AUV sensor fault detection method based on feedforward neural network interval analysis, program, equipment and storage medium

Abstract

The invention discloses an AUV sensor fault detection method based on feedforward neural network interval analysis, a program, equipment and a storage medium, and belongs to the field of autonomous underwater robot fault detection. The method comprises the steps of training a feedforward neural network based on system fault-free data, constructing an input and output mapping relation, propagating an input interval boundary layer by layer and calculating upper and lower boundaries of network output by combining characteristics of a neural network monotone increasing activation function and an interval operation rule, and finally obtaining a network output boundary based on interval analysis. An adaptive threshold for fault detection is generated in conjunction with boundaries of measured noise and network errors. The interval analysis method which does not need a model and is high in calculation efficiency is adopted, the method is suitable for real-time online monitoring of AUV multi-sensor system faults, the calculation complexity is remarkably reduced, bounded noise and system uncertainty in the underwater environment are effectively processed, and meanwhile a more compact fault detection threshold interval is generated.

Description

Technical Field

[0001] The present invention belongs to the field of autonomous underwater robot fault detection, and in particular relates to an AUV sensor fault detection method, program, device and storage medium based on feedforward neural network interval analysis. Background Art

[0002] With the continuous deepening of marine resource development, AUVs play a vital role in the fields of marine resource development, marine scientific research, and underwater engineering operations. AUVs are widely used in tasks such as seabed topography mapping, resource exploration, pipeline inspection, and environmental monitoring. They can replace humans in high-risk operations in extreme environments such as high pressure, low temperature, and strong corrosion, significantly improving the efficiency and safety of ocean exploration. However, the complexity and uncertainty of the deep-sea environment (such as unknown ocean current disturbances, sensor noise, and equipment aging) make AUVs prone to sensor failures during operation. If such failures are not detected in time, the mission may be interrupted at best, and equipment damage or even environmental accidents may occur at worst. Therefore, real-time and accurate fault diagnosis of AUV sensors has become one of the key technologies to ensure the safe and stable operation of AUVs.

[0003] Traditional AUV sensor fault diagnosis methods rely primarily on accurate system models, such as Kalman filters and their derivatives. These methods establish dynamic and observation models of the system, use filtering algorithms to estimate the system state, and detect faults by comparing the estimated value with the actual measured value. However, underwater AUVs are subject to fluid dynamic disturbances, sensor noise, and environmental uncertainty, making it difficult to establish an accurate dynamic model. This is especially true for components with significant nonlinear characteristics, such as thrusters and hydrophones. Model mismatch can lead to missed or false fault detection.

[0004] In recent years, data-driven fault diagnosis methods have attracted widespread attention due to their ability to effectively utilize the system's historical operating data and avoid the complex model building process. Among them, neural networks, as a powerful nonlinear function approximation tool, have been widely used in the field of fault diagnosis. However, most existing neural network-based fault diagnosis methods require a large number of fault samples for training. In the actual operation of AUVs, fault samples are often difficult to obtain, and the fault types are diverse and unevenly distributed, which leads to an imbalance in the training data and seriously affects the performance of fault diagnosis. In addition, AUV sensor measurement data is usually interfered with by unknown but bounded noise. This noise can cause deviations between the output of the neural network and the actual measurement value, thereby increasing the difficulty of fault diagnosis.

[0005] To address these issues, the present invention proposes an AUV sensor fault detection method based on interval analysis using a feedforward neural network. This method utilizes actual sensor measurement data to derive an adaptive threshold for fault detection. Compared to traditional semidefinite programming-based methods that assume a Gaussian distribution for system uncertainty and employ an ellipsoidal confidence set to describe noise, which introduces significant conservatism, the present invention only requires that the noise interval be bounded. By combining interval analysis with a neural network, this method provides a more computationally efficient and less conservative solution for AUV sensor fault diagnosis, particularly suitable for dynamic underwater environments with unknown models and complex noise. Summary of the Invention

[0006] Aiming at the problem of system fault detection with unknown but bounded measurement noise interference, the present invention proposes an AUV sensor fault detection method based on feedforward neural network interval analysis method.

[0007] The present invention provides an AUV sensor fault detection method based on feedforward neural network interval analysis, comprising:

[0008] Step 1: Obtain the input data and sensor output data of the AUV system when there is no fault, and build a training set;

[0009] Step 2: Construct a feedforward neural network and train it using the training set to obtain the optimal weight matrix and bias vector;

[0010] Step 3: Based on the optimal weight matrix and bias vector, combined with the inter-layer characteristics of the feedforward neural network and the interval operation rules, the interval analysis method is used to propagate the input interval of the neural network layer by layer to calculate the upper and lower bounds of the network output;

[0011] Step 4: Combine the upper and lower bounds of the network output with the upper and lower bounds of the measurement noise and feedforward neural network error to determine the threshold for fault detection;

[0012] Step 5: Determine whether a system fault occurs by comparing the measured output to see if it exceeds the fault detection threshold boundary.

[0013] Furthermore, in step 2, the feedforward neural network includes an input layer, a hidden layer, and an output layer;

[0014] The input layer is: For the former s u System input, For the former s y System output;

[0015] The hidden layer uses a monotonically increasing activation function. Each hidden layer first performs a linear affine transformation and then performs a nonlinear activation function operation. The hidden layer is:

[0016]

[0017] z η =φ(ζ η )

[0018] Among them, z η is the output vector of the ηth layer, η=2,…,l-1; is the weight matrix of the nth layer; is the bias vector; φ() is the activation function of the neuron; z η-1 is the output of the η-1th layer; ζ η represents the intermediate data before the activation of the n-1th hidden layer;

[0019] The output layer is: the predicted value of the sensor data.

[0020] Furthermore, in step 3, the activation function is a monotonically increasing l-layer feedforward neural network, whose network input is Satisfy the bounded interval Then the interval boundary of the network output z satisfies:

[0021]

[0022] Among them, W l + =max{0,W η}, W l - =W l + -W l , W l is the optimal weight matrix of the lth layer; b l is the optimal weight matrix of the lth layer; and z l-1 It is calculated iteratively in the following way:

[0023]

[0024] For η=2,…,l-1, we have:

[0025]

[0026] in, W η is the optimal weight matrix of the ηth layer; b η is the optimal weight matrix of the ηth layer; the upper and lower boundaries of noise and are two known vectors;

[0027] Furthermore, in step 4, in the case of no fault, yk The interval boundaries are designed as follows:

[0028]

[0029] in, and z k,l is the output boundary of the neural network layer l corresponding to the training k-th data; the feedforward neural network error are two known constants.

[0030] Furthermore, in step 5, the fault detection strategy is:

[0031]

[0032] The present invention also provides a computer device / equipment / system, comprising a memory, a processor, and a computer program stored in the memory, wherein when the processor executes the computer program, the steps of the AUV sensor fault detection method based on feedforward neural network interval analysis are implemented.

[0033] The present invention also provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of any of the above-mentioned AUV sensor fault detection methods based on feedforward neural network interval analysis.

[0034] The present invention also provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of any of the above-mentioned AUV sensor fault detection methods based on feedforward neural network interval analysis.

[0035] The beneficial effects of the present invention are:

[0036] 1. The proposed AUV sensor fault detection method based on feedforward neural network interval analysis is more consistent with the noise characteristics of actual AUVs in marine environments. Even when the interference and noise are unknown but bounded, interval analysis can propagate layer by layer using bounded inputs, demonstrating broad applicability and versatility. In contrast, traditional semidefinite programming methods typically assume that the system's noise and interference follow a Gaussian distribution, which can be overly conservative in practical applications, as noise and interference in real systems are often difficult to accurately model.

[0037] 2. The proposed AUV sensor fault detection method based on feedforward neural network interval analysis utilizes simple interval operations and monotonic activation function characteristics to propagate interval boundaries layer by layer to obtain the boundaries of the network output, thereby calculating a more accurate adaptive threshold that more closely matches the actual output range, significantly improving the reliability and accuracy of fault detection. In contrast, traditional semidefinite programming methods use conservative estimates when calculating neural network outputs due to quadratic constraint construction and ellipsoidal domain approximation, resulting in overly loose fault detection thresholds and difficulty in effectively detecting actual faults.

[0038] 3. The proposed AUV sensor fault detection method based on feedforward neural network interval analysis transforms complex nonlinear transformations into linear interval propagation. Its computational complexity is only related to the number of neural network layers and neurons. Simple interval operations can be used to obtain the bounds of the network output, significantly improving computational efficiency and meeting real-time requirements. In contrast, traditional semidefinite programming methods require the online solution of complex linear matrix inequalities, which are computationally complex and time-consuming, making them difficult to meet the real-time fault detection requirements of AUVs.

[0039] 4. The AUV sensor fault detection method based on feedforward neural network interval analysis proposed in the present invention does not rely on an accurate system model, and can flexibly adjust the network structure and activation function. It can realize real-time monitoring of sensor faults by training the neural network only with the normal operating data of the sensor, and can better cope with the complex and changeable working environment of the AUV during underwater exploration. In addition, by converting multiplicative faults into additive faults, it can be extended to systems with multiplicative faults, and has wider applicability and versatility. In contrast, traditional model-driven methods rely on accurate mathematical modeling of AUVs and require the design of observer structures for specific systems. Data-driven methods rely on a large number of fault samples for classification, and both are somewhat conservative. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the AUV sensor fault detection method based on the feedforward neural network interval analysis method;

[0041] Figure 2 This is the overall structural diagram of the "Beaver-II" AUV system;

[0042] Figure 3 This is a comparison chart between the neural network fitting curve and the actual output curve of the "Beaver-II" AUV;

[0043] Figure 4 The result diagram of the straight-line speed and adaptive threshold curve of the "Beaver-II" AUV when the sensor fails;

[0044] Figure 5The result diagram of the heading angle and its adaptive threshold curve of the "Beaver-II" AUV when the sensor fails. DETAILED DESCRIPTION

[0045] The present invention will be further described below with reference to the accompanying drawings.

[0046] The present invention discloses an AUV sensor fault detection method based on feedforward neural network interval analysis. For discrete-time systems, a feedforward neural network is first constructed using the input and output data of the AUV system when it is fault-free. The feedforward neural network is used for neural network training so that it can approximate the mapping relationship of the fault-free system. Then, by utilizing the monotonicity of the activation function, the positive and negative decomposition of the weight matrix is ​​performed layer by layer with interval arithmetic operations to calculate the upper and lower bounds of the neural network output. The upper and lower bounds of the measurement noise and network error are combined to determine the final adaptive threshold used for fault detection. Finally, by comparing the actual measurement output with the adaptive threshold, it is determined whether the system has a fault.

[0047] The definition lemma required for this invention is as follows:

[0048] Lemma 1: For satisfying the constraint n-dimensional real vector and constant matrix The following inequality holds:

[0049]

[0050] Among them, A + Represents the positive part of the matrix A, that is, the absolute value of all positive elements in the matrix, while the negative elements are zero. - represents the negative part of the matrix A, that is, the absolute value of all negative elements in the matrix, while the positive elements are zero.

[0051] Definition 1: l-layer feedforward neural network N: The structure is:

[0052] z1=ζ, (2a)

[0053]

[0054] in, and They correspond to the output data and input data of the feedforward neural network N, represents the weight matrix of the ηth layer, is the bias vector, Represents the intermediate data of the ηth layer and the nonlinear activation function of the ηth layer.

[0055] Has the following form:

[0056]

[0057] Among them, ψ η : is the activation function of a single neuron.

[0058] The specific steps include:

[0059] Step 1: Based on the "Beaver-II" AUV experimental platform independently built by the laboratory, the feedforward neural network is constructed and trained using the input and output data of the AUV system when there is no fault.

[0060] According to the time series characteristics of AUV sensor data, a feedforward neural network N is constructed, which consists of an input layer, a hidden layer, and an output layer. The input layer receives a time series vector consisting of historical system input and sensor output, the hidden layer uses a monotonically increasing activation function (such as ReLU, Sigmoid function), and the output layer outputs the predicted value of the sensor data.

[0061] Collect system input data u during normal operation of AUV k (such as thruster control voltage) and sensor output data y k (such as straight-line speed, heading angle), construct training samples. The input vector will be composed of the previous s u System input and former s y system Output vector As the network training input, that is:

[0062]

[0063] The sensor output y at the current moment k As a sample, the Levenberg-Marquardt algorithm is used to train the neural network until the fitting function is close to the true value, and the optimal weight matrix W is obtained. η and the bias vector b η , used for subsequent interval operation methods.

[0064] Step 2: Combining the monotonically increasing characteristics of neural network layers with interval operation rules, use the interval analysis method to propagate the input interval of the neural network layer by layer and calculate the upper and lower bounds of the network output.

[0065] Because neural networks have complex nonlinear characteristics, it is difficult to directly use the relationship between their output and input to obtain the output boundary. However, all divided layers have linear and simple nonlinear characteristics, so it is easy to analyze the relationship between the output and input of a single layer and calculate the output boundary of the network by propagating the boundary layer by layer. Therefore, based on the principle of layer-by-layer interval analysis and Lemma 1, the weight matrix is ​​decomposed into positive and negative decomposition, and the output interval calculation method of Theorem 1 is proposed:

[0066] Theorem 1: For a l-layer feedforward neural network N constructed according to formulas (2a)-(2c) and with all activation functions being monotonically increasing, if its network input ζ satisfies the interval bounded condition, then its network output is also interval bounded. In addition, the interval upper and lower bounds and z It is given by:

[0067]

[0068] in, and z l-1 It is calculated iteratively in the following way:

[0069]

[0070] For η=2,…,l-1, we have:

[0071]

[0072] According to (5) in Theorem 1, for each layer of the neural network, the upper and lower bounds of the input, as well as the weight matrix and bias vector of the layer are known. The upper and lower bounds of the output are calculated, and the output interval of the last layer is used as the output range of the entire neural network to ensure that the range can cover all possible measured outputs under normal operating conditions.

[0073] Step 3: Combine the boundaries of the network output with the upper and lower bounds of measurement noise and neural network error to determine the threshold for fault detection.

[0074] Consider the unknown but bounded nature of the measurement noise, namely:

[0075]

[0076] Ideal output The actual output satisfies the following relationship:

[0077]

[0078] Fault-free data of the control system is usually easy to obtain. Assume that the neural network N is trained based on sufficient and adequate data so that it can satisfy the following equation:

[0079]

[0080] in

[0081]

[0082] Although obtained and However, in practice, it is impossible to obtain accurate noise-free ideal output. However, the actual measured data (such as propeller control voltage, heading angle, and straight-line speed) obtained by AUV during tank experiments are easy to obtain. Therefore, the network output z obtained by neural network training can be used as the k As the actual output in the absence of faults.

[0083] In summary, Theorem 2 is proposed based on Theorem 1 to calculate y in the case of no fault. k The interval boundary can be used as an adaptive threshold for fault detection:

[0084] Theorem 2: Assume that the measurement noise v k Positional but bounded For a fault-free discrete-time system, given a l-layer feedforward neural network N trained with fault-free data, the system output adaptive threshold for fault detection is and y k is given by:

[0085]

[0086] in, and z k,l To train the output boundary of the neural network layer l corresponding to the kth data, the kth data and the lth layer are corresponding; the upper bound of the neural network output and the lower bound z k,l Given by:

[0087]

[0088] in

[0089]

[0090] in, For η=2,…,l-1, such that The upper and lower limits of the neural network input and Calculated as follows:

[0091]

[0092] According to the output range of the neural network obtained by interval analysis, combined with the measurement noise generated by the AUV in the pool experiment and the upper and lower bounds of the error generated during the neural network training process, the adaptive threshold of fault detection is calculated layer by layer using (13) in Theorem 2. and y k .

[0093] Step 4: Determine whether the system has a fault by comparing whether the measured output exceeds the fault detection threshold. If the measured output exceeds the threshold range, a fault alarm is triggered.

[0094] The adaptive threshold provided by Theorem 1 represents the measured output z of the neural network k Based on Theorem 1 and Theorem 2, combined with the system noise and error constraints, the adaptive threshold provided represents the measured output y in the absence of faults. k Therefore, if the AUV does not fail during operation, the measurement output will always be within the adaptive threshold range. Based on this, the following fault detection strategy can be derived:

[0095]

[0096] In addition, the method proposed in this invention can be extended to systems with multiplicative faults. The multiplicative faults of the actuators can be described as:

[0097]

[0098] in, is the actual output of the actuator, Describe the impact of the failure.

[0099] In theory, a multiplicative fault can be converted into an additive fault as follows:

[0100] u f,k =u k -κu k =u k +f k (19)

[0101] Among them, f k is an additive fault. Similarly, the multiplicative fault of the sensor can also be converted into an additive fault. Therefore, by converting the multiplicative fault into an additive fault, the proposed fault detection method can be extended to systems with multiplicative faults.

[0102] Example 1

[0103] In order to verify the feasibility and effectiveness of the fault detection method proposed in the present invention, the "Beaver-II" AUV is selected as the AUV experimental platform. The specific implementation method of the present invention is described below based on the "Beaver-II" AUV experimental platform and the accompanying drawings.

[0104] The length, width and height of the "Beaver-II" AUV are 0.8m, 0.5m and 0.4m respectively, and its mass in air is 50kg. Figure 2 As shown in the figure, the Beaver-II AUV is equipped with a digital compass and depth sensor. These sensors, along with a Doppler velocimeter and depth gauge, are mounted on the hull to monitor the Beaver-II's depth, attitude, and speed. The power and electronics compartments are symmetrically mounted above the AUV, with the digital compass affixed above them and the depth gauge mounted below.

[0105] The "Beaver-II" AUV can achieve four degrees of freedom of movement: straight sailing, bow turning, lateral movement and heave. The four degrees of freedom of the "Beaver-II" AUV are achieved through the thrust generated by the thrusters. The "Beaver-II" AUV has three pairs of thrusters symmetrically arranged on it: main thrusters, side thrusters and vertical thrusters.

[0106] A method for detecting faults in AUV sensors based on feedforward neural network interval analysis, comprising:

[0107] Step 1: Obtain the input data and sensor output data of the AUV system when there is no fault, and build a training set;

[0108] Step 2: Construct a feedforward neural network and train it using the training set to obtain the weight matrix and bias vector;

[0109] According to Definition 1, a feedforward neural network N consists of a series of layers, where the output of each layer is the input of the next layer. The first layer calculated by (2a) is the input layer, and the neural network N obtains the network input based on this layer. The last layer calculated by (2c) is the output layer, and the neural network N gives the network output based on this layer. The layer calculated by (2b) between the input layer and the output layer is the hidden layer, and the nth hidden layer is the n+1th layer of the neural network N. Each hidden layer performs a linear affine transformation, followed by a nonlinear activation function operation, as follows:

[0110]

[0111] z η =φ(ξ η ) (twenty one)

[0112] where η = 2,..., l - 1, ζ η denotes the intermediate data before the activation of the η-1th hidden layer.

[0113] Step three: According to the weight matrix and bias vector, combining the characteristics of the feedforward neural network layers and the interval operation rules, the input interval of the neural network is propagated layer by layer using the interval analysis method, and the upper and lower bounds of the network output are calculated.

[0114] Before building and training the neural network, first, the interval bounds of the neural network output need to be obtained, that is, when the network input ζ satisfies the following interval bounded condition:

[0115]

[0116] The interval boundary of the network output satisfies:

[0117]

[0118] Since the neural network has complex nonlinear characteristics, it is difficult to directly use the relationship between its output and input to obtain the boundary of the output. All the divided layers have linear and simple nonlinear characteristics, so it is easy to analyze the relationship between the output and input of a single layer, and the boundary of the network output can be calculated by propagating the boundary layer by layer. Therefore, based on the principle of layer-by-layer interval analysis and Lemma 1, Theorem 1 (equations (5), (6), (7)) is proposed.

[0119] The proof is as follows:

[0120] First, analyze the bounded condition of the input layer. Substituting (22) into (2a) gives:

[0121]

[0122] Next, the propagation process in the hidden layer is derived. The upper and lower bounds of the output of the η-1th layer are denoted as and z η-1 respectively, and the boundary of the input of the ηth layer is and z η-1 Therefore, for the linear affine transformation (20) in the ηth layer, according to Lemma 1, the following inequalities can be obtained:

[0123] ξ η ≤ξ η ≤ξ η (25)

[0124] where

[0125]

[0126] In addition, according to (3) and (21), the following equation holds true in the activation function operation:

[0127] z η (i)=ψ(ξ η (i)) (27)

[0128] Since ψ is monotonically increasing, based on the properties of monotonically increasing functions, we can obtain from (27):

[0129]

[0130] in

[0131]

[0132] The hidden layer of the feedforward neural network N is a series of layers with the structure (20). The output of one hidden layer is the input of the next hidden layer. Therefore, combined with the initial condition (7), for η = 2, ..., l-1, z can be derived iteratively through (25) and (28). l-1 the border.

[0133] Finally, according to (6), the input of the output layer is given by the upper bound and z l-1 Lower Bound Constraint,Applying Lemma 1 to (2c), we can obtain the bounds of the network output,through (5).

[0134] Step 4: Combine the upper and lower bounds of the network output with the upper and lower bounds of the measurement noise and feedforward neural network error to determine the threshold for fault detection;

[0135] Based on the neural network interval analysis method proposed in Theorem 1, when the network input ξ interval is bounded, the network output can be determined After obtaining the interval analysis results, they can be used to calculate the adaptive threshold for fault detection by combining the measurement noise and neural network error.

[0136] Consider the following discrete-time system:

[0137]

[0138] in, and are the state vector, system input, system output, measurement noise, added actuator faults, and sensor faults, respectively. and is an unknown continuous function.

[0139] During the operation of the AUV, by analyzing the disturbance caused by the error between the identification system and the actual system and the historical data of the sensor measurement noise, and removing a few abnormal values ​​with large amplitudes, the boundary of the disturbance and measurement noise can be determined. These values ​​change within this boundary at every moment. During the operation of the AUV, its motion state changes within the specified range, so the measurement noise v of the AUV system k The boundaries of can be assumed to satisfy the following conditions:

[0140]

[0141] Among them, the upper and lower boundaries of noise and are two known vectors.

[0142] In the absence of faults, the system (30) can be expressed as

[0143]

[0144] Among them, F(x k ,u k ) by adding f a,k =0Substitute into F(x k ,u k ,f a,k ) to calculate.

[0145] Since the mapping F and H are unknown, an interval analysis method based on a feedforward neural network is used to analyze the dynamic system. According to the time series input and output of the system (32), a feedforward neural network is constructed. Its weight matrix and bias vector are calculated through neural network training. During the training process, the previous s u System input and former s y system Output vector As the network training input, that is:

[0146]

[0147] At the same time, the current system output y k As the corresponding network training output. The ideal output in the noise-free case is defined as:

[0148]

[0149] The ideal output and actual output satisfy the following relationship:

[0150]

[0151] Fault-free data of the control system is usually easy to obtain. Assume that the neural network N is trained based on sufficient and adequate data so that it can satisfy the following equation:

[0152]

[0153] in

[0154]

[0155] in, are two known constants.

[0156] Although obtained and However, in practice, it is impossible to obtain an accurate noise-free ideal output. However, the actual measured data (such as propeller control voltage, heading angle, and straight-line speed) obtained by the AUV during the tank experiment are easy to obtain. According to (33) and the assumption (31), the input of the feedforward neural network is interval-bounded.

[0157] According to the above discussion, Theorem 2 gives the value of y in the case of no fault. k The interval boundary calculation method of is used as the adaptive threshold for fault detection. y k and The value of is calculated by formulas (13), (14), (15), and (16).

[0158] The proof is as follows:

[0159] First, we derive the boundary of the network input. Since the system inputs are all known fixed values, for j = ks u ,…,k-1,u j The upper and lower bounds are both u j ,Right now:

[0160] u j ≤u j ≤u j (39)

[0161] At the same time, according to the definition of ideal output, for all m=ks y ,…,k-1, the following equation holds:

[0162]

[0163] According to (31) and (40), we can get:

[0164]

[0165] Substituting (39) and (41) into (33) yields:

[0166]

[0167] in, and Defined by (16).

[0168] Then, according to the result of Theorem 1, given the neural network input interval (42), the interval boundary of the neural network output can be obtained through (14)-(16).

[0169] Finally, according to Theorem 2, the system output y is calculated under the condition of no fault k The border and y k , and use it as the adaptive threshold for fault detection. According to (36), the system output in the absence of noise is The boundaries are:

[0170]

[0171] Substituting (35) into (42) yields:

[0172]

[0173] Add v to both sides of the inequality k , the system output y in the absence of faults k It can be expressed as:

[0174]

[0175] in, and y k The value of is the calculation method of (13) in Theorem 2.

[0176] Example 2

[0177] Specific simulation experiment of “Beaver-II” AUV fault detection.

[0178] First, a "Beaver-II" AUV was tested in a water tank. During the experiment, the "Beaver-II" AUV maintained a stable speed and attitude from startup to reaching a preset steady state. The "Beaver-II" AUV's straight-line navigation was primarily achieved by the thrust of its two main thrusters, while heading control was achieved by adjusting the thrust difference between the two main thrusters. The thrust of the two main thrusters is determined by the control voltage, and the corresponding thrust models are:

[0179] The relationship between the left thruster control voltage and thrust:

[0180] Forward: T1=6.7785*V-4.0768 (46)

[0181] Backward: T1=7.5499*V+5.878 (47)

[0182] The relationship between the right thruster control voltage and thrust:

[0183] Forward: T2=6.7703*V-4.22 (48)

[0184] Backward: T2=7.0137*V+7.4725 (49)

[0185] Where V is the control voltage, ranging from -5V to 5V.

[0186] Because accurate modeling of the Beaver-II AUV is difficult to achieve, a data-driven approach was used to construct its mathematical model. Based on 200 sets of input data (u1 and u2) of the left and right thruster control voltages, as well as the output data of the straight-line speed ρ and heading angle ψ, measured from the sensor system, a four-layer feedforward neural network (4 neurons in the input layer, 8 neurons in the first hidden layer, 4 neurons in the second hidden layer, and 2 neurons in the output layer) with a monotonically increasing RELU activation function was constructed. Its structure is as follows:

[0187]

[0188] The feedforward neural network N is trained with 200 sets of system input and measurement output data of two observation quantities, where the ratio of data used for training, data used for verification and data used for testing is 0.7:0.15:0.15, that is, 140 sets of data are used to train the fitting data of the network output, and 30 sets of data are used to verify whether overfitting occurs, until the fitting effect closest to the real data is obtained, such as Figure 3 shown.

[0189] Among them, the optimal weight matrices W0, W1, W2 and bias vectors b0, b1, b2 obtained based on neural network training are as follows:

[0190]

[0191]

[0192] The method proposed in this invention is effective for all monotonically increasing activation functions. For the RELU nonlinear activation function used in the experiment, if its input is a vector It can be expressed as:

[0193]

[0194] In the tank experiment, the left and right thrusts of the AUV were set as:

[0195] u1=6.7785*V-4.0768

[0196] u2=6.7703*V-4.22

[0197] Sampling time T s = 0.02s, AUV measurement noise v k The following unknown but bounded conditions are satisfied:

[0198] -0.1≤v k ≤0.1

[0199] A sudden sensor fault is added at the 100th time step to demonstrate the effectiveness of the proposed method in fault detection:

[0200]

[0201] Next, the interval analysis method proposed in this invention is tested by adding a sudden fault. The simulation results are as follows: Figure 4 、 5 As shown in Figure 2, it can be seen that before the sensor failure occurs, the system output is always within the adaptive threshold range and is close to the fitting value of the neural network. However, after the failure occurs, y k The threshold value quickly exceeds the threshold value range, which indicates that a fault has occurred. In addition, to verify the superiority of the method proposed in this invention, the adaptive threshold value obtained by the method is compared with the threshold value obtained by the semidefinite programming method using MATLAB R2024a and YALMIP toolbox. According to the comparison chart, it can be seen that the threshold value obtained by the proposed method is less conservative and has better fault detection performance, while the semidefinite programming method is less conservative due to y k Most of the time it is within the threshold range, making it difficult to detect sensor failure.

[0202] In summary, this paper proposes a method for AUV sensor fault detection based on feedforward neural network interval analysis. By constructing a feedforward neural network model, using interval analysis techniques to propagate input intervals layer by layer to calculate output boundaries, and combining measurement noise and training error to generate adaptive detection thresholds, this method overcomes the bottlenecks of traditional methods in computational efficiency, threshold accuracy, model dependence, and anti-interference capabilities. This method effectively handles bounded noise and system uncertainty in underwater environments, reduces computational complexity, improves detection accuracy, and can effectively reduce the conservatism of traditional methods. It is suitable for real-time online fault detection of AUV sensors and improves the reliability and robustness of AUVs under complex operating conditions and unknown models.

[0203] In particular, in some preferred embodiments of the present application, a computer device is also provided, comprising a memory and a processor and a computer program stored in the memory, wherein the processor implements the steps of the AUV sensor fault detection method based on feedforward neural network interval analysis in any of the above embodiments when executing the computer program.

[0204] In some other preferred embodiments of the present application, a computer readable storage medium is also provided, having stored thereon a computer program / instructions, wherein the computer program is executed by a processor to implement the steps of the AUV sensor fault detection method based on feedforward neural network interval analysis in any of the above embodiments.

[0205] It is understood by those skilled in the art that all or part of the processes of the above-mentioned embodiments can be completed by a computer program instructing related hardware, and the computer program can be stored in a non-volatile computer readable storage medium. The computer program, when executed, can include the processes of the above-mentioned embodiments of the AUV sensor fault detection method based on feedforward neural network interval analysis, which will not be repeated here.

[0206] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present description, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, the skilled in the art can combine and combine the different embodiments or examples described in the present description and the features of the different embodiments or examples without contradiction.

[0207] In addition, the terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "N" is at least two, for example, two, three, etc., unless otherwise specifically limited.

[0208] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing a custom logical function or step of a process, and the scope of the preferred embodiments of the invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of the invention pertain.

[0209] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or N wires (electronic devices), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and a portable compact disc read-only memory (CDROM). Furthermore, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing it in another suitable manner if necessary, and then storing it in a computer memory.

[0210] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having logic gate circuits for implementing logic functions on data signals, an application-specific integrated circuit having suitable combinational logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0211] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0212] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing module, or each unit may exist physically separately, or two or more units may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they may also be stored in a computer-readable storage medium.

[0213] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and are not to be construed as limiting the present invention. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for detecting AUV sensor faults based on feedforward neural network interval analysis, characterized in that: The steps include: Step 1: Obtain the input data and sensor output data of the AUV system when there is no fault, and build a training set; Step 2: Construct a feedforward neural network and train it using the training set to obtain the optimal weight matrix and bias vector; Step 3: Based on the optimal weight matrix and bias vector, combined with the inter-layer characteristics of the feedforward neural network and the interval operation rules, the interval analysis method is used to propagate the input interval of the neural network layer by layer to calculate the upper and lower bounds of the network output; Step 4: Combine the upper and lower bounds of the network output with the upper and lower bounds of the measurement noise and feedforward neural network error to determine the threshold for fault detection; Step 5: Determine whether a system fault occurs by comparing the measured output to see if it exceeds the fault detection threshold boundary.

2. The AUV sensor fault detection method based on feedforward neural network interval analysis according to claim 1 is characterized in that: In step 2, the feedforward neural network includes an input layer, a hidden layer, and an output layer; The input layer is: For the former s u System input, For the former s y System output; The hidden layer uses a monotonically increasing activation function. Each hidden layer first performs a linear affine transformation and then performs a nonlinear activation function operation. The hidden layer is: z η =φ(ζ η ) Among them, z η is the output vector of the ηth layer, η=2,...,l-1; is the weight matrix of the nth layer; is the bias vector; φ() is the activation function of the neuron; z η-1 is the output of the η-1th layer; ζ n represents the intermediate data before the activation of the n-1th hidden layer; The output layer is: the predicted value of the sensor data.

3. The AUV sensor fault detection method based on feedforward neural network interval analysis according to claim 2 is characterized in that: In step 3, the activation function is a monotonically increasing l-layer feedforward neural network, whose network input is Satisfy the bounded interval Then the interval boundary of the network output z satisfies: Among them, W l + =max{0,W l }, W l - =W l + -W l , W l is the optimal weight matrix of the lth layer; b l is the optimal weight matrix of the lth layer; and z l-1 Iterate the calculation in the following way: For η=2,…,l-1, we have: in, W η is the optimal weight matrix of the ηth layer; b η is the optimal weight matrix of the ηth layer; the upper and lower boundaries of noise and are two known vectors.

4. The AUV sensor fault detection method based on feedforward neural network interval analysis according to claim 1 is characterized in that: In step 4, in the case of no fault, y k The interval boundaries are designed as follows: in, and z k,l is the output boundary of the neural network layer l corresponding to the training k-th data; the feedforward neural network error are two known constants.

5. The AUV sensor fault detection method based on feedforward neural network interval analysis according to claim 1 is characterized in that: In step 5, the fault detection strategy is:

6. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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