scholarly journals Stochastic order-based optimal design of a surface reservoir–irrigation district system

2012 ◽  
Vol 15 (2) ◽  
pp. 591-606 ◽  
Author(s):  
Hosein Alizadeh ◽  
S. Jamshid Mousavi
Keyword(s):  
Optimal Design ◽  
Stochastic Order ◽  
Pso Algorithm ◽  
Expected Value ◽  
Irrigation District ◽  
Stochastic Orders ◽  
Stochastic Programs ◽  
Mathematical Programs ◽  
Expected Gain ◽  
Global Optima

This paper explores the effects of streamflow uncertainty and the type of stochastic order, which is used for comparing stochastic variables, on optimal design of a reservoir multi-crop irrigation district system. Four nonlinear mathematical programs with an economic objective function including deterministic, stochastic-EXP with expected value order, stochastic-SD with stochastic dominance (SD) order, and stochastic-EGCL with expected gain-confidence limit (EGCL) order were developed. Afterwards, the approaches of successive linear programming (SLP) and PSO–MC, which combines particle swarm optimization (PSO) algorithm and Monte Carlo simulation (MC), to solve the programs were selected. Hajiarab Irrigation District located in Ghazvin Province of Iran was used as a case study and the results obtained from using different programs and solution approaches were analyzed and compared. Among the solution approaches, SLP could not solve the programs other than the deterministic one while PSO–MC could find at least good solutions, if not the global optima, for all the programs. Among the main decision variables, the stochastic programs resulted in a reduced size of irrigation district compared with that obtained by the deterministic program. Moreover, the programs using stochastic orders other than a simple expected value converged at solutions different from the solution reached by the expected value-based program.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

Active disturbance rejection motion control of spherical robot with parameter tuning

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Manlu Liu ◽  
Rui Lin ◽  
Maotao Yang ◽  
Anaid V. Nazarova ◽  
Jianwen Huo
Keyword(s):  
Motion Control ◽  
Disturbance Rejection ◽  
Parameter Tuning ◽  
Pso Algorithm ◽  
State Equation ◽  
Expected Value ◽  
Spherical Robot ◽  
Motion Controller ◽  
Actual Case ◽  
Content Type

Purpose The characteristics of spherical robots, such as under-drive, non-holonomic constraints and strong coupling, make it difficult to establish its motion control model accurately. To improve the anti-interference performance of spherical robots in practical engineering, this paper proposes a spherical robot motion controller based on auto-disturbance rejection control (ADRC) with parameter tuning. Design/methodology/approach This paper considers the influences of the spherical shell, internal frame and pendulum on the movement of the spherical robot during the rotation to establish the multi-body dynamics model of the XK-I spherical robot. Due to the serious coupling problem of the dynamic model, the motion control state equation is constructed using linearization and decoupling. The XK-I spherical robot PSO-ADRC motion controller with parameter tuning function is designed by combining the state equation with the particle swarm optimization (PSO) algorithm. Finally, experiments are performed to evaluate the feasibility of PSO-ADRC in an actual case compared to ADRC, PSO-PID and PID. Findings By analyzing the required time to reach the expected value, the control stability and the fluctuation range of the standard deviation after reaching the expected value, the superiority of PSO-ADRC to ADRC, PSO-PID and PID is demonstrated in terms of the speed and anti-interference ability. Practical implications The proposed method can be applied to the robot control field. Originality/value A parameter-tuning method for auto-disturbance-rejection motion control of the spherical robot is proposed. According to the experimental results, the anti-interference ability of the spherical robot moving on uneven ground is improved. Therefore, it provides a foundation for the autonomous environmental monitoring of the spherical robot equipped with sensors.

PRESERVATION OF STOCHASTIC ORDERS UNDER MIXTURES OF EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (4) ◽  
pp. 655-666 ◽  
Author(s):  
Jarosław Bartoszewicz ◽  
Magdalena Skolimowska
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Order ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Dispersive Order ◽  
Mixing Distributions ◽  
Convex Transform Order ◽  
Star Order

Recently, Bartoszewicz [5,6] considered mixtures of exponential distributions treated as the Laplace transforms of mixing distributions and established some stochastic order relations between them: star order, dispersive order, dilation. In this article the preservation of the likelihood ratio, hazard rate, reversed hazard rate, mean residual life, and excess wealth orders under exponential mixtures is studied. Some new preservation results for the dispersive order are given, as well as the preservation of the convex transform order, and the star one is discussed.

Sign in / Sign up

Export Citation Format

Share Document