A method for fault detection of unmanned vessels based on TNL-type interval observers

Abstract

This invention provides a fault detection method for unmanned surface vessels (USVs) based on a TNL-type interval observer, relating to the field of ship safety. First, a suitable coordinate system is selected, and considering the influence of ocean waves on the USV, a state-space model of the USV's asymmetric motion under disturbance is constructed. Then, a TNL-type interval observer with an auxiliary matrix is ​​designed. This interval observer relaxes the non-negativity constraint and has higher degrees of freedom. Furthermore, using H... ∞ The technology optimizes estimation performance to minimize errors. Based on this, interval estimation is performed on the measurement output, and a fault detection scheme is constructed by combining the output. Compared with traditional methods, the fault detection scheme of this invention has a smaller threshold interval, is more sensitive to system faults, and can effectively solve the fault detection problem of unmanned vessels in complex environments, possessing broad practical and research value.

Description

Technical Field

[0001] This invention belongs to the field of ship safety, and in particular relates to a fault detection method for unmanned ships based on a TNL-type interval observer. Background Technology

[0002] With the integration of new technologies such as network communication and cloud computing into ship technology, ships are becoming increasingly modern and intelligent, and unmanned surface vessels (USVs), similar to other unmanned systems, are gaining public attention. Compared to traditional manned vessels, USVs are better able to adapt to various environments and complete more complex and dangerous tasks. During missions, USVs' actuators and other components can malfunction due to harsh marine weather conditions and unpredictable sea currents. Once a malfunction occurs, the USV's control performance is affected, leading to mission failure, and in severe cases, damage to the ship's sophisticated and expensive equipment, resulting in losses. Therefore, research on fault detection methods for USV systems is of great significance in enhancing their safety and reliability.

[0003] The key to fault detection lies in the generation and evaluation of residuals that reflect the difference between the actual and expected system behavior. The estimates generated by the observer can be considered as the expected behavior of the system and can be used to generate residuals. In recent years, interval observers, as a supplement to general observers, can provide an interval estimate of the system, limiting the range of states. Therefore, interval observers can both generate residuals and provide a range for residual evaluation, making them a simple and efficient fault detection device. The focus of fault detection methods based on interval observers is the design of the interval observer, and the core of interval observer design is ensuring non-negativity. Therefore, the gain matrix of the interval observer must ensure both observer stability and non-negativity, and such a gain matrix is ​​not always easy to find. Existing methods based on coordinate transformation relax the requirement of ensuring non-negativity in the gain matrix design, but the introduction of the coordinate transformation matrix increases the range of the estimation interval, thus significantly reducing the effectiveness of fault detection. Therefore, the design of interval observers that relax the non-negativity constraint and have a smaller estimation interval, making them more suitable for fault detection, requires further research. Summary of the Invention

[0004] This invention addresses the issue of actuator failures in unmanned surface vessels (USVs), aiming to design a fault detection method based on a TNL-type interval observer, combined with H... ∞ Technological improvements have been made to enhance the estimation accuracy of the interval observer, providing better fault detection capabilities.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A fault detection method for unmanned surface vessels based on a TNL-type interval observer is implemented through the following steps:

[0007] Step 1: Establish a suitable coordinate system, take into account the interference of ocean waves on the unmanned vessel, model the dynamic behavior of the asymmetric motion of the unmanned vessel on the water surface, and then obtain a simplified state space model;

[0008] Step 2: Based on the state-space model of the asymmetric motion of the unmanned vessel system obtained in Step 1, construct a TNL-type interval observer with an auxiliary matrix;

[0009] Step 3: Based on the TNL-type interval observer obtained in Step 2, construct the estimation error system and utilize H ∞ The parameter matrix of the interval observer is designed to improve estimation performance and minimize error;

[0010] Step 4: Based on the improved estimation accuracy interval observer designed in the above steps, the interval estimate of the state is generated, the interval estimate of the measurement output is performed, and the output value is used to construct a fault detection scheme.

[0011] Furthermore, the detailed process of selecting the coordinate system and establishing the state-space model of the unmanned vessel's asymmetric motion in step one is as follows:

[0012] By writing Newton's laws in a fixed-space coordinate system, we obtain the fundamental equations for the asymmetric motion of the unmanned vessel's port and starboard sides with components along the transverse axis:

[0013]

[0014]

[0015]

[0016] in, h o f o For the ship's effective mass, force, heading angle, and roll angle in the Y direction; and N represents the moment of inertia relative to the Z and X axes. o and K o These represent the moments relative to the Z and X axes, respectively; X represents the longitudinal axis (stern to bow), Y represents the longitudinal axis (pointing to starboard), and Z represents the normal axis (pointing downward).

[0017] Using Taylor expansion and Laplace transform, the transfer function of the unmanned surface vessel's motion can be obtained as follows:

[0018]

[0019]

[0020]

[0021] Where v(s), ψ(s), φ(s), and δ(s) are v(t) (sway velocity), ψ(t) (heading angle), and δ(s) (yaw rate). Laplace transforms of (roll angle) and δ(t) (rudder deflection angle); and ω n Here, w represents the damping coefficient and the undamped natural frequency. ψ (s) and w ψ (t)(interference with heading angle caused by ocean waves) and (Interference with rudder deflection caused by ocean waves; T) r and T v k is a given time constant. vr K dr K dv K vp and K dp Given the gain.

[0022] The controllable rudder deflection angle δ(t) is selected as the known control input u(t) of the unmanned vessel. The state-space model of the asymmetric motion of the unmanned vessel system, namely the motion of the sway, yaw, and roll subsystems, is as follows:

[0023]

[0024] in, System state x(t) = [v(t) r(t) φ(t) p(t) ψ(t)] T r(t) is the yaw speed, p(t) is the roll rate; the disturbance from the waves is denoted as w(t) = [w ψ (t) w φ (t)] T ;y t For measurement output; C is a known matrix. t The disturbances from the waves received by the heading angle and rudder deflection are unknown, but their impact can usually be estimated within a certain range, that is, the upper and lower limits of the disturbance are generally known.

[0025] Furthermore, given that the upper and lower bounds of the system's initial state are known, the specific construction process of the TNL-type interval observer with auxiliary matrix described in step two is as follows:

[0026] First, the system state equations are rewritten in a form that facilitates the construction of TNL-type interval observers:

[0027] For any matrix T, the state equation satisfies

[0028]

[0029] Based on the above equation, for matrices T and N that satisfy T+NC=I, according to the state-space expression, we can obtain...

[0030]

[0031] Furthermore, the final state expression is rewritten in the following form:

[0032]

[0033]

[0034] Then, based on the rewritten state expression, the following TNL-type interval observer is constructed:

[0035]

[0036]

[0037]

[0038]

[0039] in, and represents the intermediate variables for the upper and lower estimates of the interval observer; L is the gain matrix of the interval observer. and J Upper and lower auxiliary matrices to relax the nonnegativity restriction of the interval observer; and x (t) represents the upper interval estimate and lower interval estimate of the state, respectively; and w (t) represents the upper and lower bounds of the interference.

[0040] Furthermore, the error system described in step three is constructed as follows:

[0041] Definition of estimation error and lower estimation error e (t)=x(t)- x (t), the dynamic characteristics of the upper and lower estimation errors are as follows:

[0042]

[0043]

[0044] By combining the lower estimation error and the lower estimation error, we can consider the compact form of the error. The dynamic characteristics of this error system are:

[0045]

[0046] in,

[0047]

[0048] To ensure the non-negativity and stability of the interval observer while simultaneously improving estimation accuracy, the parameter matrix of the interval observer is designed as follows:

[0049] From T+NC=I, we can obtain and then Where S is an arbitrary matrix, for The generalized inverse of the matrix transforms the design of two matrices, T and N, into the design of a single matrix S.

[0050] To obtain the parameter matrix of the interval observer, construct the following semidefinite programming problem:

[0051] Minγ

[0052]

[0053]

[0054] Where e1 = [I5; 0], Let P be a diagonal positive definite matrix. For any matrix G, sym{G} denotes the sum of matrix G and its transpose. G≥0 means that all elements of matrix G are greater than or equal to 0. Let G be a negative definite matrix, * denote a symmetric term in the matrix, and I and 0 denote the identity matrix and zero matrix of appropriate dimension; for a vector α, diag{α} denotes a diagonal matrix with elements of α as diagonal elements.

[0055] Solving the above optimization problem yields the following results:

[0056] Interval observer gain matrix L = P -1 L P ,

[0057] Auxiliary matrix J =P -1 J P ,

[0058] Other parameter matrices

[0059] e2=[0;0;0;0;0;1].

[0060] Furthermore, the interval observer error satisfies the following performance:

[0061] ||e(t)||≤γ||ζ(t)||.

[0062] Furthermore, the specific design process of the fault detection scheme described in step four is as follows:

[0063] Step 3 solves the semidefinite programming problem to obtain the interval observer parameter matrix. By satisfying the first constraint, the error system matrix is ​​guaranteed. It is a Metzler matrix (a matrix with non-negative off-diagonal elements), which ensures that the error is non-negative, i.e., e(t)≥0; the stability of the error system is ensured by satisfying the second constraint condition.

[0064] Therefore, the interval estimates of the upper and lower intervals of state x(t) provided by the interval observer satisfy the following conditions:

[0065]

[0066] in, and x (t) are all bounded.

[0067] From the algebraic relationship between the state and its upper and lower interval estimates in the above equation, we can obtain the interval estimate of the measurement output when the system is operating normally without faults.

[0068]

[0069] Based on the algebraic relationship between the measurement output and its interval estimation in the above formula, the final fault detection scheme is designed as follows:

[0070] If y(t)- y (t)≥0 or Then it is determined that no system fault has occurred;

[0071] If y(t)- y (t)<0 and If so, it is determined that the system actuator has malfunctioned.

[0072] Compared with the prior art, the beneficial effects of the present invention are shown as follows:

[0073] (1) This invention solves the problem of fault detection of unmanned vessel systems in complex water environments. The threshold generated by the interval observer simplifies the fault detection process and is more suitable for fault detection than ordinary observers.

[0074] (2) The TNL-type interval observer constructed in this invention has more design parameters and higher degrees of freedom than the general interval observer. Furthermore, the introduction of an auxiliary matrix relaxes the non-negativity constraint, making the structure of the interval observer more flexible.

[0075] (3) This invention utilizes H ∞The technology improves the estimation accuracy of the interval observer, obtaining a detection threshold that is as small as possible, resulting in stronger fault detection capabilities. Attached Figure Description

[0076] Figure 1 The motion coordinate system established by this invention to achieve asymmetric motion behavior modeling of unmanned vessels;

[0077] Figure 2 A schematic diagram of the fault detection principle of the unmanned vessel based on the TNL type section observer designed for this invention;

[0078] Figure 3 The flowchart for unmanned vessel fault detection based on a TNL-type interval observer designed for this invention is shown. Detailed Implementation

[0079] The following is in conjunction with the appendix Figure 1 , 2 The invention will be explained in further detail in section 3.

[0080] The present invention describes a method for detecting faults in unmanned surface vessels based on a TNL-type interval observer, such as... Figure 3 As shown, it includes the following steps:

[0081] Step 1: Select and establish a suitable coordinate system. Considering the interference of ocean waves on the unmanned vessel, model the dynamic behavior of the asymmetric motion of the unmanned vessel on the water surface, and then obtain a simplified state-space model.

[0082] like Figure 1 As shown, a coordinate system is established with the unmanned vessel's center of gravity as the origin O, the direction from bow to stern as the positive X-axis, the direction from the center of the circle to the starboard side as the positive Y-axis, and the vertical downward direction as the positive Z-axis. By applying Newton's laws to this coordinate system using Taylor expansion and Laplace transform, the equations of motion for the unmanned vessel's asymmetric motion are obtained, leading to the transfer function of the unmanned vessel's motion:

[0083]

[0084]

[0085]

[0086] Where v(s), ψ(s), φ(s), and φ(s) are the Laplace transforms of the sway velocity v(t), heading angle ψ(t), roll angle φ(t), and rudder deflection angle δ(t), respectively; w ψ (s) and These represent the disturbances to the heading angle and rudder deflection caused by ocean waves, respectively; ζ and ω nFor the damping coefficient and the undamped natural frequency, the rest are given constants or gain matrices.

[0087] The operable rudder deflection angle δ(t) can be used as a known input u(t) to convert the transfer function of the above unmanned vessel motion into a state-space expression:

[0088]

[0089] y(t)=Cx(t)

[0090] in, Let r(t) and p(t) represent the system state, respectively, and let r(t) and p(t) represent the yaw rate and roll rate, respectively; the disturbance caused by the waves is denoted as . y t Let C be the measurement output generated by the sensor, and let C be a known dimensionless matrix.

[0091] Step 2: Based on the state equation of the unmanned vessel's motion obtained in the above steps, construct a TNL-type interval observer with an auxiliary matrix.

[0092] Using T and N, which can be converted into the identity matrix by T+NC=I, the system state equations are rewritten as:

[0093]

[0094]

[0095] Assume that the upper and lower bounds of the disturbance caused by the waves and the upper and lower bounds of the initial state are known, i.e., satisfying and of w (t), and x (0) is known. Under this assumption, a TNL-type interval observer is constructed:

[0096]

[0097]

[0098]

[0099]

[0100] in, and L is the intermediate variable for the upper and lower estimates of the interval observer; and J Here are the gain matrix and upper and lower auxiliary matrices for the interval observer. and x(t) represents the upper and lower interval estimates of the state.

[0101] Step 3: Based on the TNL-type interval observer obtained in the above steps, construct the observer error system and utilize H... ∞ Technological improvements enhance estimation performance, minimizing errors.

[0102] Define the upper and lower interval estimation error vectors as follows:

[0103]

[0104] e (t)=x(t)- x (t)

[0105] The dynamic characteristics of the up and down estimation errors, i.e., the up and down estimation error system, are as follows:

[0106]

[0107]

[0108] Combining the upper and lower estimation errors yields the estimation error.

[0109]

[0110] Its dynamic characteristics are

[0111]

[0112] in,

[0113]

[0114]

[0115] The parameter matrix of the interval observer, which improves the accuracy of interval estimation and minimizes the estimation error, is obtained by solving the following optimization problem;

[0116] Minγ

[0117] St

[0118]

[0119]

[0120] in, e1 = [I5; 0], P is restricted to a diagonal positive definite matrix, I and 0 denote the identity matrix and zero matrix of appropriate dimension; for a vector α, diag{α} denotes a diagonal matrix with elements in α as diagonal elements, L P , J -P S P Let be the matrix to be solved;

[0121] Based on the matrix obtained from solving the above semidefinite programming problem, we can obtain

[0122] The gain matrix is ​​L = P -1 L P

[0123] The auxiliary matrix is J =P -1 J P

[0124] The parameter matrices of the remaining interval observers are

[0125]

[0126] e2 = [0; 0; 0; 0; 0; 1]

[0127] The various observer parameter matrices obtained from the above optimization problem guarantee the stability and non-negativity of the interval observers. Meanwhile, the estimation error satisfies the following performance...

[0128]

[0129] Step 4: Based on the interval estimation of the state designed in the above steps, construct a fault detection scheme using the measurement output and its interval estimation.

[0130] When no faults occur, the upper and lower interval estimates generated by the interval observer satisfy...

[0131]

[0132] Based on this, from the output equation y=Cx(t), we can obtain the upper and lower estimates of the output.

[0133]

[0134]

[0135] And the upper and lower output estimates satisfy

[0136]

[0137] Based on this principle, the fault detection scheme was designed as follows:

[0138] If y(t)- y (t)≤0 and The system will then issue an alarm to indicate that a fault has occurred;

[0139] If y(t)- y (t)>0 or If so, it is assumed that no system fault has occurred.

[0140] In this invention, references to certain symbols and explanations of some details are assumed to be based on generally accepted basic knowledge within the relevant field. The specific implementation processes described above are merely for providing a clear and intuitive explanation of this invention and are not intended to limit the scope of protection of this invention. Any technical improvements or derivative technologies based on this invention fall within the scope of protection of this invention.

Claims

1. A fault detection method for unmanned surface vessels based on a TNL-type interval observer, characterized in that, Includes the following: By establishing a suitable coordinate system and taking into account the interference of ocean waves on the unmanned vessel, the dynamic behavior of the unmanned vessel's asymmetric motion under disturbance is modeled, thereby obtaining a simplified state-space model. Based on the state-space model of the asymmetric motion of the unmanned vessel, a TNL-type interval observer with an auxiliary matrix is ​​constructed. Based on the TNL-type interval observer described above, an estimation error system is constructed, and the H∞ technique is used to design the interval observer parameter matrix to improve the estimation performance and minimize the error. Based on the interval estimate of the state generated by the interval observer with improved estimation accuracy, the measurement output is interval estimated, and a fault detection scheme is constructed by combining the measurement output. Establish a suitable coordinate system, and considering the interference of ocean waves on the unmanned surface vessel (USV), model the dynamic behavior of the USV's asymmetric motion under disturbance. Establish a coordinate system with the unmanned vessel's center of gravity as the origin, the direction from bow to stern as the positive x-axis, the direction from the origin to starboard as the positive y-axis, and the vertical direction downwards as the positive z-axis (normal axis). Applying Newton's laws to this coordinate system, we can derive the fundamental equations for the unmanned vessel's asymmetric motion with components along the x-axis on both sides: in, , , and f o For the ship's effective mass, force, heading angle, and roll angle in the Y-axis direction, and N represents the moment of inertia relative to the Z-axis and X-axis. o and K o This represents the torque relative to the Z and X axes; Using Taylor expansion and Laplace transform, the transfer function of the unmanned surface vessel's asymmetric motion is obtained from the fundamental equations of the aforementioned asymmetric motion. Among them, v(s), ψ(s), φ(s), δ(s), w ψ (t) and w φ (s) is v(t), ψ(t), φ(t), δ(s), w ψ (s) and w φ The Laplace transform of (s), where v(t) is the sway velocity, ψ(t) is the heading angle, φ(t) is the roll angle, and δ(t) is the rudder deflection angle, w ψ (t) and w φ (t) represent the disturbances caused by sea waves to the heading angle and rudder deflection angle, respectively, ζ and ω. n T represents the damping coefficient and the undamped natural frequency. r and T v For a given time constant, K vr K dr K dv K vp and K dp Given a gain; Based on the transfer function of the unmanned vessel's asymmetric motion described above, and treating the rudder deflection angle as a known control input, i.e., control input u(t) = δ(t), the state-space model of the unmanned vessel's asymmetric motion can be obtained as follows: in, State x(t)=[v(t) r(t) φ (t) p(t) ψ(t)] T r(t) is the yaw speed, p(t) is the roll rate, and w(t) = [w ψ (t)w φ (t)] T y t For the measurement output, C is a known appropriate dimension matrix; For the state-space model of asymmetric motion of unmanned surface vessels, a TNL-type interval observer with an auxiliary matrix is ​​constructed as follows: Using matrices T and N that satisfy T+NC=I, the state equations in the state-space model can be written as follows: Introducing auxiliary moment vectors further rewrites the state equations as follows: Assuming that the disturbances from the ocean waves and the initial state, though unknown, have known boundaries, a TNL-type interval observer with an auxiliary matrix is ​​constructed based on the rewritten state expression. in, For upper and lower estimation of intermediate variables, L is the interval observer gain matrix. and The upper and lower auxiliary matrices are used to relax the nonnegativity restriction of the interval observer. and For the upper and lower bounds of interference, and For the upper and lower interval estimates of the state, (TE) + It is a matrix obtained by taking the sum of each element in TE and comparing it to the value that is larger than 0. (TE) - = (TE) + -TE; For the aforementioned TNL-type interval observer, the upper estimation error The dynamic characteristics of the estimation error are as follows: The dynamic characteristics are Combined compact upper and lower estimation error to obtain error This error dynamic system is in, ； Using H ∞ The interval observer parameter matrix, which improves estimation performance while minimizing error, is obtained by solving the following optimization problem. in, e1 = [I5; 0], P is restricted to a diagonal positive definite matrix, for any matrix G, sym{G} denotes the sum of matrix G and its transpose, G≥0 means that all elements of matrix G are greater than or equal to 0, G<0 means that G is a negative definite matrix, * denotes the omitted symmetric terms in a symmetric matrix, I and 0 denote the identity matrix and zero matrix of appropriate dimension; for vector α, diag{α} denotes a diagonal matrix with elements in α as diagonal elements, γ is the optimization performance index, LP, S P Let be the matrix to be solved; Then, the parameter matrices of the interval observer are solved as follows: Gain matrix L = P -1 LP Auxiliary matrix Other parameter matrices Furthermore, the interval observer error meets the performance requirements. ||e(t)||≤ γ ||ζ(t)||; Based on the interval estimates of the state generated by the interval observer with improved estimation accuracy, the measurement output is then interval estimated, and a fault detection scheme is constructed by combining the measurement output. When there are no faults in the system, the interval observer gain matrix that satisfies the constraints in the optimization problem guarantees the non-negativity and stability of the interval observer, that is, the upper and lower interval estimates satisfy... and , <∞ Based on the algebraic relationship of the above states, the measured output is estimated from the output equation y = Cx(t) over an interval. in For the upper interval estimation of the measurement output, For the lower interval estimate of the measurement output, and satisfying Based on the algebraic relationship of the above measurement outputs, a fault detection scheme is designed. like or If so, it is determined that no system fault has occurred; like - <0 and - If the value is greater than 0, the system will issue an alarm to indicate that a fault has occurred.

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