Statistical Optimization of Regulators Employing a Binary Error Criterion

1959 ◽  
Vol 81 (2) ◽  
pp. 254-261
Author(s):  
J. H. Milsum
Keyword(s):  
Computer Experiments ◽  
Analog Computer ◽  
Statistical Linearization ◽  
Error Criterion ◽  
Linearization Technique ◽  
Density Distributions ◽  
Error Magnitude ◽  
The Mean ◽  
Probability Density Distributions ◽  
Reference Input

The problem is considered of minimizing total costs of a regulator subject to both a steady reference input and a statistical load disturbance. A binary error criterion is used which directly relates the error magnitude to the economic penalty entailed by the error. In contrast it is not easy to relate the mean-square error to economic penalty. Experimental work shows that the amplitude probability density distributions in saturating loops are altered sufficiently from the Gaussian that the statistical linearization technique does not predict results with satisfactory accuracy in many cases of interest. The use of modified distributions alleviates this problem, but analog computer experiments provide the most satisfactory attack for complicated situations and are easily instrumented.

Structure of the Mean Velocity and Turbulence in Premixed Axisymmetric Acetylene Flames

1994 ◽  
Vol 116 (3) ◽  
pp. 631-642 ◽  
Author(s):  
M. Matovic ◽  
S. Oka ◽  
F. Durst
Keyword(s):  
Flow Field ◽  
Probability Density ◽  
Turbulent Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Common Features ◽  
Density Distributions ◽  
The Mean ◽  
Probability Density Distributions ◽  
Insight Into

Laser-Doppler measurements of axial mean velocities and the corresponding rms values of turbulent velocity fluctuations are reported for premixed, axisymmetric, acetylene flames together with the probability density distributions of the turbulent velocity fluctuations. All this information provides an insight into the structure of the flow field. Characteristic zones of the flow field are defined that show common features for all acetylene flames studied by the authors. These features are discussed in the paper and are suggested to characterize, in general, interesting parts of the flames.

Spectral and Probability-Density Nature of Square-Prism Separation-Reattachment Wall Pressures

1978 ◽  
Vol 100 (4) ◽  
pp. 485-492 ◽  
Author(s):  
J. B. Wedding ◽  
J. M. Robertson ◽  
J. A. Peterka ◽  
R. E. Akins
Keyword(s):  
Probability Density ◽  
Wake Flow ◽  
Statistical Nature ◽  
Additional Information ◽  
Density Distributions ◽  
Square Prism ◽  
Pressure Fields ◽  
The Mean ◽  
Non Gaussian ◽  
Probability Density Distributions

The statistical nature of the fluctuating pressures associated with the separation-reattachment flow were studied for a two-dimensional square prism in uniform flow for low (0.33 percent) and high (10.4 percent) turbulence levels. Studies were also made with a splitter plate to inhibit the feedback effect arising from vortex shedding. The nature of the separation reattachment flow was charcterized by use of the measured value of the mean and fluctating pressure fields. Spectral distribution of the unsteady pressures reveals strong energy spikes at the Strenthal frequency which are eliminated by the pressure of the splitler plate. Probability density distributions indicate appreciably non-Gaussian nature only in the wake. Additional information is presented on the variation with angle of the Strouhal frequency for the wake flow.

A Phenomenological Theory of Socioeconomic Systems with Spatial Interactions

1982 ◽  
Vol 14 (7) ◽  
pp. 869-888 ◽  
Author(s):  
P F Lesse
Keyword(s):  
Lagrange Multipliers ◽  
Average Cost ◽  
Phenomenological Theory ◽  
Traffic Flows ◽  
Spatial Interactions ◽  
Practical Application ◽  
Density Distributions ◽  
Expected Values ◽  
Probability Density Distributions ◽  
The Relationship

This paper deals with a class of models which describe spatial interactions and are based on Jaynes's principle. The variables entering these models can be partitioned in four groups: (a) probability density distributions (for example, relative traffic flows), (b) expected values (average cost of travel), (c) their duals (Lagrange multipliers, traffic impedance coefficient), and (d) operators transforming probabilities into expected values. The paper presents several dual formulations replacing the problem of maximizing entropy in terms of the group of variables (a) by equivalent extreme problems involving groups (b)-(d). These problems form the basis of a phenomenological theory. The theory makes it possible to derive useful relationships among groups (b) and (c). There are two topics discussed: (1) practical application of the theory (with examples), (2) the relationship between socioeconomic modelling and statistical mechanics.

Assembly variation analysis of complicated products based on rigid–flexible hybrid vector loop

2018 ◽  
Vol 233 (10) ◽  
pp. 2099-2114 ◽  
Author(s):  
Zhenyu Liu ◽  
Shien Zhou ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Probability Density ◽  
Loop Model ◽  
Feature Points ◽  
Variation Analysis ◽  
Manufacturing Error ◽  
Density Distributions ◽  
Mechanical Products ◽  
Flexible Parts ◽  
Probability Density Distributions ◽  
Product Assembly

The performance of mechanical products is closely related to their key feature errors. It is essential to predict the final assembly variation by assembly variation analysis to ensure product performance. Rigid–flexible hybrid construction is a common type of mechanical product. Existing methods of variation analysis in which rigid and flexible parts are calculated separately are difficult to meet the requirements of these complicated mechanical products. Another methodology is a result of linear superposition with rigid and flexible errors, which cannot reveal the quantitative relationship between product assembly variation and part manufacturing error. Therefore, a kind of complicated products’ assembly variation analysis method based on rigid–flexible vector loop is proposed in this article. First, shapes of part surfaces and sidelines are estimated according to different tolerance types. Probability density distributions of discrete feature points on the surface are calculated based on the tolerance field size with statistical methods. Second, flexible parts surface is discretized into a set of multi-segment vectors to build vector-loop model. Each vector can be orthogonally decomposed into the components representing position information and error size. Combining the multi-segment vector set of flexible part with traditional rigid part vector, a uniform vector-loop model is constructed to represent rigid and flexible complicated products. Probability density distributions of discrete feature points on part surface are regarded as inputs to calculate assembly variation values of products’ key features. Compared with the existing methods, this method applies to the assembly variation prediction of complicated products that consist of both rigid and flexible parts. Impact of each rigid and flexible part’s manufacturing error on product assembly variation can be determined, and it provides the foundation of parts tolerance optimization design. Finally, an assembly example of phased array antenna verifies effectiveness of the proposed method in this article.

scholarly journals A new Description of Probability Density Distributions of Polar Mesospheric Clouds (PMC)

2018 ◽  
Author(s):  
Uwe Berger ◽  
Gerd Baumgarten ◽  
Jens Fiedler ◽  
Franz-Josef Lübken
Keyword(s):  
Probability Density ◽  
Mass Density ◽  
Particle Radius ◽  
Number Density ◽  
Data Set ◽  
Statistical Probability ◽  
Polar Mesospheric Clouds ◽  
Density Distributions ◽  
Mesospheric Clouds ◽  
Probability Density Distributions

Abstract. In this paper we present a new description about statistical probability density distributions (pdfs) of Polar Mesospheric Clouds (PMC) and noctilucent clouds (NLC). The analysis is based on observations of maximum backscatter, ice mass density, ice particle radius, and number density of ice particles measured by the ALOMAR RMR-lidar for all NLC seasons from 2002 to 2016. From this data set we derive a new class of pdfs that describe the statistics of PMC/NLC events which is different from previously statistical methods using the approach of an exponential distribution commonly named g-distribution. The new analysis describes successfully the probability statistic of ALOMAR lidar data. It turns out that the former g-function description is a special case of our new approach. In general the new statistical function can be applied to many kinds of different PMC parameters, e.g. maximum backscatter, integrated backscatter, ice mass density, ice water content, ice particle radius, ice particle number density or albedo measured by satellites. As a main advantage the new method allows to connect different observational PMC distributions of lidar, and satellite data, and also to compare with distributions from ice model studies. In particular, the statistical distributions of different ice parameters can be compared with each other on the basis of a common assessment that facilitate, for example, trend analysis of PMC/NLC.

scholarly journals Distributions of Two Atoms Collisions over the Surface of the Condensed Phase

2021 ◽  
Vol 248 ◽  
pp. 01022
Author(s):  
Sergey Zheltov ◽  
Leonid Pletnev
Keyword(s):  
Potential Barrier ◽  
Condensed Phase ◽  
Evaporation Rate ◽  
Computer Experiments ◽  
Knudsen Layer ◽  
Graphics Processors ◽  
Rigid Spheres ◽  
Density Distributions ◽  
The Monte Carlo Method ◽  
Cuda Technology

The processes of heat and mass transfer are closely related to the evaporation of a substance from the surface of the condensed phase. The interaction of outgoing molecules from the surface of the condensed phase with condensed phase molecules plays a fundamental role. A simpler case of evaporation is the departure of atoms from the surface of the condensed phase, i.e. the atoms overcome the potential barrier on the surface of the condensed phase. Depending on the evaporation rate, a Knudsen layer appears above the surface of the condensed phase. In this paper, based on the model of rigid spheres, the density distributions of the collision distances and the average values of the collision distances of two atoms emitted simultaneously from the surface of the condensed phase above the surface are analyzed. Distributions of the collision distance depending on the surface temperature, the size of the potential barrier, and the size of the evaporation area are obtained. Computer experiments were performed using the Monte Carlo method. To obtain the results of numerical simulation, a parallel algorithm adapted to calculations on graphics processors with CUDA technology was developed.

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