We see some xi's from a Bernoulli distribution.

我努利分布中看到了一些xi。

That’s called the kinetic energy density, and it’s the second term of Bernoulli’s equation.

这就是所谓动能密度， 它是努利方程第二。

The mean of this Bernoulli distribution is going to be P2.

这个努利分布均值将是 P2。

The first term in Bernoulli's equation takes that energy, and divides it by volume.

努利方程第一是 能量除以体。

That's called the kinetic energy density, and it's the second term of Bernoulli's equation.

这称为动能密度， 它是努利方程第二。

The results showed that the Euler-Bernoulli model underestimates deformation but overestimates internal forces of tunnels.

结果表明，Euler-Bernoulli 模型低估了隧道变形，但高估了隧道内力。

Because the Euler-Bernoulli beam regards the shearing stiffness as an infinite value.

因为 Euler-Bernoulli 梁将剪切刚度视为无限值。

The key is stability, and the essence is using aerodynamics, which is fundamentally based on Bernoulli's principle.

关键是稳定性， 而本质是使用空气动力学，这根本上是基于努利原理。

And then the variance of this Bernoulli distribution is going to be these two proportions multiplied.

然后这个努利分布方差就是这两个比例。

Therefore, the Euler-Bernoulli beam model has an enormous limitation in reflecting the dislocation deformation between adjacent rings.

因此，Euler-Bernoulli 梁模型在反映相邻环之间位错变形方面存在巨大局限性。

Now with this definition of this-- and this is the most general definition of a Bernoulli Distribution.

现在有了这个定义——这是努利分布最一般定义。

The segmental lining ring was considered as a Euler-Bernoulli model, yet the shearing dislocation of segmental ring was excluded.

将节段衬环视为 Euler-Bernoulli 模型，但排除了节段环剪切位错。

Nevertheless, scholars noticed that the Euler-Bernoulli model failed to indicate the dislocation between rings, while it widely occurred in in-service shield tunnels.

尽管如此，学者注意到 Euler-Bernoulli 模型未能指示环之间位错，而它广泛发生在服役盾构隧道中。

The existing tunnel is equivalent to a continuous Euler–Bernoulli beam placed on a Pasternak foundation.

现有隧道相当于放置在 Pasternak 基础上连续 Euler-Bernoulli 梁。

A Euler–Bernoulli beam with a Pasternak foundation was used as a simplified model for tunnel stress analysis.

使用带有 Pasternak 基础 Euler-Bernoulli 梁作为隧道应力分析简化模型。

To figure out really the formulas for the mean and the variance of a Bernoulli Distribution if we don't have the actual numbers.

如果我没有实际数字，要真正找出努利分布均值和方差公式。

A Euler–Bernoulli beam on a Pasternak foundation was used as a simplified model to analyze the stress of the existing tunnel.

使用 Pasternak 基础上 Euler-Bernoulli 梁作为简化模型来分析现有隧道应力。

In the method proposed in this paper, Euler–Bernoulli beams are used to simulate the bending deformation of existing tunnels.

在本文中提出方法中，使用 Euler-Bernoulli 梁来模拟现有隧道弯曲变形。

And then we'll come up with general formulas for the mean and variance and standard deviation of this distribution, which is actually called the Bernoulli Distribution.

然后我会得出这个分布均值、方差和标准差通用公式，这实际上被称为努利分布。

In initial studies, the tunnel model in the LECM was conceptualized as a longitudinal continuous Euler-Bernoulli beam, as its simple computation and flexibility in complex analysis.

在初步研究中，LECM 中隧道模型被概念化为纵向连续 Euler-Bernoulli 梁，因为它计算简单，在复杂分析中具有灵活性。