基于灰色系统理论的滑行艇运动姿态预报研究
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摘要
滑行艇具有机动灵活、造价低、日常营运费用省等优点，因而得到了广泛应用。为了能够设计出有效的自动控制系统，需要建立预报模型对滑行艇的运动姿态或运动趋势进行实时的、精确的预报。滑行艇在波浪上航行时，实际海浪情况的复杂性造成了滑行艇运动的复杂性，其运动常常是几种简单运动的叠加，即各个自由度之间存在着一定程度上的耦合影响。这使得对滑行艇的运动姿态进行精确预报具有相当的难度。同时由于滑行艇的运动姿态具有高速性和很强的随机性等特点，利用大量的原始数据来建立其运动预报的模型将是不现实的，并且也很难取得良好的效果。根据滑行艇运动的特点，结合灰色系统理论对原始数据要求不高、预报精度高等优点，本文提出利用灰色系统理论中的MGM(1,N)模型对滑行艇的运动姿态进行预报。
首先，分析了滑行艇运动系统具有的灰色特性，其中包括各个自由度之间关系，以及滑行艇运动与海浪等影响因素的灰色特性，为灰色系统理论在滑行艇运动姿态预报中的应用打下了基础。另外，MGM(1,N)模型自提出之后，在许多领域都有了成功的应用，本文针对MGM(1,N)模型理论体系进行了研究，并给出了MGM(1,N)模型的基本形式、参数矩阵的定义及定理的证明，为模型的后续理论研究奠定了基础。
其次，针对滑行艇运动姿态的特点和灰色系统理论新信息优先的原理，提出了新增一组数据和新增一批数据之后，MGM(1,N)模型参数矩阵的计算方法。由于滑行艇的运动姿态具有高速性和很强的随机性等特点，一次性的利用原始数据建立MGM(1,N)模型对滑行艇运动姿态进行预报的精度和时间都是有限的。因此，为延长预报时间、提高预报精度，必须不断将新采集的数据和原始数据结合在一起更新所建立的MGM(1,N)模型的参数矩阵。同时由于灰色系统理论的特点如果原始数据过多，预报的效果反而不一定好，因此在引入新的数据的同时还需要剔除较早的一组数据。基于分块矩阵的理论，本文分别提出了在新增一组数据和新增一批数据之后，MGM(1,N)模型参数矩阵估计的递推公式，建立递推MGM(1,N)模型。
再者，将递推MGM(1,N)模型应用于滑行艇的运动姿态预报，并与原始MGM(1,N)模型进行数值分析比较。基于滑行艇模型在水池波浪环境中的运动姿态数据，进行了大量的数值仿真实验，结果表明利用递推MGM(1,N)模型对滑行艇运动姿态进行预报是可行的，能够成功地反映滑行艇运动规律,具有合理、有效的趋势分析与较高的预报精度。
最后，提出通过利用李亚普诺夫稳定性理论对滑行艇运动系统建立的MGM(1,N)模型的参数矩阵进行分析，给出滑行艇运动系统稳定性分析。
Planing craft is widely used because of its advantages such as flexible, low cost, lowroutine maintenance cost. To design an effective automatic control system of planing craft, aprediction model should be built to predict its motion attitude real-timely and precisely.While sailing in wave, the complexity of the actual wave condition the complexity of themotion of the planing craft. The motion usually is the superposition of several kinds ofsimple motion, that is to say, there are coupling influences among the each degree offreedom to a certain extent. This makes it quite difficult to predict the motion attitude ofplaning craft accurately. Meanwhile, because of the characteristics such as high speed andrandom, it is unrealistic to build a model to predict the motion of planing craft by using amass of original data and hard to get a good predictive effect. According to thecharacteristics of the motion of planing craft, and combined with the advantages of greysystem such as not high demand for the original data and high precision for predicting, amethod to predict the motion attitude of planing craft by using the MGM(1,N) model in greysystem theory was proposed by this paper.
Firstly, the grey characteristics of planing craft motion system were analyzed, includingthe relationship among the each degree of freedom, and the grey characteristics of thefactors such as wave that affect the motion of planing craft. This makes a foundation for theapplication of grey system theory in the prediction of planing craft motion. Besides, SinceMGM(1,N) model was proposed, it has been applied in many areas, therefore, this paperresearch on the theoretical system of MGM(1,N) model. The basic form of MGM(1,N)model, the definition of parameter matrix, the proof of the theory are given, which lay agood foundation for the subsequent theory research.
Secondly, according to the characteristics of planing craft motion attitude and thepriority principle of new information in grey system theory, this paper proposes therecurrence formula of MGM(1,N) model’s parameter matrix after a group and a batch ofdata was newly added. Because of the characteristics such as high speed and randomness,the predicting accuracy and time are limited by predicting the motion attitude of planing craft using the huge original data to build a MGM(1,N) model. Therefore, to prolongpredicting time and improve predicting accuracy, the newly acquired data should becombined with the former data to update the parameter matrix of MGM(1,N) model.Simultaneously, because of the characteristic of grey system is that the more original datamay lead to a worse predicting effect, the prior data should be eliminated after the new datais added into the model. Based on the theory of block matrix, this paper proposes therecurrence formula of the parameter matrix of MGM(1,N) model after a group and a batchof data is newly added, named recurrence MGM(1,N) model.
Thirdly, this paper applies recurrence MGM(1,N) model into the prediction of motionattitude of planing craft. Based on a large number of motion attitude data of planing craftsailing in the environment of wave tank is acquired, and the numerical simulation test iscarried out. The results of numerical simulation test show that using recurrence MGM(1,N)model to predict planing motion attitude is feasible and can get a good prediction effect. Sothe method proposed by this paper can reflect the planing craft motion mechanismsuccessfully, and had rational and effective functions of analyzing trend and forecasting.
Finally, the stability analysis method of the motion system of planing craft is proposedby using the Lyapunov stability theory.
首先，分析了滑行艇运动系统具有的灰色特性，其中包括各个自由度之间关系，以及滑行艇运动与海浪等影响因素的灰色特性，为灰色系统理论在滑行艇运动姿态预报中的应用打下了基础。另外，MGM(1,N)模型自提出之后，在许多领域都有了成功的应用，本文针对MGM(1,N)模型理论体系进行了研究，并给出了MGM(1,N)模型的基本形式、参数矩阵的定义及定理的证明，为模型的后续理论研究奠定了基础。
其次，针对滑行艇运动姿态的特点和灰色系统理论新信息优先的原理，提出了新增一组数据和新增一批数据之后，MGM(1,N)模型参数矩阵的计算方法。由于滑行艇的运动姿态具有高速性和很强的随机性等特点，一次性的利用原始数据建立MGM(1,N)模型对滑行艇运动姿态进行预报的精度和时间都是有限的。因此，为延长预报时间、提高预报精度，必须不断将新采集的数据和原始数据结合在一起更新所建立的MGM(1,N)模型的参数矩阵。同时由于灰色系统理论的特点如果原始数据过多，预报的效果反而不一定好，因此在引入新的数据的同时还需要剔除较早的一组数据。基于分块矩阵的理论，本文分别提出了在新增一组数据和新增一批数据之后，MGM(1,N)模型参数矩阵估计的递推公式，建立递推MGM(1,N)模型。
再者，将递推MGM(1,N)模型应用于滑行艇的运动姿态预报，并与原始MGM(1,N)模型进行数值分析比较。基于滑行艇模型在水池波浪环境中的运动姿态数据，进行了大量的数值仿真实验，结果表明利用递推MGM(1,N)模型对滑行艇运动姿态进行预报是可行的，能够成功地反映滑行艇运动规律,具有合理、有效的趋势分析与较高的预报精度。
最后，提出通过利用李亚普诺夫稳定性理论对滑行艇运动系统建立的MGM(1,N)模型的参数矩阵进行分析，给出滑行艇运动系统稳定性分析。
Planing craft is widely used because of its advantages such as flexible, low cost, lowroutine maintenance cost. To design an effective automatic control system of planing craft, aprediction model should be built to predict its motion attitude real-timely and precisely.While sailing in wave, the complexity of the actual wave condition the complexity of themotion of the planing craft. The motion usually is the superposition of several kinds ofsimple motion, that is to say, there are coupling influences among the each degree offreedom to a certain extent. This makes it quite difficult to predict the motion attitude ofplaning craft accurately. Meanwhile, because of the characteristics such as high speed andrandom, it is unrealistic to build a model to predict the motion of planing craft by using amass of original data and hard to get a good predictive effect. According to thecharacteristics of the motion of planing craft, and combined with the advantages of greysystem such as not high demand for the original data and high precision for predicting, amethod to predict the motion attitude of planing craft by using the MGM(1,N) model in greysystem theory was proposed by this paper.
Firstly, the grey characteristics of planing craft motion system were analyzed, includingthe relationship among the each degree of freedom, and the grey characteristics of thefactors such as wave that affect the motion of planing craft. This makes a foundation for theapplication of grey system theory in the prediction of planing craft motion. Besides, SinceMGM(1,N) model was proposed, it has been applied in many areas, therefore, this paperresearch on the theoretical system of MGM(1,N) model. The basic form of MGM(1,N)model, the definition of parameter matrix, the proof of the theory are given, which lay agood foundation for the subsequent theory research.
Secondly, according to the characteristics of planing craft motion attitude and thepriority principle of new information in grey system theory, this paper proposes therecurrence formula of MGM(1,N) model’s parameter matrix after a group and a batch ofdata was newly added. Because of the characteristics such as high speed and randomness,the predicting accuracy and time are limited by predicting the motion attitude of planing craft using the huge original data to build a MGM(1,N) model. Therefore, to prolongpredicting time and improve predicting accuracy, the newly acquired data should becombined with the former data to update the parameter matrix of MGM(1,N) model.Simultaneously, because of the characteristic of grey system is that the more original datamay lead to a worse predicting effect, the prior data should be eliminated after the new datais added into the model. Based on the theory of block matrix, this paper proposes therecurrence formula of the parameter matrix of MGM(1,N) model after a group and a batchof data is newly added, named recurrence MGM(1,N) model.
Thirdly, this paper applies recurrence MGM(1,N) model into the prediction of motionattitude of planing craft. Based on a large number of motion attitude data of planing craftsailing in the environment of wave tank is acquired, and the numerical simulation test iscarried out. The results of numerical simulation test show that using recurrence MGM(1,N)model to predict planing motion attitude is feasible and can get a good prediction effect. Sothe method proposed by this paper can reflect the planing craft motion mechanismsuccessfully, and had rational and effective functions of analyzing trend and forecasting.
Finally, the stability analysis method of the motion system of planing craft is proposedby using the Lyapunov stability theory.
引文
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