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"Ohsaki, Makoto"
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Sequential mixture of Gaussian processes and saddlepoint approximation for reliability-based design optimization of structures
This paper presents an efficient optimization procedure for solving the reliability-based design optimization (RBDO) problem of structures under aleatory uncertainty in material properties and external loads. To reduce the number of structural analysis calls during the optimization process, mixture models of Gaussian processes (MGPs) are constructed for prediction of structural responses. The MGP is used to expand the application of the Gaussian process model (GPM) to large training sets for well covering the input variable space, significantly reducing the training time, and improving the overall accuracy of the regression models. A large training set of the input variables and associated structural responses is first generated and split into independent subsets of similar training samples using the Gaussian mixture model clustering method. The GPM for each subset is then developed to produce a set of independent GPMs that together define the MGP as their weighted average. The weight vector computed for a specified input variable contains the probability that the input variable belongs to the projection of each subset onto the input variable space. To calculate the failure probabilities and their inverse values required during the process of solving the RBDO problem, a novel saddlepoint approximation is proposed based on the first three cumulants of random variables. The original RBDO problem is replaced by a sequential deterministic optimization (SDO) problem in which the MGPs serve as surrogates for the limit-state functions in probabilistic constraints of the RBDO problem. The SDO problem is strategically solved for exploring a promising region that may contain the optimal solution, improving the accuracy of the MGPs in that region, and producing a reliable solution. Two design examples of a truss and a steel frame demonstrate the efficiency of the proposed optimization procedure.
Journal Article
Reinforcement learning for optimum design of a plane frame under static loads
A new method is presented for optimum cross-sectional design of planar frame structures combining reinforcement learning (RL) and metaheuristics. The method starts from RL jointly using artificial neural network so that the action taker, or the agent, can choose a proper action on which members to be increased, reduced or kept their size. The size of the neural network is compressed into small numbers of inputs and outputs utilizing story-wise decomposition of the frame. The trained agent is used in the process of generating a neighborhood solution during optimization with simulated annealing (SA) and particle swarm optimization (PSO). Because the proposed method is able to explore the solution space efficiently, better optimal solutions can be found with less computational cost compared with those obtained solely by metaheuristics. Utilization of RL agent also leads to high-quality optimal solutions regardless of variation of parameters of SA and PSO or initial solution. Furthermore, once the agent is trained, it can be applied to optimization of other frames with different numbers of stories and spans.
Journal Article
Geometry and topology optimization of plane frames for compliance minimization using force density method for geometry model
A new method is proposed for simultaneous optimization of shape, topology and cross section of plane frames. Compliance against specified loads is minimized under constraint on structural volume. Difficulties caused by the melting nodes can be alleviated to some extent by introducing force density as design variables for defining the geometry, where the side constraints are assigned for force density to indirectly avoid the existence of extremely short members. Force density method is applied to an auxiliary cable-net model with different boundary and loading conditions so that the regularity of force density matrix is ensured by positive force densities. Sensitivity coefficients of the objective and constraint functions with respect to the design variables are also explicitly calculated. After the optimal geometry of the frame is obtained, the topology is further improved by removing the thin members and combining closely spaced nodes. It is demonstrated in the numerical examples of three types of frames that rational geometry and topology can be achieved using the proposed method, and the effect of bending moment on the optimal solution is also discussed.
Journal Article
Correction to: Gaussian mixture model for robust design optimization of planar steel frames
A Correction to this paper has been published:
https://doi.org/10.1007/s00158-020-02789-9
Journal Article
Gaussian mixture model for robust design optimization of planar steel frames
A new method is presented for an application of the Gaussian mixture model (GMM) to a multi-objective robust design optimization (RDO) of planar steel frame structures under aleatory (stochastic) uncertainty in material properties, external loads, and discrete design variables. Uncertainty in the discrete design variables is modeled in the wide range between the smallest and largest values in the catalog of the cross-sectional areas. A weighted sum of Gaussians is statistically trained based on the sampled training data to capture an underlying joint probability distribution function (PDF) of random input variables and the corresponding structural response. A simple regression function for predicting the structural response can be found by extracting the information from a conditional PDF, which is directly derived from the captured joint PDF. A multi-objective RDO problem is formulated with three objective functions, namely, the total mass of the structure, and the mean and variance values of the maximum inter-story drift under some constraints on design strength and serviceability requirements. The optimization problem is solved using a multi-objective genetic algorithm utilizing the trained GMM for calculating the statistical values of objective and constraint functions to obtain Pareto-optimal solutions. Since the three objective functions are highly conflicting, the best trade-off solution is desired and found from the obtained Pareto-optimal solutions by performing fuzzy-based compromise programming. The robustness and feasibility of the proposed method for finding the RDO of planar steel frame structures with discrete variables are demonstrated through two design examples.
Journal Article
Multiobjective robust shape and topology optimization of plane frames using order statistics
This paper presents a worst-case approach to robust optimization of plane frame structures under variation in uncertain parameters. The optimization procedure is first implemented without considering uncertainty, resulting in an optimal structure that may be unstable without bending stiffness. Based on such optimal solution, we then take variation in uncertain parameters into consideration and estimate the quantile response or trimmed mean of order statistics, where the quantile response is used as a relaxation of worst value of structural response. In order to obtain robust optimal solutions at various robustness levels, a multiobjective optimization problem is formulated and solved to simultaneously minimize the several order statistics or trimmed means with different orders. It is demonstrated in the numerical examples that the optimal distribution of cross-sectional areas of elements vary with the change of robustness level, and the convergence by using trimmed mean as estimation of quantile response is better than that of the simple order statistics.
Journal Article
Deep reinforcement learning-based critical element identification and demolition planning of frame structures
This paper proposes a framework for critical element identification and demolition planning of frame structures. Innovative quantitative indices considering the severity of the ultimate collapse scenario are proposed using reinforcement learning and graph embedding. The action is defined as removing an element, and the state is described by integrating the joint and element features into a comprehensive feature vector for each element. By establishing the policy network, the agent outputs the Q value for each action after observing the state. Through numerical examples, it is confirmed that the trained agent can provide an accurate estimation of the Q values, and handle problems with different action spaces owing to utilization of graph embedding. Besides, different behaviors can be learned by varying hyperparameters in the reward function. By comparing the proposed method and the conventional sensitivity index-based methods, it is demonstrated that the computational cost is considerably reduced because the reinforcement learning model is trained offline. Besides, it is proved that the Q values produced by the reinforcement learning agent can make up for the deficiencies of existing indices, and can be directly used as the quantitative index for the decision-making for determining the most expected collapse scenario, i.e., the sequence of element removals.
Journal Article
A design tool for globally developable discrete architectural surfaces using Ricci flow
This paper presents an approach for the design of discrete architectural surfaces that are globally developable; that is, having zero Gaussian curvature at every interior node. This kind of architectural surface is particularly suitable for fast fabrication at a low cost, since their curved geometry can be developed into a plane. This highly non‐linear design problem is broken down into two sub‐problems: (1) find the member lengths of a triangular mesh that lead to zero Gaussian curvature, by employing the discrete surface Ricci flow developed in the field of discrete differential geometry; (2) realize the final geometry by solving an optimization problem, subject to the constraints on member lengths as well as the given boundary. It is demonstrated by the numerical examples that both of these two sub‐problems can be solved with small computational costs and sufficient accuracy. In addition, the Ricci flow algorithm has an attractive feature—the final design is conformal to the initial one. Conformality could result in higher structural performance, because the shape of each panel is kept as close as possible to its initial design, suppressing possible distortion of the panels. This paper further presents an improved circle packing scheme implemented in the discrete surface Ricci flow to achieve better conformality, while keeping its simplicity in algorithm implementation as in the existing Thurston's scheme .
Journal Article
Investigation of equivalent correlation coefficient based on the Mehler’s formula
Purpose
Conversion of the correlated random variables into independent variables, especially into independent standard normal variables, is the common technology for estimating the statistical moments of response and evaluating reliability of random system, in which calculating the equivalent correlation coefficient is an important component. The purpose of this paper is to investigate an accurate, efficient and easy to implement estimation method for the equivalent correlation coefficient of various incomplete probability systems.
Design/methodology/approach
First, an approach based on the Mehler’s formula for evaluating the equivalent correlation coefficient is introduced, then, by combining with polynomial normal transformations, this approach is improved to be valid for various incomplete probability systems, which is named as the direct method. Next, with the convenient linear reference variables for eight frequently used random variables and the approximation of the Rosenblatt transformation introduced, a further improved implementation without iteration process is developed, which is named as the simplified method. Finally, several examples are investigated to verify the characteristics of the proposed methods.
Findings
The results of the examples in this paper show that both the proposed two methods are of high accuracy, by comparison, the proposed simplified method is more effective and convenient.
Originality/value
Based on the Mehler’s formula, two practical implementations for evaluating the equivalent correlation coefficient are proposed, which are accurate, efficient, easy to implement and valid for various incomplete probability systems.
Journal Article