快速双非凸回归算法及其电力数据预测应用

为适应产能输出、运营效益等电力数据预测应用，文中提出一种快速双非凸回归(double nonconvex regression，DNR)预测算法。首先，将经典稀疏编码分类技术解释为预测回归模型，并划分为训练阶段和测试阶段，使之适合标量预测应用；其次，针对经典Lasso模型存在的稀疏性不足以及噪声拟合单一问题，该算法通过l_p范数约束逼近原始稀疏编码问题的误差重构项和系数正则项，具有更为灵活的模型形式和应用范围。最后，通过交替方向乘子框架实现了重构系数的优化升级策略。为确保ADMM优化子问题具有快速解，提出一种改进的迭代阈值规则用于更新非凸l_p约束项，解决了原始算法陷入的局部最优问题。在电力企业实际运行产出和运营指标数据上的实验结果表明，DNR在预测效果和预测效率上均优于经典的支持向量机、BP神经网络以及非凸约束预测方法。

Fast double nonconvex regression algorithm for forecast of electric power data

In this paper, we propose a new forecasting algorithm called double nonconvex regression (DNR) for the fast forecast of electricity power data such as the outputs of production ability and operational benefit. First, we reinterpret the typical sparse coding classification method as a regression model for forecasting, and further divide the model into training and testing phases to fit scalar-quantity forecasts. Next, we transform the constraints of representation residuals and coefficient regularization into a nonconvex l_p norm for better approximation and broader application. Lastly, we adopt the alternating direction method of multipliers algorithm to optimize the formulated forecast problem. To achieve a fast update rule for l_p norm constrained subproblems, we propose a new iterative threshold method that avoids the local minimum issue. Compared with typical methods such as the SVM, BP neural network, and nonconvex regularization methods, the proposed algorithm achieves surprisingly good experimental results for electricity power data.