Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

Pollini, Nicolò; Lavan, Oren

doi:10.1007/s00158-017-1858-2

Cited by 37 publications

(24 citation statements)

References 30 publications

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“…53 Moreover, to ensure the consistency of the sensitivity calculated, we rely on the so called discretize-then-differentiate adjoint variable method. [65][66][67] According to this method, the discrete version of the governing equilibrium (Equation A1) is considered in the gradient calculation.…”

Section: Sensitivity Analysis and Computational Considerationsmentioning

confidence: 99%

Fail‐safe optimization of viscous dampers for seismic retrofitting

Pollini

2020

Earthq Engng Struct Dyn

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This paper presents a new optimization approach for designing minimum-cost fail-safe distributions of fluid viscous dampers for seismic retrofitting. Failure is modeled as either complete damage of the dampers or partial degradation of the dampers' properties. In general, this leads to optimization problems with large number of constraints. This may result in high computational costs if all the constraints are simultaneously considered during the optimization analysis. Thus, to reduce the computational effort, the use of a working-set optimization algorithm is proposed in this paper. The main idea is to solve a sequence of relaxed optimization subproblems with a small subset of all constraints. The algorithm terminates once a solution of a subproblem is found that satisfies all the constraints of the problem. The retrofitting cost is minimized with constraints on the interstory drifts at the peripheries of frame structures. The structures considered are subjected to a realistic ensemble of ground motions, and their response is evaluated with time-history analyses. The transient optimization problem is efficiently solved with a gradient-based sequential linear programming algorithm. The gradients of the response functions are calculated with a consistent adjoint sensitivity analysis procedure. Promising results attained for 3-D irregular frames are presented and discussed. The numerical results highlight the fact that the optimized layout and size of the dampers can change significantly even for moderate levels of damage.

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Section: Sensitivity Analysis and Computational Considerationsmentioning

confidence: 99%

Fail‐safe optimization of viscous dampers for seismic retrofitting

Pollini

2020

Earthq Engng Struct Dyn

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“…For the tuning procedure of the parameter ρ , we relied on the procedure discussed in Pollini et al During the nonlinear time‐history structural analysis, the response of each damper in each time‐step is approximated with a fourth‐order Runge‐Kutta method as suggested by Kasai and Oohara . A similar approach has been used in Akcelyan et al and by the authors in Reference Pollini et al…”

Section: Governing Equationsmentioning

confidence: 99%

“…The gradient of the aggregated constraint (ie,

\nabla_{x} {\overset{d}{true}}_{c}

), on the other hand, requires an adjoint sensitivity analysis. To ensure the consistency of the sensitivity calculated, we relied on the discretize‐then‐differentiate adjoint variable method, similarly to Pollini et al Ultimately, the outcome of the adjoint sensitivity analysis is the vector

\nabla_{c_{d}}^{T} {\overset{d}{true}}_{c} = ([], \frac{\partial {\overset{d}{true}}_{c}}{\partial c_{d 1}} ⋯ \frac{\partial {\overset{d}{true}}_{c}}{\partial c_{d N d}})

. The complete derivatives are computed with the chain rule:

\frac{d {\overset{d}{true}}_{c}}{d x_{1}} = \frac{d {\overset{c}{true}}_{d}}{d x_{1}} \frac{\partial {\overset{d}{true}}_{c}}{\partial {\overset{c}{true}}_{d}}; \frac{d {\overset{d}{true}}_{c}}{d x_{2}} = \frac{d {\overset{c}{true}}_{d}}{d x_{2}} \frac{\partial {\overset{d}{true}}_{c}}{\partial {\overset{c}{true}}_{d}}; \frac{d {\overset{d}{true}}_{c}}{d y_{1}} = \frac{d {\overset{c}{true}}_{d}}{d y_{1}} \frac{\partial {\overset{d}{true}}_{c}}{\partial {\overset{c}{true}}_{d}}; \frac{d {\overset{d}{true}}_{c}}{d y_{2}} = \frac{d {\overset{c}{true}}_{d}}{d y_{2}} \partial true...

…”

Section: Gradient‐based Optimizationmentioning

confidence: 99%

“…The gradient of the aggregated constraint (ie, ∇ xdc ), on the other hand, requires an adjoint sensitivity analysis. To ensure the consistency of the sensitivity calculated, we relied on the discretize-then-differentiate adjoint variable method, similarly to Pollini et al 45 Ultimately, the outcome of the adjoint sensitivity analysis is the vector ∇ T c dd c = . The complete derivatives are computed with the chain rule:…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Moreover, it is in this loop that the vector of the dampers' forces is approximated with a fourth‐order Runge‐Kutta approximation. () The inner loop is denoted by the index j . In this loop, the state determination for each element is contained.…”

Section: Governing Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Optimization‐based minimum‐cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers

Pollini

Lavan

2018

Earthq Engng Struct Dyn

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Summary In this paper, we discuss an optimization‐based approach for minimum‐cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers. The proposed approach accounts also for moment‐axial interaction in the structural elements, to consider a more realistic coupling between added dampers and retrofitted structure. The design variables of the problem are the damping coefficients of the dampers. Indirectly, the design involves also the stiffness coefficients of the supporting braces. In the optimization analysis, we minimize a realistic retrofitting cost function with constraints on inter‐story drifts under a suite of ground motion records. The cost function includes costs related to the topological and mechanical properties of the dampers' designs. The structure is modeled with a mixed finite element approach, where the hysteretic behavior is defined at the beams' and columns' cross sections level. We consider damper‐brace elements with a visco‐elastic behavior characterized by the Maxwell model. The dampers' viscous behavior is defined by a fractional power law. Promising results obtained for a two‐story, a nine‐story, and a 20‐story 2‐D frames are presented and discussed.

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A new reduced model of damped moment frame for rapid optimization of viscous damper placement

Akehashi

Takewaki

2022

Japan Architectural Review

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A new model reduction method is presented for moment‐resisting frames with viscous dampers. The proposed method considers (1) the interactive effect of added damping between the horizontal‐vertical directions and (2) the direct effect with regard to the vertical direction different from the conventional static condensation method. When brace‐type dampers are treated, these effects cannot be neglected originally. The proposed method gives a better correspondence of the fundamental eigenmode with that of the non‐reduced moment frame than the static condensation method. In addition, the proposed reduced model can accurately evaluate the maximum interstory drifts of the non‐reduced moment frame. The proposed model reduction method is formulated in the frequency domain. The frequency dependency of the stiffness matrix and the damping matrix of the reduced model is investigated. The influences of the added damping matrix by viscous dampers on the natural circular frequencies, the damping ratios and the participation vectors are also investigated. Finally, it is demonstrated through a numerical example that the displacement‐based optimization of the damper allocation can be accurately and rapidly conducted by using the reduced models throughout the optimization process.

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Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

Cited by 37 publications

References 30 publications

Fail‐safe optimization of viscous dampers for seismic retrofitting

Fail‐safe optimization of viscous dampers for seismic retrofitting

Optimization‐based minimum‐cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers

A new reduced model of damped moment frame for rapid optimization of viscous damper placement

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