Sensitivity of Optimum Solutions of Problem Parameters

Sobieszczanski‐Sobieski, Jaroslaw; Barthélémy, Jean‐François; Riley, Kathleen M.

doi:10.2514/3.51191

Cited by 155 publications

(9 citation statements)

References 7 publications

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“…Here, z k is treated as a fixed parameter. In order to attain the first-order sensitivity of a model at an optimal solution with respect to a parameter, which is located in the objective function and constraints, we use the partial derivative of the Lagrange function of the model 42–44 : ∂∂zk[∑i=1lαi∗−12∑i=1l∑j=1lαi∗normalαj∗yiyjK(xi○z,xj○z)+λ(true∑i=1lαi∗yi)−∑i=1lμi(1)normalαi∗+∑i=1lμi(2)(normalαi∗−C)]|z=z∗newline=−12∑i=1l<...>…”

Section: Feature Selection Algorithm Based On Nonlinear Support Vecmentioning

confidence: 99%

Big data approach to batch process monitoring: Simultaneous fault detection and diagnosis using nonlinear support vector machine-based feature selection

Onel

Kieslich

Guzman

et al. 2018

Computers & Chemical Engineering

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This paper presents a novel data-driven framework for process monitoring in batch processes, a critical task in industry to attain a safe operability and minimize loss of productivity and profit. We exploit high dimensional process data with nonlinear Support Vector Machine-based feature selection algorithm, where we aim to retrieve the most informative process measurements for accurate and simultaneous fault detection and diagnosis. The proposed framework is applied to an extensive benchmark dataset which includes process data describing 22,200 batches with 15 faults. We train fault and time-specific models on the prealigned batch data trajectories via three distinct time horizon approaches: one-step rolling, two-step rolling, and evolving which varies the amount of data incorporation during modeling. The results show that two-step rolling and evolving time horizon approaches perform superior to the other. Regardless of the approach, proposed framework provides a promising decision support tool for online simultaneous fault detection and diagnosis for batch processes.

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Section: Feature Selection Algorithm Based On Nonlinear Support Vecmentioning

confidence: 99%

Big data approach to batch process monitoring: Simultaneous fault detection and diagnosis using nonlinear support vector machine-based feature selection

Onel

Kieslich

Guzman

et al. 2018

Computers & Chemical Engineering

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“…The sensitivity analysis method was proposed early in 1980s by Sobieszczanski-Sobieski et al to study the sensitivity of optimum solution of problem parameters. The basic principle of sensitivity analysis is to get the derivative of the optimum solution to multiple variables and then obtain the optimum solution and the corresponding variables via calculating the weight factors of different variables [16]. Besides, a working status factor of the BSS system based on displacement is defined as the control objective.…”

Section: The Static Control Model Based On Minimal Displacementmentioning

confidence: 99%

A Static Control Algorithm for Adaptive Beam String Structures Based on Minimal Displacement

Shen

Cheng

Yang

et al. 2013

Mathematical Problems in Engineering

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The beam string structure (BSS) is a type of prestressed structure and has been widely used in large span structures nowadays. The adaptive BSS is a typical smart structure that can optimize the working status itself by controlling the length of active struts via certain control device. The control device commonly consists of actuators in all struts and sensors on the beam. The key point of the control process is to determine the length adjustment values of actuators according to the data obtained by preinstalled sensors. In this paper, a static control algorithm for adaptive BSS has been presented for the adjustment solution. To begin with, an optimization model of adaptive BSS with multiple active struts is established, which uses a sensitivity analysis method. Next, a linear displacement control process is presented, and the adjustment values of struts are calculated by a simulated annealing algorithm. A nonlinear iteration procedure is used afterwards to calibrate the results of linear calculation. Finally, an example of adaptive BSS under different external loads is carried out to verify the feasibility and accuracy of the algorithm. And the results also show that the adaptive BSS has much better adaptivity and capability than the noncontrolled BSS.

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“…One of them provides the derivatives of the optimal objective and design variables, but requires second derivatives of the behaviour variables. The other does not require the second derivatives, but generates the derivatives of the optimal objective only' 13,14 '.…”

Section: (3)mentioning

confidence: 99%

Multidisciplinary design optimisation (MDO) methods: their synergy with computer technology in the design process

Sobieszczanski‐Sobieski

1999

Aeronaut. j.

Self Cite

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The paper identifies speed, agility, human interface, generation of sensitivity information, task decomposition, and data transmission (including storage) as important attributes for a computer environment to have in order to support engineering design effectively. It is argued that when examined in terms of these attributes the presently available environment can be shown to be inadequate. A radical improvement is needed, and it may be achieved by combining new methods that have recently emerged from multidisciplinary design optimisation (MDO) with massively parallel processing computer technology. The caveat is that, for successful use of that technology in engineering computing, new paradigms for computing will have to be developed - specifically, innovative algorithms that are intrinsically parallel so that their performance scales up linearly with the number of processors. It may be speculated that the idea of simulating a complex behaviour by interaction of a large number of very simple models may be an inspiration for the above algorithms; the cellular automata are an example. Because of the long lead time needed to develop and mature new paradigms, development should begin now, even though the widespread availability of massively parallel processing is still a few years away.

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Sensitivity of Optimum Solutions of Problem Parameters

Cited by 155 publications

References 7 publications

Big data approach to batch process monitoring: Simultaneous fault detection and diagnosis using nonlinear support vector machine-based feature selection

Big data approach to batch process monitoring: Simultaneous fault detection and diagnosis using nonlinear support vector machine-based feature selection

A Static Control Algorithm for Adaptive Beam String Structures Based on Minimal Displacement

Multidisciplinary design optimisation (MDO) methods: their synergy with computer technology in the design process

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