WO2021185044A1 - 基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质 - Google Patents

基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质 Download PDF

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WO2021185044A1
WO2021185044A1 PCT/CN2021/077910 CN2021077910W WO2021185044A1 WO 2021185044 A1 WO2021185044 A1 WO 2021185044A1 CN 2021077910 W CN2021077910 W CN 2021077910W WO 2021185044 A1 WO2021185044 A1 WO 2021185044A1
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dictionary
heavy metal
wastewater treatment
metal wastewater
samples
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French (fr)
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黄科科
文昊飞
阳春华
朱红求
李勇刚
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中南大学
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F1/00—Treatment of water, waste water, or sewage
    • C02F1/008—Control or steering systems not provided for elsewhere in subclass C02F
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F1/00—Treatment of water, waste water, or sewage
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F1/00—Treatment of water, waste water, or sewage
    • C02F1/46—Treatment of water, waste water, or sewage by electrochemical methods
    • C02F1/461—Treatment of water, waste water, or sewage by electrochemical methods by electrolysis
    • C02F1/463—Treatment of water, waste water, or sewage by electrochemical methods by electrolysis by electrocoagulation
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F2101/00—Nature of the contaminant
    • C02F2101/10—Inorganic compounds
    • C02F2101/20—Heavy metals or heavy metal compounds
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F2209/00—Controlling or monitoring parameters in water treatment
    • C02F2209/005—Processes using a programmable logic controller [PLC]
    • C02F2209/006—Processes using a programmable logic controller [PLC] comprising a software program or a logic diagram
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F2209/00—Controlling or monitoring parameters in water treatment
    • C02F2209/05—Conductivity or salinity
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F2209/00—Controlling or monitoring parameters in water treatment
    • C02F2209/06—Controlling or monitoring parameters in water treatment pH
    • C—CHEMISTRY; METALLURGY
    • C02—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F—TREATMENT OF WATER, WASTE WATER, SEWAGE, OR SLUDGE
    • C02F2209/00—Controlling or monitoring parameters in water treatment
    • C02F2209/40—Liquid flow rate

Definitions

  • the invention belongs to the field of heavy metal wastewater treatment, and in particular relates to an intelligent monitoring method, device and storage medium for abnormal working conditions in a heavy metal wastewater treatment process based on migration learning.
  • Flocculation-electrochemical technology is one of the effective ways to realize the deep purification of heavy metal wastewater.
  • This technology uses electrochemical technology to perform advanced treatment on the wastewater treated by the traditional flocculation sedimentation process, which can reduce the consumption of chemicals, and can save electricity compared with a single electro-flocculation treatment of wastewater.
  • the effect of the existing flocculation-electrochemical technology on wastewater treatment is affected by many process factors (such as pH value, current density, conductivity, etc.).
  • heavy metal wastewater has uncertainties due to its sources, including climate change, man-made destruction, accidental pollution, and the unclear mechanism of many internal biochemical reaction processes. It is difficult to describe the characteristics of heavy metal wastewater with a clear mathematical relationship. .
  • the ion concentration distribution of heavy metal wastewater from different sources is quite different, and its treatment effect needs to be obtained after a long period of offline testing.
  • the treatment conditions of heavy metal wastewater from different sources mainly rely on the experience of the craftsmen to make judgments, and it is often difficult to accurately identify the normal and abnormal conditions of the treatment process. When abnormal conditions occur, it is difficult to effectively reduce the concentration of heavy metal ions in the wastewater. If the treatment process is not adjusted in time, the treatment result will affect the effect of the next process.
  • the manual treatment method is subjectively blind, especially when the source of heavy metal wastewater changes, the accuracy of working condition recognition is low.
  • the present invention proposes a migration learning-based An intelligent monitoring method, device and storage medium for abnormal working conditions in a heavy metal wastewater treatment process.
  • the method can adapt to heavy metal wastewater from different sources and accurately identify the working conditions of the treatment process.
  • Dictionary learning is an efficient way of data representation. This method assumes that the signal can be sparsely represented, that is, expressed as a product of a dictionary and its sparse coding. By learning and storing a dictionary with a small amount of data, high-dimensional signals can be restored Data, which is very effective for the processing of high-dimensional data. Because it can reduce the calculation and storage load of high-dimensional data, dictionary learning has received more and more attention.
  • This technical solution uses historical data including pH value, current density, conductivity, initial heavy metal concentration, flow rate and other indicators during the treatment process to model historical data.
  • different sources of wastewater are taken into consideration.
  • the initial heavy metal concentration has a different time series distribution, and the detection effect of the model obtained using historical data may not be guaranteed. Therefore, offline testing is performed on the treatment results of heavy metal wastewater with uncertain sources, and the data under normal operating conditions are selected according to the test results (that is, the data that the concentration of heavy metal ions in the wastewater is effectively reduced) and the history of normal operating conditions under the determined source
  • the data is fused, and the historical model is transferred and learned to realize the detection of abnormal conditions in the wastewater treatment process from different sources.
  • an intelligent monitoring method for abnormal working conditions of heavy metal wastewater treatment process based on migration learning includes:
  • Step 1.1 Collection of historical samples
  • y i represents the i-th heavy metal wastewater treatment history sample with a fixed source, 1 ⁇ i ⁇ N s , each sample contains m wastewater indicators ⁇ pH value, current density, conductivity, initial heavy metal concentration, flow rate ⁇ , N s represents The number of samples included in Y SD;
  • Step 1.2 According to the principle of sparse representation, use dictionary D 1 and sparse code X to represent Y SD to construct the objective function of offline dictionary learning, and obtain the optimal initial dictionary D SD corresponding to Y SD by solving the objective function of offline dictionary learning, and sparse coding and D SD X SD corresponds;
  • the final value of the dictionary D 1 is D SD , each column of the initial value of D 1 is a randomly selected sample, and D 1 has K columns; the final value of the sparse coding X is X SD ; X SD represents Y SD sparse encoding in D SD, D SD each column represents a dictionary atom;
  • T is usually set to 2;
  • the K-SVD method is used to solve the objective function of the offline dictionary learning, and the dictionary D 1 and the sparse code X are continuously updated until the optimal initial dictionary D SD corresponding to Y SD is obtained.
  • the K-SVD method is used to solve the problem. Specifically, K samples are randomly selected from Y SD as the initial value of the dictionary D SD , and the sparse code X SD is obtained by the orthogonal matching pursuit algorithm; the dictionary D 1 is updated by column, For example, when updating the k-th column of dictionary atoms, it can be written as follows, Represents the kth row in X.
  • E k is equal to Define collection Express The index set of the index where the non-zero item is located, Express The i-th element of, N means The number of elements in. Define ⁇ k as N ⁇
  • matrix, its value at ( ⁇ k (i),i) is 1, and the rest are 0. ⁇ k and After E k is multiplied, the original matrix can be contracted, right After doing singular value decomposition, Get d k u(:,1), After the column-by-column update is completed, the orthogonal matching pursuit algorithm is used to alternately update the sparse code X SD . After a certain number of iterations, the optimal initial dictionary D SD is obtained .
  • Use sensors to collect historical samples of effective heavy metal wastewater treatment with unknown sources The set of effective samples with unknown sources is Y TD ; according to the principle of sparse representation, use the initial dictionary D SD and the corresponding sparse code X to represent Y TD to construct heavy metal wastewater treatment after unknown sources
  • the objective function of the sparse coding corresponding to the data sample is solved through migration learning to obtain the optimal sparse coding X p corresponding to the effective sample set Y TD whose source is unknown, and then the corresponding optimal dictionary is obtained by using X p;
  • D p represents the interpolation dictionary in the migration learning process
  • T is the set value of the number of non-zero elements in the sparse coding matrix
  • 0 represent two norm and zero norm, respectively
  • x i represents the i-th column in X.
  • the optimal dictionary corresponding to the effective sample set Y TD whose source is unknown is solved;
  • X p represents the sparse code obtained during the p-th iteration
  • E is the identity matrix
  • the calculation of the reconstruction error refers to the two-norm calculation between the sample collection value of the reconstruction error to be calculated and the representative value of the sample using the extended dictionary and the corresponding sparse coding.
  • nuclear density estimation to obtain the control limits in the working conditions of the heavy metal wastewater treatment process refers to calculating the nuclear density function according to the following formula for the reconstruction error of historical samples with unknown sources, and using the nuclear density function under a set confidence level The value of as the corresponding control limit:
  • e is the distribution of reconstruction error of the historical sample whose source is unknown to be fitted
  • e i is the reconstruction error of the i-th historical sample whose source is unknown
  • H is the bandwidth matrix
  • n is the total number of historical samples
  • K [ ⁇ ] indicates the kernel function; It refers to the curve fitted by historical samples e i with unknown historical sources under a given bandwidth matrix H.
  • the kernel function uses a Gaussian kernel function, the bandwidth matrix uses a diagonal matrix, and the confidence is set to 0.98;
  • y f is an abnormal sample in the wastewater treatment process
  • y i y f - ⁇ i f i
  • y i is to isolate the i-th dimension index of y f , and the values of other dimension indexes remain unchanged.
  • f i is the reconstruction amplitude of the i-th dimension index in y f ;
  • x ri is the sparse comb code of y i under the extended dictionary, and the initial value of x ri is the sparse code of y f under the extended dictionary;
  • Re i is the reconstruction error of the i-th wastewater indicator in y f on the extended dictionary,
  • D TD represents the extended dictionary;
  • ⁇ i represents the direction selection vector, if the i-th element in the vector is 1, it means that the i indicators, other elements are all 0, ⁇ i ⁇ R m ; with They are the result values obtained after optimizing x ri and f i through the argmin objective function.
  • the first dimension variable represents the pH value
  • an intelligent monitoring device for abnormal working conditions in a heavy metal wastewater treatment process based on migration learning is characterized in that it includes:
  • Offline dictionary building module using historically collected heavy metal wastewater treatment data samples from a fixed source to build an offline dictionary
  • Extended dictionary building module using historically collected data samples of effective heavy metal wastewater treatment with unknown sources to perform migration learning on offline dictionaries to build extended dictionaries;
  • the control limit generation module is used to calculate the reconstruction error of all historical samples using the extended dictionary, and uses the kernel density estimation method to calculate the control limit in the working conditions of the heavy metal wastewater treatment process based on the reconstruction error of all historical samples;
  • the abnormal working condition judgment module is used to calculate the reconstruction error of the data to be monitored obtained online according to the extended dictionary, and compare the reconstruction error of the data to be monitored with the control limit, and judge whether the current heavy metal wastewater treatment process is abnormal according to the comparison result .
  • a computer storage medium is used to store a program, and when the program is executed, it is used to realize the above-mentioned intelligent monitoring method for abnormal working conditions of a heavy metal wastewater treatment process based on migration learning.
  • the present invention provides an intelligent monitoring method, device and storage medium for abnormal working conditions of heavy metal wastewater treatment process based on migration learning.
  • wastewater sources are different, the data distribution of wastewater from different sources is quite different.
  • the traditional method is difficult to accurately identify the working conditions of the heavy metal wastewater treatment process; through the data fusion of the heavy metal wastewater treatment process from different sources, it can automatically realize the intelligent identification of abnormal working conditions in the heavy metal wastewater treatment process of different sources; specifically, the use of fixed sources heavy metal wastewater treatment process normal sample Y SD, normal samples Y TD small amount of unknown origin heavy metal wastewater treatment process; firstly by learning Y SD obtained its data in the dictionary D SD, and then consider the different Y SD and Y TD distribution, Using the method of transfer learning, the characteristics of Y TD are integrated into the dictionary learning process, and a dictionary D TD with stronger generalization ability is obtained.
  • D TD not only considers the characteristics of Y SD , but also considers the distribution difference of Y TD into the model. It has stronger data representation ability, so it can accurately identify abnormal conditions of heavy metal wastewater from different sources online .
  • the method does not require prior knowledge of the process, can adaptively adapt to the uncertain factors in the wastewater treatment system, can more accurately detect changes in related indicators in the process, and realize timely detection and early warning.
  • Figure 1 is a schematic diagram of a specific process of an example of the present invention.
  • an intelligent monitoring method for abnormal working conditions in a heavy metal wastewater treatment process based on migration learning includes:
  • Step 1.1 Collection of historical samples
  • y i represents the i-th heavy metal wastewater treatment history sample with a fixed source, 1 ⁇ i ⁇ N s , each sample contains m wastewater indicators ⁇ pH value, current density, conductivity, initial heavy metal concentration, flow rate ⁇ , N s represents The number of samples included in Y SD;
  • Step 1.2 According to the principle of sparse representation, use dictionary D 1 and sparse code X to represent Y SD to construct the objective function of offline dictionary learning, and obtain the optimal initial dictionary D SD corresponding to Y SD by solving the objective function of offline dictionary learning, and sparse coding and D SD X SD corresponds;
  • the final value of the dictionary D 1 is D SD , and each column of the initial value of D 1 is a randomly selected sample, and D 1 has K columns; the final value of the sparse encoding X is X SD ; X SD represents Y SD sparse encoding in D SD, D SD each column represents a dictionary atom;
  • T is usually set to 2;
  • the K-SVD method is used to solve the objective function of the offline dictionary learning, and the dictionary D 1 and the sparse code X are continuously updated until the optimal initial dictionary D SD corresponding to Y SD is obtained.
  • the K-SVD method is used to solve the problem. Specifically, K samples are randomly selected from Y SD as the initial value of the dictionary D SD , and the sparse code X SD is obtained by the orthogonal matching pursuit algorithm; the dictionary D 1 is updated by column, For example, when updating the k-th column of dictionary atoms, it can be written as follows, Represents the kth row in X.
  • E k is equal to Define collection Express
  • ⁇ k N ⁇
  • ⁇ k and After E k is multiplied, the original matrix can be contracted, right After doing singular value decomposition, Get d k u(:,1), After the column-by-column update is completed, the orthogonal matching pursuit algorithm is used to alternately update the sparse code X SD . After a certain number of iterations, the optimal initial dictionary D SD is obtained .
  • Use sensors to collect historical samples of effective heavy metal wastewater treatment with unknown sources The set of effective samples with unknown sources is Y TD ; according to the principle of sparse representation, use the initial dictionary D SD and the corresponding sparse code X to represent Y TD to construct heavy metal wastewater treatment after unknown sources
  • the objective function of the sparse coding corresponding to the data sample is solved through migration learning to obtain the optimal sparse coding X p corresponding to the effective sample set Y TD whose source is unknown, and then the corresponding optimal dictionary is obtained by using X p;
  • D p represents the interpolation dictionary in the migration learning process
  • T is the set value of the number of non-zero elements in each column of the sparse coding matrix
  • 0 represent two norm and zero norm, respectively
  • x i represents the i-th column in X.
  • the objective function of the dictionary corresponding to the heavy metal wastewater treatment data sample of unknown source is constructed, and the source is the unknown effective sample set Y TD corresponding to Optimal dictionary
  • X p represents the sparse code obtained during the p-th iteration
  • E is the identity matrix
  • the use of nuclear density estimation to obtain the control limits in the working conditions of the heavy metal wastewater treatment process refers to the calculation of the nuclear density function based on the reconstruction error of historical samples of unknown source according to the following formula, and the value of the nuclear density function under the set confidence level As the corresponding control limit:
  • e is the distribution of reconstruction error of the historical sample whose source is unknown to be fitted
  • e i is the reconstruction error of the i-th historical sample whose source is unknown
  • H is the bandwidth matrix
  • n is the total number of historical samples
  • K [ ⁇ ] indicates the kernel function; It refers to the curve fitted by historical samples e i with unknown historical sources under a given bandwidth matrix H.
  • the kernel function uses a Gaussian kernel function, the bandwidth matrix uses a diagonal matrix, and the confidence is set to 0.98;
  • the calculation of the reconstruction error refers to the two-norm calculation between the sample acquisition value of the reconstruction error to be calculated and the representative value of the sample using the extended dictionary and the corresponding sparse code.
  • anomaly detection and anomaly index isolation are carried out on the working conditions of the wastewater treatment process:
  • y f is an abnormal sample in the wastewater treatment process
  • y i y f - ⁇ i f i
  • y i is to isolate the i-th dimension index of y f , and the values of other dimension indexes remain unchanged.
  • f i is the reconstruction amplitude of the i-th dimension index in y f ;
  • x ri is the sparse comb code of y i under the extended dictionary, and the initial value of x ri is the sparse code of y f under the extended dictionary;
  • Re i is the reconstruction error of the i-th wastewater indicator in y f on the extended dictionary,
  • D TD represents the extended dictionary;
  • ⁇ i represents the direction selection vector, if the i-th element in the vector is 1, it means that the i indicators, other elements are all 0, ⁇ i ⁇ R m ; with They are the result values obtained after optimizing x ri and f i through the argmin objective function.
  • the first dimension variable represents the pH value
  • the pH can be stabilized by changing the dosage of chemicals in the future, thereby ensuring the normal operation of the wastewater treatment process.
  • an embodiment of the present invention also provides an intelligent monitoring device for abnormal working conditions in a heavy metal wastewater treatment process based on migration learning, including:
  • Offline dictionary building module using historically collected heavy metal wastewater treatment data samples from a fixed source to build an offline dictionary
  • Extended dictionary building module using historically collected data samples of effective heavy metal wastewater treatment with unknown sources to perform migration learning on offline dictionaries to build extended dictionaries;
  • the control limit generation module is used to calculate the reconstruction error of all historical samples using the extended dictionary, and use the kernel density estimation method to calculate the control limit in the working conditions of the heavy metal wastewater treatment process based on the reconstruction error of all historical samples;
  • the industrial system abnormality judgment module is used to calculate the reconstruction error of the data to be monitored online according to the extended dictionary, compare the reconstruction error of the data to be monitored with the control limit, and judge whether the current heavy metal wastewater treatment process is abnormal according to the comparison result .
  • each unit module in the various embodiments of the present invention can be concentrated in one processing unit, or each unit module can exist alone physically, or two or more unit modules can be integrated into one unit module. It can be implemented in the form of hardware or software.
  • the embodiment of the present invention also provides a computer storage medium for storing a program.
  • the program When executed, it is used to realize a migration learning-based intelligent monitoring method for abnormal working conditions in a heavy metal wastewater treatment process. For its beneficial effects, see Method Part of the beneficial effects will not be repeated here.
  • this application can be provided as methods, systems, or computer program products. Therefore, this application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, this application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.
  • computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing equipment to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction device.
  • the device implements the functions specified in one process or multiple processes in the flowchart and/or one block or multiple blocks in the block diagram.
  • These computer program instructions can also be loaded on a computer or other programmable data processing equipment, so that a series of operation steps are executed on the computer or other programmable equipment to produce computer-implemented processing, so as to execute on the computer or other programmable equipment.
  • the instructions provide steps for implementing the functions specified in one process or multiple processes in the flowchart and/or one block or multiple blocks in the block diagram.

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Abstract

一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质，基于迁移学习的重金属废水处理过程异常工况智能化监测，通过对不同来源的重金属废水处理过程数据融合，能够自动的实现不同来源的重金属废水处理过程异常工况智能识别；具体为利用来源固定的重金属废水处理过程的正常样本Y SD、少量来源未知的重金属废水处理过程的正常样本Y TD；首先通过对Y SD进行学习得到其数据表示字典D SD，然后考虑到Y SD和Y TD分布不同，采用迁移学习的方法，将Y TD的特征融入到字典学习过程，得到泛化能力更强的字典D TD。基于迁移学习的重金属废水处理过程异常工况智能化监测方法无需过程先验知识，能自适应的适应废水处理系统中的不确定性因素，能够更加准确的检测过程中相关指标的变化，实现及时地检测与预警。

Description

基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质 技术领域
本发明属于重金属废水处理领域，特别涉及一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质。
背景技术
作为地球上不可替代的自然资源与环境资源，水的储量与质量与人类的生存发展息息相关。随着近些年工业的高速发展，工业废水尤其是重金属废水对环境污染非常严重和对人类危害非常深远。同时，重金属在环境中稳定性高、难降解、迁移范围广，正逐渐成为全球性环境问题。
絮凝—电化学技术是实现重金属废水深度净化的有效途径之一。该技术用电化学技术对经传统絮凝沉淀过程处理后的废水进行深度处理，可以减少药剂的消耗，与单一的电絮凝处理废水相比，又可以节约电能。一方面，现有絮凝—电化学技术对废水的处理效果受多种过程因素(如pH值、电流密度、电导率等)的影响。另一方面，重金属废水因其来源等存在不确定性，包括气候变化、人为破坏、偶然污染、内部许多生物化学反应过程的机理不明确等，难以用明确的数学关系对重金属废水的特征进行描述。除此之外，不同来源的重金属废水的离子浓度分布差异较大，其处理效果需要经过长时间离线化验才能获取。目前，针对不同来源的重金属废水的处理工况主要依赖于工艺人员的经验进行判断，往往难以准确的识别处理过程的正常工况和异常工况。当异常工况发生时，难以有效地降低废水中的重金属离子浓度，如未对处理过程进行及时调整，其处理结果会影响下一个工序的效果。而人工处理方式操作主观盲目性大，尤其是当重金属废水来源发生变化时，其工况识别准确性较低。
发明内容
本发明为了准确识别不同来源的重金属废水处理过程的异常工况，同时克服不同来源重金属离子各浓度数据带来的数据分布畸变导致模型失配带来的问题，本发明提出一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质，该方法能够适应不同来源重金属废水，准确识别处理过程的工况。
字典学习是一种高效的数据表示方式，该方法假设信号能进行稀疏表示，即表示为一个字典和其稀疏编码的乘积形式，通过学习并存储一个小数据量的字典，便能还原高维信号数据，这对于高维数据的处理是卓有成效的。由于能够减少高维数据的计算与存储负荷，字典学习受到了越来越多关注。
本技术方案通过对包含处理过程中pH值、电流密度、电导率、初始重金属浓度、流量 等指标在内的历史数据进行建模，在对废水处理过程进行在线监测时，考虑到不同来源的废水其初始重金属浓度的时间序列上分布不同，使用历史数据得到的模型，其检测效果可能得不到保障。因此，对来源不确定的重金属废水的处理结果进行离线化验，根据化验结果选取其正常工况下的数据(即废水中重金属离子浓度得到有效降低的数据)和确定来源下的正常工况的历史数据进行融合，通过对历史模型进行迁移学习，实现不同来源下的废水处理过程的异常工况检测。
本发明的技术方案如下：
一方面，一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法，包括：
1)利用历史采集的来源固定的重金属废水处理数据样本，构建来源固定的重金属废水处理数据样本的离线字典；
2)利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，获得来源未知的有效重金属废水处理数据样本对应的扩展字典；
3)利用扩展字典，计算来源未知下的有效重金属废水处理数据样本的重构误差，并基于所述重构误差，利用核密度估计获得重金属废水处理过程工况中的控制限；
4)计算待监测数据y t在扩展字典D TD下的重构误差，若计算得到的重构误差小于控制限，则认为当前重金属废水处理过程未出现异常，否则，则认为当前重金属废水处理过程出现异常。
进一步地，所述来源固定的重金属废水处理数据样本的离线字典的构建过程如下：
步骤1.1：历史样本采集；
利用传感器采集来源固定的重金属废水处理历史样本，来源固定的样本集合为Y SD；
Figure PCTCN2021077910-appb-000001
y i表示来源固定的第i个重金属废水处理历史样本，1≤i≤N s，每个样本包含m个废水指标{pH值、电流密度、电导率、初始重金属浓度、流量}，N s表示Y SD中包含的样本个数；
步骤1.2：依据稀疏表示原理，利用字典D 1和稀疏编码X表示Y SD，构建离线字典学习的目标函数，并通过求解离线字典学习的目标函数，获得Y SD对应的最优初始字典D SD，以及与D SD对应的稀疏编码X SD；
Figure PCTCN2021077910-appb-000002
Figure PCTCN2021077910-appb-000003
其中，字典D 1的初始取值为从历史样本集合Y SD中随机选取的K个样本按列排列形成的矩阵，K＝10*m，T为稀疏编码矩阵中的每一列非零元素个数设定值，
Figure PCTCN2021077910-appb-000004
和||·|| 0分别表示二范数和零范数；x i表示X中的第i列。
字典D 1的最终取值即为D SD，D 1的初始值中每一列是一个随机选取的样本，且D 1具有K列；稀疏编码X的最终取值即为X SD；X SD表示Y SD在D SD下的稀疏编码，D SD中每一列表示一个字典原子；
T的取值通常设置为2；
进一步地，采用K-SVD方法对所述离线字典学习的目标函数进行求解，不断更新字典D 1和稀疏编码X，直到获得Y SD对应的最优初始字典D SD。
采用K-SVD方法进行求解，具体地，从Y SD随机选取K个样本作为字典D SD的初始值，利用正交匹配追踪算法求得稀疏编码X SD后；按列对字典D 1进行更新，例如更新第k列字典原子时，可写成如下形式，
Figure PCTCN2021077910-appb-000005
表示X中的第k行。
Figure PCTCN2021077910-appb-000006
其中，E k等于
Figure PCTCN2021077910-appb-000007
定义集合
Figure PCTCN2021077910-appb-000008
表示
Figure PCTCN2021077910-appb-000009
中非零项所在索引的索引集，
Figure PCTCN2021077910-appb-000010
表示
Figure PCTCN2021077910-appb-000011
的第i个元素，N表示
Figure PCTCN2021077910-appb-000012
中的元素个数。定义Ω k为N×|ω k|矩阵，它在(ω k(i),i)处的值为1，其余值均为0。将Ω k与
Figure PCTCN2021077910-appb-000013
E k相乘后即可收缩原矩阵，
Figure PCTCN2021077910-appb-000014
Figure PCTCN2021077910-appb-000015
对
Figure PCTCN2021077910-appb-000016
做奇异值分解后，
Figure PCTCN2021077910-appb-000017
得到d k＝u(:,1)，
Figure PCTCN2021077910-appb-000018
当逐列更新完之后，则利用正交匹配追踪算法交替更新稀疏编码X SD。迭代更新一定次数后，得到最优的初始字典D SD。
进一步地，所述利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，获得扩展字典的过程如下：
利用传感器采集来源未知的有效重金属废水处理历史样本，来源未知的有效样本集合为 Y TD；依据稀疏表示原理，利用初始字典D SD和对应的稀疏编码X表示Y TD，构建未知来源后重金属废水处理数据样本对应的稀疏编码的目标函数，通过迁移学习，求解获得来源为未知的有效样本集合Y TD对应的最优稀疏编码X p，再利用X p获得对应的最优字典；
Figure PCTCN2021077910-appb-000019
Figure PCTCN2021077910-appb-000020
其中，D p表示迁移学习过程中的插值字典，D p的初始值表示来源固定的重金属废水处理数据样本的离线字典对应的最优初始字典D SD，即当p＝0时，D 0＝D SD；T为稀疏编码矩阵中的非零元素个数设定值，
Figure PCTCN2021077910-appb-000021
和||·|| 0分别表示二范数和零范数；x i表示X中的第i列。
进一步地，通过构建来源未知的重金属废水处理数据样本对应的字典的目标函数，求解来源为未知的有效样本集合Y TD对应的最优字典；
Figure PCTCN2021077910-appb-000022
其中，λ表示调节参数，取值范围为[1,10]；D表示待求的字典，通过迭代求得的最终字典赋值给D p+1，D p+1表示求得的来源为未知的有效样本集合Y TD对应的最优字典；
求解过程如下：
通过对
Figure PCTCN2021077910-appb-000023
进行求导，获得插值字典的更新结果，
Figure PCTCN2021077910-appb-000024
再通过对扩展字典的字典原子进行缩放，
Figure PCTCN2021077910-appb-000025
不断重复该过程，直到
Figure PCTCN2021077910-appb-000026
δ表示停止阈值，停止阈值设置为0.01；
X p表示第p次迭代过程中，得到的稀疏编码，
Figure PCTCN2021077910-appb-000027
是X p的转置，E是单位矩阵，
Figure PCTCN2021077910-appb-000028
和
Figure PCTCN2021077910-appb-000029
表示扩展字典D TD的第1列和第K列。
进一步地，所述重构误差的计算是指待计算重构误差的样本采集值和该样本用扩展字典与对应稀疏编码的表示值之间的二范数计算。
进一步地，利用核密度估计获得重金属废水处理过程工况中的控制限，是指按照以下公式对来源未知的历史样本的重构误差计算核密度函数，且以核密度函数在设定置信度下的取值作为对应控制限：
Figure PCTCN2021077910-appb-000030
其中，e是表示待拟合的来源未知的历史样本的重构误差的分布，e i表示第i个来源未知的历史样本的重构误差，H表示带宽矩阵，n表示历史样本的总数，K[·]表示核函数；
Figure PCTCN2021077910-appb-000031
是指在给定带宽矩阵H下，通过历来源未知的历史样本e i拟合出的曲线。
在本实例中，核函数采用高斯核函数，带宽矩阵采用对角线矩阵，置信度设置为0.98；
进一步地，通过设置异常废水指标定位目标函数，依次设置方向选择向量，计算每个废水指标在扩展字典下的重构误差，直到异常样本上的异常幅值收敛，确定异常废水指标；
Figure PCTCN2021077910-appb-000032
Figure PCTCN2021077910-appb-000033
Figure PCTCN2021077910-appb-000034
其中，y f为废水处理过程存在异常的样本，y i＝y f-ξ if i，y i是对y f的第i维指标进行隔离，且其他维指标的取值保持不变的待重构样本，f i是y f中第i维指标的重构幅值；x ri为y i在扩展字典下的稀梳编码，x ri的初始值为y f在扩展字典下的稀疏编码；Re i是y f中第i个废水指标在扩展字典上的重构误差，D TD表示扩展字典；ξ i表示方向选择向量，若该向量上第i个元素为1，表示此次选择了第i个指标，其他元素全为0，ξ i∈R m；
Figure PCTCN2021077910-appb-000035
和
Figure PCTCN2021077910-appb-000036
分别是通过argmin目标函数对x ri和f i进行优化后得到的结果值。
不断改变方向选择向量选取的指标，例如，第1维变量表示pH值，ξ 1＝[1,0，0，...0，0] T表示对pH值的一个选择向量，通过找到最小的重构误差对应的i值，确定异常指标；
另一方面，一种基于迁移学习的重金属废水处理过程异常工况智能化监测装置，其特征在于，包括：
离线字典建立模块，利用历史采集的来源固定的重金属废水处理数据样本，构建离线字典；
扩展字典建立模块，利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，构建扩展字典；
控制限生成模块，用于利用扩展字典计算所有历史样本的重构误差，并采用核密度估计方法，基于所有历史样本的重构误差计算重金属废水处理过程工况中的控制限；
工况异常判断模块，用于根据扩展字典计算在线获取的待监测数据的重构误差，并将待监测数据的重构误差与控制限比较，根据比较结果判断当前重金属废水处理过程工况是否异常。
另一方面，一种计算机存储介质，用于存储程序，所述程序被执行时，用于实现上述一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法。
有益效果
本发明提出一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法、装置及存储介质，考虑到重金属废水处理过程中，废水来源各异，不同来源的废水其数据的分布差异较大，传统的方法难以准确识别重金属废水处理过程的工况；通过对不同来源的重金属废水处理过程数据融合，能够自动的实现不同来源的重金属废水处理过程异常工况智能识别；具体为利用来源固定的重金属废水处理过程的正常样本Y SD、少量来源未知的重金属废水处理过程的正常样本Y TD；首先通过对Y SD进行学习得到其数据表示字典D SD，然后考虑到Y SD和Y TD分布不同，采用迁移学习的方法，将Y TD的特征融入到字典学习过程，得到泛化能力更强的字典D TD。考虑到D TD既考虑了Y SD的特征，同时又将Y TD的分布差异性考虑到模型中，其具有更强的数据表示能力，因此能够在线准确的识别不同来源的重金属废水的异常工况。该方法无需过程先验知识，能自适应的适应废水处理系统中的不确定性因素，能够更加准确的检测过程中相关指标的变化，实现及时地检测与预警。
附图说明
图1为本发明实例的具体流程示意图。
具体实施方式
下面将结合附图和实例对本发明做进一步的说明。
如图1所示，本实例中，一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法包括：
1)利用历史采集的来源固定的重金属废水处理数据样本，构建来源固定的重金属废水处理数据样本的离线字典；
所述来源固定的重金属废水处理数据样本的离线字典的构建过程如下：
步骤1.1：历史样本采集；
利用传感器采集来源固定的重金属废水处理历史样本，来源固定的样本集合为Y SD；
Figure PCTCN2021077910-appb-000037
y i表示来源固定的第i个重金属废水处理历史样本，1≤i≤N s，每个样本包含m个废水指标{pH值、电流密度、电导率、初始重金属浓度、流量}，N s表示Y SD中包含的样本个数；
步骤1.2：依据稀疏表示原理，利用字典D 1和稀疏编码X表示Y SD，构建离线字典学习的目标函数，并通过求解离线字典学习的目标函数，获得Y SD对应的最优初始字典D SD，以及与D SD对应的稀疏编码X SD；
Figure PCTCN2021077910-appb-000038
其中，字典D 1的初始取值为从历史样本集合Y SD中随机选取的K个样本按列排列形成的矩阵，K＝10*m，T为稀疏编码矩阵中每一列的非零元素个数设定值，
Figure PCTCN2021077910-appb-000039
和||·|| 0分别表示二范数和零范数；x i表示X中的第i列。
字典D 1的最终取值即为D SD，D 1的初始值中每一列是一个随机选取的样本，且D 1具有K列；稀疏编码X的最终取值即为X SD；X SD表示Y SD在D SD下的稀疏编码，D SD中每一列表示一个字典原子；
T的取值通常设置为2；
采用K-SVD方法对所述离线字典学习的目标函数进行求解，不断更新字典D 1和稀疏编码X，直到获得Y SD对应的最优初始字典D SD。
采用K-SVD方法进行求解，具体地，从Y SD随机选取K个样本作为字典D SD的初始值，利用正交匹配追踪算法求得稀疏编码X SD后；按列对字典D 1进行更新，例如更新第k列字典原子时，可写成如下形式，
Figure PCTCN2021077910-appb-000040
表示X中的第k行。
Figure PCTCN2021077910-appb-000041
其中，E k等于
Figure PCTCN2021077910-appb-000042
定义集合
Figure PCTCN2021077910-appb-000043
表示
Figure PCTCN2021077910-appb-000044
中非零项所在索引的索引集。定义Ω k为N×|ω k|矩阵，它在(ω k(i),i)处的值为1，其余值均为0。将Ω k与
Figure PCTCN2021077910-appb-000045
E k相乘后即可收缩原矩阵，
Figure PCTCN2021077910-appb-000046
对
Figure PCTCN2021077910-appb-000047
做奇异值分解后，
Figure PCTCN2021077910-appb-000048
得到d k＝u(:,1)，
Figure PCTCN2021077910-appb-000049
当逐列更新完之后，则利用正交匹配追踪算法交替更新稀疏编码X SD。迭代更新一定次数后，得到最优的初始字典D SD。
2)利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，获得来源未知的有效重金属废水处理数据样本对应的扩展字典；
所述利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，获得扩展字典的过程如下：
利用传感器采集来源未知的有效重金属废水处理历史样本，来源未知的有效样本集合为Y TD；依据稀疏表示原理，利用初始字典D SD和对应的稀疏编码X表示Y TD，构建未知来源后重金属废水处理数据样本对应的稀疏编码的目标函数，通过迁移学习，求解获得来源为未知的有效样本集合Y TD对应的最优稀疏编码X p，再利用X p获得对应的最优字典；
Figure PCTCN2021077910-appb-000050
其中，D p表示迁移学习过程中的插值字典，D p的初始值表示来源固定的重金属废水处理数据样本的离线字典对应的最优初始字典D SD，即当p＝0时，D 0＝D SD；T为稀疏编码矩阵中每一列的非零元素个数设定值，
Figure PCTCN2021077910-appb-000051
和||·|| 0分别表示二范数和零范数；x i表示X中的第i列。
为了不断减小新分布数据的表示误差，并且同时保持插值字典模型的连续性，通过构建来源未知的重金属废水处理数据样本对应的字典的目标函数，求解来源为未知的有效样本集合Y TD对应的最优字典；
Figure PCTCN2021077910-appb-000052
其中，λ表示调节参数，取值范围为[1,10]；D表示待求的字典，通过迭代求得的最终字典赋值给D p+1，D p+1表示求得的来源为未知的有效样本集合Y TD对应的最优字典；
求解过程如下：
通过对
Figure PCTCN2021077910-appb-000053
进行求导，获得插值字典的更新结果：
Figure PCTCN2021077910-appb-000054
为了保证表示字典原子的L2范数等于1，再通过对扩展字典的字典原子进行缩放：
Figure PCTCN2021077910-appb-000055
不断重复(3)-(6)，直到
Figure PCTCN2021077910-appb-000056
δ表示停止阈值，停止阈值设置为0.01；
X p表示第p次迭代过程中，得到的稀疏编码，
Figure PCTCN2021077910-appb-000057
是X p的转置，E是单位矩阵，
Figure PCTCN2021077910-appb-000058
和
Figure PCTCN2021077910-appb-000059
表示扩展字典D TD的第1列和第K列。
Figure PCTCN2021077910-appb-000060
3)利用扩展字典，计算来源未知下的有效重金属废水处理数据样本的重构误差，并基于所述重构误差，利用核密度估计获得重金属废水处理过程工况中的控制限；
利用核密度估计获得重金属废水处理过程工况中的控制限，是指按照以下公式对来源未知的历史样本的重构误差计算核密度函数，且以核密度函数在设定置信度下的取值作为对应控制限：
Figure PCTCN2021077910-appb-000061
其中，e是表示待拟合的来源未知的历史样本的重构误差的分布，e i表示第i个来源未知的历史样本的重构误差，H表示带宽矩阵，n表示历史样本的总数，K[·]表示核函数；
Figure PCTCN2021077910-appb-000062
是指在给定带宽矩阵H下，通过历来源未知的历史样本e i拟合出的曲线。
在本实例中，核函数采用高斯核函数，带宽矩阵采用对角线矩阵，置信度设置为0.98；
4)计算待监测数据y t在扩展字典D TD下的重构误差，若计算得到的重构误差小于控制限，则认为当前重金属废水处理过程未出现异常，否则，则认为当前重金属废水处理过程出现异常。
重构误差的计算是指待计算重构误差的样本采集值和该样本用扩展字典与对应稀疏编码的表示值之间的二范数计算。
基于得到的字典模型对废水处理过程工况进行异常检测及异常指标隔离：
通过设置异常废水指标定位目标函数，依次设置方向选择向量，计算每个废水指标在扩展字典下的重构误差，直到异常样本上的异常幅值收敛，确定异常废水指标；
Figure PCTCN2021077910-appb-000063
Figure PCTCN2021077910-appb-000064
Figure PCTCN2021077910-appb-000065
其中，y f为废水处理过程存在异常的样本，y i＝y f-ξ if i，y i是对y f的第i维指标进行隔离，且其他维指标的取值保持不变的待重构样本，f i是y f中第i维指标的重构幅值；x ri为y i在扩展字典下的稀梳编码，x ri的初始值为y f在扩展字典下的稀疏编码；Re i是y f中第i个废水指标在扩展字典上的重构误差，D TD表示扩展字典；ξ i表示方向选择向量，若该向量上第i个元素为1，表示此次选择了第i个指标，其他元素全为0，ξ i∈R m；
Figure PCTCN2021077910-appb-000066
和
Figure PCTCN2021077910-appb-000067
分别是通过argmin目标函数对x ri和f i进行优化后得到的结果值。
不断改变方向选择向量选取的指标，例如，第1维变量表示pH值，ξ 1＝[1,0，0，...0，0] T表示对pH值的一个选择向量，通过找到最小的重构误差对应的i值，确定异常指标；
通过异常隔离能够找出废水处理过程中可能的问题，例如如果发现异常是由pH导致，未来可以通过改变药剂添加量实现pH的稳定，进而保证废水处理过程的正常运行。
基于上述方法，本发明实施例还提供一种基于迁移学习的重金属废水处理过程异常工况智能化监测装置，包括：
离线字典建立模块，利用历史采集的来源固定的重金属废水处理数据样本，构建离线字典；
扩展字典建立模块，利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，构建扩展字典；
控制限生成模块，用于利用扩展字典计算所有历史样本的重构误差，并采用核密度估计方法，基于所有历史样本的重构误差计算重金属废水处理过程工况中的控制限；
工业系统异常判断模块，用于根据扩展字典计算在线获取的待监测数据的重构误差，并将待监测数据的重构误差与控制限比较，根据比较结果判断当前重金属废水处理过程工况是否异常。
应当理解，本发明各个实施例中的功能单元模块可以集中在一个处理单元中，也可以是各个单元模块单独物理存在，也可以是两个或两个以上的单元模块集成在一个单元模块中，可以采用硬件或软件的形式来实现。
本发明实施例还提供一种计算机存储介质，用于存储程序，所述程序被执行时，用于实现一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法，其有益效果参见方法部分的有益效果，在此不再赘述。
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多 个方框中指定的功能的步骤。
最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，尽管参照上述实施例对本发明进行了详细的说明，所属领域的普通技术人员应当理解：依然可以对本发明的具体实施方式进行修改或者等同替换，而未脱离本发明精神和范围的任何修改或者等同替换，其均应涵盖在本发明的权利要求保护范围之内。

Claims (10)

  1. 一种基于迁移学习的重金属废水处理过程异常工况智能化监测方法，其特征在于，包括：
    1)利用历史采集的来源固定的重金属废水处理数据样本，构建来源固定的重金属废水处理数据样本的离线字典；
    2)利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，获得来源未知的有效重金属废水处理数据样本对应的扩展字典；
    3)利用扩展字典，计算来源未知下的有效重金属废水处理数据样本的重构误差，并基于所述重构误差，利用核密度估计获得重金属废水处理过程工况中的控制限；
    4)计算待监测数据y t在扩展字典D TD下的重构误差，若计算得到的重构误差小于控制限，则认为当前重金属废水处理过程未出现异常，否则，则认为当前重金属废水处理过程出现异常。
  2. 根据权利要求1所述的方法，其特征在于，所述来源固定的重金属废水处理数据样本的离线字典的构建过程如下：
    步骤1.1：历史样本采集；
    利用传感器采集来源固定的重金属废水处理历史样本，来源固定的样本集合为Y SD；
    Figure PCTCN2021077910-appb-100001
    y i表示来源固定的第i个重金属废水处理历史样本，1≤i≤N s，每个样本包含m个废水指标{pH值、电流密度、电导率、初始重金属浓度、流量}，N s表示Y SD中包含的样本个数；
    步骤1.2：依据稀疏表示原理，利用字典D 1和稀疏编码X表示Y SD，构建离线字典学习的目标函数，并通过求解离线字典学习的目标函数，获得Y SD对应的最优初始字典D SD，以及与D SD对应的稀疏编码X SD；
    Figure PCTCN2021077910-appb-100002
    Figure PCTCN2021077910-appb-100003
    其中，字典D 1的初始取值为从历史样本集合Y SD中随机选取的K个样本按列排列形成的矩阵，K＝10*m，T为稀疏编码矩阵中的每一列非零元素个数设定值，
    Figure PCTCN2021077910-appb-100004
    和||·|| 0分别表示二范数和零范数；x i表示X中的第i列。
  3. 根据权利要求2所述的方法，其特征在于，采用K-SVD方法对所述离线字典学习的目 标函数进行求解，不断更新字典D 1和稀疏编码X，直到获得Y SD对应的最优初始字典D SD。
  4. 根据权利要求1所述的方法，其特征在于，所述利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，获得扩展字典的过程如下：
    利用传感器采集来源未知的有效重金属废水处理历史样本，来源未知的有效样本集合为Y TD；依据稀疏表示原理，利用初始字典D SD和对应的稀疏编码X表示Y TD，构建未知来源后重金属废水处理数据样本对应的稀疏编码的目标函数，通过迁移学习，求解获得来源为未知的有效样本集合Y TD对应的最优稀疏编码X p，再利用X p获得对应的最优字典；
    Figure PCTCN2021077910-appb-100005
    Figure PCTCN2021077910-appb-100006
    其中，D p表示迁移学习过程中的插值字典，D p的初始值表示来源固定的重金属废水处理数据样本的离线字典对应的最优初始字典D SD，即当p＝0时，D 0＝D SD；T为稀疏编码矩阵中的非零元素个数设定值，
    Figure PCTCN2021077910-appb-100007
    和||·|| 0分别表示二范数和零范数；x i表示X中的第i列。
  5. 根据权利要求4所述的方法，其特征在于，通过构建来源未知的重金属废水处理数据样本对应的字典的目标函数，求解来源为未知的有效样本集合Y TD对应的最优字典；
    Figure PCTCN2021077910-appb-100008
    其中，λ表示调节参数，取值范围为[1,10]；D表示待求的字典，通过迭代求得的最终字典赋值给D p+1，D p+1表示求得的来源为未知的有效样本集合Y TD对应的最优字典；
    求解过程如下：
    通过对
    Figure PCTCN2021077910-appb-100009
    求导，获得插值字典的更新结果，
    Figure PCTCN2021077910-appb-100010
    再通过对扩展字典的字典原子进行缩放，
    Figure PCTCN2021077910-appb-100011
    不断重复该过程，直到
    Figure PCTCN2021077910-appb-100012
    δ表示停止阈值，停止阈值设置为0.01；
    X p表示第p次迭代过程中，得到的稀疏编码，
    Figure PCTCN2021077910-appb-100013
    是X p的转置，E是单位矩阵，
    Figure PCTCN2021077910-appb-100014
    和
    Figure PCTCN2021077910-appb-100015
    表示扩展字典D TD的第1列和第K列。
  6. 根据权利要求1所述的方法，其特征在于，所述重构误差的计算是指待计算重构误差的样本采集值和该样本用扩展字典与对应稀疏编码的表示值之间的二范数计算。
  7. 根据权利要求1所述的方法，其特征在于，利用核密度估计获得重金属废水处理过程工况中的控制限，是指按照以下公式对来源未知的历史样本的重构误差计算核密度函数，且以核密度函数在设定置信度下的取值作为对应控制限：
    Figure PCTCN2021077910-appb-100016
    其中，e是表示待拟合的来源未知的历史样本的重构误差的分布，e i表示第i个来源未知的历史样本的重构误差，H表示带宽矩阵，n表示历史样本的总数，K[·]表示核函数；
    Figure PCTCN2021077910-appb-100017
    是指在给定带宽矩阵H下，通过历来源未知的历史样本e i拟合出的曲线。
  8. 根据权利要求1所述的方法，其特征在于，通过设置异常废水指标定位目标函数，依次设置方向选择向量，计算每个废水指标在扩展字典下的重构误差，直到异常样本上的异常幅值收敛，确定异常废水指标；
    Figure PCTCN2021077910-appb-100018
    Figure PCTCN2021077910-appb-100019
    Figure PCTCN2021077910-appb-100020
    其中，y f为废水处理过程存在异常的样本，y i＝y f-ξ if i，y i是对y f的第i维指标进行隔离，且其他维指标的取值保持不变的待重构样本，f i是y f中第i维指标的重构幅值；x ri为y i在扩展字典下的稀梳编码，x ri的初始值为y f在扩展字典下的稀疏编码；Re i是y f中第i个废水指标在扩展字典上的重构误差，D TD表示扩展字典；ξ i表示方向选择向量，若该向量上第i个元素为1，表示此次选择了第i个指标，其他元素全为0，ξ i∈R m；
    Figure PCTCN2021077910-appb-100021
    和
    Figure PCTCN2021077910-appb-100022
    分别是通过argmin目标函数对x ri和f i进行优化后得到的结果值。
  9. 一种基于迁移学习的重金属废水处理过程异常工况智能化监测装置，其特征在于，包括：
    离线字典建立模块，利用历史采集的来源固定的重金属废水处理数据样本，构建离线字典；
    扩展字典建立模块，利用历史采集的来源未知的有效重金属废水处理数据样本，对离线字典进行迁移学习，构建扩展字典；
    控制限生成模块，用于利用扩展字典计算所有历史样本的重构误差，并采用核密度估计 方法，基于所有历史样本的重构误差计算重金属废水处理过程工况中的控制限；
    工业系统异常判断模块，用于根据扩展字典计算在线获取的待监测数据的重构误差，并将待监测数据的重构误差与控制限比较，根据比较结果判断当前重金属废水处理过程工况是否异常。
  10. 一种计算机存储介质，其特征在于，用于存储程序，所述程序被执行时，用于实现如权利要求1-8任一所述的方法。
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