Oltean Gabriel, Ivanciu Laura-Nicoleta
Department of Bases of Electronics, Technical University of Cluj-Napoca, Romania.
PLoS One. 2016 Jan 8;11(1):e0146602. doi: 10.1371/journal.pone.0146602. eCollection 2016.
The design and verification of complex electronic systems, especially the analog and mixed-signal ones, prove to be extremely time consuming tasks, if only circuit-level simulations are involved. A significant amount of time can be saved if a cost effective solution is used for the extensive analysis of the system, under all conceivable conditions. This paper proposes a data-driven method to build fast to evaluate, but also accurate metamodels capable of generating not-yet simulated waveforms as a function of different combinations of the parameters of the system. The necessary data are obtained by early-stage simulation of an electronic control system from the automotive industry. The metamodel development is based on three key elements: a wavelet transform for waveform characterization, a genetic algorithm optimization to detect the optimal wavelet transform and to identify the most relevant decomposition coefficients, and an artificial neuronal network to derive the relevant coefficients of the wavelet transform for any new parameters combination. The resulted metamodels for three different waveform families are fully reliable. They satisfy the required key points: high accuracy (a maximum mean squared error of 7.1x10-5 for the unity-based normalized waveforms), efficiency (fully affordable computational effort for metamodel build-up: maximum 18 minutes on a general purpose computer), and simplicity (less than 1 second for running the metamodel, the user only provides the parameters combination). The metamodels can be used for very efficient generation of new waveforms, for any possible combination of dependent parameters, offering the possibility to explore the entire design space. A wide range of possibilities becomes achievable for the user, such as: all design corners can be analyzed, possible worst-case situations can be investigated, extreme values of waveforms can be discovered, sensitivity analyses can be performed (the influence of each parameter on the output waveform).
事实证明，如果仅涉及电路级仿真，那么复杂电子系统（尤其是模拟和混合信号系统）的设计和验证将是极其耗时的任务。如果采用一种经济高效的解决方案来在所有可想象的条件下对系统进行广泛分析，那么可以节省大量时间。本文提出了一种数据驱动的方法，用于构建快速评估且准确的元模型，该元模型能够根据系统参数的不同组合生成尚未模拟的波形。必要的数据通过对汽车行业的电子控制系统进行早期仿真获得。元模型的开发基于三个关键要素：用于波形表征的小波变换、用于检测最优小波变换并识别最相关分解系数的遗传算法优化，以及用于针对任何新的参数组合推导小波变换相关系数的人工神经网络。针对三种不同波形族生成的元模型完全可靠。它们满足所需的关键点：高精度（基于单位归一化波形的最大均方误差为7.1×10⁻⁵）、高效性（构建元模型的计算量完全可承受：在通用计算机上最多18分钟）以及简单性（运行元模型不到1秒，用户只需提供参数组合）。这些元模型可用于非常高效地生成新波形，针对相关参数的任何可能组合，从而提供探索整个设计空间的可能性。用户可以实现广泛的可能性，例如：可以分析所有设计角落、可以研究可能的最坏情况、可以发现波形的极值、可以进行敏感性分析（每个参数对输出波形的影响）。
