For example, at this point of discontinuity a variation in the design parameter may cause a node to come into contact, frictional behavior to change from sticking to sliding, or a material point to transition from elastic to inelastic behavior. The formulation of DSA presented above provides a brief introduction to the way DSA is implemented in ABAQUS; however, due to some simplifications, the discussion is not relevant to a large number of nonlinear mechanical problems, especially those involving history-dependent behavior of the structure modeled. Design sensitivity analysis (DSA) is the study of how the measurable outputs of a model change with respect to changes in its design variables (Martins and Hwang 2013).It plays a key role in gradient-based optimization (Zhang and Kang 2014; Xiao et al. The restarted analysis will follow all the DSA propagation rules that are applicable to a regular analysis. Concise Reliability for Engineers, Reviewed: February 3rd, 2016 Published: April 13th, 2016, Total Chapter Downloads on intechopen.com. A.} Shape design parameters are not valid for rigid surfaces. The design sensitivity analysis (DSA) capability provides the derivatives of certain output variables with respect to specified design parameters. It is important to ensure that the variations defined by the uncertainty and sensitivity analysis Design Variables will have the intended effect. As it follows from Equation (12), the scatter of y can be reduced by reducing the standard deviation sx,k or the sensitivity of y to the changes of xk (coefficient ak). A few of the reasons to do this include: To identify the design parameters that have significant impact on the model behavior. A full discussion of DSA theory is given in Design sensitivity analysis, Section 2.18.1 of the ABAQUS Theory Manual. The DSA theory is presented from the perspective of computing the required derivatives analytically, first for static stress analysis and then for frequency analysis. In this form, the output is highly dependent on the design variable value. Design computations using the Carreau-Yasuda fluid model demonstrate the analysis and design sensitivity analysis given above and illustrate the effect of representing the low-strain rate near-constant viscosity in the constitutive model. Quiz is loading You must sign in or sign up to start the quiz. You must first complete [] Hence you can not start it again. The responses available for DSA are a subset of the list of ABAQUS output variables and are known as design responses; the specified input quantities are known as design parameters. Use a representative simulation period instead of the whole annual simulation. To help speed simulations, you could consider using one or more of these techniques: Complex optimisation with a large number of design variables and options makes it difficult to find clearly distinguishable trends. Several groups of computations are carried out, and in each group, only one variable (xi) is changed, whereas the others keep their nominal values x1,0, x2,0, , xn,0, corresponding to the design point. After having obtained the corrected standard deviation sxi', the lower (L) and upper (U) allowable limit for the input quantity xj can be determined as. This approach is computationally expensive since an entire equilibrium problem must be solved for each perturbation, but it is easily implemented. Furthermore, sensitivity analysis methods are used to assess how physically coherent the analyzed surrogates are. Also from SAGE Publishing. Even their most fundamental characteristics, for example a resistor's resistance, will be at least . The expression obtained by dividing Equation (10) or (12) by the total scatter sy2 gives the relative proportions of individual factors in the total scatter, The square root of scatter (10) is the standard deviation sy. Therefore, is a direct measure of the magnitude of the eigenvalue sensitivity and is also convenient since this term already must be calculated to obtain the eigenvalue sensitivity. The DSA calculations require the gradients of the design-dependent input data with respect to the design parameters. *Address all correspondence to: jaroslav.mencik@upce.cz. The objective of robust design optimization is the optimization of the product performance while minimizing the sensitivity of the performance to uncertainties, which has been widely applied to aerospace engineering (Xiong et al. An adequately large sample size (i.e., 800 samples) has been generated for the parametric sensitivity analysis as the input for each faade orientation using the extended FAST process. The discussion below is divided into two sections depending on the characteristics of the eigenvalue problem: distinct eigenvalues and repeated eigenvalues. Our team is growing all the time, so were always on the lookout for smart people who want to help us reshape the world of scientific publishing. 3. The decision will also depend on the costs related to the individual adjustments. III.Series. Variations of a general design functional are expressed in explicit form with respect to variations of all design variables; i.e,, material properties, applied loads, prescribed . The easiest way is to reduce the scatter of L. However, even if this scatter were zero, the variation coefficient of compliance would be vC' = 0.033, which is much more than demanded. Each input quantity has coefficient of variation vl = vw = vt = vE = v = 0.01 = 1%. For example, specifying a sizing frequency of n will cause ABAQUS/Design to determine new perturbation sizes at every n increments or eigenmodes. With a focus only on the important variables, the optimisation results are cleaner, quicker and easily understandable. Due to the history dependence, the incremental displacement sensitivities for the current increment depend on the sensitivities of the state variables at the beginning of the increment, in the same sense that incremental displacements depend on the state variables at the beginning of the increment for equilibrium analyses. The semi-analytic approach is used in ABAQUS and can be viewed as a compromise between the analytic and global finite difference approaches. The output variables for which sensitivities are computed are called design responses or simply responses. It includes the determination of the relevant operating conditions, the computations of the . When an eigenvalue repeats R times, the eigenvectors associated with are linearly independent but not uniqueany linear combination of these eigenvectors is also an eigenvector. An adjoint approach, derived from the reciprocal theorem and the theory of convolution, is used to formulate design sensitivities for linear elastodynamic systems. Both first- and secondorder sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. A. Jurado & F. Nieto School of Civil Engineering, University of Corua, Campus de Elvia, Spain Abstract One of the main difficulties in the design of long span suspension bridges is the stability under wind . This paper deals with design sensitivity calculation by the direct differentiation method for isoparametric curved shell elements. The reduction of variance of yk can be attained by more accurate manufacturing or by better control and sorting out the components that are out of the tolerance limits. More accurate value is obtained if all input variables, x1, x2, , xn are considered as random in the Monte Carlo simulations, and the scatter is calculated from all values yj. 3 in Chapter 15). If an appropriate perturbation size is already known for a particular design parameter (from previous analyses of similar problems, for example), economy can be gained by applying this perturbation size directly rather than having ABAQUS/Design automatically find the perturbation size. Following a sensitivity analysis approach, based on a sparse formulation, a useful method was presented for the design of power systems [213]. Static procedure. One must respect that the deviations of some input quantities influence the output in one direction, whereas the deviations of other quantities can have the opposite influence. Today, computer aided engineering (CAE) has been used for supporting engineers in tasks such as analysis, simulation, design, manufacture, etc. These regression functions correspond to the cuts through the response surface (Fig. 5.6.2.4 Design sensitivity analysis. Quantities that are functions of design parameters are referred to as being design dependent. Since we need to calculate the sensitivity of an incremental (perturbation) response, the sensitivity of the stress and load stiffening effects must be known at the end of the base step. The basic idea of this approach, as outlined in the section on static DSA, is to compute some of the required intermediate derivatives using finite differencing. In Sensitivity Analysis two important things need to be done in variable definition which will typically be different from optimisation: Therefore, despite the theoretical possibility of doing Sensitivity Analysis for more than one output at a time, DesignBuilder recommends, as a good practice, that sensitivity analysis of each output is set up separately and as a precursor to Optimisation. author = "Tortorelli, {D. In such cases, the response must be evaluated for each possible value of every discontinuous quantity. The scalar s is taken as the projection of this matrix onto an eigenvector . Both first- and secondorder sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Let R and P be the numbers of design responses and design parameters, respectively. Open Access is an initiative that aims to make scientific research freely available to all. Let R and P be the numbers of design responses and design parameters, respectively. The determination of suitable tolerances will be illustrated on the following example, adapted from [9]. The above optimization can be performed even if the scatter sy2 from the preliminary design is smaller than the allowable value. This also means that acceptable scatter of y can sometimes be achieved with lower demands on the accuracy of input parameters. Its position should ensure the low sensitivity of the output parameters to the deviations of input quantities from nominal values. More. The procedure depends on whether the variability is random or deterministic. The constants at individual terms correspond to their exponents in Equation (6), and the signs depend on whether the quantity was in the numerator or denominator. As discussed above, the perturbation sizing algorithm is applied simultaneously to all modes associated with a repeated eigenvalue. Use the following option to specify the design parameters: The following are restrictions on design parameters: Design parameters can be associated only with floating point data. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. After the design point has been found, the sensitivity analysis could be made to show the influence of the variations of input variables on the variability of the output [].The results may be used for setting the tolerances of input quantities to keep the output in the allowable range. If the perturbation sizing algorithm is applied to a mode with a distinct eigenvalue, is taken as the eigenvector associated with this mode. The theory presented below assumes that all the eigenvalues are distinct (i.e., no repeated eigenvalues). Then, an approximate expression is obtained by regression fitting the response computed for several combinations of input variables (Fig. The issue of obtaining accurate sensitivities with respect to design shape parameters using this method has been discussed extensively in the literature (for example, Pedersen et al., 1989; Barthelemy and Haftka, 1990; Fenyes and Lust, 1991; and Van Keulen and De Boer, 1998). The responses and response sensitivities (see Specifying responses above) are output only to the output database (sensitivity output to the data file and results file is not supported). This can be achieved by a suitable choice of nominal values of input quantities and by setting their tolerances. The available responses are a subset of the existing output variables. The finite difference interval must be chosen carefully. As an example, you can choose to obtain the derivatives of stresses with respect to Young's modulus; stress is the response, and Young's modulus is the design parameter. The resultant expression, involving the changes of all variables, is, and the relative sensitivity of the stiffness is. Discover which parameters have the greatest effect on system behavior, enabling you to increase model robustness, reduce model complexity and design optimal experiments . This approach is difficult to implement, but it is efficient and yields exact sensitivities. Both first- and secondorder sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. With this assumption, the tolerance of y can be reduced from y to y' by reducing the standard deviation of y from the original value sy to sy'. Design sensitivity is defined as a response change per unit design variable change. Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. In such case, it is better to study the influence of deviations of input quantities by modeling the response without simplifications. Both approaches will be illustrated on an example [9]. In book: Handbook of Design and Analysis of Experiments (pp.627 -673) Chapter: Design for Sensitivity Analysis; Publisher: Chapman & Hall/CRC; Editors: Angela Dean, Max Morris, John Stufken, Derek . Continuum design sensitivity formulas are derived from the material derivative in continuum mechanics and the variational form of the governing equation. UR - http://www.scopus.com/inward/record.url?scp=0002645387&partnerID=8YFLogxK, UR - http://www.scopus.com/inward/citedby.url?scp=0002645387&partnerID=8YFLogxK, Powered by Pure, Scopus & Elsevier Fingerprint Engine 2022 Elsevier B.V, We use cookies to help provide and enhance our service and tailor content. As can be seen in Design sensitivity analysis, Section 2.18.1 of the ABAQUS Theory Manual, the accuracy of the DSA solution is dictated by both the accuracy of the numerically computed derivatives and, for nonlinear static analysis, the accuracy of the tangent stiffness matrix. The repeated eigenvalue case is considered in the next section. Design sensitivity analysis :computational issues of sensitivity equation methods / Lisa G.Stanley,Dawn L.Stewart. xj,0 is the nominal (design) value and k is a constant (e.g. A common mistake for new users is to request these variables without switching on the option. This is conducted to gain insights into the relationship between the microscale geometry and the acoustic material parameters of a generic bar-lattice design . This makes the DSA module a very efficient add-on to the equilibrium analysis enabling sensitivity computations at a relatively low cost. By default, the incremental DSA formulation is used. 2016 The Author(s). For the calculation of Sensitivity Analysis, go to the Data tab in excel and then select What if . Both first- and secondorder sensitivities are derived as well as first-order sensitivities for symmetric . The approximate value of the total scatter is obtained by summing up the partial scatters. Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Good design ensures that the important output quantities will always lie within the allowable limits. This discussion will build upon the concepts and terminology described in Design sensitivity analysis for static stress analysis, so it is recommended that the previous section be read first. In most cases, the more variables that are defined in the analysis, the more runs will be required to achieve more acceptance results. Often, the response function must be found by numerical solution (e.g. Shape sensitivity analysis for structural performance measures has been developed for many years (Choi and Kim 2006) and was briefly discussed in Chapter 4. Uncertainty and sensitivity analysis studies require hundreds or even thousands of simulations to be carried out and so can be extremely time/calculation intensive.
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