以下为句子列表：
英文: Analytical solutions for plates with various boundary conditions were developed using the state space approach.
中文: 采用状态空间法得到了各种边界条件组合条件下板的解析解。
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英文: By means of the state space model of variations propagation, the objective function was built and genetic algorithm was applied for the optimization of sensors' coordinates.
中文: 该方法利用薄板装配偏差流传递的状态空间模型确定优化设计的目标函数，采用遗传算法实现测点在多工位间坐标位置的优化设计。
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英文: Keywords: VBARX, system identification, state space model, modal parameters.
中文: 关键词：VBARX、系统识别、状态空间、模态参数。
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英文: The six methods are as follows: the supperposition method, the state space method, the complex mode method, the direct integral method, the numerical method for solving the initial-value problem of first-order ordinary differential coupled equations with
中文: 这六种方法是：振型叠加法、状态空间法、复模态法、直接积分法、一阶常微分方程组初值问题的数值解法和时域有限元法。
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英文: To solve the problem that the PH distribution proposed changes the state space of system, the value iteration algorithm for the semi-Markov decision process is improved to get the optimal inspection and maintenance policy.
中文: 将位相型(PH)分布引入模型后，决策过程的状态空间发生变化，为了获得适用于原有模型假设的检测与维修优化策略，提出了一种改进的值迭代算法。
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