• Korean Chemical Engineering Research
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• v.61 no.4
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• pp.542-549
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• 2023

Since the growing interest in surrogate modeling, there has been continuous research aimed at simulating nonlinear chemical processes using data-driven machine learning. However, the opaque nature of machine learning models, which limits their interpretability, poses a challenge for their practical application in industry. Therefore, this study aims to analyze chemical processes using Explainable Artificial Intelligence (XAI), a concept that improves interpretability while ensuring model accuracy. While conventional sensitivity analysis of chemical processes has been limited to calculating and ranking the sensitivity indices of variables, we propose a methodology that utilizes XAI to not only perform global and local sensitivity analysis, but also examine the interactions among variables to gain physical insights from the data. For the ammonia synthesis process, which is the target process of the case study, we set the temperature of the preheater leading to the first reactor and the split ratio of the cold shot to the three reactors as process variables. By integrating Matlab and Aspen Plus, we obtained data on ammonia production and the maximum temperatures of the three reactors while systematically varying the process variables. We then trained tree-based models and performed sensitivity analysis using the SHAP technique, one of the XAI methods, on the most accurate model. The global sensitivity analysis showed that the preheater temperature had the greatest effect, and the local sensitivity analysis provided insights for defining the ranges of process variables to improve productivity and prevent overheating. By constructing alternative models for chemical processes and using XAI for sensitivity analysis, this work contributes to providing both quantitative and qualitative feedback for process optimization.

• Journal of the Korean Geotechnical Society
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• v.23 no.1
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• pp.39-49
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• 2007

In this study, quantitative sensitivity analysis on rockfill material influencing the dam crest settlement of CFRD (Concrete-Faced Rockfill Dam) subjected to earthquake loading was carried out. The purpose of this study is to indicate the most important input parameter from the results of sensitivity analysis, to show the quantitative variation of settlement at the crest of CFR type dam during earthquake with this input parameter, and to recommend the approximate estimation method of the settlement on the crest of CFRD subjected to earthquake loading. The statistic characteristics of rockfill parameters which were obtained from large triaxial tests were evaluated. The total 108 dynamic numerical analyses (2 input earthquake, 2 magnitudes for each earthquake, 27 rockfill material property combinations) on CFRD were conducted. The global sensitivity analysis was carried out using the results of numerical analysis. From the sensitivity analysis, It was found that the crest settlement of the CFRD subjected to earthquake was absolutely affected by the shear modulus of rockfill material irrespective of the input earthquakes and the magnitude of input acceleration. On the contrary, it was found that the effect of cohesion and friction angle of rockfill was negligible. From the results of sensitivity analysis and numerical analysis, the approximate estimation method of the settlement on the crest of CFRD subjected to earthquake loading was recommended on condition that the rockfill shear modulus and simple dam information was known.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1320-1327
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in this flow problem.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1852-1860
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• 1991

A shape design sensitivity of the elastic deformation due to a change of traction boundary condition is presented. The solution of governing equations for a linear elasticity problem is obtained by finite element method and the traction boundary is defined by design variables. The performance functional to be considered involves both the domain and boundary integral. Variations of geometry can be defined as design velocity. Using material derivative concept and adjoint equations, the design sensitivity is derived by Lagrange multiplier method. For a given geometry of a structure, the change of traction boundary is described by the tangential component of the design velocity only. The final result for the shape design sensitivity is formulated as the boundary integral form, the integrand is defined by tangential component of design velocity and first order derivatives of parameters. Numerical implementation of design sensitivity is discussed and is compared with the difference of the actual values.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.8
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• pp.11-17
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• 2021

This paper describes the time rate of change of dynamic response of a cantilever beam inserted with a damping element, such as bonding, which is excited under a general force at various locations. A sensitivity analysis was performed in a finite element model to show that two types of second-order algebraic governing equations were used to predict the rate of change of dynamic displacement: one is related to the modal coordinate linked to a physical coordinate, and the other to the design parameter of the time rate of change of displacement. The sensitivity differential equation formulation includes more complicated terms compared with that of the undamped cantilever beam. The sensitivities of the dynamic response were observed by changing the location of the excitation force, displacement extraction, and cross-sectional area of the beam. The analytical results obtained by this suggested theory showed a relatively good agreement when compared with those obtained using the commercial finite element program. The suggested analysis procedure enables the prediction of the response sensitivity for any finite element model of the dynamic system.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.7
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• pp.90-99
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• 1996

In the area of assembly process of micro-chips and electronic parts on the printed circuit board, surface mounting device(SMD) is used as a fundamental tool. Generally speaking, the motion of the SMD is based on the ball screw system operated by any type of actuators. The ball screw system is a mechanical transformed which converts the mechanical rotational motion to the translational one. Also, this system could be considered as an efficient motion device against mechanical backlash and friction. Therefore a dynamic modeling and state sensitivity analysis of the ball screw system in SMD have to be done in the initial design stage. In this paper, a simple mathematical dynamic model for this system and the sensit- ivity analysis are mentioned. Especially, the bond graph approach is used for graphical modeling of the dynamic system before analysis stage. And the direct differentiation method is used for the state sensit- ivity analysis of the system. Finally, some trends for the state variables with respect to the design variables could be suggested for the better design and faster operating based on the results of dynamic and state sensitivity.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.398-401
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• 2001

There are two methods to calculate design sensitivity such as direct differentiation method and adjoint method. A sort of direct differentiation method for design sensitivity analysis costs too much when number of design variables is much larger than the number of response functions whose design sensitivity analyses are required. Therefore, an adjoint method is suggested for the case that the dimension of design variables is lager than the number of response function. An adjoint method is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation, requiring only the eigenvalue and its associated eigenvectors for mode being differentiated. This method has been extended to the repeated eigenvalue problem. In this paper, we propose an adjoint method for deign sensitivity analysis of damped vibratory systems with distinct eigenvalues.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.354-357
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• 2004

In this paper, a sensitivity analysis technique is presented for performing effective structural optimization of bus system. Design sensitivities are analyzed on natural frequency of bus substructures using super-element. Vibration modes of substructure, which large affect on the global vibration mode of bus B.I.W., are found through the sensitivity analysis using the chain rule. And design variables, which are determined from the sensitivity analysis, are changed through optimum design.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1478-1485
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• 1993

A shape optimization problem is formulated to determine the optimal position of heating lines in a compression molding die. The objective of the problem is that the cavity surface would be maintained by a prescribed uniform temperature. A boundary integral equation for the sensitivity of the temperature in terms of hole position is derived using the method of shape design sensitivity analysis. The boundary element method is employed to analyze the temperature and sensitivity field of the die. The sensitivity calculation algorithm is incorporated in an optimization routine. To demonstrate a numerical implementation, an example problem arising in thermal design of a compression molding die is dealt with, showing that the number of heating lines chosen for the die strongly affects the ultimate uniformity of the cavity surface temperature.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.119-124
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• 2001

A general procedure to implement the sensitivity analysis of PSC flexural members is proposed based on the analytical calculation of the gradients of stresses and strains with respect to the 21 design variables in a closed format. The formulation covers the long term losses including concrete creep, shrinkage, and PS steel relaxation as well as load effects. The derived formulation is applied to the rectangular section PSC beam with prestressing and nonprestressing steels for the sensitivity analysis. The analytically calculated sensitivity results are compared with those numerically calculated.