A pipeline assembly process adaptive state estimation method based on variational quantum circuit

Abstract

The application provides a pipeline assembly process adaptive state estimation method based on a variational quantum circuit. The method uses the superposition and entanglement characteristics of quantum states to construct a variational quantum circuit based on quantum coding, encodes a time-dependent noise sequence into a high-dimensional Hilbert space, and thus captures the complex time-dependent characteristics of the sequence. By constructing an adaptive variational quantum circuit optimization mechanism and deeply integrating it with a Kalman filter framework, adaptive state estimation of the pipeline assembly process is achieved. The method solves the key problems of low estimation accuracy and slow convergence speed of traditional state estimation methods in a time-dependent non-independent and identically distributed noise environment, significantly improves the estimation performance and dynamic adjustment capability in a complex noise scenario, and provides key technical support for the application of quantum computing enhanced perception and control technology in the field of intelligent assembly.

Description

Technical Field

[0001] This invention proposes an adaptive state estimation method for pipeline assembly processes based on variable quantum circuits. This method utilizes the superposition and entanglement properties of quantum states to construct a quantum-encoded variable quantum circuit, encoding time-dependent noise sequences into a high-dimensional Hilbert space to capture their complex time-dependent characteristics. By constructing an adaptive variable quantum circuit optimization mechanism and deeply integrating it with the Kalman filter framework, adaptive state estimation of the pipeline assembly process is achieved. This method solves the key problems of low estimation accuracy and slow convergence speed of traditional state estimation methods in time-dependent, non-independent, and identically distributed noise environments, significantly improving estimation performance and dynamic adjustment capabilities in complex noise scenarios. It provides crucial technical support for the application of quantum computing-enhanced sensing and control technologies in the field of intelligent assembly. Background Technology

[0002] The rapid development of sensing and artificial intelligence technologies has driven the widespread application of state estimation and predictive control in fields such as industrial automation and autonomous driving. Especially in intelligent assembly line workshops, high-precision and highly interference-resistant real-time state estimation has become a key technology for achieving precision operation and closed-loop control. Its applications cover scenarios such as robotic arm trajectory tracking, workpiece positioning, assembly force control, and overall production line efficiency optimization.

[0003] Traditional adaptive state estimation methods based on the Kalman filter framework correct estimation accuracy by adjusting the noise covariance matrix online. However, the effectiveness of such methods relies on the assumption that the noise is independently and identically distributed in time. In actual assembly line processes, sensing units generally exhibit significant time-dependent characteristics due to crosstalk or environmental disturbances. For non-stationary signals with time dependence and non-independent and identically distributed characteristics, their time-varying statistical properties cause the noise modeling of traditional adaptive mechanisms to fail. Therefore, designing a high-precision, high-response adaptive state estimation method for time-dependent non-stationary noise scenarios is crucial.

[0004] For the modeling of non-stationary sequences, existing research improves the robustness of state estimation by constructing noise modeling based on classical autoregressive or long short-term memory networks and estimating noise covariance online. However, the stringent requirements of real-time performance, accuracy, and adaptive adjustment capabilities in assembly line environments pose a core challenge: First, traditional methods have limited ability to characterize the temporal correlation of high-dimensional nonlinear systems; second, the difficulty in balancing accuracy and computational efficiency in real-time estimation leads to significant estimation delays and convergence speed bottlenecks in dealing with rapidly changing non-stationary noise, limiting their practical application in high-speed, precision assembly scenarios. Therefore, it is essential to develop more robust and adaptive state estimation algorithms to meet the core requirements of high accuracy, strong anti-interference, and real-time response in current assembly line processes, thereby improving production line efficiency. Furthermore, increasing the automation level of the assembly process can effectively reduce reliance on highly skilled operators, significantly reducing the high operating costs associated with manual labor. Summary of the Invention

[0005] This invention proposes an adaptive state estimation method for pipeline assembly processes based on variable quantum circuits. This method utilizes the superposition and entanglement properties of quantum states to construct a quantum-encoded variable quantum circuit, encoding time-dependent noise sequences into a high-dimensional Hilbert space to capture their complex time-dependent characteristics. By constructing an adaptive variable quantum circuit optimization mechanism and deeply integrating it with the Kalman filter framework, adaptive state estimation of the pipeline assembly process is achieved. This method solves the key problems of low estimation accuracy and slow convergence speed of traditional state estimation methods in time-dependent, non-independent, and identically distributed noise environments, significantly improving estimation performance and dynamic adjustment capabilities in complex noise scenarios. It provides crucial technical support for the application of quantum computing-enhanced sensing and control technologies in the field of intelligent assembly.

[0006] 1. An adaptive state estimation method for pipeline assembly processes based on variable quantum circuits, characterized by constructing the state space and historical noise sequence of assembly units, constructing a variable quantum circuit based on quantum encoding, establishing an adaptive variable quantum circuit optimization mechanism, and using the Kalman filter framework for pipeline assembly process state prediction to achieve adaptive state estimation of the assembly process, comprising the following steps:

[0007] (1) Constructing the state space and historical noise sequence of the assembly unit ① In the scenario of the assembly workshop, each assembly unit consists of an execution unit and a sensing and measurement unit. The assembly unit is used to assemble a circular workpiece with a radius of 1.5m; the execution unit contains a 3-DOF robotic arm; Let be the true state vector at the k-th time step during the assembly process, which includes 9 dimensions: its own end position (3-dimensional), three-axis velocity (3-dimensional), and three-axis acceleration (3-dimensional); the corresponding system noise is . The maximum time step for each assembly round is 300. The matrix describing the dynamics of the execution unit has dimensions of . ;

[0008] ② The sensing and measurement unit for acquiring data during the assembly process consists of a vision sensor and a position sensor installed at the end of the actuator of the execution unit. The observation matrix of the sensing measurement unit has dimensions of . ; This is the observation vector of the sensing measurement unit at the k-th time step. The observation dimensions include a total of 6 dimensions, including the end position of the actuator (3-dimensional), the end velocity (3-dimensional), and the corresponding observation noise is... ;in and For time-dependent, non-independent, and identically distributed noise, construct the state space and observation model of the assembly unit as follows:

[0009] (1)

[0010] ③ Collect historical measurement data of the end effector of the execution unit during the assembly process, and calculate the historical noise vector of the sensor according to formula (1). and ;

[0011] ④ Calculate the historical noise vectors for the first 5 time steps in sequence, following step ③. and Then the corresponding historical noise sequence was obtained. and ;

[0012] (2) Constructing a variable quantum circuit based on quantum coding ① The constructed variable quantum circuit contains a total of 10 qubits; the historical noise sequence and Input to a pre-built variable quantum circuit;

[0013] ②The historical noise sequence and Encoded as a rotation angle sequence and , can be expressed as

[0014] (2)

[0015] The rotation angle sequence of the j-th qubit in the sequence is as follows: and ; and These are rotation angle sequences. and The rotation angle value of the j-th qubit at the i-th index; the initial quantum state of the noise sequence is... ;

[0016] ③ The sequence encoded as rotation angles is parameterized through a rotation gate; this operation is performed using a function. This means that the function expression is ;

[0017] ④ Quantum entanglement is added through a controlled NOT gate, which uses a function. This indicates that c and c+1 represent the control bit and target bit of the controlled NOT gate, respectively, and the function expression is: ;

[0018] ⑤ The variable quantum circuit constructed in steps ①-④ can be used to encode the rotation angle sequence into the corresponding quantum state. and Its calculation formula is

[0019] (3)

[0020] (4)

[0021] in Represents the Kronic operation; Represents the multiplication symbol;

[0022] ⑥ The output quantum state described in step ⑤ and Observations were conducted using Pauli operators. The observation of the quantum state can be expressed as follows:

[0023] ;

[0024] Using Pauli operators For quantum states and Observations were conducted to obtain the rotation angle sequence. and The quantum expectation value sequence related to the statistical properties and Its calculation formula is

[0025] (5)

[0026] (6)

[0027] in and These are rotation angle sequences. and The expected value of quantum observation at the i-th index; and They represent the use of Pauli operators. For quantum states and The set of observations observed;

[0028] (3) Establish an adaptive variable quantum circuit optimization mechanism ① The quantum expectation sequence described in step (2) and Through a quantum neural network module, adaptive parameter updates are achieved, and the calculation formula is as follows:

[0029] (7)

[0030] (8)

[0031] in Let be the encoding function of the quantum neural network, denoted as: ; Let be the adaptive weight parameter vector of the neural network, where Quantum expectation value Weight parameters; and This is the output value of the quantum neural network; the quantum neural network module adopts a fully connected feedforward architecture, and the input layer receives a 10-dimensional feature vector concatenated from the expected sequence of quantum observations, which is represented as... The hidden layer contains 64 hidden units; the output layer generates a concatenated 15-dimensional noise prediction vector obtained by equations (7) and (8). The network training uses batch gradient descent optimization with a batch size of 128.

[0032] ②Use and The time-varying covariance matrix of the state noise and measurement noise of the assembly process at the current moment can be obtained. and The estimated value is calculated using the following formula:

[0033] (9)

[0034] (10)

[0035] in , ;

[0036] ③ The optimization process of the quantum neural network described above employs minimizing the likelihood loss function of the state estimation. , can be expressed as

[0037] (11)

[0038] in , ;

[0039] ④ Optimize the weight parameters of the quantum neural network using gradient descent. and ,in To optimize the learning rate of the weight parameters, it is set to 0.1; the calculation formula is as follows:

[0040] (12)

[0041] in, This indicates the direction of parameter updates; the right side of the arrow indicates the weight parameters used to estimate the covariance matrix at the next time step.

[0042] (4) Prediction of process status in pipeline assembly using the Kalman filter framework

[0043] ①The time-varying covariance matrix estimated in step (3) and An extended Kalman filter framework is input to estimate the precise pose of the end effector of the assembly process unit relative to the workpiece in real time.

[0044] ② Input the posterior state estimate from the previous time step. Predicting the prior value at the current time step using the state space matrix. The calculation formula is as follows:

[0045] (13)

[0046] ③ Based on the posterior covariance matrix of the previous time step And the process noise covariance matrix estimated by quantum neural networks Predicting the prior covariance matrix The calculation formula is as follows:

[0047] (14)

[0048] in The noise driving matrix has dimensions of . ;

[0049] ④ Based on the current prior covariance matrix Observation matrix And the observation noise covariance matrix estimated by quantum neural network Calculate the Kalman gain at the current time step. The calculation formula is as follows:

[0050] (15)

[0051] ⑤ Utilizing the current observation vector For prior predicted values Make corrections; via Kalman gain Fusion of prior state predictions With observation residuals Output the predicted state vector and posterior covariance matrix The calculation formula is as follows:

[0052] (16)

[0053] (17)

[0054] The state prediction of the assembly line process is realized through equations (16) and (17); steps (1)-(4) in this claim constitute a complete iterative process, and the algorithm stops iterating when the number of iterations is 1000.

[0055] 2. The method according to claim 1, characterized in that: the method first constructs the state space and historical noise sequence of the assembly unit, then constructs a variable quantum circuit based on quantum coding, and establishes an adaptive variable quantum network optimization mechanism, and finally uses the Kalman filter framework to predict the state of the pipeline assembly process; repeating steps (1)-(4) in claim 1 can realize adaptive state estimation of the pipeline assembly process under time-dependent non-independent identically distributed noise. Attached Figure Description

[0056] Figure 1 Framework diagram of an adaptive state estimation method for pipeline assembly process based on variable quantum circuits

[0057] Figure 2 For trajectory tracking effect diagram

[0058] Figure 3 The total error estimation curve

[0059] Figure 4 A graph showing the total RMSE estimation. Detailed Implementation

[0060] 1. An adaptive state estimation method for pipeline assembly processes based on variable quantum circuits, characterized by constructing the state space and historical noise sequence of assembly units, constructing a variable quantum circuit based on quantum encoding, establishing an adaptive variable quantum circuit optimization mechanism, and using the Kalman filter framework for pipeline assembly process state prediction to achieve adaptive state estimation of the assembly process, comprising the following steps:

[0061] (1) Constructing the state space and historical noise sequence of the assembly unit ① In the scenario of the assembly workshop, each assembly unit consists of an execution unit and a sensing and measurement unit. The assembly unit is used to assemble a circular workpiece with a radius of 1.5m; the execution unit contains a 3-DOF robotic arm; Let be the true state vector at the k-th time step during the assembly process, which includes 9 dimensions: its own end position (3-dimensional), three-axis velocity (3-dimensional), and three-axis acceleration (3-dimensional); the corresponding system noise is . The maximum time step for each assembly round is 300. The matrix describing the dynamics of the execution unit has dimensions of . ;

[0062] ② The sensing and measurement unit for acquiring data during the assembly process consists of a vision sensor and a position sensor installed at the end of the actuator of the execution unit. The observation matrix of the sensing measurement unit has dimensions of . ; This is the observation vector of the sensing measurement unit at the k-th time step. The observation dimensions include a total of 6 dimensions, including the end position of the actuator (3-dimensional), the end velocity (3-dimensional), and the corresponding observation noise is... ;in and For time-dependent, non-independent, and identically distributed noise, construct the state space and observation model of the assembly unit as follows:

[0063] (1)

[0064] ③ Collect historical measurement data of the end effector of the execution unit during the assembly process, and calculate the historical noise vector of the sensor according to formula (1). and ;

[0065] ④ Calculate the historical noise vectors for the first 5 time steps in sequence, following step ③. and Then the corresponding historical noise sequence was obtained. and ;

[0066] (2) Constructing a variable quantum circuit based on quantum coding ① The constructed variable quantum circuit contains a total of 10 qubits; the historical noise sequence and Input to a pre-built variable quantum circuit;

[0067] ②The historical noise sequence and Encoded as a rotation angle sequence and , can be expressed as

[0068] (2)

[0069] The rotation angle sequence of the j-th qubit in the sequence is as follows: and ; and These are rotation angle sequences. and The rotation angle value of the j-th qubit at the i-th index; the initial quantum state of the noise sequence is... ;

[0070] ③ The sequence encoded as rotation angles is parameterized through a rotation gate; this operation is performed using a function. This means that the function expression is ;

[0071] ④ Quantum entanglement is added through a controlled NOT gate, which uses a function. This indicates that c and c+1 represent the control bit and target bit of the controlled NOT gate, respectively, and the function expression is: ;

[0072] ⑤ The variable quantum circuit constructed in steps ①-④ can be used to encode the rotation angle sequence into the corresponding quantum state. and Its calculation formula is

[0073] (3)

[0074] (4)

[0075] in Represents the Kronic operation; Represents the multiplication symbol;

[0076] ⑥ The output quantum state described in step ⑤ and Observations were conducted using Pauli operators. The observation of the quantum state can be expressed as follows:

[0077] ;

[0078] Using Pauli operators For quantum states and Observations were conducted to obtain the rotation angle sequence. and The quantum expectation value sequence related to the statistical properties and Its calculation formula is

[0079] (5)

[0080] (6)

[0081] in and These are rotation angle sequences. and The expected value of quantum observation at the i-th index; and They represent the use of Pauli operators. For quantum states and The set of observations observed;

[0082] (3) Establish an adaptive variable quantum circuit optimization mechanism ① The quantum expectation sequence described in step (2) and Through a quantum neural network module, adaptive parameter updates are achieved, and the calculation formula is as follows:

[0083] (7)

[0084] (8)

[0085] in Let be the encoding function of the quantum neural network, denoted as: ; Let be the adaptive weight parameter vector of the neural network, where Quantum expectation value Weight parameters; and This is the output value of the quantum neural network; the quantum neural network module adopts a fully connected feedforward architecture, and the input layer receives a 10-dimensional feature vector concatenated from the expected sequence of quantum observations, which is represented as... The hidden layer contains 64 hidden units; the output layer generates a concatenated 15-dimensional noise prediction vector obtained by equations (7) and (8). The network training uses batch gradient descent optimization with a batch size of 128.

[0086] ②Use and The time-varying covariance matrix of the state noise and measurement noise of the assembly process at the current moment can be obtained. and The estimated value is calculated using the following formula:

[0087] (9)

[0088] (10)

[0089] in , ;

[0090] ③ The optimization process of the quantum neural network described above employs minimizing the likelihood loss function of the state estimation. , can be expressed as

[0091] (11)

[0092] in , ;

[0093] ④ Optimize the weight parameters of the quantum neural network using gradient descent. and ,in To optimize the learning rate of the weight parameters, it is set to 0.1; the calculation formula is as follows:

[0094] (12)

[0095] in, This indicates the direction of parameter updates; the right side of the arrow indicates the weight parameters used to estimate the covariance matrix at the next time step.

[0096] (4) Prediction of process status in pipeline assembly using the Kalman filter framework

[0097] ①The time-varying covariance matrix estimated in step (3) and An extended Kalman filter framework is input to estimate the precise pose of the end effector of the assembly process unit relative to the workpiece in real time.

[0098] ② Input the posterior state estimate from the previous time step. Predicting the prior value at the current time step using the state space matrix. The calculation formula is as follows:

[0099] (13)

[0100] ③ Based on the posterior covariance matrix of the previous time step And the process noise covariance matrix estimated by quantum neural networks Predict the prior covariance matrix The calculation formula is as follows:

[0101] (14)

[0102] in The noise driving matrix has dimensions of . ;

[0103] ④ Based on the current prior covariance matrix Observation matrix And the observation noise covariance matrix estimated by quantum neural network Calculate the Kalman gain at the current time step. The calculation formula is as follows:

[0104] (15)

[0105] ⑤ Utilizing the current observation vector For prior predicted values Make corrections; via Kalman gain Fusion of prior state predictions With observation residuals Output the predicted state vector and posterior covariance matrix The calculation formula is as follows:

[0106] (16)

[0107] (17)

[0108] The state prediction of the assembly line process is realized through equations (16) and (17); steps (1)-(4) in this claim constitute a complete iterative process, and the algorithm stops iterating when the number of iterations is 1000.

[0109] 2. The method according to claim 1, characterized in that: the method first constructs the state space and historical noise sequence of the assembly unit, then constructs a variable quantum circuit based on quantum coding, and establishes an adaptive variable quantum network optimization mechanism, and finally uses the Kalman filter framework to predict the state of the pipeline assembly process; repeating steps (1)-(4) in claim 1 can realize adaptive state estimation of the pipeline assembly process under time-dependent non-independent identically distributed noise.

Claims

1. An adaptive state estimation method for pipeline assembly processes based on variable quantum circuits, characterized in that, The process involves constructing the state space and historical noise sequence of an assembly unit, building a quantum-encoded variable quantum circuit, establishing an adaptive variable quantum circuit optimization mechanism, and using a Kalman filter framework for pipeline assembly process state prediction to achieve adaptive state estimation of the assembly process. The steps include: (1) Constructing the state space and historical noise sequence of the assembly unit ① In the scenario of the assembly workshop, each assembly unit consists of an execution unit and a sensing and measurement unit. The assembly unit is used to assemble a circular workpiece with a radius of 1.5m; the execution unit contains a 3-DOF robotic arm; This is the true state vector at the k-th time step during the assembly process, which includes 9 dimensions, including its own end position, triaxial velocity, and triaxial acceleration; the corresponding process noise is... The maximum time step for each assembly round is 300. The matrix describing the dynamics of the execution unit has dimensions of . ; ② The sensing and measurement unit for acquiring data during the assembly process consists of a vision sensor and a position sensor installed at the end of the actuator of the execution unit. The observation matrix of the sensing measurement unit has dimensions of . ; This is the observation vector of the sensing measurement unit at the k-th time step. The observation dimensions include 6 dimensions, including the end position and end velocity of the actuator. The corresponding observation noise is... ;in and For time-dependent, non-independent, and identically distributed noise, construct the state space and observation model of the assembly unit as follows: (1)； ③ Collect historical measurement data of the end effector of the execution unit during the assembly process, and calculate the historical noise vector of the sensor according to formula (1). and ; ④ Calculate the historical noise vectors for the first 5 time steps in sequence, following step ③. and Then the corresponding historical noise sequence was obtained. and ; (2) Constructing a variable quantum circuit based on quantum coding ① The constructed variable quantum circuit contains a total of 10 qubits; the historical noise sequence and Input to a pre-built variable quantum circuit; ②The historical noise sequence and Encoded as a rotation angle sequence and , can be expressed as (2) The rotation angle sequence of the j-th qubit in the sequence is as follows: and ; and These are rotation angle sequences. and The rotation angle value of the j-th qubit at the i-th index; the initial quantum state of the noise sequence is... ; ③ The sequence encoded as rotation angles is parameterized through a rotation gate; this operation is performed using a function. This means that the function expression is ; ④ Quantum entanglement is added through a controlled NOT gate, which uses a function. This indicates that c and c+1 represent the control bit and target bit of the controlled NOT gate, respectively, and the function expression is: ; ⑤ The variable quantum circuit constructed through steps ①-④ can be used to encode the rotation angle sequence into the corresponding quantum state. and Its calculation formula is (3)； (4)； in Represents the Kronic operation; Represents the multiplication symbol; ⑥ Output quantum state in step ⑤ and Observations were conducted using Pauli operators. The output quantum state can be observed and expressed as ； Using Pauli operators For quantum states and Observations were conducted to obtain the rotation angle sequence. and The quantum expectation value sequence related to the statistical properties and Its calculation formula is (5)； (6)； in and These are rotation angle sequences. and The expected value of quantum observation at the i-th index; and They represent the use of Pauli operators. For quantum states and The set of observations observed; (3) Establish an adaptive variable quantum circuit optimization mechanism ① The quantum expectation value sequence described in step (2) and Through a quantum neural network module, adaptive parameter updates are achieved, and the calculation formula is as follows: (7)； (8)； in Let be the encoding function of the quantum neural network, denoted as: ; Let be the adaptive weight parameter vector of the neural network, where Quantum expectation value Weight parameters; Quantum expectation value Weight parameters; and This is the output value of the quantum neural network; the quantum neural network module adopts a fully connected feedforward architecture, and the input layer receives a 10-dimensional feature vector concatenated from the expected sequence of quantum observations, which is represented as... The hidden layer contains 64 hidden units; the output layer generates a concatenated 15-dimensional noise prediction vector obtained by equations (7) and (8). The network training uses batch gradient descent optimization with a batch size of 128. ②Use and It is possible to obtain the time-varying covariance matrix of the process noise and observation noise at the current moment of the assembly process. and The estimated value is calculated using the following formula: (9)； (10)； in , ; ③ The optimization process of the quantum neural network described above employs minimizing the likelihood loss function of the state estimation. , can be expressed as (11)； in , ; ④ Optimize the weight parameter vector of the quantum neural network using gradient descent. and ,in To optimize the learning rate of the weight parameters, it is set to 0.1; the calculation formula is as follows: (12)； in, This indicates the direction of parameter updates; the right side of the arrow indicates the weight parameters used to estimate the covariance matrix at the next time step. (4) Prediction of process status in pipeline assembly using the Kalman filter framework ①The time-varying covariance matrix estimated in step (3) and An extended Kalman filter framework is input to estimate the precise pose of the end effector of the assembly process unit relative to the workpiece in real time. ② Input the posterior state estimate from the previous time step. Predicting the prior value at the current time step using the state space matrix. The calculation formula is as follows: (13)； ③ Based on the posterior covariance matrix of the previous time step And the time-varying covariance matrix of process noise estimated by quantum neural networks Predict the prior covariance matrix The calculation formula is as follows: (14)； in The noise driving matrix has dimensions of . ; ④ Based on the current prior covariance matrix Observation matrix and the time-varying covariance matrix of observation noise estimated by quantum neural networks. Calculate the Kalman gain at the current time step. The calculation formula is as follows: (15)； ⑤ Utilizing the current observation vector For prior predicted values Make corrections; via Kalman gain Fusion of prior predictions With observation residuals Output the predicted state vector and the posterior covariance matrix at the current time The calculation formula is as follows: (16)； (17)； The state prediction of the assembly line process is realized through equations (16) and (17); steps (1)-(4) constitute a complete iterative process, and the algorithm stops iterating when the number of iterations is 1000.

2. The method according to claim 1, characterized in that: The method first constructs the state space and historical noise sequence of the assembly unit, then constructs a variable quantum circuit based on quantum coding, and establishes an adaptive variable quantum network optimization mechanism. Finally, it uses the Kalman filter framework to predict the state of the pipeline assembly process. The iterative steps (1)-(4) can realize adaptive state estimation of the pipeline assembly process under time-dependent non-independent and identically distributed noise.

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