Floating structures oscillate in waves, where these wave-induced motions may be critical for various marine operations. An important consideration is thereby given to the sea states at the planning and operating stages for an offshore project. The most important information extracted from a sea state is the directional wave spectrum, indicating wave direction, significant wave height, and wave spectrum peak period. Among several available methods of measuring and estimating the directional wave spectrum, the wave buoy analogy technique based on vessel motion responses is an in situ and almost real-time solution without extra costs of devices. If the forms of the wave spectra are not predefined in the estimation, the method is called a nonparametric approach. Its most remarkable advantage is the flexible form, but the smoothness should be regulated. After the discrete Fourier transform has been applied to the measured vessel motions, smoothing is necessary. However, this process results in disturbed vessel cross-spectra and a lowpass characteristic of the windowing function. This paper presents a nonparametric approach for directional wave spectrum estimation based on vessel motion responses. It introduces novel smoothness constraints using Bézier surface and includes a more robust estimate using L1 optimization. Both techniques are applied to the wave buoy analogy for the first time. Numerical simulations are conducted to verify the proposed algorithm.

浮动结构在波浪中振荡，这些波浪引起的运动对于各种海上作业可能至关重要。因此，在海上项目的计划和运营阶段，要对海州进行重要考虑。从海况中提取的最重要的信息是定向波谱，指示波向，有效波高和波谱峰值周期。在测量和估计方向波谱的几种可用方法中，基于船舶运动响应的浮标类比技术是一种现场且几乎实时的解决方案，无需额外的设备成本。如果在估算中未预定义波谱的形式，则该方法称为非参数方法。它最显着的优点是柔性形式，但应调节平滑度。在将离散傅里叶变换应用于所测得的船只运动之后，必须进行平滑处理。但是，此过程会导致血管互谱受到干扰，并导致开窗功能的低通特性。本文提出了一种基于船舶运动响应的定向波谱估计的非参数方法。它使用Bézier曲面引入了新颖的平滑度约束，并使用L1优化包括了更可靠的估计。两种技术都首次应用于浮标类比。进行了数值模拟，以验证所提出的算法。本文提出了一种基于船舶运动响应的定向波谱估计的非参数方法。它引入了使用Bézier曲面的新颖的平滑度约束，并包括了使用L1优化的更鲁棒的估计。两种技术都首次应用于浮标类比。进行了数值模拟，以验证所提出的算法。本文提出了一种基于船舶运动响应的定向波谱估计的非参数方法。它使用Bézier曲面引入了新颖的平滑度约束，并使用L1优化包括了更可靠的估计。两种技术都首次应用于浮标类比。进行了数值模拟，以验证所提出的算法。