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双语推荐：状态转移矩阵

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研究了一类特殊张量及其简单性质。从 Markov 链的转移概率矩阵出发,考虑到多步转移概率矩阵中所存储的信息仅表示从状态 i 经 n 步到达状态 j 的总概率,而无法从中直接读出转移过程途经各状态i 1,i 2,…,im-1的概率,因此提出了可用张量来存储相应的信息,称之为转移过程张量。在此基础上提出了超随机张量的概念,并根据 Chapman-Kolmogorov 方程证明了某些转移过程张量即为超随机张量。此外,研究了超随机张量的一些简单性质。
A special kind of tensor and its simple nature were studied and proved.Since the information stored in n-step transition probability matrix only expresses the total probability from state i to j in ex-actly n steps,and cannot give the probability of going from i to j via the states of i 1 ,i 2 ,…,im-1 ,a con-cept of transition process tensor was proposed to store these probabilities.Moreover,it also gave the definition of super stochastic tensor,according to Chapman-Kolmogorov equations,it was proved that some transition process tensors were super stochastic tensors.Some properties of super stochastic tensor were also studied.

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针对模拟电路运行过程中存在的不确定性,对传统的隐马尔可夫模型(HMM)进行了改进,将模型中满足不变性的状态转移概率矩阵改为时变状态转移概率矩阵,使之更符合实际情况。在状态初期为了防止状态转移概率发生过度更新,设置了更新概率控制因子。采用线性辨别分析(LDA)方法对测量信号进行特征提取,用于HMM的训练和测试,从而实现模拟电路早期故障的识别和诊断。仿真结果表明,改进后的HMM具有更强的故障识别和诊断能力。
Due to the uncertainties that exist in the running of the analog circuits, the traditional Hidden Markov Model (HMM)approach is improved. The state transition probability matrix of the traditional model is replaced by time-varying one that more satisfies the actual situation. An updating control factor is introduced for avoiding the excess updating of the state transition probability in the initial stage of each state. The Linear Discriminant Analysis(LDA)is used to reduce dimensionality and remove redundancy of the voltage feature vectors, which are for HMM’s training and testing in order to achieve recognition and diagnosis of the incipient faults in analog circuit. The experimental results indicate that the improved HMM has better fault recognition capability than the traditional HMM.

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将小波变换与符号时间序列分析相结合,引入工程领域的D-Markov模型,提出了一种用于金融波动变化模式识别和异常检测的方法。波动序列经过离散小波变换,产生小波系数序列,将小波系数序列符号化产生符号时间序列,建立符号时间序列的D-Markov模型,并求状态转移概率矩阵,计算各状态转移概率矩阵的状态概率向量与标准状态转移概率矩阵的状态概率向量之间的欧拉距离,从而得到异常度。基于得到的异常度识别金融波动变化模式,检测异常波动的发生。以上证综指的5分钟序列为样本实证分析,对该方法的可行性和有效性进行了验证。
Through the introduction of D -Markov model in the field of engineering , combined with the wavelet transform and symbolic time series analysis , a method of financial volatility pattern recognition and anomaly detection was put forward . Wavelet coefficient sequence was generated from the discrete wavelet transform of volatility series .Then, the D-Markov model of symbolic time series , which was the wavelet coefficient sequence after symbolization , was build to get the state transition prob-ability matrix.Subsequently , anomaly measure as the standard Euclidean distance between state probability vectors of states tran -sition probability matrixes and state probability vector under standard volatility series was computed .Financial volatility pattern was recognized and abnormal volatility was detected based on the anomaly measure .With high frequency data whose sampling in-terval was 5 minutes from Shanghai Stock Exchange Composite Index , the feasibility and validity of this method

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在不确定规划领域中，不确定状态转移系统求规划解常常会搜索大量无用的状态和动作，造成冗余计算。获得不确定状态转移系统的状态可达关系可以避免无用搜索、减少冗余计算，为系统提供引导信息。以非循环可达关系为基础，定义矩阵的计算规则，使用系统的邻接矩阵来计算可达矩阵。同时首次提出了循环可达关系的分类、二可达关系等，并设计了求循环可达关系的算法，且以实例证明了算法的有效性和正确性。在不确定规划中获得状态之间的可达性关系，在求规划解的过程中可以删除大量无用的状态动作序偶，降低问题规模。提高求解规划问题的效率。
It is frequent to search a lot of useless states and actions which can result in redundant calculations in solving planning problems over a non-deterministic state-transition system in non-determinate plan field. Getting state accessibility relation for the nondeterministic state-transition system can avoid useless searching, reduce redundant calculations and create a guided information for the nondeterministic state-transition system. Based on acyclic reachability relation , this paper defined the calculation rules of matrix multiplication, classification of circular reachability relation and two-reachability relation. It aslo presented the method to get circular reachability relation and designed an algorithm for this. The example proves the validity and correctness of the algorithm. If the non-determinate plan has the information of state accessibility, it can delete useless states and actions to reduce the size of the problem and improve solution efficiency of solving planning prob

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研究一类不完全转移率信息的Markov跳变奇异系统的Η∞控制问题，提出连续Markov跳变奇异系统的新型有界实引理，并将其推广到不完全转移率条件。进一步设计Η∞状态反馈控制器，使得闭环系统在转移率部分未知的条件下随机可容许，且满足Η∞性能γ。所得结论涵盖了奇异矩阵模态依赖情形，且表示为严格线性矩阵不等式形式，利于工程实现。最后，通过仿真算例表明了所提出方法的有效性和优越性。
The Η∞ control problem of Markov jump singular systems with incomplete transition rates is discussed. A new bounded real lemma for continuous time Markov jump singular systems is derived and then expanded to systems with partial transition rates. Moreover, an Η∞controller is designed to make sure that the closed-loop systems are admissible and satisfy Η∞criteria. The given method also covers the systems with the mode-dependent singular matrix and the controller is designed in terms of a set of strict linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness and advantages of the proposed method.

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目前文本水印算法多基于文本外在特征,很少利用文本内容上的内在关联性,通过对文本句子的主语和宾语进行指代冗余分析,构造用于嵌入水印的指代冗余矩阵,再根据水印信息和矩阵编码规则确定指代冗余矩阵修改位置,利用实体状态编码和状态转移操作修改原文本完成水印嵌入。该算法可以抵抗格式变换、同义词替换等攻击,具有较低的文本修改率和较好的鲁棒性。
Most of the current text watermarking algorithms are based on external features of text, but sel-dom the internal relationship of text content is used . This paper constructs the coreference redundancy ma-trix as the direct carrier by analyzing the coreference redundancy of the sentences’ subjects and objects in the text, locates the coreference redundancy matrix elements which need to be modified according to the watermarking information and matrix coding rules, then revises the original text based on the entity status coding and state transfer operations. This algorithm can resist the attacks of the format changing, synonym substitution and so on with a lower modification rate and better robustness.

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针对椭圆轨道误差传播问题,提出了一种基于T-H方程状态转移矩阵的初始误差传播特性分析方法。首先将空间目标真实状态和预报状态对应于一"实"一"虚"两个近距离空间目标,把预报误差看作"虚"目标相对"实"目标的相对运动,利用空间目标近距离相对运动理论来研究预报误差的特性。然后引入T-H方程状态转移矩阵分析初始误差的传播,得到了各个方向误差传播的规律。最后进行仿真验证,分别使用蒙特卡洛法和文中方法计算了典型椭圆轨道的误差传播,并与STK高精度轨道预报模型(HPOP)进行对比,得到结果的相对误差大都在2%以内,并与理论分析结果的趋势一致,证实了该方法的正确性。
To study the initial error propagation of elliptical orbit , a new method was developed based on the state transition matrix of T-H equation . Firstly , the true state and predict state of one space object can be considered as two objects :a real one and a virtual one . Considering predict error as relative motion between these two objects , the relative motion theory was used to study the characteristic of error propagation . Secondly , the state transition matrix of T-H equation was introduced to analyze the propagation of initial error , with which the trend of error propagation in each direction was obtained . Finally ,a simulation case was designed to validate the correctness of the new method ,and the Monte-Carlo method and the new method were used to calculate error propagation of typical elliptical orbit . The results were compared with the HPOP′s results . Most of the relative error is less than 2% , and is consistent with the trend of the theoretical analysis results .

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海上升压站是风电场电能传输的关键环节。针对海上升压站电气设备的可靠性研究,提出了一种新颖的基于马尔可夫过程的建模方法。首先对升压站电气设备的运行状态进行划分,确定其二状态马尔可夫模型,其次分析基本元件的连接形式,建立其状态转移概率矩阵和转移概率密度矩阵。在此基础上根据马尔可夫方程建立海上风电场升压站内主要设备变压器、母线,电缆等的可靠性模型,并分析了升压站系统的可靠性指标,最后根据某海上风电场的具体数据,结合所建立的升压站电气设备的可靠性模型,对此风电场的升压站系统的可靠性指标进行计算分析。
Offshore substation is the key to offshore wind farm power energy transmission. A novel modeling method based on Markov process was put forward for reliability research of offshore substation electrical equipment. Firstly, operation condition of electrical equipment was divided in order to determine the two state Markov model. Secondly, through analysis of connection form of basic electrical element, its state transition probability matrix and a transition probability density matrix were established. The reliability model of major offshore wind farm substation equipment such as transformers, bus-bar, and cable was established based on Markov equation. The reliability index of the offshore wind farm substation systems was analyzed. Finally, on the basis of some offshore wind farm specific data, combining with the reliability model, the reliability index of the offshore wind farm substation system was analyzed.

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为了量化特高压直流（UHVDC）系统可靠性及其参数灵敏度，提出了可靠性分层等值模型和改进频率和持续时间（F&D）算法。基于UHVDC系统结构和运行特点，计及多容量水平、换流变压器接线形式和单端整体备用模式，将其划分若干个子系统，分别建立状态空间，逐层向上等值，得到整个系统状态空间。传统F&D法需人工查找和计算等值转移频率后才可计算出等值转移率，易出错且计算量随着状态空间维数增加。基于矩阵描述的改进F&D算法，可直接建立等值前后转移率矩阵关系，以及系统可靠性指标对底层元件可靠性参数的灵敏度分解关系。算例分析结果表明，所提模型和算法能够定量评估UHVDC系统可靠性，明确了影响UHVDC可靠性的关键参数和薄弱环节，证实了方法的可行性与有效性。
To quantify reliability and parametric sensitivity of the ultra HVDC (UHVDC) system, hierarchical models for reliability equivalent and improved F&D method are newly proposed. Based on the system configuration and the operation characteristics, multiple capacity levels, transformer winding connections, and single station sharing spare are considered. The UHVDC system is classified to several sub-systems, whose state spaces are derived and combined to yield the whole state space. The traditional frequency and duration (F&D) method necessitates manual search and calculating transition frequency to acquire transition rate, which is fallible, and the calculation efforts increases with the states. Improved F&D method based on matrix description yields relation of the transition matrices before and after equivalence. Sensitivity between system reliability indices and components’ reliability parameters is finally derived. Numerical results show that the proposed model and algorithm

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给出了一种交互多模型（interacting multiple model，IMM）算法中 Markov 转移概率矩阵在线修正的方法，并将平方根容积卡尔曼滤波器（square-root cubature Kalman filter，SRCKF）引入到 IMM 算法中，提出一种时变转移概率的机动目标跟踪 IMM-SRCKF 算法。该算法利用当前量测中包含的模式信息，对 IMM 算法中的转移概率矩阵进行实时递推估计，避免了常规 IMM 算法中转移概率先验确定的困难，提高了模型切换速度和跟踪精度；同时，SRCKF 以目标状态协方差的平方根进行迭代更新，确保了滤波过程中协方差矩阵的对称性和半正定性，改善了数值精度和稳定性。仿真实验结果表明，该算法对机动目标的跟踪性能优于常规的 IMM 及 IMM-CKF算法。
An on-line updating method of Markov transition probability for the interacting multiple model (IMM)algorithm is proposed,and the square-root cubature Kalman filter(SRCKF)is introduced into IMM,so a novel time-varying Markov transition IMM-SRCKF algorithm is obtained.Using real-time recursive estimation method based on the system mode information implicit in the current measurements,the proposed algorithm ef-fectively avoids the problem of prior determination of the Markov transition probability matrix in traditional IMM.Furthermore,SRCKF propagates the square root of the covariance in filter interaction so that it guaran-tees the symmetry and positive semi-definiteness of the covariance matrix and greatly improves the numerical stability and numerical accuracy.Simulation results show that the proposed algorithm has better tracking per-formance and higher efficiency compared with the conventional IMM and IMM-CKF.

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