Tomographic Image Reconstruction Based on Minimization of Symmetrized Kullback-Leibler Divergence

Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation. We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance.

Discrete Topology Optimization of Structures Without Uncertainty

The topology of a structure is defined by its genus or number of handles. When the topology of a structure is optimized, its topology might be changed if the material state of a design cell is switched from solid to void or vice versa. In discrete topology optimization, each design cell is either solid or void and there is no topology uncertainty from any grey design cell. Point connection might cause topology uncertainty and is eradicated when hybrid discretization model is used for discrete topology optimization. However, the topology solution of an optimized structure might be uncertain when its design domain is discretized differently, which is commonly called mesh dependence problem. In this paper, the degree of genus based topology optimization strategy is introduced to circumvent this topology uncertainty. With this strategy, the genus of an optimized structure is constrained during its topology optimization process. There is no topology uncertainty even if different design domain discretizations are used. The introduced strategy is used for discrete topology optimization of structures that have multiple loading points in this paper. The presented discrete topology optimization procedure is demonstrated by examples with different degrees of genus and loading conditions.

The Uncertainty Elimination in Discrete Topology Optimization of Compliant Mechanisms

Topology uncertainty leads to different topology solutions and makes topology optimization ambiguous. Point connection and grey cell might cause topology uncertainty. They are both eradicated when hybrid discretization model is used for discrete topology optimization. A common topology uncertainty in the current discrete topology optimization stems from mesh dependence. The topology solution of an optimized compliant mechanism might be uncertain when its design domain is discretized differently. To eliminate topology uncertainty from mesh dependence, the genus based topology optimization strategy is introduced in this paper. The topology of a compliant mechanism is defined by its genus which is the number of holes in the compliant mechanism. With this strategy, the genus of an optimized compliant mechanism is actively controlled during its topology optimization process. There is no topology uncertainty when this strategy is incorporated into discrete topology optimization. The introduced topology optimization strategy is demonstrated by examples with different degrees of genus.

The Discrete Topology Optimization of Structures Using the Improved Hybrid Discretization Model

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty caused by any intermediate material state. In this paper, the improved hybrid discretization model is introduced for the discrete topology optimization of structures. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. The dangling and redundant solid design cells are completely eliminated from topology solutions in the improved hybrid discretization model to avoid sharp protrusions. The local stress constraint is directly imposed on each triangular analysis cell to make the designed structure safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. The presented discrete topology optimization procedure is illustrated by two topology optimization examples of structures.

The Improved Hybrid Discretization Model for the Discrete Topology Optimization of Compliant Mechanisms

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty problem caused by any intermediate material state. In this paper, the improved hybrid discretization model is introduced for the discrete topology optimization of compliant mechanisms. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into triangular analysis cells. The dangling and redundant solid design cells are removed from topology solutions in the improved hybrid discretization model to promote the material utilization. To make the designed compliant mechanisms safe, the local stress constraint is directly imposed on each triangular analysis cell. To circumvent the geometrical bias against the vertical design cells, the binary bit-array genetic algorithm is used to search for the optimal topology. Two topology optimization examples of compliant mechanisms are solved based on the proposed improved hybrid discretization model to verify its effectiveness.