In this work, a novel learning-based on-line adaptive shape predictive model is developed to represent the 3D surface of the formed shape after springback in single point incremental forming (SPIF). The model can be updated in each step to predict the forming shapes in future prediction horizons given a new potential tool path, with on-line collected historic geometrical data and their corresponding tool path in previous steps. Furthermore, this model is incorporated into a sequential coupled constrained model predictive control algorithm (MPC), to optimize the potential step-down and step-over sizes in future steps, to minimize the geometric error of the whole formed part in SPIF. Two different geometric shapes, a benchmark truncated cone (with only convex geometric feature) and a non-convex dog-bone (with varying convex and concave feature), are selected for the experimental testing of the new developed on-line adaptive model predictive control algorithm (AMPC). This paper presents the detailed data acquisition and modelling process, on-line feedback control algorithms and experimental validation. The experimental results indicated that the maximum geometric error in the concerned region for the benchmark truncated cone shape and the complex non-convex dog-bone shape can be successfully decreased from above 1.25 mm without control to below 0.75 mm with the current adaptive MPC controller, which cannot be achieved with our previous non-adaptive MPC controller. This is believed to be the first attempt to incorporate a learning-based nonlinear adaptive predictive model with a model predictive controller for tool path optimization in incremental forming. The adaptive model predictive controller (AMPC) demonstrated in this work may provide a powerful tool for geometric accuracy improvement for production of complex geometric shapes in varying forming conditions in incremental sheet forming in the future.

在这项工作中，开发了一种新颖的基于学习的在线自适应形状预测模型，以表示单点增量成形（SPIF）回弹后成形形状的3D表面。可以在每个步骤中更新模型，以在给定新的潜在刀具路径的情况下在未来的预测范围内预测成形形状，并在先前的步骤中使用在线收集的历史几何数据及其对应的刀具路径。此外，此模型已合并到顺序耦合约束模型预测控制算法（MPC）中，以优化未来步骤中的潜在降级和跨步尺寸，以最小化SPIF中整个成型零件的几何误差。两种不同的几何形状，一个基准截头圆锥体（仅具有凸形几何特征）和一个非凸形狗骨（具有变化的凸形和凹形特征），选择用于新开发的在线自适应模型预测控制算法（AMPC）的实验测试。本文介绍了详细的数据采集和建模过程，在线反馈控制算法和实验验证。实验结果表明，使用当前的自适应MPC控制器，基准截头圆锥形状和复杂的非凸狗骨形状在相关区域的最大几何误差可以成功地从1.25 mm以上降低到0.75 mm以下，这是我们以前的非自适应MPC控制器无法实现的。相信这是将基于学习的非线性自适应预测模型与模型预测控制器相结合的首次尝试，该模型预测控制器用于增量成形中的刀具路径优化。