WO2022077180A1 - 确定无味卡尔曼滤波器的模型参数的方法、装置和系统 - Google Patents

确定无味卡尔曼滤波器的模型参数的方法、装置和系统 Download PDF

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WO2022077180A1
WO2022077180A1 PCT/CN2020/120476 CN2020120476W WO2022077180A1 WO 2022077180 A1 WO2022077180 A1 WO 2022077180A1 CN 2020120476 W CN2020120476 W CN 2020120476W WO 2022077180 A1 WO2022077180 A1 WO 2022077180A1
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detection data
denoised
sensor
data
value
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French (fr)
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冯程
施尼盖斯·丹尼尔
田鹏伟
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西门子（中国）有限公司
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Priority to CN202080104961.0A priority patent/CN116113981A/zh
Priority to EP20956962.3A priority patent/EP4227891A4/en
Publication of WO2022077180A1 publication Critical patent/WO2022077180A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06T5/70—Denoising; Smoothing
    • 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
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/044—Recurrent networks, e.g. Hopfield networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/09—Supervised learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/60—Image enhancement or restoration using machine learning, e.g. neural networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20081—Training; Learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20084—Artificial neural networks [ANN]

Definitions

  • the present invention relates to the technical field of data filtering, and in particular, to a method, device and system for determining model parameters of a tasteless Kalman filter.
  • the Kalman Filter (KF) and its variants are widely used in condition monitoring processing in application environments such as Industrial Control Systems (ICS).
  • ICS Industrial Control Systems
  • the original version of the Kalman filter is often applied to linear dynamic state-space models to monitor the state of physical processes under noisy sensor measurements.
  • EKF Extended Kalman Filter
  • ULF Unscented Kalman Filter
  • UKF is easy to implement and generally has better accuracy than EKF.
  • Embodiments of the present invention propose a method, apparatus and system for determining model parameters of UKF.
  • the method of determining the model parameters of the UKF including:
  • the trained neural network model is determined as the state transition function of UKF.
  • means for determining model parameters of the UKF comprising:
  • the data acquisition module is used to acquire the detection data of the sensor
  • a first determination module configured to determine the noise distribution of the sensor and the denoised detection data based on the detection data
  • a training module for training a neural network model using the denoised detection data
  • the second determination module is used for determining the trained neural network model as the state transition function of the UKF.
  • a memory for storing detection data of a physical quantity by a sensor and state data of an actuator, wherein the actuator is adapted to perform actions based on instructions related to the detection data;
  • a processor configured to: acquire the detection data and the state data from the memory; determine the noise distribution of the sensor and the denoised detection data based on the detection data; The detected data and the state data are used as training data to train a neural network model; the trained neural network model is determined as the state transition function of UKF.
  • the fourth aspect provides ICS, including:
  • the first interface coupled with the sensor
  • the second interface is coupled with the actuator
  • UKF for acquiring detection data from a sensor based on the first interface, and acquiring the state data from the actuator based on the second interface; and generating denoised detection data based on the detection data and the state data ; wherein the UKF determines the model parameters as described in any of the above methods.
  • an unscented Kalman filter for determining model parameters by applying the method described in any one of the above.
  • an apparatus for determining model parameters of UKF comprising a processor and a memory; an application program executable by the processor is stored in the memory, for causing the processor to execute as described in any of the above A method for determining the model parameters of the UKF.
  • a computer-readable storage medium having stored therein computer-readable instructions for performing the method of determining model parameters of the UKF as described in any of the above.
  • the embodiment of the present invention does not need to establish a mathematical model of process dynamics, determines the noise distribution of the sensor and the denoised detection data through the detection data of the sensor, and then uses the denoised detection data to train to be good at capturing nonlinear process dynamics Therefore, the state transition function of UKF can be automatically learned from the detection data, which improves the usability of UKF.
  • it also includes: determining the residual distribution between the predicted value of the sensor output by the trained neural network model and the detected value of the sensor as the process noise matrix of the UKF; A diagonal matrix in which the variances of the noise distributions are arranged is determined as the measurement noise matrix of the UKF.
  • the embodiment of the present invention can quickly calculate the process noise matrix and the measurement noise matrix of the UKF based on the residual distribution and noise distribution between the predicted value and the detected value of the output of the trained neural network model, without manually specifying the process noise matrix. and measurement noise matrices, thus avoiding reliance on expertise, further increasing the usability of UKF.
  • the determining the sensor noise distribution and the denoised detection data based on the detection data includes: setting the original value of the denoised detection data; based on the original value of the denoised detection data value and the detection data, iteratively calculate the sensor noise distribution and the denoised detection data, wherein each iteration includes: based on the last iteration value of the denoised detection data and the detection data, determine the sensor The current iteration value of the noise distribution; based on the current iteration value of the sensor noise distribution and the detection data, the current iteration value of the denoised detection data is determined; using the denoised detection data The current iteration value updates the previous iteration value of the denoised detection data.
  • the embodiments of the present invention can quickly and accurately determine the sensor noise distribution and the denoised detection data through iterative calculation.
  • an industrial control system including an actuator; it also includes: acquiring state data of the actuator in the industrial control system; and using the denoised detection data to train a neural network model includes: : Use the denoised detection data and the state data as training data to train the neural network model.
  • the embodiment of the present invention can improve the accuracy of the neural network model by further acquiring the state data of the actuator, and further using the state data of the actuator as training data to train the neural network model, and is especially suitable for applications that usually include sensors and actuators. ICS.
  • FIG. 1 is an exemplary flowchart of a method for determining model parameters of UKF according to an embodiment of the present invention.
  • FIG. 2 is an exemplary structural diagram of a system for determining model parameters of UKF according to an embodiment of the present invention.
  • FIG. 3 is an exemplary structural diagram of an ICS according to an embodiment of the present invention.
  • Figure 4 is an exemplary schematic diagram of an ICS comprising a UKF according to an embodiment of the present invention.
  • FIG. 5 is a comparison diagram of a first simulation effect between an embodiment of the present invention and the prior art.
  • FIG. 6 is a comparison diagram of a second simulation effect between an embodiment of the present invention and the prior art.
  • FIG. 7 is a first exemplary structural diagram of an apparatus for determining model parameters of UKF according to an embodiment of the present invention.
  • FIG. 8 is a second exemplary structural diagram of an apparatus for determining model parameters of UKF according to an embodiment of the present invention.
  • z ⁇ tw:t-1 ⁇ , u ⁇ tw:t-1 ⁇ are model inputs, representing sensor measurements and actuator states for the previous w time steps, respectively; is the model output, representing the predicted sensor measurements at the current time step; ⁇ is the parameter to be estimated, e.g. by taking a given log of time series data (consisting of sensor measurements and actuator states in the ICS) , which minimizes the mean squared error between the predicted sensor measurement and its actual value. According to the model's predictions, when the Euclidean distance between the predicted sensor measurement and its observed value exceeds a certain threshold An alert will sound.
  • f() is a nonlinear state transition or process function, which obtains the state of the physical process and the actuator at time t-1, and outputs the expected state of the physical process at time t
  • Q is the covariance matrix of process noise
  • h ( ) is the measurement function that maps the state of the physical process to the sensor measurement space
  • R is the covariance matrix of the sensor measurement noise.
  • UKF can use the following two steps to update x t and P t .
  • Step 1 Prediction Step
  • the prior mean and covariance of the state distribution at time t are computed.
  • some sigma function such as using Van der Merwe's Scaled Sigma Point Algorithm, a set of sigma points X and their corresponding state distributions at time t-1 are generated Weights W m , W c :
  • the sigma points are cleverly chosen to represent the state distribution with only a few points.
  • the selected sigma points are passed through the process function f() as follows:
  • the mean and covariance of the previous state distribution at time t can be computed by a tasteless transformation function as follows:
  • Step 2 Update Steps:
  • the posterior mean and covariance of the state distribution at time t are computed.
  • the mean and covariance of the measurement sigma points are calculated by a tasteless transformation function, where:
  • the Kalman gain can be obtained by the following formula:
  • a Neural Unflavored Kalman Filter (Neural UKF) is proposed in which the state transition function is represented by a neural network to capture nonlinear process dynamics such as in ICS systems. Additionally, embodiments of the present invention propose a method to learn neural UKFs from data, rather than manually designing UKFs. That is, model parameters in UKF, such as state transition functions (i.e. neural networks), process noise matrices, and measurement noise matrices, are all learned automatically from the data. Therefore, the embodiments of the present invention not only significantly reduce the difficulty of using UKF for condition monitoring of ICS, but also provide a technical solution for establishing an accurate condition monitoring model.
  • state transition functions i.e. neural networks
  • process noise matrices i.e. neural networks
  • measurement noise matrices measurement noise matrices
  • FIG. 1 is an exemplary flowchart of a method for determining model parameters of UKF according to an embodiment of the present invention.
  • the method includes:
  • Step 101 Acquire detection data of the sensor.
  • Step 102 Based on the detection data, determine the noise distribution of the sensor and the detection data after denoising.
  • Step 103 Use the denoised detection data to train a neural network model.
  • Step 104 Determine the trained neural network model as the state transition function of the tasteless Kalman filter.
  • the embodiment of the present invention does not need to establish a mathematical model of process dynamics, determines the noise distribution of the sensor and the denoised detection data through the detection data of the sensor, and then uses the denoised detection data to train to be good at capturing nonlinear process dynamics Therefore, the state transition function of UKF can be automatically learned from the detection data, which improves the usability of UKF.
  • the state data of the actuator is further determined in step 101; in step 103, the denoised detection data is used as training data, and training the neural network model includes: using the denoised detection data and the state data as training data to train the neural network model.
  • the accuracy of the neural network model can be improved, especially for ICS that usually include sensors and actuators.
  • the method further includes: determining the residual distribution between the predicted value of the sensor and the detected value of the sensor output by the trained neural network model as the process noise matrix of the UKF;
  • the variance of the noise distribution is merged into the diagonal matrix, which is determined as the measurement noise matrix of the UKF. Specifically, by combining the variance of the noise distribution of the sensor determined in step 102 into a diagonal matrix, the covariance matrix of the sensor measurement noise can be automatically generated.
  • the embodiment of the present invention quickly calculates the process noise matrix and measurement noise matrix of the UKF based on the residual distribution and noise distribution between the predicted value and the detected value of the output of the trained neural network model, without manually specifying the process noise matrix. and measurement noise matrices, thus avoiding reliance on expertise, further increasing the usability of UKF.
  • determining the noise distribution of the sensor and the denoised detection data based on the detection data in step 102 includes: setting the original value of the denoised detection data; based on the denoised detection data The original value and the detection data, iteratively calculate the sensor noise distribution and the denoised detection data, wherein each iteration includes: based on the last iteration value of the denoised detection data and the detection data, determine the The current iteration value of the sensor noise distribution; based on the current iteration value of the sensor noise distribution and the detection data, determine the current iteration value of the denoised detection data; use the denoised detection data The current iteration value of , updates the last iteration value of the denoised detection data.
  • the embodiments of the present invention can quickly and accurately determine the sensor noise distribution and the denoised detection data through iterative calculation.
  • D ⁇ 1:T ⁇ can be collected by running the ICS in a "vacuum environment" (inaccessible from the corporate network) for a period of time to capture the normal operation of the system.
  • Step 2 Learn the measurement noise of the sensor
  • n sensor measurements can be expressed as follows:
  • a random forest regressor may be used to construct virtual sensors. Specifically, to construct k virtual sensors for the physical process monitored by sensor i, define F k ( ) as a random forest regressor consisting of k decision trees. Then, train a random forest regressor that accepts input using the dataset t D ⁇ 1:T ⁇ and u t to predict After training the random forest model, each decision tree in the trained model can be treated as a virtual sensor, resulting in k virtual sensors for the physical process.
  • Step 3 Learn the state transition function and process noise matrix
  • feedforward neural network (FNN) models feedforward neural network (FNN) models and recurrent neural network (RNN) models:
  • Step 4 Specify the Measurement Function
  • the measurement function is relatively easy to specify, it just maps the state of the physical process into the measurement space. In particular, when process j is monitored by sensor i, let
  • the neural UKF constructed based on the above model parameters can be applied to condition monitoring.
  • ⁇ t and ⁇ t be the mean and covariance of the measured sigma points at time t, when alarm when. This means that the Mahalanobis distance between the observed measurement and the predicted distribution exceeds a predetermined threshold.
  • the value of ⁇ can be adjusted by setting an acceptable false positive rate by using neural UKF for anomaly detection of training data.
  • an embodiment of the present invention also proposes a system for determining model parameters of the UKF.
  • FIG. 2 is an exemplary structural diagram of a system for determining model parameters of UKF according to an embodiment of the present invention.
  • the system 20 includes:
  • the memory 21 is used to store the detection data of the physical quantity by the sensor and the state data of the actuator, wherein the actuator is adapted to perform actions based on the instructions related to the detection data;
  • the denoised detection data and the state data are used as training data to train a neural network model; the trained neural network model is determined as the state transition function of UKF.
  • the processor 22 is configured to: determine the residual distribution between the predicted value of the sensor and the detected value of the sensor output by the trained neural network model as the UKF process noise matrix; the diagonal matrix obtained by merging the variance of the noise distribution is determined as the measurement noise matrix of the UKF.
  • the processor 22 is configured to: set the original value of the de-noised detection data; based on the original value of the de-noised detection data and the detection data, iteratively calculate the sensor noise distribution and denoised detection data, wherein each iteration includes: determining the current iteration value of the sensor noise distribution based on the previous iteration value of the denoised detection data and the detection data; The current iteration value of the noise distribution of the sensor and the detection data, determine the current iteration value of the denoised detection data; update the denoised detection data with the current iteration value of the denoised detection data The last iteration value of the detection data.
  • the model parameters of the UKF are determined based on the detection data of the sensors and the state data of the actuators stored in the memory 21 , and the UKF is subsequently determined based on the model parameters of the UKF.
  • the system 20 can generate the UKF based on historical data in the memory 21 .
  • the model parameters of the UKF can also be determined based on the real-time detection data obtained by the real-time detection and the real-time state data of the actuator, and then the UKF can be determined based on the model parameters of the UKF.
  • the UKF of the embodiments of the present invention can be applied in various application environments, such as in ICS.
  • ICS consists of integrated hardware and software components designed to monitor and control industrial processes and are typically deployed in critical infrastructure such as water treatment plants, power grids and natural gas pipelines. Unlike traditional IT systems, the consequences of ICS deviating from normal operation can cause significant physical damage to equipment, the environment, and even human life. Proactive monitoring of the physical conditions that must be maintained for ICS to function properly is critical to improving the safety and reliability of such systems, enabling early detection of abnormal system states, allowing timely mitigation measures, such as fault checks, system closure.
  • FIG. 3 is an exemplary structural diagram of an ICS according to an embodiment of the present invention.
  • FIG. 3 depicts the architecture of a generic ICS, which includes a physical layer 307 , a control layer 303 and a supervisory control layer 301 .
  • Field devices such as sensors 305 and actuators 306 in physical layer 307 report and modify physical process states through signals sent and received by programmable logic controllers (PLCs) and remote terminal units (RTUs) 304 located in control layer 303 .
  • PLCs programmable logic controllers
  • RTUs remote terminal units
  • FIG 4 is an exemplary schematic diagram of an ICS comprising a UKF according to an embodiment of the present invention.
  • the ICS30 includes:
  • the second interface 32 is coupled with the actuator
  • UKF33 for acquiring detection data 35 from the sensor via the bus 34 based on the first interface 31, acquiring the status data 36 from the actuator via the bus 34 based on the second interface 32; based on the detection data 35 and the State data 36 generates denoised detection data 37; wherein UKF 33 determines model parameters using the method described in any of the above.
  • the control layer 303 obtains data from sensors 305 (eg, water level sensors, flow meters, and water quality sensors). Based on the data received from the sensors 305, the control layer 303 issues commands to the actuators 306 to perform specific actions, such as turning pumps on or off and valves on or off.
  • the supervisory control layer 301 includes a data acquisition and supervisory control system (SCADA), a human-machine interface (HMI), an engineering workstation, and a data historian component 302 . They communicate directly with the control layer 303 to provide higher level supervisory monitoring and control functions, and can also connect to wider corporate systems and networks through a "demilitarized zone" not shown in Figure 3. Condition monitoring mechanisms are typically deployed in this layer, and in the control layer 303, sensor measurements and actuator states are continuously checked to ensure that the physical process is in a controlled state.
  • Typical applications of embodiments of the present invention are described below.
  • the neural UKF proposed by embodiments of the present invention is used for anomaly detection on public ICS data logs collected from a Safe Water Treatment (SWaT) testbed.
  • SWaT Safe Water Treatment
  • the SWaT test bed is a scaled-down water treatment plant with a six-stage filtration process to purify raw water.
  • 6 PLCs are deployed in conjunction with 24 sensors and 27 actuators to control the entire process.
  • SWaT data logs are collected by running SWaT from an empty state to a fully operational state without interruption. 11 days in total. During the first 7 days, the device was operating under normal conditions, i.e. immune to any attack. In the remaining 4 days, 36 different types of attacks were launched on the SWaT testbed, including single-stage single-point attack, single-stage multi-point attack, multi-stage single-point attack and multi-stage multi-point attack against the water treatment process .
  • the dataset contains all sensor and actuator values collected every second for the stated duration.
  • Each data point contains 53 attributes, of which 24 are continuous sensor readings and 27 are discrete actuator states.
  • the neural UKF was learned using the method shown in this embodiment of the invention using data logs from the first 7 days (downsampled to a data point every 10 seconds), and then the learned The resulting neural UKF detected abnormal process states under attack in the remaining 4 days of data logs.
  • FNNs and RNNs (implemented as LSTM networks]) as state transition functions.
  • Two residual-based anomaly detection models based on FNN and RNN respectively with the same structure as the prediction model are used as benchmark models.
  • TPR true positive rate
  • FPR false positive rate
  • FIG. 5 is a comparison diagram of a first simulation effect of an embodiment of the present invention on the prior art.
  • the abscissa is the false positive rate (FPR), and the ordinate is the true positive rate (TPR).
  • Curve 51 is the simulation curve of UKF based on RNN proposed by the embodiment of the present invention.
  • curve 52 is the simulation curve of UKF based on FNN proposed by the embodiment of the present invention;
  • curve 53 is the prior art, based on RNN residual error The simulation curve of the model;
  • the curve 54 is the simulation curve of the prior art model based on FNN residuals.
  • FIG. 6 is a comparison diagram of a second simulation effect of an embodiment of the present invention on the prior art.
  • Figure 6 shows the number of attack types that can be detected by various methods under different FPR conditions.
  • the abscissa is the false positive rate, and the ordinate is the number of detected attack types.
  • Curve 61 is the UKF based on RNN proposed by the method of the present invention;
  • curve 62 is the simulation curve of the prior art model based on RNN residuals;
  • Curve 63 is the simulation curve of UKF based on FNN proposed by the method of the present invention ;
  • Curve 64 is a simulation curve of a prior art model based on FNN residuals.
  • the embodiments of the present invention use the UKF algorithm to monitor the hidden state of the physical process and can detect abnormal behaviors more accurately compared to the residual error-based method of ICS condition monitoring based directly on noise sensor measurements. Moreover, the embodiments of the present invention propose a method for automatically learning UKF from data, instead of manually designing UKF requiring high system knowledge and mathematical expertise, thereby significantly reducing the difficulty of applying UKF for condition monitoring in practice. Also, embodiments of the present invention use a neural network to capture the state transition function in the UKF. This enables the neural UKF to monitor ICS with highly nonlinear system dynamics compared to traditional Kalman filter-based algorithms.
  • FIG. 7 is a first exemplary structural diagram of an apparatus for determining model parameters of UKF according to an embodiment of the present invention.
  • the apparatus 700 for determining model parameters of UKF includes:
  • a first determination module 702 configured to determine the noise distribution of the sensor and the denoised detection data based on the detection data
  • a training module 703, configured to train a neural network model by using the denoised detection data
  • the second determination module 704 is configured to determine the trained neural network model as the state transition function of UKF.
  • a third determination module 705 is further included, configured to determine the residual distribution between the predicted value of the sensor and the detected value of the sensor output by the trained neural network model as the UKF Process noise matrix; a diagonal matrix obtained by merging the variance of the noise distribution is determined as the measurement noise matrix of the UKF.
  • the first determination module 702 is configured to set the original value of the denoised detection data; based on the original value of the denoised detection data and the detection data, iteratively calculate the sensor noise distribution and denoised detection data, wherein each iteration includes: determining the current iteration value of the sensor noise distribution based on the previous iteration value of the denoised detection data and the detection data; The current iteration value of the noise distribution and the detection data determine the current iteration value of the denoised detection data; update the denoised detection data using the current iteration value of the denoised detection data. Last iteration value.
  • the data acquisition module 701 is further configured to acquire the state data of the actuator; the training module 703 is configured to use the denoised detection data and the state data as training data to train the neural network model.
  • FIG. 8 is a second exemplary structural diagram of an apparatus for determining model parameters of UKF according to an embodiment of the present invention.
  • the apparatus 800 for determining model parameters of UKF includes a memory 802 and a processor 801; the memory 802 stores an application program executable by the processor 801, for causing the processor 801 to execute the above The described method for determining the model parameters of the unscented Kalman filter.
  • the hardware modules in various embodiments may be implemented mechanically or electronically.
  • a hardware module may include specially designed permanent circuits or logic devices (eg, special purpose processors, such as FPGAs or ASICs) for performing specific operations.
  • Hardware modules may also include programmable logic devices or circuits (eg, including general-purpose processors or other programmable processors) temporarily configured by software for performing particular operations.
  • programmable logic devices or circuits eg, including general-purpose processors or other programmable processors
  • the present invention also provides a machine-readable storage medium storing instructions for causing a machine to perform a method as described herein.
  • a system or device equipped with a storage medium on which software program codes for realizing the functions of any one of the above-described embodiments are stored, and make the computer (or CPU or MPU of the system or device) ) to read and execute the program code stored in the storage medium.
  • a part or all of the actual operation can also be completed by an operating system or the like operating on the computer based on the instructions of the program code.
  • the program code read from the storage medium can also be written into the memory provided in the expansion board inserted into the computer or into the memory provided in the expansion unit connected to the computer, and then the instructions based on the program code make the device installed in the computer.
  • the CPU on the expansion board or the expansion unit or the like performs part and all of the actual operations, so as to realize the functions of any one of the above-mentioned embodiments.
  • Embodiments of storage media for providing program code include floppy disks, hard disks, magneto-optical disks, optical disks (eg, CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), Magnetic tapes, non-volatile memory cards and ROMs.
  • the program code may be downloaded from a server computer or cloud over a communications network.

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Abstract

确定无味卡尔曼滤波器(UKF)的模型参数的方法和装置。方法包括：获取传感器的检测数据；基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；利用所述去噪后的检测数据训练神经网络模型；将训练后的神经网络模型确定为UKF的状态转移函数。可以从检测数据中自动学习UKF的模型参数，尤其适用于工业控制系统(ICS)的状态监测等多种应用环境。

Description

确定无味卡尔曼滤波器的模型参数的方法、装置和系统 技术领域
本发明涉及数据滤波技术领域，尤其涉及确定无味卡尔曼滤波器的模型参数的方法、装置和系统。
背景技术
由于传感器测量的噪声性质，卡尔曼滤波器(Kalman Filter,KF)及其变体被广泛用于诸如工业控制系统(Industrial Control System，ICS)等应用环境的状态监视处理中。特别是，卡尔曼滤波器的原始版本通常应用于线性动态状态空间模型，以在噪声传感器测量下监视物理过程的状态。对于具有非线性过程动力学的系统，扩展卡尔曼滤波器(Extended Kalman Filter,EKF)和无味卡尔曼滤波器(Unscented Kalman Filter,UKF)是两个常见选择。在实践中，与EKF相比，UKF易于实施并且通常具有更好的准确性。
尽管UKF得到了广泛的认可，但UKF的设计在实践中仍然颇具挑战性。具体而言，要应用UKF，首先需要系统识别步骤以建立过程动力学的数学模型，即设计作为UKF的模型参数之一的状态转移函数。然而，对于具有高度非线性过程动力学的系统，此步骤通常非常困难，甚至不可行，这会显著降低UKF的可用性。
另外，需要在系统动力学和传感器知识方面具有很高的专业知识，才可以在状态空间模型中指定同样作为UKF模型参数的过程噪声矩阵和测量噪声矩阵。因此这两个矩阵通常设计不正确，导致UKF模型设计不良。
发明内容
本发明实施方式提出确定UKF的模型参数的方法、装置和系统。
第一方面，确定UKF的模型参数的方法，包括：
获取传感器的检测数据；
基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；
利用所述去噪后的检测数据训练神经网络模型；
将训练后的神经网络模型确定为UKF的状态转移函数。
第二方面，提供确定UKF的模型参数的装置，包括：
数据获取模块，用于获取传感器的检测数据；
第一确定模块，用于基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；
训练模块，用于利用所述去噪后的检测数据训练神经网络模型；
第二确定模块，用于将训练后的神经网络模型确定为所述UKF的状态转移函数。
第三方面，提供确定UKF的系统，包括：
存储器，用于保存传感器对物理量的检测数据以及执行器的状态数据，其中所述执行器适配于基于与所述检测数据相关的指令执行动作；
处理器，被配置用于：从所述存储器获取所述检测数据和所述状态数据；基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；将所述去噪后的检测数据和所述状态数据作为训练数据，训练神经网络模型；将所述训练后的神经网络模型确定为UKF的状态转移函数。
第四方面，提供ICS，包括：
第一接口，与传感器耦合；
第二接口，与执行器耦合；
UKF，用于基于所述第一接口从传感器获取检测数据，基于所述第二接口从所述执行器获取所述状态数据；基于所述检测数据和所述状态数据生成去噪后的检测数据；其中所述UKF如上任一项所述方法确定出模型参数。
第五方面，提供应用如上任一项所述方法确定出模型参数的无味卡尔曼滤波器。
第六方面，提供确定UKF的模型参数的装置，包括处理器和存储器；所述存储器中存储有可被所述处理器执行的应用程序，用于使得所述处理器执行如上任一项所述的确定UKF的模型参数的方法。
第七方面，提供计算机可读存储介质，其中存储有计算机可读指令，该计算机可读指令用于执行如上任一项所述的确定UKF的模型参数的方法。
可见，本发明实施方式无需建立过程动力学的数学模型，通过传感器的检测数据确定出传感器的噪音分布和去噪后的检测数据，再利用去噪后的检测数据去训练善于捕获非线性过程动力学的神经网络模型，因此可以从检测数据中自动学习出UKF的状态转移函数，提高了UKF的可用性。
对于上述任一方面，优选地，还包括：将训练后的神经网络模型输出的传感器的预测值与所述传感器的检测值之间的残差分布，确定为所述UKF的过程噪音矩阵；将所述噪音分布的方差排列成的对角矩阵，确定为所述UKF的测量噪声矩阵。
可见，本发明实施方式基于训练后的神经网络模型的输出的预测值与检测值之间的残差分布以及噪音分布，快速计算出UKF的过程噪音矩阵和测量噪声矩阵，无需人工指定过程噪音矩阵和测量噪声矩阵，从而避免了对专业知识的依赖，进一步提高了UKF的可用性。
对于上述任一方面，优选地，所述基于检测数据，确定传感器噪音分布和去噪后的检测数据包括：设置去噪后的检测数据的原始值；基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；基于所述传感器噪音分布的本次迭代值与所述检测数据，确定所述去噪后的检测数据的本次迭代值；利用所述去噪后的检测数据的本次迭代值更新所述去噪后的检测数据的上次迭代值。
因此，本发明实施方式通过迭代计算，可以快速准确地确定传感器噪音分布和去噪后的检测数据。
对于上述任一方面，优选地，应用于包括执行器的工业控制系统；还包括：获取工业控制系统中的所述执行器的状态数据；所述利用去噪后的检测数据训练神经网络模型包括：将所述去噪后的检测数据和所述状态数据作为训练数据，训练所述神经网络模型。
因此，本发明实施方式通过进一步获取执行器的状态数据，并进一步将执行器的状态数据作为训练数据以训练神经网络模型，可以提高神经网络模型的精准度，尤其适用于通常包含传感器和执行器的ICS中。
附图说明
图1为本发明实施方式的确定UKF的模型参数的方法的示范性流程图。
图2为本发明实施方式的确定UKF的模型参数的系统的示范性结构图。
图3为本发明实施方式的ICS的示范性结构图。
图4为本发明实施方式包含UKF的ICS的示范性示意图。
图5为本发明实施方式与现有技术的第一仿真效果对比图。
图6为本发明实施方式与现有技术的第二仿真效果对比图。
图7为本发明实施方式的确定UKF的模型参数的装置的第一示范性结构图。
图8为本发明实施方式的确定UKF的模型参数的装置的第二示范性结构图。
其中，附图标记如下：
Figure PCTCN2020120476-appb-000001
Figure PCTCN2020120476-appb-000002
Figure PCTCN2020120476-appb-000003
具体实施方式
为了使本发明的技术方案及优点更加清楚明白，以下结合附图及实施方式，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施方式仅仅用以阐述性说明本发明，并不被配置为用于限定本发明的保护范围。
为了描述上的简洁和直观，下文通过描述若干代表性的实施方式来对本发明的方案进行阐述。实施方式中大量的细节仅被配置为用于帮助理解本发明的方案。但是很明显，本发明的技术方案实现时可以不局限于这些细节。为了避免不必要地模糊了本发明的方案，一些实施方式没有进行细致地描述，而是仅给出了框架。下文中，“包括”是指“包括但不限于”，“根据……”是指“至少根据……，但不限于仅根据……”。由于汉语的语言习惯，下文中没有特别指出一个成分的数量时，意味着该成分可以是一个也可以是多个，或可理解为至少一个。
迄今为止，ICS中的大多数状态监视机制都依赖于预测模型，该模型基于先前的传感器测量值和执行器状态来预测每个时间步的传感器测量值，并且如果预测的测量值与其观测值之间的残余误差超过具体阈值则报警。基本的预测模型可以采用许多不同的形式，例如包括自回归(AR)模型，线性动态状态空间模型和其他基于深度神经网络的回归模型。但是，所有预测模型都可以表示为高级函数：
Figure PCTCN2020120476-appb-000004
其中z {t-w：t-1}，u {t-w：t-1}是模型输入，分别代表前w个时间步的传感器测量值和执行器状态；
Figure PCTCN2020120476-appb-000005
是模型输出，代表当前时间步长的预测传感器测量值；θ是待估计的参数，例如，通过在给定的时间序列数据日志(由ICS中的传感器测量值和执行器状态组成)的情况下，最小化预测的传感器测量值与其实际值之间的均方误差。根据模型的预测，当预测的传感器测量值与 其观测值之间的欧几里德距离超过特定阈值时
Figure PCTCN2020120476-appb-000006
将发出警报。
针对非线性状态空间模型和UKF进行说明：
在不失一般性的前提下，考虑具有M个物理过程的ICS，并由N个传感器和K个执行器进行监控。我们假设M≤N，以便每个物理过程都由至少一个传感器监视。令x t是时间t处物理过程的隐藏状态，z t是时间t处来自传感器的测量值，u t是时间t处执行器的状态。系统动力学可以用非线性动态状态空间模型表示，如下所示：
x t＝f(x t-1，u t-1)+Q；
z t＝h(x t)+R；
其中f()是一个非线性状态转换或过程函数，它在t-1时刻获取物理过程和执行器的状态，并在t时刻输出物理过程的预期状态；Q是过程噪声的协方差矩阵；h()是将物理过程的状态映射到传感器测量空间的测量函数；R是传感器测量噪声的协方差矩阵。
以x t-1和P t-1为t-1时刻时过程状态分布的均值向量和协方差矩阵，UKF可以使用以下两个步骤来更新x t和P t。
第一步：预测步骤
在预测步骤中，计算时间t处状态分布的先验平均值和协方差。首先，通过一些西格玛(sigma)函数，例如使用范德默威(Van der Merwe)的标度Sigma点算法(Scaled Sigma Point Algorithm)，生成一组sigma点X及其在时间t-1时状态分布的相应权重W m，W c：
X，W m，W c＝sigma_function(x t-1，P t-1)；
巧妙地选择sigma点，以只有几个点表示状态分布。通过如下过程函数f()传递选定的sigma点：
Y＝f(X，u t-1)；
可以通过无味变换函数按如下方式计算时间t处先前状态分布的均值和协方差：
Figure PCTCN2020120476-appb-000007
Figure PCTCN2020120476-appb-000008
第二步：更新步骤：
在更新步骤中，计算时间t时状态分布的后验均值和协方差，即x t和P t。首先，使用测量函数h()将先验的sigma点映射到测量空间中：
L＝h(Y)；
通过无味变换函数计算得出测量sigma点的均值和协方差，其中：
Figure PCTCN2020120476-appb-000009
Figure PCTCN2020120476-appb-000010
卡尔曼增益可通过以下公式获得：
Figure PCTCN2020120476-appb-000011
然后，可以更新：
Figure PCTCN2020120476-appb-000012
Figure PCTCN2020120476-appb-000013
通常在设计UKF时，需要手动指定函数f()，h()以及噪声矩阵Q和R，这就既需要设计人员有专业知识，还降低UKF的可用性。
在本发明实施方式中，提出了神经无味卡尔曼滤波器(Neural UKF)，其中状态转换函数由神经网络表示，以捕获诸如ICS系统中的非线性过程动力学。另外，本发明实施方式提出了一种从数据中学习神经UKF的方法，而不是手动设计UKF。也就是说，UKF中的模型参数(比如，状态转移函数(即神经网络)、过程噪声矩阵和测量噪声矩阵)都是从数据中自动学习的。因此，本发明实施方式不仅显著降低了将UKF用于ICS的状态监测的难度，而且提供了建立精确的状态监测模型的技术方案。
图1为本发明实施方式的确定UKF的模型参数的方法的示范性流程图。
如图1所示，该方法包括：
步骤101：获取传感器的检测数据。
步骤102：基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据。
步骤103：利用所述去噪后的检测数据训练神经网络模型。
步骤104：将所述训练后的神经网络模型确定为所述无味卡尔曼滤波器的状态转移函数。
可见，本发明实施方式无需建立过程动力学的数学模型，通过传感器的检测数据确定出传感器的噪音分布和去噪后的检测数据，再利用去噪后的检测数据去训练善于捕获非线性过程动力学的神经网络模型，因此可以从检测数据中自动学习出UKF的状态转移函数，提高了UKF的可用性。
考虑到在很多应用环境(比如，ICS)中，通常还布置有基于传感器对物理过程的检测数据而执行控制动作的执行器。优选地，在一个实施方式中，在步骤101中进一步确定执行器的状态数据；步骤103中将去噪后的检测数据作为训练数据，训练神经网络模型包括：将所述去噪后的检测数据和所述状态数据作为训练数据，训练所述神经网络模型。
因此，通过进一步获取执行器的状态数据，并进一步将执行器的状态数据作为训练数据以训练神经网络模型，可以提高神经网络模型的精准度，尤其适用于通常包含传感器和执行器的ICS。
在一个实施方式中，还包括：将训练后的神经网络模型输出的、传感器的预测值与所述传感器的检测值之间的残差分布，确定为所述UKF的过程噪音矩阵；将所述噪音分布的方差合并出的对角矩阵，确定为所述UKF的测量噪声矩阵。具体地，通过将步骤102中确定的传感器的噪音分布的方差合并为对角矩阵，可以自动生成传感器测量噪声的协方差矩阵。
可见，本发明实施方式基于训练后的神经网络模型的输出的预测值与检测值之间的残差分布以及噪音分布，快速计算出UKF的过程噪音矩阵和测量噪声矩阵，无需人工指定过程噪音矩阵和测量噪声矩阵，从而避免了对专业知识的依赖，进一步提高了UKF的可用性。
在一个实施方式中，步骤102中基于检测数据，确定所述传感器的噪音分布和去噪后的检测数据包括：设置去噪后的检测数据的原始值；基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；基于所述传感器噪音分布的本次迭代值与所述检测数据，确定所述去噪后的检测数据的本次迭代值；利用所述去噪后的检测数据的本次迭代值更新所述去噪后的检测数据的上次迭代值。
因此，本发明实施方式通过迭代计算，可以快速准确地确定传感器噪音分布和去噪后的检测数据。
下面以应用到ICS为例，详细描述本发明实施方式从数据中学习UKF的详细算法。具体包括：
步骤1：数据收集
在数据收集步骤中，可以让ICS以T个时间步长运行，然后收集数据D {1：T}＝{d 1，d 2，...，d T}，其中d t＝{z t，u t}。假设数据D {1：T}中没有异常信号。在实践中，可以通过以“真空环境”(无法从公司网络进行访问)运行ICS一段时间来收集D {1：T}，以捕获系统运行的正常情况。
步骤2：学习传感器的测量噪声
考虑由n个传感器监视的物理过程。令
Figure PCTCN2020120476-appb-000014
为传感器i的收集测量值，其中i＝1:n。令x {1：T}＝{x 1，x 2，...，x T}为物理过程的隐藏状态。此外，还假定
Figure PCTCN2020120476-appb-000015
其中
Figure PCTCN2020120476-appb-000016
是方差为
Figure PCTCN2020120476-appb-000017
的零平均高斯噪声。对于i＝1:n，建议使用最大似然估计从
Figure PCTCN2020120476-appb-000018
推断
Figure PCTCN2020120476-appb-000019
具体来说，可以将n个传感器测量值的似然值表示如下：
Figure PCTCN2020120476-appb-000020
然后，令
Figure PCTCN2020120476-appb-000021
得到：
Figure PCTCN2020120476-appb-000022
最小化负对数似然值，得到：
Figure PCTCN2020120476-appb-000023
由于有两组参数要优化，因此使用块坐标下降法来解决上述优化问题。
具体来说，通过固定x {1：T}，可以得到：
Figure PCTCN2020120476-appb-000024
通过固定c {1：n}，得到：
Figure PCTCN2020120476-appb-000025
迭代地重复上述步骤，直到收敛为止，以便两次连续迭代之间的物理过程的隐藏状态范数小于阈值，即最优x {1：T}和c {1：n}可以通过最大化测量值的似然值得到。在使用上述方法推断系统中所有传感器的传感器噪声后，可以设置
Figure PCTCN2020120476-appb-000026
这意味着传感器的测量噪声是独立的。
在上述描述中，假设每个物理过程都由多个传感器监控。尽管传感器冗余在ICS中非常普遍，但是在物理过程仅由单个传感器监视的情况下，仍然可以通过为物理过程构造虚拟传感器来应用本发明实施方式。
在本发明实施方式，可以使用随机森林回归器来构建虚拟传感器。具体来说，要为由传感器i监视的物理过程构造k个虚拟传感器，将F k()定义为由k个决策树组成的随机森林回归器。然后，训练随机森林回归器，该回归器使用数据集t D {1：T}接受输入
Figure PCTCN2020120476-appb-000027
和u t来预测
Figure PCTCN2020120476-appb-000028
训练随机森林模型后，可以将训练模型中的每个决策树都视为一个虚拟传感器，从而获得用于物理过程的k个虚拟传感器。
步骤3：学习状态转移函数和过程噪声矩阵
在上一步中，不仅导出了传感器噪声矩阵R，还导出了受监视物理过程的隐藏状态。令x {1：T}＝{x 1，x 2，...，x T}表示导出的物理过程的隐藏状态，可以训练神经网络模型以捕获状态转换函数f()。其中，神经网络模型有很多选择。
比如：可以考虑两种类型的模型，前馈神经网络(FNN)模型和递归神经网络(RNN)模型：
FNN(x t-1，u t-1；θ)；
RNN(x {t-w：t-1}，u {t-w：t-1}；θ)；
取决于选择的模型，令
Figure PCTCN2020120476-appb-000029
或RNN(x {t-w：t-1}，u {t-w：t-1}；θ)，可以使用反向传播优化以下损耗函数：
Figure PCTCN2020120476-appb-000030
训练完神经网络模型后，可以根据
Figure PCTCN2020120476-appb-000031
的统计值，得出t＝1:T的过程噪声矩阵Q。
步骤4：指定测量函数
测量函数相对容易指定，它只是将物理过程的状态映射到测量空间中。特别地，当进程j由传感器i监视时，让
Figure PCTCN2020120476-appb-000032
然后，可以将基于上述模型参数构建的神经UKF应用于状态监测。
在监视阶段中，令μ t和Σ t为时间t的测量sigma点的均值和协方差，当
Figure PCTCN2020120476-appb-000033
时报警。这意味着观察到的测量值和预测分布的马氏距离超过了预定的阈值。可以通过将神经UKF用于训练数据的异常检测来设置可接受的误报率来调整τ的值。
基于上述描述，本发明实施方式还提出了确定UKF的模型参数的系统。
图2为本发明实施方式的确定UKF的模型参数的系统的示范性结构图。
如图2所示，该系统20，包括：
存储器21，用于保存传感器对物理量的检测数据以及执行器的状态数据，其中所述执行器适配于基于与所述检测数据相关的指令执行动作；
处理器22，经由总线23与存储器21耦合，其被配置用于：从所述存储器21获取所述检测数据和所述状态数据；基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；将所述去噪后的检测数据和所述状态数据作为训练数据，训练神经网络模型；将所述训练后的神经网络模型确定为UKF的状态转移函数。
在一个实施方式中，所述处理器22，被配置用于：将训练后的神经网络模型输出的、传感器的预测值与所述传感器的检测值之间的残差分布，确定为所述UKF的过程噪音矩阵；将所述噪音分布的方差合并出的对角矩阵，确定为所述UKF的测量噪声矩阵。
在一个实施方式中，所述处理器22，被配置用于：设置去噪后的检测数据的原始值；基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；基于所述传感器噪音分布的本次迭代值与所述检测数 据，确定所述去噪后的检测数据的本次迭代值；利用所述去噪后的检测数据的本次迭代值更新所述去噪后的检测数据的上次迭代值。
在图2所示的系统20中，基于在存储器21中保存的传感器的检测数据以及执行器的状态数据确定UKF的模型参数，后续基于UKF的模型参数确定UKF。因此，系统20可以基于存储器21中的历史数据生成UKF。实际上，还可以基于实时检测获取的实时检测数据以及执行器的实时状态数据确定UKF的模型参数，并再基于该UKF的模型参数确定UKF。
可以将本发明实施方式的UKF应用到各种应用环境中，比如应用到ICS中。
ICS由旨在监视和控制工业过程的集成硬件和软件组件组成，通常部署在关键基础设施中，例如水处理厂、电网和天然气管道。与传统的IT系统不同，ICS偏离正常运行的后果可能会对设备，环境乃至人类生命造成重大物理损害。对ICS正常运行所必须维持的物理状况的主动监视对于提高此类系统的安全性和可靠性至关重要，可以实现对系统异常状态的早期检测，从而可以及时采取缓解措施，例如故障检查，系统关闭。
图3为本发明实施方式的ICS的示范性结构图。图3描述了通用ICS的体系结构，其中包括物理层307、控制层303和监督控制层301。物理层307中的传感器305和执行器306等现场设备通过位于控制层303中的可编程逻辑控制器(PLC)和远程终端单元(RTU)304发送和接收的信号来报告和修改物理过程状态。
图4为本发明实施方式包含UKF的ICS的示范性示意图。在图4中，ICS30包括：
第一接口31，与传感器耦合；
第二接口32，与执行器耦合；
UKF33，用于基于第一接口31经由总线34从传感器获取检测数据35，基于所述第二接口32经由总线34从所述执行器获取所述状态数据36；基于所述检测数据35和所述状态数据36生成去噪后的检测数据37；其中UKF33应用如上任一项所述方法确定出模型参数。
下面以水分配系统为实例，描述本发明实施方式的UKF的应用过程。
在水分配系统中，控制层303从传感器305(例如水位传感器、流量计和水质传感器)获取数据。基于从传感器305接收到的数据，控制层303向执行器306发出命令以执行特定的动作，例如打开或关闭泵以及打开或关闭阀。监督控制层301包含数据采集与监视控制系统(SCADA)、人机交互界面(HMI)、工程工作站和数据历史记录器组件302。它们直接与控制层303通信，以提供更高级别的监督监视和控制功能，并且还可以通过未在图3中显示的“隔离区(demilitarized zone)”与更广泛的公司系统和网络连接。状态监视机制通常部署在该层中，在控制层303中，连续检查传感器的测量值和执行器状态，以确保物理过程处于 受控状态。
下面描述本发明实施方式的典型应用。比如，处理水厂状态监测实验。将本发明实施方式提出的神经UKF用于从安全水处理(SWaT)测试台收集的公共ICS数据日志上的异常检测。
具体来说，SWaT试验床是按比例缩小的水处理厂，具有六级过滤工艺以净化原水。6个PLC与24个传感器和27个执行器协同工作部署以控制整个过程。SWaT数据日志是通过以下方式收集的：通过不间断运行SWaT从空状态到完全运行状态。总共11天。在最初的7天中，该设备在正常条件下运行，即不受任何攻击。在剩下的4天内，在SWaT测试平台上发起了36种不同类型的攻击，包括针对水处理过程的单阶段单点攻击、单阶段多点攻击、多阶段单点攻击和多阶段多点攻击。数据集包含在所述持续时间内每秒收集的所有传感器和执行器值。每个数据点包含53个属性，其中24个是连续的传感器读数，27个是离散的执行器状态。在没有SWaT系统动力学的任何先验知识的情况下，使用前7天的数据日志(每10秒降采样到一个数据点)，使用本发明实施方式所示的方法学习神经UKF，然后将学习到的神经UKF在剩余4天的数据日志中检测受到攻击的异常过程状态。
具体来说，考虑使用FNN和RNN(实现为LSTM网络])作为状态转换函数。使用了两个分别基于FNN和RNN且结构与预测模型相同的、基于残差的异常检测模型作为基准模型。
首先使用以下四个用于异常检测的模型来显示真实阳性率(TPR)，其中伪阳性率(FPR)从0到0.1变化(ROC曲线)：
图5为本发明实施方式对现有技术的第一仿真效果对比图。
在图5中，横坐标为假阳性率(FPR)，纵坐标为真阳性率(TPR)。曲线51为采用本发明实施方式提出的、基于RNN的UKF的仿真曲线；曲线52为采用本发明实施方式提出的、基于FNN的UKF的仿真曲线；曲线53为现有技术的、基于RNN残差的模型的仿真曲线；曲线54为现有技术的、基于FNN残差的模型的仿真曲线。
从图5(ROC曲线)中可以看出，与基于FNN和RNN残差的检测模型相比，FNN神经UKF和RNN神经UKF可以实现更高的TPR。此外，如果针对某攻击类型的TPR大于0.1，认为可以检测到该攻击类型。
图6为本发明实施方式对现有技术的第二仿真效果对比图。图6展示在不同FPR情况下各种方法可以检测到的攻击类型数量。
在图6中，横坐标为假阳性率，纵坐标为检测到的攻击类型数目。曲线61为采用本发明方式提出的、基于RNN的UKF；曲线62为现有技术的、基于RNN残差的模型的仿真曲线； 曲线63为采用本发明方式提出的、基于FNN的UKF的仿真曲线；曲线64为现有技术的、基于FNN残差的模型的仿真曲线。
从图6能够看出，与基于残差的模型相比，使用神经UKF可以检测更多的攻击类型。实验表明，与常用的基于残留错误的方法相比，本发明实施方式可以更准确地检测异常行为。
因此，与直接基于噪声传感器测量进行ICS状态监测的基于残留误差的方法相比，本发明实施方式使用UKF算法监测物理过程的隐藏状态，可以更精确地检测异常行为。而且，本发明实施方式提出了一种从数据自动学习UKF的方法，而不是手动设计需要高系统知识和数学专业知识的UKF，从而显著降低了在实践中应用UKF进行状态监测的难度。还有，本发明实施方式使用神经网络来捕获UKF中的状态转换函数。与传统的基于卡尔曼滤波的算法相比，这使得神经UKF能够以高度非线性的系统动力学来监视ICS。
基于上述描述，本发明实施方式还提出了确定UKF的模型参数的装置。图7为本发明实施方式的确定UKF的模型参数的装置的第一示范性结构图。
如图7所示，确定UKF的模型参数的装置700包括：
数据获取模块701，用于获取传感器的检测数据；
第一确定模块702，用于基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；
训练模块703，用于利用所述去噪后的检测数据训练神经网络模型；
第二确定模块704，用于将所述训练后的神经网络模型确定为UKF的状态转移函数。
在一个实施方式中，还包括第三确定模块705，用于将训练后的神经网络模型输出的、传感器的预测值与所述传感器的检测值之间的残差分布，确定为所述UKF的过程噪音矩阵；将所述噪音分布的方差合并出的对角矩阵，确定为所述UKF的测量噪声矩阵。
在一个实施方式中，所述第一确定模块702，用于设置去噪后的检测数据的原始值；基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；基于所述传感器噪音分布的本次迭代值与所述检测数据，确定所述去噪后的检测数据的本次迭代值；利用所述去噪后的检测数据的本次迭代值更新去噪后的检测数据的上次迭代值。
在一个实施方式中，所述数据获取模块701，还用于获取执行器的状态数据；所述训练模块703，用于将所述去噪后的检测数据和所述状态数据作为训练数据，训练所述神经网络 模型。
图8为本发明实施方式的确定UKF的模型参数的装置的第二示范性结构图。
在图8中，确定UKF的模型参数的装置800包括一个存储器802和一个处理器801；存储器802中存储有可被处理器801执行的应用程序，用于使得处理器801执行如上任一项所述的确定无味卡尔曼滤波器的模型参数的方法。
需要说明的是，上述各流程和各结构图中不是所有的步骤和模块都是必须的，可以根据实际的需要忽略某些步骤或模块。各步骤的执行顺序不是固定的，可以根据需要进行调整。各模块的划分仅仅是为了便于描述采用的功能上的划分，实际实现时，一个模块可以分由多个模块实现，多个模块的功能也可以由同一个模块实现，这些模块可以位于同一个设备中，也可以位于不同的设备中。
各实施方式中的硬件模块可以以机械方式或电子方式实现。例如，一个硬件模块可以包括专门设计的永久性电路或逻辑器件(如专用处理器，如FPGA或ASIC)用于完成特定的操作。硬件模块也可以包括由软件临时配置的可编程逻辑器件或电路(如包括通用处理器或其它可编程处理器)用于执行特定操作。至于具体采用机械方式，或是采用专用的永久性电路，或是采用临时配置的电路(如由软件进行配置)来实现硬件模块，可以根据成本和时间上的考虑来决定。
本发明还提供了一种机器可读的存储介质，存储用于使一机器执行如本文所述方法的指令。具体地，可以提供配有存储介质的系统或者装置，在该存储介质上存储着实现上述实施例中任一实施方式的功能的软件程序代码，且使该系统或者装置的计算机(或CPU或MPU)读出并执行存储在存储介质中的程序代码。此外，还可以通过基于程序代码的指令使计算机上操作的操作系统等来完成部分或者全部的实际操作。还可以将从存储介质读出的程序代码写到插入计算机内的扩展板中所设置的存储器中或者写到与计算机相连接的扩展单元中设置的存储器中，随后基于程序代码的指令使安装在扩展板或者扩展单元上的CPU等来执行部分和全部实际操作，从而实现上述实施方式中任一实施方式的功能。
用于提供程序代码的存储介质实施方式包括软盘、硬盘、磁光盘、光盘(如CD-ROM、CD-R、CD-RW、DVD-ROM、DVD-RAM、DVD-RW、DVD+RW)、磁带、非易失性存储卡和ROM。可选择地，可以由通信网络从服务器计算机或云上下载程序代码。
以上所述，仅为本发明的较佳实施方式而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范 围之内。
上文通过附图和优选实施例对本发明进行了详细展示和说明，然而本发明不限于这些已揭示的实施例。基与上述多个实施例,本领域技术人员可以知晓，可以组合上述不同实施例中的代码审核手段得到本发明更多的实施例，这些实施例也在本发明的保护范围之内。

Claims (15)

  1. 确定无味卡尔曼滤波器的模型参数的方法(100)，其特征在于，包括：
    获取(101)传感器的检测数据；
    基于所述检测数据，确定(102)所述传感器的噪音分布和去噪后的检测数据；
    利用所述去噪后的检测数据训练(103)神经网络模型；
    将训练后的神经网络模型确定(104)为无味卡尔曼滤波器的状态转移函数。
  2. 根据权利要求1所述的方法(100)，其特征在于，还包括：
    将训练后的神经网络模型输出的传感器的预测值与所述传感器的检测值之间的残差分布，确定为所述无味卡尔曼滤波器的过程噪音矩阵；
    将所述噪音分布的方差排列成的对角矩阵，确定为所述无味卡尔曼滤波器的测量噪声矩阵。
  3. 根据权利要求1所述的方法(100)，其特征在于，基于所述检测数据，确定(102)所述传感器的噪音分布和去噪后的检测数据包括：
    设置去噪后的检测数据的原始值；
    基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：
    基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；
    基于所述传感器噪音分布的本次迭代值与所述检测数据，确定所述去噪后的检测数据的本次迭代值；
    利用所述去噪后的检测数据的本次迭代值更新所述去噪后的检测数据的上次迭代值。
  4. 根据权利要求1所述的方法(100)，其特征在于，所述方法应用于包括执行器的工业控制系统，还包括：
    获取所述工业控制系统中执行器的状态数据；
    利用所述去噪后的检测数据训练(103)神经网络模型包括：将所述去噪后的检测数据和所述状态数据作为训练数据，训练(103)所述神经网络模型。
  5. 确定无味卡尔曼滤波器的模型参数的装置(700)，其特征在于，包括：
    数据获取模块(701)，用于获取传感器的检测数据；
    第一确定模块(702)，用于基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；
    训练模块(703)，用于利用所述去噪后的检测数据训练神经网络模型；
    第二确定模块(704)，用于将训练后的神经网络模型确定为无味卡尔曼滤波器的状态转移函数。
  6. 根据权利要求5所述的装置(700)，其特征在于，还包括：
    第三确定模块(705)，用于将训练后的神经网络模型输出的、传感器的预测值与所述传感器的检测值之间的残差分布，确定为所述无味卡尔曼滤波器的过程噪音矩阵；将所述噪音分布的方差排列成的对角矩阵，确定为所述无味卡尔曼滤波器的测量噪声矩阵。
  7. 根据权利要求5所述的装置(700)，其特征在于，
    所述第一确定模块(702)，用于设置去噪后的检测数据的原始值；基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；基于所述传感器噪音分布的本次迭代值与所述检测数据，确定所述去噪后的检测数据的本次迭代值；利用所述去噪后的检测数据的本次迭代值更新去噪后的检测数据的上次迭代值。
  8. 根据权利要求5所述的装置(700)，其特征在于，所述装置(700)应用于包括执行器的工业控制系统；其中：
    所述数据获取模块(701)，还用于获取工业控制系统中执行器的状态数据；
    所述训练模块(703)，用于将所述去噪后的检测数据和所述状态数据作为训练数据，训练所述神经网络模型。
  9. 确定无味卡尔曼滤波器的模型参数的系统(20)，其特征在于，包括：
    存储器(21)，用于保存传感器对物理量的检测数据以及执行器的状态数据，其中所述执行器适配于基于与所述检测数据相关的指令执行动作；
    处理器(22)，被配置用于：
    从所述存储器(21)获取所述检测数据和所述状态数据；
    基于所述检测数据，确定所述传感器的噪音分布和去噪后的检测数据；
    将所述去噪后的检测数据和所述状态数据作为训练数据，训练神经网络模型；
    将所述训练后的神经网络模型确定为无味卡尔曼滤波器的状态转移函数。
  10. 根据权利要求9所述的系统(20)，其特征在于，
    所述处理器(22)，被配置用于：
    将训练后的神经网络模型输出的传感器的预测值与所述传感器的检测值之间的残差分布， 确定为所述无味卡尔曼滤波器的过程噪音矩阵；将所述噪音分布的方差排列成的对角矩阵，确定为所述无味卡尔曼滤波器的测量噪声矩阵。
  11. 根据权利要求9所述的系统(20)，其特征在于，
    所述处理器(22)，被配置用于：
    设置去噪后的检测数据的原始值；
    基于所述去噪后的检测数据的原始值和所述检测数据，迭代计算传感器噪音分布和去噪后的检测数据，其中每次迭代包括：
    基于所述去噪后的检测数据的上次迭代值和所述检测数据，确定所述传感器噪音分布的本次迭代值；
    基于所述传感器噪音分布的本次迭代值与所述检测数据，确定所述去噪后的检测数据的本次迭代值；
    利用所述去噪后的检测数据的本次迭代值更新所述去噪后的检测数据的上次迭代值。
  12. 工业控制系统(30)，其特征在于，包括：
    第一接口(31)，与传感器耦合；
    第二接口(32)，与执行器耦合；
    无味卡尔曼滤波器(33)，用于基于所述第一接口(31)从传感器获取检测数据(35)，基于所述第二接口(32)从所述执行器获取所述状态数据(36)；基于所述检测数据(35)和所述状态数据(36)生成去噪后的检测数据(37)；
    其中所述无味卡尔曼滤波器(33)应用权利要求1-4中任一项所述方法(100)确定出模型参数。
  13. 应用权利要求1-4中任一项所述方法(100)确定出模型参数的无味卡尔曼滤波器。
  14. 确定无味卡尔曼滤波器的模型参数的装置(800)，其特征在于，包括处理器(801)和存储器(802)；
    所述存储器(802)中存储有可被所述处理器(801)执行的应用程序，用于使得所述处理器(801)执行如权利要求1至4中任一项所述的确定无味卡尔曼滤波器的模型参数的方法(100)。
  15. 计算机可读存储介质，其特征在于，其中存储有计算机可读指令，该计算机可读指 令用于执行如权利要求1至4中任一项所述的确定无味卡尔曼滤波器的模型参数的方法(100)。
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