非均匀采样数据系统的辨识及其应用研究
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摘要
非均匀采样数据系统的输入刷新和（或）输出采样呈现不等时间间隔，是一类更为广泛的多率采样数据系统。受到硬件设备的限制、经济条件的制约和环境因素的影响，这类系统在石油、化工、食品、医药等过程工业中普遍存在。然而，由于传统辨识方法和控制理论大多仅适用于单率采样数据系统，目前非均匀采样数据系统的辨识和控制水平仍然十分有限。因此，本文对非均匀采样数据系统的辨识问题进行深入研究，并探讨辨识方法在推理控制和软测量建模中的应用，具有重要的理论意义和实用价值。论文的主要工作包括以下几个方面：
(1)在不同噪声干扰条件下研究了输入非均匀采样数据系统的辨识问题。首先，基于递阶梯度迭代搜索原理，推导了白噪声干扰输入非均匀采样数据系统输出误差模型的梯度迭代辨识算法。该算法的辨识性能优于辅助模型随机梯度算法，但是计算量却远小于最小二乘迭代算法。其次，推导了有色噪声干扰输入非均匀采样数据系统Box-Jenkins模型的基于滤波的递推最小二乘辨识算法。通过对系统模型参数和噪声模型参数进行交互估计，有效降低了算法的计算量并提高了估计精度。
(2)针对有色噪声干扰条件下的输入输出同步非均匀采样数据系统，基于提升技术推导了描述这类系统的Box-Jenkins模型，并提出了相应的辅助模型多新息广义增广随机梯度辨识算法。该算法通过新息扩展，充分利用了可获得的数据信息，能够有效提高辨识性能。另外，考虑到提升状态空间模型涉及因果约束问题，而提升传递函数模型参数过多、结构过于复杂，都不便于输入输出同步非均匀采样数据系统的辨识和控制。通过引入时变后移算子，提出了一种结构简单的新型传递函数模型，并提出了该模型的辅助模型最小二乘辨识算法。
(3)基于快速均匀刷新的输入数据和慢速非均匀采样且具有不确定延迟的输出数据，利用最大期望算法，将不确定延迟看作隐变量，提出了快速单率有限脉冲响应模型参数和不确定延迟的交互估计方法。进一步基于辨识得到的有限脉冲响应模型，分别利用最小二乘算法和最大期望算法，提出了快速单率输出误差模型的两种参数估计方法。仿真例子和实验结果表明，提出的辨识方法能够有效克服不确定延迟对辨识性能的影响，给出高精度的参数估计。
(4)针对输入快速非均匀刷新、输出慢速均匀采样的系统，推导了可测输出与非均匀损失输出采样点上传递函数模型之间的数学关系，利用这一关系和辨识得到的可测输出点的模型参数，对损失输出点的模型参数进行估计；基于估计的模型对下一个非均匀采样点的输出进行预测，根据最小方差原理提出了输入非均匀采样数据系统的推理自适应控制算法。进一步借助于辅助变量，提出了未知有色噪声干扰下非均匀采样数据系统的推理控制方法。
(5)针对一个实际的输出非均匀采样数据系统――直流蒸汽发生器，基于混合建模方法建立了蒸汽含量的软测量模型。首先，根据热量平衡原理推导了该过程的简单机理模型，利用温度、流量等常规过程变量对蒸汽含量进行实时估计；其次，利用蒸汽含量的实验室分析数据对机理模型的输出进行在线偏差补偿，以增强软测量模型的自适应能力；同时，利用预报误差方法优化模型参数和补偿项的加权系数，以获得精度最高的软测量模型；最后，对过程变量进行在线异常值检测和处理，以确保软测量模型在实际运行过程中的可靠性。
The non-uniformly sampled-data (NUSD) systems with irregular sampling intervalsfor the inputs and/or outputs are a class of more general multirate sampled-data systems.Due to hardware limitations, economic considerations and environmental impacts, suchNUSD systems can be widely found in petroleum, chemical, food, medicine and otherprocess industries. However, since traditional identifcation methods and control theoryare designed mainly for single-rate sampled-data systems, research on identifcation andcontrol of the NUSD systems is still relatively sparse. Therefore, this thesis focuses ondevelopment of new identifcation algorithms for the NUSD systems and investigates theirapplications in the inferential control design and the soft sensor development, which hasimportant theoretical signifcance and practical values. The major contribution of thisthesis includes:
(1) Identifcation of the input NUSD systems under diferent noise interferences is stud-ied. First, a gradient-based iterative algorithm is derived for the output error modelof the input NUSD systems with white noise. The proposed algorithm not only hasbetter identifcation performance than the auxiliary model based stochastic gradi-ent algorithm, but also has lower computational cost than the least squares basediterative algorithm. Furthermore, a fltering based recursive least squares algorithmis derived for the Box-Jenkins model of the input NUSD systems with colored noise.The proposed algorithm interactively estimates the parameters of the system modeland the noise model; thus has low computational load and high estimation accuracy.
(2) For the synchronous input-output NUSD systems with colored noises, the Box-Jenkins model is derived based on the lifting technique, and an auxiliary modelbased multi-innovation generalized extended stochastic gradient algorithm is pre-sented for the model identifcation. The proposed algorithm makes full use of theavailable data and improves the identifcation performance via innovation expan-sion. Considering that the lifted state-space model involves causality constraintproblem and the corresponding transfer function model is quite complicated withtoo many parameters, neither one is convenient for identifcation and control ofthe synchronous input-output NUSD systems. Therefore, a novel transfer functionmodel is derived by introducing a time-varying backward shift operator, and anauxiliary based least squares algorithm is developed for its identifcation.
(3) An Expectation-Maximization (EM) based identifcation algorithm is developed forthe output NUSD systems with uncertain sampling delays, where the uncertain delays are considered as the hidden states, and the parameters of the underlyingfast-rate fnite impulse response model are estimated along with the delays. Fur-thermore, two algorithms are proposed to recover the approximated fast-rate outputerror model by using the least square algorithm and the EM algorithm, respectively.The simulation examples and experimental results illustrate that the proposed al-gorithm can overcome the negative impacts of uncertain delays on the identifcationperformance, and provide parameter estimates with high precision.
(4) For the input NUSD systems with fast non-uniformly updated inputs and slowlysampled outputs, the mathematical relationship between the transfer function modelof the sampled outputs and the non-uniform missing outputs is derived. Basedon this relationship and using the identifed model of the sampled outputs, themodels of the missing outputs can be estimated. Then by using the estimatedmodel to predict the output at the next non-uniform sampling instant, an inferentialadaptive control algorithm is proposed for the input NUSD systems according tothe minimum variance criterion. By using the auxiliary variables, the proposedinferential control scheme is further extended to the input NUSD systems disturbedby unknown colored noises.
(5) For a practical output NUSD system, i.e., the once-through steam generator, softsensors based on hybrid modeling technique are developed to predict its steamqualities. First, simplifed frst-principle models are derived according to the en-ergy balance equations, thus the steam qualities can be estimated online throughtemperatures, fows and other process variables. Then, to improve the adaptabilityof the soft sensors, of-line lab analyses of steam qualities are adopted to rectifythe frst-principle model predictions via bias compensation; and to obtain high-performance soft sensors, the predication error method is applied to optimize themodel parameters and the weighting factor in the bias update equation. Further-more, online outlier detection and rejection are considered to ensure the reliabilityof the developed soft sensors.
(1)在不同噪声干扰条件下研究了输入非均匀采样数据系统的辨识问题。首先，基于递阶梯度迭代搜索原理，推导了白噪声干扰输入非均匀采样数据系统输出误差模型的梯度迭代辨识算法。该算法的辨识性能优于辅助模型随机梯度算法，但是计算量却远小于最小二乘迭代算法。其次，推导了有色噪声干扰输入非均匀采样数据系统Box-Jenkins模型的基于滤波的递推最小二乘辨识算法。通过对系统模型参数和噪声模型参数进行交互估计，有效降低了算法的计算量并提高了估计精度。
(2)针对有色噪声干扰条件下的输入输出同步非均匀采样数据系统，基于提升技术推导了描述这类系统的Box-Jenkins模型，并提出了相应的辅助模型多新息广义增广随机梯度辨识算法。该算法通过新息扩展，充分利用了可获得的数据信息，能够有效提高辨识性能。另外，考虑到提升状态空间模型涉及因果约束问题，而提升传递函数模型参数过多、结构过于复杂，都不便于输入输出同步非均匀采样数据系统的辨识和控制。通过引入时变后移算子，提出了一种结构简单的新型传递函数模型，并提出了该模型的辅助模型最小二乘辨识算法。
(3)基于快速均匀刷新的输入数据和慢速非均匀采样且具有不确定延迟的输出数据，利用最大期望算法，将不确定延迟看作隐变量，提出了快速单率有限脉冲响应模型参数和不确定延迟的交互估计方法。进一步基于辨识得到的有限脉冲响应模型，分别利用最小二乘算法和最大期望算法，提出了快速单率输出误差模型的两种参数估计方法。仿真例子和实验结果表明，提出的辨识方法能够有效克服不确定延迟对辨识性能的影响，给出高精度的参数估计。
(4)针对输入快速非均匀刷新、输出慢速均匀采样的系统，推导了可测输出与非均匀损失输出采样点上传递函数模型之间的数学关系，利用这一关系和辨识得到的可测输出点的模型参数，对损失输出点的模型参数进行估计；基于估计的模型对下一个非均匀采样点的输出进行预测，根据最小方差原理提出了输入非均匀采样数据系统的推理自适应控制算法。进一步借助于辅助变量，提出了未知有色噪声干扰下非均匀采样数据系统的推理控制方法。
(5)针对一个实际的输出非均匀采样数据系统――直流蒸汽发生器，基于混合建模方法建立了蒸汽含量的软测量模型。首先，根据热量平衡原理推导了该过程的简单机理模型，利用温度、流量等常规过程变量对蒸汽含量进行实时估计；其次，利用蒸汽含量的实验室分析数据对机理模型的输出进行在线偏差补偿，以增强软测量模型的自适应能力；同时，利用预报误差方法优化模型参数和补偿项的加权系数，以获得精度最高的软测量模型；最后，对过程变量进行在线异常值检测和处理，以确保软测量模型在实际运行过程中的可靠性。
The non-uniformly sampled-data (NUSD) systems with irregular sampling intervalsfor the inputs and/or outputs are a class of more general multirate sampled-data systems.Due to hardware limitations, economic considerations and environmental impacts, suchNUSD systems can be widely found in petroleum, chemical, food, medicine and otherprocess industries. However, since traditional identifcation methods and control theoryare designed mainly for single-rate sampled-data systems, research on identifcation andcontrol of the NUSD systems is still relatively sparse. Therefore, this thesis focuses ondevelopment of new identifcation algorithms for the NUSD systems and investigates theirapplications in the inferential control design and the soft sensor development, which hasimportant theoretical signifcance and practical values. The major contribution of thisthesis includes:
(1) Identifcation of the input NUSD systems under diferent noise interferences is stud-ied. First, a gradient-based iterative algorithm is derived for the output error modelof the input NUSD systems with white noise. The proposed algorithm not only hasbetter identifcation performance than the auxiliary model based stochastic gradi-ent algorithm, but also has lower computational cost than the least squares basediterative algorithm. Furthermore, a fltering based recursive least squares algorithmis derived for the Box-Jenkins model of the input NUSD systems with colored noise.The proposed algorithm interactively estimates the parameters of the system modeland the noise model; thus has low computational load and high estimation accuracy.
(2) For the synchronous input-output NUSD systems with colored noises, the Box-Jenkins model is derived based on the lifting technique, and an auxiliary modelbased multi-innovation generalized extended stochastic gradient algorithm is pre-sented for the model identifcation. The proposed algorithm makes full use of theavailable data and improves the identifcation performance via innovation expan-sion. Considering that the lifted state-space model involves causality constraintproblem and the corresponding transfer function model is quite complicated withtoo many parameters, neither one is convenient for identifcation and control ofthe synchronous input-output NUSD systems. Therefore, a novel transfer functionmodel is derived by introducing a time-varying backward shift operator, and anauxiliary based least squares algorithm is developed for its identifcation.
(3) An Expectation-Maximization (EM) based identifcation algorithm is developed forthe output NUSD systems with uncertain sampling delays, where the uncertain delays are considered as the hidden states, and the parameters of the underlyingfast-rate fnite impulse response model are estimated along with the delays. Fur-thermore, two algorithms are proposed to recover the approximated fast-rate outputerror model by using the least square algorithm and the EM algorithm, respectively.The simulation examples and experimental results illustrate that the proposed al-gorithm can overcome the negative impacts of uncertain delays on the identifcationperformance, and provide parameter estimates with high precision.
(4) For the input NUSD systems with fast non-uniformly updated inputs and slowlysampled outputs, the mathematical relationship between the transfer function modelof the sampled outputs and the non-uniform missing outputs is derived. Basedon this relationship and using the identifed model of the sampled outputs, themodels of the missing outputs can be estimated. Then by using the estimatedmodel to predict the output at the next non-uniform sampling instant, an inferentialadaptive control algorithm is proposed for the input NUSD systems according tothe minimum variance criterion. By using the auxiliary variables, the proposedinferential control scheme is further extended to the input NUSD systems disturbedby unknown colored noises.
(5) For a practical output NUSD system, i.e., the once-through steam generator, softsensors based on hybrid modeling technique are developed to predict its steamqualities. First, simplifed frst-principle models are derived according to the en-ergy balance equations, thus the steam qualities can be estimated online throughtemperatures, fows and other process variables. Then, to improve the adaptabilityof the soft sensors, of-line lab analyses of steam qualities are adopted to rectifythe frst-principle model predictions via bias compensation; and to obtain high-performance soft sensors, the predication error method is applied to optimize themodel parameters and the weighting factor in the bias update equation. Further-more, online outlier detection and rejection are considered to ensure the reliabilityof the developed soft sensors.
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