Non-Linear Random Vibrations Using Second-Order Adjoint and Projected Differentiation Methods

This paper proposes a new computationally efficient methodology for random vibrations of nonlinear vibratory systems using a time-dependent second-order adjoint variable (AV2) method, and a second-order projected differentiation (PD2) method. The proposed approach is called AV2-PD2. The vibratory system can be excited by stationary Gaussian or non-Gaussian random processes. A Karhunen-Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. A second-order adjoint approach is used to obtain the required first and second-order output derivatives accurately by solving as many sets of equations of motion (EOMs) as the number of KL random variables. These derivatives are used to compute the marginal CDF of the output process with second-order accuracy. Then, a second-order projected differentiation method calculates the autocorrelation function of each output process with second-order accuracy, at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). The total number of solutions of the EOM scales linearly with the number of input KL random variables and the number of output processes. The efficiency and accuracy of the proposed approach is demonstrated using a non-linear Duffing oscillator problem under a quadratic random excitation.

Output process of the M|GI|1 is an asymptotical renewal process

Most of the studies on models with retrials are devoted to the research of the number of applications in the system or in the source of repeated calls using asymptotic and numerical approaches or simulation. Although one of the main characteristics that determines the quality of the communication system is the number of applications served by the system per unit of time. Information on the characteristics of the output processes is of great practical interest, since the output process of one system may be incoming to another. The results of the study of the outgoing flows of queuing networks are widely used in the modeling of computer systems, in the design of data transmission networks and in the analysis of complex multi-stage production processes. In this paper, we have considered a single server system with redial, the input of which receives a stationary Poisson process. The service time in considered system is a random value with an arbitrary distribution function B(x). If the customer enters the system and finds the server busy, it instantly joins the orbit and carries out a random delay there during an exponentially distributed time. The object of study is the output process of this system. The output is characterized by the probability distribution of the number of customers that have completed service for time t. We have provided the study using asymptotic analysis method under low rate of retrials limit condition. We have shown in the paper that the output of retrial queue M|GI|1 is an asymptotical renewal process. Moreover, the lengths of the intervals in output process are the sum of an exponential random value with the parameter lambda + kappa and a random variable with the distribution function B(x). The results of a numerical experiment show that the probability distributions of the number of served customers in the system are practically the same for significantly different distribution laws B(x) of service time if the service times have the same first two moments.

Estimation of portfolio efficiency considering social responsibility: Evidence from the multi-horizon diversification DEA

With the introduction of the concept of social responsibility investment/green investment, more and more investors have realized the importance of such investment, which has prompted portfolio managers to more comprehensively consider both financial and non-financial performance of portfolios in different time horizons. DEA (Data Envelopment Analysis), as a data-driven evaluation approach, has been widely used in performance evaluation of portfolios. However, the existing studies are mostly limited to single-horizon problems, and the evaluation indicators are mostly financial indicators, while ignoring the impact of non-financial indicators (e.g., social responsibility indicators). More importantly, the input-output process of portfolios in the multi-horizon framework also needs to be clarified. In this paper, we first define the input-output process of portfolios from the multi-horizon perspective, and then propose the corresponding stochastic output possibility sets based on portfolio returns and social responsibility indicators. We use the expectation and variance measures to derive the deterministic estimation of the above stochastic sets, where the expectations and variances of portfolio returns and social responsibility indicators are all regarded as outputs. We construct the multi-horizon diversification DEA models both with and without social responsibility constraints. Finally, we select the 20 component stocks of China ESG100 index to illustrate the difference between the multi-horizon models and the single-horizon models, and further discuss the impact of social responsibility on the portfolio efficiency and its ranking. The empirical results show that compared with the single-horizon models, the proposed models can provide portfolio managers with an improvement strategy to balance the performance of portfolio returns and social responsibility indicators in different time horizons. Further, we also find that the social responsibility has a greater impact on the portfolio efficiency and its ranking, especially when the portfolio managers pay more attention to the social responsibility performance.

A novel gradient current density output mode for effective electrochemical oxidative degradation of dye wastewater by boron-doped diamond (BDD) anode

In order to solve the problems of high energy consumption and low current efficiency in electrochemical oxidation (EO) degradation under the traditional constant output process (COP), a gradient output process (GOP) of current density is proposed in this paper. That is, the current density is gradually reduced in a fixed degradation time, and the Reactive Blue 19 simulated dye wastewater was used as the degradation target. The general applicability of the process was further confirmed by studying the optimal gradient current density output parameters, the dye concentration, electrolyte concentration and other dye compounds with different molecular structures. The corresponding results show that the chemical oxygen demand (COD) removal (78%) and the color removal (100%) under the GOP are similar to those in the COP, and the overall energy consumption is reduced by about 50% compared with that in the traditional constant current mode. Moreover, the current efficiency in the middle and late stages of EO process has increased by 8.6 times compared with COP.

Spectral method of analysis and optimal estimation in linear stochastic systems

It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multiplicative noise. The obtained results are applied to solve the output process analysis problem and the optimal estimation problem.

Direct Adaptive Controllers for a Multi Input Multi Output Process

Control of nonlinear dynamic systems is of great practical importance, since virtually all real world systems belong to this class. The prevalent approach is to use a model of the process linearized about the steady state operating point to design linear controllers. The Multi Input Multi Output (MIMO) process considered in this paper has varying system dynamics. This paper focuses on the performance evaluation of multi-loop Adaptive MIT(AMIT) controller and Adaptive PI(API) controller with vanishing adaptation technique for a laboratory interacting coupled tank MIMO process.