, this work integrates a neural network (NN)-based detection method and a Lyapunov-based model predictive controller for a class of nonlinear systems. A chemical process example is used to illustrate the application of the proposed NN-based detection and LMPC methods to handle cyber-attacks. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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12 pages, 1437 KiB

Open AccessArticle

Kinematics in the Information Age

by Brendon Smeresky, Alexa Rizzo and Timothy Sands

Mathematics 2018, 6(9), 148; https://doi.org/10.3390/math6090148 - 27 Aug 2018

Cited by 12 | Viewed by 5660

Abstract

Modern kinematics derives directly from developments in the 1700s, and in their current instantiation, have been adopted as standard realizations…or templates that seem unquestionable. For example, so-called aerospace sequences of rotations are ubiquitously accepted as the norm for aerospace applications, owing from a [...] Read more.

Modern kinematics derives directly from developments in the 1700s, and in their current instantiation, have been adopted as standard realizations…or templates that seem unquestionable. For example, so-called aerospace sequences of rotations are ubiquitously accepted as the norm for aerospace applications, owing from a recent heritage in the space age of the late twentieth century. With the waning of the space-age as a driver for technology development, the information age has risen with the advent of digital computers, and this begs for re-evaluation of assumptions made in the former era. The new context of the digital computer defines the use of the term “information age” in the manuscript title and further highlights the novelty and originality of the research. The effects of selecting different Direction Cosine Matrices (DCM)-to-Euler Angle rotations on accuracy, step size, and computational time in modern digital computers will be simulated and analyzed. The experimental setup will include all twelve DCM rotations and also includes critical analysis of necessary computational step size. The results show that the rotations are classified into symmetric and non-symmetric rotations and that no one DCM rotation outperforms the others in all metrics used, yielding the potential for trade space analysis to select the best DCM for a specific instance. Novel illustrations include the fact that one of the ubiquitous sequences (the “313 sequence”) has degraded relative accuracy measured by mean and standard deviations of errors, but may be calculated faster than the other ubiquitous sequence (the “321 sequence”), while a lesser known “231 sequence” has comparable accuracy and calculation-time. Evaluation of the 231 sequence also illustrates the originality of the research. These novelties are applied to spacecraft attitude control in this manuscript, but equally apply to robotics, aircraft, and surface and subsurface vehicles. Full article

(This article belongs to the Special Issue Mathematics and Engineering)

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