A method and device for detecting faults in downhole tool accelerometers

Abstract

This invention discloses a method and device for detecting faults in downhole tool accelerometers. Using the accelerometer and gyroscope as state variables, a generalized nonlinear system is established for the downhole tool sensor model, and linearized to obtain a generalized linear variable parameter system. Based on a T-N-L observer architecture, system state estimation error equations and residual generation equations are constructed. Based on these equations, a fault sensitivity and disturbance robustness evaluation system is established to determine the observer parameters. The sensor acquires system state values, and the residual values ​​of the current system state variables are calculated using the estimated values ​​obtained from the observer to determine the occurrence of events. The threshold for sensor fault occurrence under the current event is also calculated to determine the fault situation. The nonlinear model more accurately describes the system dynamics. Linearizing the model ensures a high degree of matching between the model and actual operating conditions while obtaining a corresponding linear variable parameter system to reduce computational load.

Description

Technical Field

[0001] This invention belongs to the field of drilling tool technology, specifically relating to a method and device for detecting faults in downhole tool accelerometers. Background Technology

[0002] In oil drilling engineering, to achieve precise monitoring and process optimization of drilling operations, it is necessary to construct a multi-source heterogeneous sensing system to collect key drilling parameters (including drilling pressure, torque, and rotational speed) in real time. Among them, the accelerometer, as one of the core sensors, provides irreplaceable dynamic sensing support for intelligent diagnosis of drilling status, drill bit performance evaluation, and drilling parameter optimization decisions by capturing dynamic parameters such as drill string vibration, downhole impact, and attitude changes in real time. Its high-frequency sampling capability of multi-dimensional vibration signals is irreplaceable in monitoring complex downhole conditions.

[0003] Due to the complexity of the working environment, especially in the oil drilling field, sensors operate for extended periods in harsh downhole conditions such as high temperatures, strong vibrations, and mud erosion, resulting in a persistently high failure rate for accelerometers. Instrument malfunctions downhole can range from affecting drilling accuracy to requiring tripping out of the well for repairs, causing significant economic losses, or even leading to accidents. Therefore, timely detection of downhole accelerometer malfunctions in their early stages is crucial for improving drilling tool reliability and reducing drilling costs.

[0004] Fault detection of downhole accelerometers requires precise modeling. Inaccurate models lead to fundamental deviations between the dynamic characteristics of the fault detection model and the actual system, directly reducing detection sensitivity and potentially causing detection failure. Due to the multi-degree-of-freedom coupled dynamics of drilling systems, downhole accelerometers exhibit strong nonlinear time-varying characteristics and multi-state coupling features, making complete physical modeling difficult. Given these complex operating conditions and modeling challenges, research on online fault detection for downhole accelerometers is crucial for improving drilling reliability and reducing operating costs. This research has significant engineering value in overcoming the bottleneck of state perception under extreme conditions and ensuring the safety of deep well drilling.

[0005] Chinese Patent Publication No. CN115467651A, published on December 13, 2022, discloses an invention entitled "Method for Detecting Intermittent Faults of Accelerometers in Rotary Steering Drilling Tool Systems." This application discloses a method for detecting intermittent faults of accelerometers in rotary steering drilling tool systems. Its shortcomings are: 1. The uncertainty between the model and the actual system is not considered when modeling the accelerometer system; 2. Fault sensitivity is not considered when designing the fault detection method.

[0006] Chinese Patent Publication No. CN118551138A, published on August 27, 2024, discloses an invention entitled "A Method for Fault Separation of Accelerometers in Rotary Steering Drilling Tool Attitude Measurement Devices under Strong Noise." This application discloses a method for fault separation of accelerometers in rotary steering drilling tool systems. Its drawback is that using a Kalman filter (EKF) to process measurement noise requires knowledge of the noise probability distribution, which is difficult to ascertain in practice.

[0007] The literature (Yang Y, Geng Y, Wang W. Sensor fault detection and isolation based on zonotopic Kalman filter for accelerometer system in drilling tools. Measurement. 2023 Feb 15;207:112329.) addresses accelerometer systems by using a zonotopic Kalman filter (ZKF) to determine the boundaries of parameter uncertainty and measurement noise. Finally, fault detection is achieved through time-varying residual boundaries derived from a combination of residuals and dynamic thresholds. The drawback of this method is that using ZKF to obtain residual and boundary information only considers the system's robustness, which may lead to insufficient sensitivity for different systems, resulting in missed fault detections. Summary of the Invention

[0008] To address the aforementioned problems, the purpose of this invention is to provide a method and device for fault detection of accelerometers in rotary steered drilling tools. First, a system model is performed on the spatial layout of the downhole accelerometer to improve the fitting accuracy with the actual system, providing a guarantee for subsequent fault detection. The system is designed with interference robustness and fault sensitivity to improve fault detection sensitivity. A fault occurrence judgment mechanism is designed to promptly alarm for accelerometer faults. To address the constraints of low computing power in the high-temperature downhole environment, the developed online accelerometer fault detection device adopts a dual-circuit board architecture. Functional decoupling distributes the computational burden on the microcontroller, and combined with a fault information hierarchical reporting mechanism, it obtains more fault information while ensuring real-time performance.

[0009] The present invention achieves the above objectives through the following technical solutions:

[0010] A method for detecting faults in downhole tool accelerometers includes:

[0011] Using accelerometers and gyroscopes as state variables, a generalized nonlinear system is established for the downhole tool sensor model, and then linearized to obtain a generalized linear variable parameter system.

[0012] Based on the TNL observer architecture, system state estimation error equation and residual generation equation are constructed. Based on the system state estimation error equation and residual generation equation, a fault sensitivity and disturbance robustness evaluation system is established, and the observer parameters are determined.

[0013] The sensor acquires the system state value, the observer obtains the estimated value, calculates the residual value of the current system state quantity to determine the occurrence of an event, and calculates the threshold for sensor failure under the current event to determine the failure situation.

[0014] Furthermore, the method for constructing the generalized nonlinear system is as follows: establish a northeast geodetic coordinate system. and the carrier coordinate system The carrier coordinate system The axis coincides with the wellbore axis, indicating the axial direction of the drill string and the carrier coordinate system. The plane formed by the axes is the cross-section of the drill bit; the accelerometer xyz axes are sequentially distributed on the xyz axes of the carrier coordinate system. When the accelerometer xyz axes coincide with the established carrier coordinate system, the vertically downward gravitational acceleration is... Decomposed into x-axis components and the y-axis component on the bottom circular plane of the well and z-axis components Therefore, the following formula is obtained:

[0015] ;

[0016] in The well inclination angle, Let be the face angle of the gravity tool. Taking the derivative of the face angle of the gravity tool, we get:

[0017] ;

[0018] in Let the angular velocity be measured by the gyroscope, and let the system state vector be... The state equations for the accelerometer and gyroscope are established as follows:

[0019] ;

[0020] in: , ;

[0021] The system's measurement equations are as follows:

[0022] ;

[0023] In the formula and For unit array, The fault distribution matrix is... For sensor measurement noise, This is the fault vector of the sensor;

[0024] The state-space representation of downhole tools is as follows:

[0025] ;

[0026] in, , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The derivative of the system state vector at time t, A constant matrix of appropriate dimension that satisfies ,in for dimensionality for polynomial nonlinear functions, For the output matrix, The noise distribution matrix is... This is the fault distribution matrix.

[0027] Furthermore, the linearization process is as follows:

[0028] for and ,definition ,in For the set of integers, For the Kronecker product, based on the Kronecker operation rules and the generalized nonlinear system model, we obtain:

[0029] ;

[0030] vector , for Define the operations on the set of 3D real numbers. and ,in For nonlinear functions exist Performing a Taylor series expansion at this point, we obtain:

[0031] ;

[0032] in The Taylor coefficient matrix is... Let be the order of the Taylor series expansion. It is the set of non-negative integers. , Let be the Lagrange remainder coefficient matrix. , , , System status exist The estimated value of the time.

[0033] Furthermore, the Lagrange remainder is processed as follows:

[0034] ;

[0035] in ,definition , ,in Operations, If the vector is a vector, then find the magnitude of the vector. Given a matrix, find the maximum singular value of the matrix. It is a constant. , , Given the corresponding generating matrix, we finally obtain:

[0036] ;

[0037] in , For unknown uncertain terms and ;Will Unfold, and you get:

[0038] ;

[0039] in For a variable parameter state matrix, This represents the unknown uncertainties after linearization.

[0040] Furthermore, the method for obtaining a generalized linear variable parameter system based on the downhole tool linearization system involves processing the output equations:

[0041] ;

[0042] in , and These are the corresponding dimension matrices; the downhole tool linearization system is augmented, and defined as follows: , , , ,in , , , , , , This results in the following augmented system:

[0043] ;

[0044] in , , , , , , , ;

[0045] The augmented system is discretized using the Euler method to obtain the corresponding generalized linear variable parameter system model:

[0046] ;

[0047] in , , Sampling time, , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The system state vector at any given time. For the system matrix, The uncertainties after linearization For the output matrix, The noise distribution matrix is... This is the fault distribution matrix; For a variable parameter matrix, it is expressed in the following form:

[0048] ;

[0049] in It includes polyhedron for The number of vertices, for The first corresponding to the variable parameter matrix One vertex, For weighted functions, ,satisfy:

[0050] .

[0051] Furthermore, the method for establishing the TNL observer is as follows:

[0052] For the obtained generalized linear system, a TNL observer is established;

[0053] The residual system equations are divided into residual equations for the fault subsystem and residual equations for the disturbance subsystem;

[0054] Using finite frequency domain Sensitivity design is performed on the faulty subsystem based on the indicators, and sensitivity indicators are established; a member-based approach is adopted. The radius index is used to robustly design the interference subsystem, and a robustness index is established.

[0055] The multi-objective optimization problem of sensitivity and robustness indices is transformed into solving linear matrix inequalities, and the observer parameter matrix is ​​calculated. , , .

[0056] Furthermore, for the obtained generalized linear system, the TNL observer equation is established to obtain... System state vector observation at time 1 and Observations of the output vector at time step The calculation formula; the definition of state estimation error. residual ,in for The observed state vector of the system at time t can be obtained from the generalized linear system and TNL observer equations. Error in state estimation at time 1 and residual The calculation formula is as follows: the residual equation is divided into a fault subsystem and a disturbance subsystem to obtain the subsystem... Time error and The residual at time is , and , Using finite frequency domain index Sensitivity design is performed on the faulty subsystem, where The system's sensitivity to faults; employing a member-based approach. The radius index is used for robust design of the interference subsystem. Based on the interference subsystem, the ellipsoidal bundle of the interference subsystem error can be obtained. And satisfy:

[0057] ;

[0058] in , They are respectively Time and time The center vector, , They are respectively Time and time The generating matrix; for The parameter matrix formed by the maximum values ​​of each element in the matrix; for The center vector of the ellipsoidal bundle at time state vector. for The generation matrix of the ellipsoidal bundle of state vectors at time step; for The generation matrix of the ellipsoidal bundle of noise variation over time; for The generation matrix of the noise ellipsoidal bundle at any given time; for The generation matrix of the fault change ellipsoidal bundle at time intervals;

[0059] Finally, the multi-objective optimization problem of sensitivity and robustness indices is transformed into solving linear matrix inequalities to obtain the corresponding observer parameter matrix.

[0060] Furthermore, the ellipsoidal bundle of the interference residual subsystem is reduced in dimensionality using the following method: dimensional ellipsoidal bundle and integers , for A 3D hypercube, and satisfies ,definition To be The matrix obtained by arranging the column vectors in descending order of Euclidean norm is then the dimension-reduced matrix. ,in for The front of the matrix List, For the remaining columns, It is a diagonal matrix, and ,in express The One element, express The absolute value of the first One element, , .

[0061] Furthermore, the evaluation mechanism for fault occurrence first involves calculating... And satisfy:

[0062] ;

[0063] in For interference subsystem Time residual ellipsoidal bundle for The center vector, for The generating matrix; the fault occurrence mechanism judgment method is:

[0064] ;

[0065] in , for Time residual The One portion, for The absolute value, for The absolute value of the maximum boundary. It can be calculated using the following formula.

[0066] ;

[0067] in for Time matrix The OK, To calculate vectors The 1-norm.

[0068] A downhole tool accelerometer fault detection device includes a drill collar body. A first circuit board and a second circuit board are installed within the drill collar body. The first circuit board includes a first microprocessor and an auxiliary gyroscope. The second circuit board includes a communication interface and a second microprocessor. Accelerometer measurements are transmitted to the first and second microcontrollers via the communication interface. The first microcontroller on the first circuit board obtains observation values ​​for each state based on the data from the auxiliary gyroscope and accelerometer using a TNL observer and a linearized LPV system model. The observation values ​​obtained by the first microcontroller are transmitted to the second circuit board via SPI communication. The second microcontroller calculates the residual value of the current system state quantity based on the observation values ​​calculated by the first circuit board and the sensor measurements to determine the occurrence of an event, and calculates a threshold value for sensor fault occurrence under the current event to determine the fault situation. The fault monitoring device sends a fault alarm signal to the ground, where the residual information exceeds a multiple of the threshold value.

[0069] The beneficial effects of this invention are as follows:

[0070] This invention provides a method and device for fault detection of downhole tool accelerometers. By constructing a generalized nonlinear system model using accelerometers and gyroscopes as state variables, the dynamic characteristics of the sensors are accurately characterized, improving the model's fit with actual operating conditions. The generalized nonlinear system is linearized to ensure a high degree of model-to-actual-condition matching while obtaining a corresponding linear variable-parameter system to reduce computational load. An ellipsoidal bundle representation method is used to quantitatively describe the boundaries of uncertain information such as quantization errors and noise, obtaining a more accurate threshold. A finite-frequency domain sensitivity index is introduced to optimize the ellipsoidal bundle, improving fault detection sensitivity, and a fault detector is designed to achieve online fault detection.

[0071] The detection device employs a tiered fault information uploading mechanism and includes two sets of data processing boards. The first and second data processing boards work collaboratively, providing fault detection and model linearization functions respectively. This reduces the computational demands on the microcontroller and meets the low-power, high-reliability operation requirements of the downhole high-temperature environment. The dual-machine collaboration alleviates the computational burden during linearization, facilitating online deployment during the drilling process. Attached Figure Description

[0072] Figure 1 This is a flowchart of the downhole tool accelerometer fault detection method of the present invention;

[0073] Figure 2 This is a schematic diagram of the attitude parameters of the drilling tool;

[0074] Figure 3 Sensor spatial layout diagram for stable platform;

[0075] Figure 4 This is a decomposition diagram of the x-axis components of the carrier coordinate system;

[0076] Figure 5 This is a component decomposition diagram on the circular plane at the bottom of the well;

[0077] Figure 6 This is a flowchart illustrating the application of the present invention in a rotary steerable drilling tool attitude measurement system.

[0078] Figure 7 This is a flowchart of another embodiment of the present invention;

[0079] Figure 8 The magnitude of the added fault is the first... ( At the accelerometer Add to the shaft The magnitude of the constant bias fault;

[0080] Figure 9 The graph shows the residuals and threshold results after adding faults;

[0081] Figure 10 This is a diagram showing the results of the fault alarm.

[0082] Figure 11 This is a schematic diagram of the structure of a downhole accelerometer fault detection device;

[0083] Figure 12 This is a diagram showing the specific module relationships of the downhole accelerometer fault detection device.

[0084] Wherein: 1-First end cap, 2-Drill collar body, 3-Second circuit board, 301-First communication protection module, 302-Second microcontroller, 303-Storage module, 304-Power interface, 305-Communication interface, 306-Second communication protection module, 4-First circuit board, 401-Communication protection module, 402-First microcontroller, 403-Auxiliary gyroscope, 5-Second end cap. Detailed Implementation

[0085] In drilling tool fault detection, due to the complex relationships between various devices such as sensors, a linear model is typically established using only the accelerometer as the state variable and the gyroscope as noise. However, this method results in significant discrepancies between the system model and the actual device, leading to low fault detection accuracy. Establishing a system model with high fitting accuracy and sensitivity to faults is a key challenge. This patent focuses on a downhole accelerometer fault detection method and device. It establishes a nonlinear system using accelerometers and gyroscopes for downhole tool sensors and obtains a new accelerometer fault detection model through a linearization method for generalized nonlinear systems, thereby improving the accuracy and reliability of fault detection.

[0086] like Figure 1 As shown, a method for detecting faults in downhole tool accelerometers includes the following steps:

[0087] S101: Using accelerometers and gyroscopes as state variables, a generalized nonlinear system is established for the downhole tool sensor model. The nonlinear system is then linearized to obtain the corresponding generalized linear variable parameter (LPV) system.

[0088] In attitude measurement of accelerometer systems, gyroscopes are usually added to assist in the measurement. How to establish a mathematical model that includes all sensors is a key point and a challenge in sensor fault detection.

[0089] The parameters of the drill string's attitude downhole are defined as follows: Figure 2 As shown. Among them The wellbore inclination angle is the angle between the wellbore direction line and the vertical line. The wellbore inclination angle describes the angle by which the wellbore deviates from the vertical direction; a zero inclination angle indicates a vertical well. The angle of the gravity tool face is the direction line of the upper edge. Turn clockwise to The angle.

[0090] Spatial layout of sensors in attitude measurement system as follows Figure 3 As shown, the sensor includes a three-axis accelerometer and a gyroscope. The reason for choosing a centrally symmetrical sensor layout is that rotational acceleration is inevitably introduced during the drill's rotation, and this layout minimizes the impact of rotational acceleration. Therefore, during dynamic measurements, vibration noise can be considered the only source of interference from the gravitational component.

[0091] The attitude matrix is ​​represented using the Euler angle method. A northeast geodetic coordinate system is established. and the carrier coordinate system The carrier coordinate system The axis coincides with the wellbore axis, indicating the axial direction of the drill string and the carrier coordinate system. The plane formed by the axes is the cross-section of the drill bit. Accelerometers are distributed along the coordinate axes of the carrier coordinate system. Both the geodetic coordinate system and the carrier coordinate system conform to the right-hand rule. When rotating along the coordinate axes with the origin as the starting point, counterclockwise rotation is positive, and clockwise rotation is negative. The carrier coordinate system can be obtained by transforming the geodetic coordinate system using the current attitude angle of the drill bit.

[0092] Based on the measurement principle of a centrally symmetric accelerometer, when the xyz axes of the accelerometer coincide with the established carrier coordinate system, according to the vector decomposition rules as follows: Figure 4 and Figure 5 As shown, the vertically downward gravitational acceleration can be... Decomposed into x-axis components in the carrier coordinate system And the component on the circular plane at the bottom of the well, such as Figure 5 Decomposed into y-axis components and z-axis components Therefore, the following formula is obtained:

[0093] ;

[0094] Differentiating the angle of the gravity tool face, we get:

[0095] ;

[0096] in Let the angular velocity be measured by the gyroscope. The state equations for the accelerometer and gyroscope are established as follows:

[0097] ;

[0098] in: , .

[0099] During drilling, directional drilling tools often operate in harsh environments with high temperature, high pressure, and strong vibration. The measurements from accelerometers and gyroscopes often contain a lot of noise, and the sensors are extremely prone to damage and failure. The above model can be used to detect faults in accelerometers and gyroscopes. The measurement equations of the system are as follows:

[0100] ;

[0101] In the formula and For unit array, The fault distribution matrix is... For sensor measurement noise, This is the fault vector of the sensor.

[0102] In summary, the state-space expression of the attitude measurement system is as follows:

[0103] ;

[0104] Since it is a generalized nonlinear system, it needs to be linearized first for subsequent noise filtering and fault detection. , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The derivative of the system state vector at time t, A constant matrix of appropriate dimension that satisfies ,in for dimensionality for polynomial nonlinear functions, For the output matrix, The noise distribution matrix is... This is the fault distribution matrix.

[0105] To achieve fault detection of sensors, the aforementioned generalized nonlinear system needs to be linearized, transforming it into a linear system. This ensures a high degree of matching between the model and actual operating conditions while obtaining a corresponding linear variable parameter system to reduce computational load. and ,definition ,in For the set of integers, Expressed as the Kronecker product, then:

[0106] ;

[0107] Considering the Kronecker operation rule and the generalized nonlinear system model, we can obtain:

[0108] ;

[0109] For vectors , for The set of real numbers, acting on the function operation Defined as and ,in For nonlinear functions exist Performing a Taylor series expansion at this point, we get:

[0110] ;

[0111] in The Taylor coefficient matrix is... Let be the order of the Taylor series expansion. The larger the value, the higher the linearization accuracy. It is the set of non-negative integers. , Let Lagrange remainder coefficient matrix be the matrix of coefficients. , , , System status exist The estimated value of the time. It is any number between 0 and 1. For the reason A diagonal matrix composed of arbitrary numbers is obtained. for and Any vector between them.

[0112] To further improve the fitting accuracy, the Lagrange remainder term was processed:

[0113] ;

[0114] in .definition , ,in Operations, If the vector is a vector, then find the magnitude of the vector. Given a matrix, find the maximum singular value of the matrix. It is a constant. , , Given the corresponding generating matrix, we have:

[0115] ;

[0116] Where the unknown vector and , for The set of real numbers is given by the following form:

[0117] ;

[0118] in , For unknown uncertain terms and .

[0119] Will Expanding, we get:

[0120] ;

[0121] in For a variable parameter state matrix, For the unknown uncertainties after linearization, when When the value is taken to infinity, the uncertain term will be zero.

[0122] To meet the requirements of subsequent observer design, the linearized equations need to be transformed into a generalized linear variable parameter (LPV) system, and the output equations need to be processed:

[0123] ;

[0124] in , and These are the corresponding dimension matrices.

[0125] Then the system is augmented and defined. , , , ,in , , , Therefore, the following augmented system can be obtained:

[0126] ;

[0127] in , , , , , , , .

[0128] By discretizing the augmented system using the Euler method, the corresponding generalized linear variable parameter (LPV) system model can be obtained:

[0129] ;

[0130] in , , Sampling time, , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The system state vector at any given time. For the system matrix, The uncertainties after linearization For the output matrix, The noise distribution matrix is... The fault distribution matrix is... This is the augmented constant matrix.

[0131] For a variable parameter matrix, it can be expressed in the following form:

[0132] ;

[0133] in It includes polyhedron for The number of vertices, for The first corresponding to the variable parameter matrix One vertex, For weighted functions, ,satisfy:

[0134] .

[0135] S102: Based on the TNL observer architecture, construct the system state estimation error equation and residual generation equation, and on this basis, establish a fault sensitivity and disturbance robustness evaluation system and determine the observer parameters.

[0136] The TNL observer design method is as follows: For the obtained generalized linear system, the TNL observer is designed in the following form:

[0137] ;

[0138] in, , They are respectively The observed values ​​of the system state vector and output vector at time points. for The system state vector observation at time t, , , The observer matrix to be designed must satisfy the following conditions: .

[0139] The state estimation error is: ;

[0140] The residual is: ;

[0141] The residual system equations are thus obtained as follows:

[0142] ;

[0143] in and They are respectively Time and Error in state estimation at time t. for The system residual at time intervals, and They are respectively Continuously measure changes in noise and sensor malfunctions.

[0144] In order to design fault sensitivity and disturbance robustness for the residual system equation, the equation is divided into a fault subsystem and a disturbance subsystem for separate design.

[0145] The faulty subsystem is:

[0146] ;

[0147] in and They are respectively Time and The state estimation error of the faulty subsystem at time t. for The system residual of the faulty subsystem at any given moment.

[0148] The interference subsystem is:

[0149] ;

[0150] in and They are respectively Time and The state estimation error of the disturbance subsystem at time t. for The system residuals of the constantly disturbing subsystem.

[0151] Using finite frequency domain If the sensitivity design is applied to the faulty subsystem, then the sensitivity index is:

[0152] ;

[0153] in The sensitivity of the reaction system to faults, The larger the value, the higher the sensitivity.

[0154] Adopting a member-based approach The radius index is used for robust design of the interference subsystem. First, based on the interference subsystem, the ellipsoidal bundle of the interference residual subsystem can be obtained as follows:

[0155] ;

[0156] in Minkowski and two sets and Minkowski and defined as . Represents a linear mapping, ellipsoidal bundle With a matrix A linear mapping can be obtained through standard matrix multiplication: . For interference subsystem Time residual ellipsoidal bundle for The center vector, for The generating matrix. For interference subsystem The ellipsoidal bundle of time-state estimation error for The center vector, for The generating matrix, For interference subsystem Ellipsoidal bundle of time-state estimation error. for The parameter matrix formed by the maximum values ​​of each element. for The ellipsoidal bundle of the state vector at time step. for The center vector, for The generating matrix. for Ellipsoidal bundle of noise variation over time for The generating matrix. for An ellipsoidal beam that measures noise at all times. for The generating matrix. for Ellipsoidal bundle of fault variation over time for The generating matrix.

[0157] further, And satisfy:

[0158] The ellipsoidal bundle was used to characterize the noise and linearization error boundary.

[0159] definition of radius is Then we can get The radius index is:

[0160] ;

[0161] in and Interference subsystems Time and Error of state estimation at time step radius. For a given scalar, This represents the magnitude of the impact of disturbances on the state estimation error. Thus, the state estimation error... The radius will eventually converge to .

[0162] The multi-objective optimization problem of sensitivity and robustness indices is transformed into solving linear matrix inequalities:

[0163] ;

[0164] in and , These represent the weights of the sensitivity and robustness indices, respectively. By optimizing the above objectives, we can obtain:

[0165] ;

[0166] in , and To substitute the corresponding vertex The observer parameter matrix obtained by optimization.

[0167] S103: The system measurement values ​​are obtained by the sensor, and the residual value of the current system state quantity is calculated by the estimated value obtained by the observer to determine the occurrence of the event. The threshold for the occurrence of sensor failure under the current event is also calculated to determine the fault situation.

[0168] first, And satisfy:

[0169] .

[0170] Furthermore, the method for determining the fault occurrence mechanism is as follows: Based on the residual system equation, when the system is operating normally, the residual system equation can be approximated by the disturbance subsystem, then the residual ellipsoidal bundle... It will always contain the true residual, that is If a malfunction occurs, then This will no longer be satisfied. Therefore, a residual evaluation mechanism based on ellipsoidal bundles is proposed: ;

[0171] in , for Time residual The One portion, for The absolute value, for The absolute value of the maximum boundary. It can be calculated using the following formula:

[0172] ;

[0173] in for Time matrix The OK, For vectors The 1-norm.

[0174] In another embodiment, the rotary steerable drilling tool is a common downhole drilling tool, such as... Figure 2 As shown, the method for detecting accelerometer faults in downhole tools is applied to rotary steered drilling tools, providing a method for detecting accelerometer faults in rotary steered drilling tools, including the following steps:

[0175] S201: Based on the physical and spatial layout characteristics of the sensors in the rotary steerable drilling tool attitude measurement system, a generalized polynomial nonlinear system model of the accelerometer and gyroscope is established, and then linearized to obtain the corresponding generalized linear variable parameter (LPV) system.

[0176] Rotary steerable drilling tools are equipped with gyroscopes and accelerometers to obtain drilling information such as drilling speed and gravity tool face angle.

[0177] Reference Figure 3 The spatial arrangement of gyroscopes and accelerometers in rotary steerable drilling tools is as follows: Figure 3 As shown, its layout is centrally symmetrical, which minimizes the impact of rotational acceleration on the accelerometer.

[0178] Based on the aforementioned sensor spatial layout, a system model for the gyroscope and accelerometer can be established. Due to state coupling, the established model is a generalized polynomial nonlinear system model. To facilitate subsequent fault detection design, the model needs to be linearized. A linearization method is used to improve the model's fitting accuracy to the actual system, ultimately resulting in a generalized linear variable parameter (LPV) system.

[0179] The mathematical models for the accelerometer and gyroscope in the attitude measurement system of a rotary steerable drilling tool are as follows:

[0180] ;

[0181] in For state vectors, , and Gravity exist , , The gravitational component on the axis, ω is the angular velocity. , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The derivative of the system state vector at time t, A constant matrix of appropriate dimension that satisfies ,in for dimensionality for polynomial nonlinear functions, For the output matrix, The noise distribution matrix is... This is the fault distribution matrix. The specific system parameters are:

[0182] , , , , .

[0183] After linearizing the generalized nonlinear system, we obtain:

[0184] ;

[0185] Where the definition and , , Represented as the Kronecker product, the linearized parameters are: , , , ,in , , , , respectively, are augmentations of the original state vector, output vector, measurement noise vector, and fault vector, representing The state vector, output vector, measurement noise vector, and fault vector at each moment. It is a known generalized matrix. It is a variable parameter matrix. The uncertainty matrix caused by system linearization. , These are the measurement noise distribution matrix and the fault distribution matrix, respectively.

[0186] Pick The specific forms of each parameter are as follows:

[0187] , , , , , , , , , .

[0188] in , , , , . , Here, represents the uncertain term after linearization, where , express The number of rows here is 4. ,set up The ellipsoidal bundle of the initial state vector. State vector The center vector is also an estimate of the state vector. for The generating matrix. , , and The values ​​are 0, 1, 1, and 0 respectively. For an unknown matrix of a given dimension, only the known dimension is known. Right now The maximum singular value is less than or equal to 1.

[0189] Discretization using the Euler method yields:

[0190] ;

[0191] in For a variable parameter matrix and ,in for The vertices corresponding to the variable parameter matrix For including variable parameters multicellular The number of vertices, , For a weighted function, satisfying . , Sampling time, , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The system state vector at any given time. For the system matrix, The uncertainties after linearization For the output matrix, The noise distribution matrix is... This is the fault distribution matrix. From this, the specific forms of each parameter can be obtained as follows: , ,according to The specific form of the matrix reveals its main influence. , and These three parameters have an impact, so there are corresponding... A vertex, due to , , Since each parameter is bounded, we obtain the values ​​of each vertex and the weight function.

[0192] S202: For the generalized LPV system of rotary steerable drilling tools, a TNL observer is established to obtain the system's state estimation error equation and residual generation equation. Based on this, a fault sensitivity and disturbance robustness evaluation system is established, and the observer parameters are determined.

[0193] Based on the TNL observer architecture, the state estimation error equation and residual generation equation are established, according to the finite frequency domain. Indicators and The radius index was used to perform fault sensitivity and disturbance robustness analysis to determine the observer parameters.

[0194] The observer design method for the generalized LPV system of rotary steerable drilling tools is as follows: The TNL observer is designed as follows:

[0195] ;

[0196] in, , They are respectively The observed values ​​of the system state vector and output vector at time points. for The system state vector observation at time t, , , The observer matrix to be designed must satisfy the following conditions: .

[0197] Error in state estimation at time 1 residual , Measure noise change at all times Fault variation The residual system equations for the rotary steerable drilling tool attitude measurement system are as follows:

[0198] ;

[0199] Its fault subsystem and interference subsystem are as follows:

[0200] The faulty subsystem is:

[0201] ;

[0202] The interference subsystem is:

[0203] ;

[0204] According to the finite frequency domain Indicators for sensitivity design of faulty subsystems:

[0205] ;

[0206] Furthermore, robust design is implemented, employing... The radius index is given below; therefore, the definition of a one-dimensional ellipsoidal bundle is first:

[0207] ;

[0208] in The center vector of the ellipsoidal bundle. For Minkowski sum operations, Let be the generation matrix of the ellipsoidal bundle. For a unit hypercube, denoted as the dimension of the multicellular organism.

[0209] Then, based on the interference subsystem, the corresponding ellipsoidal bundle can be obtained as follows:

[0210] ;

[0211] in For interference subsystem Time residual ellipsoidal bundle. and Interference subsystems Time and Ellipsoidal bundle of time-state estimation error. for The parameter matrix formed by the maximum values ​​of each element. for The ellipsoidal bundle of the state vector at time step. for The center vector, for The generating matrix. for Ellipsoidal bundle of noise variation over time for The generating matrix. for An ellipsoidal beam that measures noise at all times. for The generating matrix. for Ellipsoidal bundle of fault variation over time for The generating matrix.

[0212] In this embodiment, , , , If it is a constant and does not change with time, then:

[0213] , , , .

[0214] Furthermore, the method for calculating the ellipsoidal bundle of the interference residual subsystem can be obtained as follows:

[0215] according to As can be seen from the calculation formula, there is a problem of the dimension continuously increasing during the operation. Therefore, it is necessary to reduce the dimension of the matrix. The dimension reduction process is given below:

[0216] consider dimensional ellipsoidal bundle and integers , for A 3D hypercube, and satisfies ,definition To be The matrix obtained by arranging the column vectors in descending order of Euclidean norm is then the dimension-reduced matrix. ,in for The front of the matrix List, For the remaining columns, It is a diagonal matrix, and ,in express The One element, express The absolute value of the first One element, , .

[0217] definition of radius is Then we can get The radius index is:

[0218] ;

[0219] The multi-objective optimization problem involving sensitivity and robustness indices is transformed into solving linear matrix inequalities, which can be solved using commercial solvers.

[0220] ;

[0221] in and , These are the weights for the sensitivity and robustness indicators, respectively.

[0222] The parameter matrix corresponding to each vertex is obtained by solving:

[0223] ;

[0224] in , and As vertices The corresponding observer parameter matrix.

[0225] S203: Detection accelerometer The primary target is shaft misalignment fault. System measurements are acquired via sensors, and the residual values ​​of the current system state variables are calculated using estimates obtained from observers. It is compared with a threshold to determine whether a fault has occurred.

[0226] The system acquires measured values ​​by sensors and calculates the residual values ​​of the current system state variables using the estimated values ​​generated by the observer. The residual values ​​are described by an ellipsoidal bundle, and the residual boundary under fault-free conditions can be obtained. This boundary is identified as the threshold. When the residual exceeds the threshold, a fault occurs, thus achieving the purpose of fault detection.

[0227] From the obtained observer parameter matrix and the observer equations of the rotary steered drilling tool attitude measurement system described above, the estimated value of the state vector can be obtained, and then according to... The corresponding residuals can then be obtained. Furthermore, when the system is operating normally, the residual system equations can be approximated by the disturbance subsystem, and the residual ellipsoidal bundle... It will always contain the true residual, that is If a malfunction occurs, then This will no longer be satisfied. Therefore, a residual evaluation mechanism based on ellipsoidal bundles is proposed:

[0228] ;

[0229] in , for Time Accelerometer The residual of the shaft, for The absolute value, for Residual when there is no fault The absolute value of the maximum boundary. It can be calculated using the following formula:

[0230] ;

[0231] in for Time-generating matrix The corresponding row, for The 1-norm.

[0232] like Figure 4 As shown, the residual calculation method and fault alarm logic are as follows:

[0233] S301: Model initialization, given the observer parameters designed according to the above method, set member initialization.

[0234] S302: Calculating the residuals of a generalized LPV system for a pinwheel rotary steerable drilling tool. Ellipsoidal bundle set of the interference subsystem and .

[0235] S303: By Calculate threshold .

[0236] S304: Calculate fault alarm signals .

[0237] like Figures 8-10 As shown, Figure 8 The magnitude of the added fault is the first... ( At the accelerometer Add to the shaft The magnitude of the constant bias fault. Figure 9 The graph shows the residuals and threshold results after adding the fault. Figure 10 This is a diagram showing the results of a fault alarm.

[0238] As can be seen from the detection results, the proposed method achieves high-precision fitting of nonlinear systems. The designed sensor fault detection can separate faulty ellipsoidal bundles from fault-free ellipsoidal bundles. The ellipsoidal bundles can well contain the actual residual signals. By using the inclusion relationship between the actual residual signals and the ellipsoidal bundle intervals, the correct fault alarm can be achieved, thus completing the design of fault detection under the ensemble framework.

[0239] It should be noted that the matrix dimensions mentioned in this patent have appropriate dimensions by default. The above content is a detailed description in conjunction with a specific rotary steerable drilling tool stabilization platform model, and it should not be considered that the specific implementation of this invention is limited to these descriptions.

[0240] like Figure 11 As shown, in another embodiment, an online accelerometer fault detection device suitable for high-temperature and low-computing-power environments in downholes is provided, employing a dual-circuit board architecture to reduce the microcontroller load. The main body of the device consists of a drill collar body and connecting components at both ends: a first end cover 1 connects to the front-end drill collar motor, a second end cover 5 connects to the rear-end vibration mechanism, and a second circuit board 3 and a first circuit board 4 are integrated inside the drill collar body 2 to form a distributed data processing system.

[0241] The online accelerometer fault detection device proposed in this embodiment has a hardware structure consisting of a first circuit board and a second circuit board. The first circuit board 4 includes a communication protection module 401, a first microcontroller 402, and an auxiliary gyroscope 403. The communication protection module 401 is connected to the first microcontroller 402 to ensure controller safety. Specifically, the communication protection module can be an isolation barrier to isolate external electrical equipment from the first microcontroller and prevent damage to the first microcontroller. The auxiliary gyroscope 403 provides rotational speed data. The second circuit board 3 integrates the first communication protection module 301 and the second communication protection module 306, the second microcontroller 302, the storage module 303, the power interface 304, and the communication interface 305. The communication interface 305 and the power interface 304 are responsible for external interaction and power supply, respectively. The accelerometer transmits data to the second microcontroller 302 through the communication interface 305 and to the first microcontroller 402 through the SPI bus. The first communication protection module 301 and the second communication protection module ensure data interaction security and prevent damage to the electrical interfaces. The first microcontroller 402 obtains estimated values ​​for each state based on the auxiliary gyroscope, accelerometer measurement data transmitted from the communication interface 305, and TNL observer parameters obtained from an external computer, and transmits these estimates to the second circuit board via SPI. The second microcontroller 302 executes a fault detection algorithm based on the input from the first circuit board 4, generating residuals and threshold boundaries which are then stored in the storage module.

[0242] The collaborative working mode of the first and second circuit boards mainly involves the first circuit board acquiring rotational speed data via an auxiliary gyroscope and accelerometer data from an external source via a communication interface. After obtaining state estimates using a linearized model and a given TNL observer, these estimates are transmitted to the second circuit board via SPI. The linearized model is a generalized linear variable-parameter system obtained by mathematically modeling and linearizing the downhole tool sensor model. The TNL observer constructs system state estimation error equations and residual generation equations, and establishes a fault sensitivity and disturbance robustness evaluation system based on these equations to determine the observer parameters. The second circuit board acquires system measurements from the sensors and calculates the residual values ​​of the current system state variables using the estimates obtained from the first circuit board. The system identifies the occurrence of an event and calculates the threshold for sensor failure under the current event to determine the nature of the failure.

[0243] The specific data processing methods for the first and second microcontrollers are the same as the specific steps of the downhole tool accelerometer fault detection method, and will not be repeated here.

[0244] To address the bandwidth limitations of the pulse generator, a graded signal uploading mechanism is designed: if the residual exceeds the threshold by N times, the value N is uploaded. The complete data is simultaneously stored locally for the ground system to access and analyze, thus achieving the dual functions of fault level determination and data traceability.

[0245] To meet the needs of scenarios with low computing power in downhole environments, an online accelerometer fault detection device was designed, comprising two circuit boards. The first circuit board performs state estimation and transmits the estimated value to the second circuit board, which then calculates the residuals and boundaries. The calculated residuals and boundaries determine whether a fault has occurred, and the fault is classified and uploaded according to the magnitude of the residuals to obtain more fault information.

Claims

1. A method for detecting faults in downhole tool accelerometers, characterized in that... include: Using accelerometers and gyroscopes as state variables, a generalized nonlinear system is established for the downhole tool sensor model, and then linearized to obtain a generalized linear variable parameter system. The generalized linear variable parameter system is in , , Sampling time, , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The system state vector at any given time. For the system matrix, The uncertainties after linearization For the output matrix, The noise distribution matrix is... This is the fault distribution matrix; For a variable parameter matrix, it is expressed in the following form. in It includes polyhedron for The number of vertices, for The first corresponding to the variable parameter matrix One vertex, For weighted functions, ,satisfy ； Based on the TNL observer architecture, system state estimation error equations and residual generation equations are constructed. Based on these equations, a fault sensitivity and disturbance robustness evaluation system is established, and observer parameters are determined. The method for establishing the TNL observer is as follows: For the obtained generalized linear system, a TNL observer is established; The residual system equations are divided into residual equations for the fault subsystem and residual equations for the disturbance subsystem; Using finite frequency domain Sensitivity design is performed on the faulty subsystem based on the indicators, and sensitivity indicators are established; a member-based approach is adopted. The radius index is used to robustly design the interference subsystem, and a robustness index is established. The multi-objective optimization problem of sensitivity and robustness indices is transformed into solving linear matrix inequalities, and the observer parameter matrix is ​​calculated. , , ; The sensor acquires the system state value, the observer obtains the estimated value, calculates the residual value of the current system state quantity to determine the occurrence of an event, and calculates the threshold for sensor failure under the current event to determine the failure situation.

2. The method for detecting faults in downhole tool accelerometers according to claim 1, characterized in that... The method for constructing the generalized nonlinear system is as follows: establish the northeast geodetic coordinate system. and the carrier coordinate system The carrier coordinate system The axis coincides with the wellbore axis, indicating the axial direction of the drill string and the carrier coordinate system. The plane formed by the axes is the cross-section of the drill bit; the accelerometer xyz axes are sequentially distributed on the xyz axes of the carrier coordinate system. When the accelerometer xyz axes coincide with the established carrier coordinate system, the vertically downward gravitational acceleration is... Decomposed into x-axis components and the y-axis component on the bottom circular plane of the well and z-axis components Therefore, the following formula is obtained: in The well inclination angle, Let be the face angle of the gravity tool. Taking the derivative of the face angle of the gravity tool, we get... in Let the angular velocity be measured by the gyroscope, and let the system state vector be... The state equations for the accelerometer and gyroscope are established as follows: in: , ; The system's measurement equations are as follows: In the formula and For unit array, The fault distribution matrix is... For sensor measurement noise, This is the fault vector of the sensor; The state-space representation of downhole tools is as follows: in, , , , They are respectively The system state vector, system output vector, measurement noise vector, and sensor fault vector at each moment. for The derivative of the system state vector at time t, A constant matrix of appropriate dimension that satisfies ,in for dimensionality for polynomial nonlinear functions, For the output matrix, The noise distribution matrix is... This is the fault distribution matrix.

3. The method for detecting faults in downhole tool accelerometers according to claim 2, characterized in that... The linearization process is as follows: for and ,definition ,in For the set of integers, For the Kronecker product, based on the Kronecker operation rules and the generalized nonlinear system model, we obtain: vector , for Define the operations on the set of 3D real numbers. and ,in For nonlinear functions exist Performing a Taylor series expansion at this point, we obtain... in The Taylor coefficient matrix is... Let be the order of the Taylor series expansion. It is the set of non-negative integers. , Let Lagrange remainder coefficient matrix be the matrix of coefficients. , , , System status exist The estimated value of the time.

4. The method for detecting faults in downhole tool accelerometers according to claim 3, characterized in that, Process the Lagrange remainder: in ,definition , ,in Operations, If the vector is a vector, then find the magnitude of the vector. Given a matrix, find the maximum singular value of the matrix. It is a constant. , , Given the corresponding generating matrix, we finally obtain: in , For unknown uncertain terms and ;Will Unfold, obtain in For a variable parameter state matrix, This represents the unknown uncertainties after linearization.

5. A method for detecting faults in downhole tool accelerometers according to claim 4, characterized in that... The method for obtaining a generalized linear variable parameter system based on the downhole tool linearization system is as follows: process the output equation. in , and These are the corresponding dimension matrices; the downhole tool linearization system is augmented, and defined as follows: , , , ,in , , , , , , This results in the following augmentation system. in , , , , , , , ; The augmented system is discretized using the Euler method to obtain the corresponding generalized linear variable parameter system model.

6. A method for detecting faults in downhole tool accelerometers according to claim 5, characterized in that... For the obtained generalized linear system, the TNL observer equation is established to obtain... System state vector observation at time 1 and Observations of the output vector at time step The calculation formula; the definition of state estimation error. residual ,in for The observed state vector of the system at time t can be obtained from the generalized linear system and TNL observer equations. Error in state estimation at time 1 and residual The calculation formula is as follows: the residual equation is divided into a fault subsystem and a disturbance subsystem to obtain the subsystem... Time error and The residual at time is , and , Using finite frequency domain index Sensitivity design is performed on the faulty subsystem, where The system's sensitivity to faults; employing a member-based approach. The radius index is used for robust design of the interference subsystem. Based on the interference subsystem, the ellipsoidal bundle of the interference subsystem error can be obtained. And satisfy: in , They are respectively Time and time The center vector, , They are respectively Time and time The generating matrix; for The parameter matrix formed by the maximum values ​​of each element in the matrix; for The center vector of the ellipsoidal bundle at time state vector. for The generation matrix of the ellipsoidal bundle of state vectors at time step; for The generation matrix of the ellipsoidal bundle of noise variation over time; for The generation matrix of the noise ellipsoidal bundle at any given time; for The generation matrix of the fault change ellipsoidal bundle at time intervals; , The observer parameter matrix; Finally, the multi-objective optimization problem of sensitivity and robustness indices is transformed into solving linear matrix inequalities to obtain the corresponding observer parameter matrix.

7. A method for detecting faults in downhole tool accelerometers according to claim 6, characterized in that... The dimensionality reduction of the ellipsoidal bundle of the interference residual subsystem is performed using the following method: dimensional ellipsoidal bundle and integers , for A 3D hypercube, and satisfies ,definition For the general The matrix obtained by arranging the column vectors in descending order of Euclidean norm is then the dimension-reduced matrix. ,in for The front of the matrix List, For the remaining columns, It is a diagonal matrix, and ,in express The One element, express The absolute value of the first One element, , .

8. A method for detecting faults in downhole tool accelerometers according to claim 7, characterized in that... The evaluation mechanism for fault occurrence is first to calculate... And satisfy: in For interference subsystem Time residual ellipsoidal bundle for The center vector, for The generating matrix; the fault occurrence mechanism judgment method is: in , for Time residual The One portion, for The absolute value, for The absolute value of the maximum boundary. It can be calculated using the following formula. in for Time matrix The OK, To calculate vectors The 1-norm.

9. A detection device based on the downhole tool accelerometer fault detection method according to any one of claims 1 to 8, comprising a drill collar body, characterized in that, The drill collar body is equipped with a first circuit board and a second circuit board. The first circuit board includes a first microprocessor and an auxiliary gyroscope, and the second circuit board includes a communication interface and a second microprocessor. The accelerometer measurement value is transmitted to the first microcontroller and the second microcontroller through the communication interface. The first microcontroller on the first circuit board obtains the observation value of each state based on the data from the auxiliary gyroscope and the accelerometer through a TNL observer and the linearized LPV system model. The observation value obtained by the first microcontroller is transmitted to the second circuit board through SPI communication. The second microcontroller calculates the residual value of the current system state quantity based on the observed value calculated by the first circuit board and the measured value obtained by the sensor to determine the occurrence of an event, and calculates the threshold for sensor failure under the current event to determine the fault occurrence situation; The detection device sends a fault alarm signal to the ground, and the fault alarm signal is that the residual information exceeds a multiple of a threshold.

Images