Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Rigid-Flexible Coupling Fatigue Life Reliability Study on Bonic Fish Driving Shaft

Due to the complex loads on a bionic robotic fish operating underwater, the reliability of its working mechanism has an important effect on its overall performance. By establishing a virtual prototype model for the rigid–flexible coupling of a bionic robotic fish, we obtained the instantaneous load on the caudal fin of the robotic fish based on the flapping-wing propulsion theory with MATLAB. A rigid–flexible coupled virtual prototype model for the caudal fin drive as a flexible member of the bionic robotic fish was established, and dynamic simulations were conducted on the model. The simulations revealed the weak links in the drive shaft and established a damage level indicator and fatigue reliability analysis method based on damage theory. The behavior of fatigue reliability for different stress cycles was established, and a dynamic reliability design method with great engineering application value was proposed for virtual prototypes of rigid–flexible coupled underwater bionic robots by combining the virtual prototype technology of rigid–flexible coupling with the theory of flapping wing propulsion and the theory of random load fatigue reliability.

Design of a Fuzzy Logic Controller for Short-Term Load Forecasting With Randomly Varying Load

Short-term load forecasting (STLF) is an integral component of energy management systems. In this paper, fuzzy logic-based algorithm is used for short-term load forecasting. The load changes over time and the goal is to satisfy the shift in demand and to maintain a fault as low as possible between the reference and real powers. The error in the load demand in mega-watt (MW) is compared with proposed technique as well as conventional methods. Three cases were investigated in which the load changes were 1) more random in nature, but the variance to the reference was more; 2) the random load changes were simpler, but a little different from the reference; and lastly, 3) the load changing was random, and the reference deviation was maximum. The results are analyzed for different load changes, and the corresponding results are verified using MATLAB. The deviation of the error value in load response is less experienced with a fuzzy logic controller than with a traditional system, and in fewer iterations, the objective function is also achieved.

A Novel Sooty Terns Algorithm for Deregulated MPC-LFC Installed in Multi-Interconnected System with Renewable Energy Plants

This paper introduces a novel metaheuristic approach of sooty terns optimization algorithm (STOA) to determine the optimum parameters of model predictive control (MPC)-based deregulated load frequency control (LFC). The system structure consists of three interconnected plants with nonlinear multisources comprising wind turbine, photovoltaic model with maximum power point tracker, and superconducting magnetic energy storage under deregulated environment. The proposed objective function is the integral time absolute error (ITAE) of the deviations in frequencies and powers in tie-lines. The analysis aims at determining the optimum parameters of MPC via STOA such that ITAE is minimized. Moreover, the proposed STOA-MPC is examined under variation of the system parameters and random load disturbance. The time responses and performance specifications of the proposed STOA-MPC are compared to those obtained with MPC optimized via differential evolution, intelligent water drops algorithm, stain bower braid algorithm, and firefly algorithm. Furthermore, a practical case study of interconnected system comprising the Kuraymat solar thermal power station is analyzed based on actual recorded solar radiation. The obtained results via the proposed STOA-MPC-based deregulated LFC confirmed the competence and robustness of the designed controller compared to the other algorithms.

Bending fatigue of single-wall and double-wall corrugated paperboards under sinusoidal and random loads

The bending fatigue tests of single-wall and double-wall corrugated paperboards were conducted to obtain the εrms– N curves under sinusoidal and random loads in this paper. The εrms– N equation of corrugated paperboard can be described by modified Coffin–Manson model considering the effect of mean stress. Four independent fatigue parameters are obtained for single-wall and double-wall corrugated paperboards. The εrms– N curve under random load moves left and rotates clockwise compared with that under sinusoidal load. The fatigue life under random load is much less than that under sinusoidal load, and the fatigue design of corrugated box should be based on the fatigue result under random load. The stiffness degradation and energy dissipation of double-wall corrugated paperboard before approaching fatigue failure are very different from that of single-wall one. For double-wall corrugated paperboard, two turning points occur in the stiffness degradation, and fluctuation occurs in the energy dissipation. Different from metal materials, the bending fatigue failure of corrugated paperboard is a process of wrinkle forming, spreading, and folding. The results obtained have practical values for the design of vibration fatigue of corrugated box.

Research on the Influence of Non-Stationary and Non-Gaussian Random Excitation on Structural Response Kurtosis

The stationary gaussian hypothesis is usually used to estimate the vibration fatigue life of structures. However, in actual engineering, the dynamic response of the structure usually exhibits non-stationary and non-gaussian, especially under harsh working condition or changing environment. The structural vibration fatigue life is closely related to the dynamic response characteristics, especially with respect to the structural response kurtosis used to characterize the non-Gaussian characteristics. In this paper, the influence of non-stationary and non-Gaussian random excitation on structural response kurtosis was studied by means of simulation and experiment. Firstly, by the means of simulating, the transmission law of excitation-response kurtosis was studied from three aspects, including system damping ratio, excitation frequency bandwidth, and excitation non-stationary characteristics. Then, the response kurtosis law was verified by the test results of cantilever vibration stress response. The results show that when the excitation is a stationary gaussian random load, the damping ratio and the excitation frequency bandwidth have no effect on the response kurtosis, and the response is approximately Gaussian distribution. When the excitation is stationary non-gaussian and non-stationary non-gaussian random load, if the damping ratio of the system is large, the response kurtosis is mainly affected by the damping ratio; If the damping ratio of the system is small, the frequency bandwidth and non-stationarity of the excitation have significant effects on the response kurtosis. The research results can provide support for predicting the vibration response and fatigue life of engineering structures under complex non-stationary non-gaussian random loads.

ANALYSIS OF ELECTRICAL LOAD SCHEDULES OF 10/0.4 KV TRANSFORMER SUBSTATIONS OF RESIDENTIAL AREAS FOR THE IDENTIFICATION OF STATIONARITY PLOTS

It is proposed on the electrical load graphs of transformer substations 10/0.4 kV in residential areas to allocate the stationarity areas for further modelling of load schedules and the implementation of controlling influences on the modes of consumers-regulators in order to align the overall graph of the electrical load. The relevance and complexity of the problem under consideration is caused by the fact that the load variation of transformer substations 10/0.4 kV in residential areas occurs randomly. This is due to the significant number, nomenclature and diversity of types of connected consumers, as well as the lack of deterministic connections between consumers of electricity, in addition, the random load function in the daily interval is non-stationary. In this regard, there was a need to develop the stages of selecting the areas of stationarity on the electrical load graphs of transformer substations 10/0.4 kV of residential areas. A measurement of the load graphs of 10/0,4 kV transformer substations is carried out, according to the results of which the distribution law of active and reactive power measurements is investigated. After confirming the hypothesis of normal distribution law, parametric tests are performed. Fisher's F-criterion is used to confirm the hypothesis of a constant variance, and Student's t-criterion is used to confirm the hypothesis of a constant mathematical expectation. The next stage, based on constancy of the variance and mathematical expectation, is the determination of autocorrelation coefficients of the studied random function and plotting of the autocorrelation function. To approximate the function the autocorrelation coefficients are determined by the least squares method and the autocorrelation function attenuation analysis is performed. The implementation of the defined stages allows to identify the areas of stationarity on the load graphs of transformer substations 10/0.4 kV. For a reliable description of the process of changing the load of transformer substations 10/0.4 kV the use of probabilistic-statistical method of modelling is justified that takes into account the stochastic nature of the load changes on the selected areas of stationarity.

Effective virtual inertia control using inverter optimization method in renewable energy generation

The high-level penetration of intermittent renewable power generation may limit power system inertia, resulting in system frequency instability in increasing power converter-based energy sources. To resolve this problem, virtual inertia control using distributed gray wolf optimization (DGWO) method in a synchronous generator is simulated under a distinct output fluctuation condition. First, the DGWO algorithm was established to achieve a local and global balance solution, and standard test functions were employed to verify the model convergence. Second, the key parameters that determine the effect of the virtual inertia controller in the power grid were analyzed. A DGWO-based optimization strategy to stabilize inertia was also developed. Finally, simulation results using step and random loads under a high permeability level are provided to verify the effectiveness of the proposed model. In the step load disturbance, the system can recover from the disturbance point to the stable point after 3 s under the regulation of the proposed control strategy, which is reduced by 18 s compared with the traditional control method. In the random load test, it takes only 12 s, 63 s less than the traditional one. Accordingly, the power system frequency can be stabilized more quickly from a disturbance state to a stable stage.