Deterministic and probabilistic hybrid prediction method for dynamic response of ocean dynamic cable

Abstract

The invention provides a determinacy and probabilistic hybrid prediction method for dynamic response of an ocean dynamic cable, and belongs to the field of ocean energy development. The method comprises the following steps: firstly, constructing an ocean dynamic cable full-coupling time-domain hydrodynamic analysis model, generating a dynamic response original data set, and carrying out data processing; secondly, a deterministic prediction model of the dynamic response of the ocean dynamic cable is constructed, and deterministic prediction of the dynamic response of the ocean dynamic cable is achieved; thirdly, based on a deterministic prediction result of the dynamic response of the dynamic cable, calculating a deterministic prediction error of the dynamic response, and establishing a probabilistic prediction method of the dynamic response; and finally, according to a deterministic prediction result and a probabilistic prediction result of the dynamic response of the dynamic cable, calculating and determining a prediction evaluation index and a probabilistic prediction evaluation index. According to the method, accurate and credible deterministic prediction of the random dynamic response of the dynamic cable can be improved, the uncertainty of the random dynamic response is effectively quantified, and the method has the capability of providing general modeling and efficient prediction for a monitoring and early warning system of the dynamic cable.

Description

Technical Field

[0001] The present invention belongs to the field of offshore floating energy development, and relates to a deterministic and probabilistic hybrid prediction method for the dynamic response of an ocean dynamic cable, which can provide accurate, fast and reliable dynamic response prediction technical support for the ocean dynamic cable. Background Art

[0002] At present, the challenges facing global energy reserves and ecological environment are becoming increasingly severe. Marine energy development has gradually become a key direction in the energy field and has broad development prospects. Marine energy development systems usually adopt a combination of upper floating platforms and underwater production systems. Among them, marine dynamic cables, as key equipment connecting upper floating platforms and underwater production systems, are known as the "lifeline" of marine energy development systems (DOI: / 10.1016 / j.oceaneng.2021.109742). Therefore, when marine dynamic cables are in operation, it is crucial to establish an operation and maintenance warning system to ensure the safe operation of the dynamic cable system. Due to the characteristics of marine dynamic cables with multiple materials, multi-level structures, complex underwater linear layouts, and coupled motion of upper floating platforms and dynamic cables, the dynamic response of marine dynamic cables under environmental loads shows strong nonlinearity, volatility and uncertainty. How to achieve efficient, accurate and reliable dynamic response of dynamic cables is a difficult problem to be solved urgently (DOI: / 10.1016 / j.apor.2013.03.003).

[0003] By investigating the dynamic cable response prediction technology at home and abroad, it is found that the current dynamic response calculation method is mainly based on the finite element method for system modeling and time domain coupling calculation. However, in actual engineering, the computational cost of the finite element method is huge, and it is difficult to meet the needs of rapid prediction and evaluation of the dynamic response of the dynamic cable. Therefore, achieving accurate and rapid prediction of dynamic response is crucial for evaluating the current and future structural state of the dynamic cable, which helps the operator to provide operation and maintenance suggestions before potential risks occur and minimize structural damage. In addition, due to the significant uncertainty in the prediction process of dynamic response, a single deterministic prediction only provides a single deterministic prediction value, which is difficult to fully reflect the uncertainty in the prediction of the dynamic response of the dynamic cable (DOI: / 10.1016 / j.apor.2023.103687; DOI: / 10.1016 / j.marstruc.2023.103448). Therefore, accurately and efficiently realizing the deterministic prediction of the dynamic response of the dynamic cable and quantifying the uncertainty in the prediction through probabilistic prediction technology will provide strong technical support for the monitoring and early warning system of the dynamic cable. This has important engineering significance for the field of marine energy development, can effectively improve safety and reliability, and promote the application and development of related technologies. Summary of the invention

[0004] In view of the problems in the prior art of low prediction accuracy of the dynamic response of marine dynamic cables and the inability to quantify prediction uncertainty, the present invention provides a deterministic and probabilistic hybrid prediction method for the dynamic response of marine dynamic cables, which can not only realize fast and accurate deterministic prediction of the dynamic response, but also realize reliable probabilistic prediction, thereby quantitatively evaluating the uncertainty of the prediction results.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A deterministic and probabilistic hybrid prediction method for dynamic response of a marine dynamic cable, the deterministic and probabilistic hybrid prediction method comprising the following steps:

[0007] S1. Construct a fully coupled time-domain hydrodynamic analysis model for marine dynamic cables and generate the original data set for dynamic response. The details are as follows:

[0008] S1.1. Construct a fully coupled time-domain hydrodynamic analysis model;

[0009] OrcaFlex software is used to build a fully coupled time-domain hydrodynamic analysis model of the marine dynamic cable. The fully coupled time-domain hydrodynamic analysis model is composed of an upper floating platform and a dynamic cable system. The time-domain simulation duration of the fully coupled time-domain hydrodynamic analysis model is set to 3 hours. The fully coupled time-domain hydrodynamic analysis model can fully simulate the interaction between the dynamic cable and the ocean waves and the upper floating body movement, and can accurately describe the influence of various factors on the dynamic response of the marine dynamic cable.

[0010] S1.2, extract the dynamic response original data set;

[0011] After the construction of the fully coupled time-domain hydrodynamic analysis model is completed, a 3-hour dynamic response time-domain simulation calculation is performed. The dynamic response original data set of the marine dynamic cable is extracted in batches. The dynamic response original data set includes two parts: input and output. The input includes the time series data of the wave height and the six-degree-of-freedom motion response of the upper floating platform, and the output includes the effective tension at the location where the maximum effective tension occurs and the curvature time series data at the location where the maximum curvature occurs, as follows:

[0012] p i ={H i ,X i ,Y i ,Z i ,α i ,β i ,γ i} (1)

[0013] y i ={T i eff ,C i} (2)

[0014] Among them, p i and i represents the i-th group of samples of the input and output of the original data set of the dynamic response of the marine dynamic cable, respectively. i represents the ith sample of the wave height time series data, X i , Y i and Z i represents the ith sample of the time series data of the surge, sway and heave motion response of the upper floating platform, α i , β i and γ i represents the i-th sample of the roll, pitch and bow motion response of the upper floating platform, T i eff represents the i-th sample of the effective tension time series data at the location where the maximum effective tension of the marine dynamic cable occurs, C i Represents the i-th sample of the curvature time series data at the location where the maximum curvature of the marine dynamic cable occurs.

[0015] S2: Data processing is performed on the original data set of the dynamic response of the marine dynamic cable in S1, including normalization, central moment feature extraction, and dimensional reconstruction. The details are as follows:

[0016] S2.1, dynamically responding to normalization processing of the original data set to obtain a normalized data set;

[0017] Based on the minimum-maximum scale normalization method, the input and output of the original data set of the dynamic cable dynamic response of S1 are normalized respectively, and the expression is:

[0018]

[0019] in, and Respectively represent the maximum and minimum values ​​of the i-th group of samples input in the original data set, and Respectively represent the maximum and minimum values ​​of the i-th group of samples output in the original data set, and They represent the i-th group of input and output samples in the dynamic response normalization dataset respectively.

[0020] S2.2, extracting the central moment feature of the input of the normalized data set;

[0021] The central moment feature characterizes the statistical characteristics of the data and can provide supplementary information for the prediction of dynamic response. The expression of the central moment feature of the i-th group of samples of the input of the normalized data set is:

[0022]

[0023] Where k represents the order of the central moment, represents the k-th central moment feature of the i-th group of samples input into the normalized data set, express The mean of express The variance of , M represents the data length used to extract the central moment feature.

[0024] S2.3, dimensionality-increasing reconstruction of normalized dataset input;

[0025] Will Combined with the first k-order central moment features of the i-th group of samples of the input of the normalized data set, the normalized data set input is reconstructed by increasing the dimension. By setting different k values, the reconstructed input of normalized data sets of different orders can be flexibly generated. The following three reconstructed inputs of normalized data sets are considered in the present invention, and the expressions are:

[0026]

[0027] in, They represent the reconstructed input of the normalized data set considering the first 2-order central moments, the first 3-order central moments, and the first 4-order central moments, respectively.

[0028] S3, based on the bidirectional long short-term memory neural network BiLSTM and the Bayesian optimization algorithm, builds a deterministic prediction model for the dynamic response of the marine dynamic cable, and based on the reconstructed input and output of the normalized data set of S2, realizes the deterministic prediction of the dynamic response of the marine dynamic cable, as follows:

[0029] S3.1. Divide the training set and test set of the deterministic prediction model;

[0030] First, the input of the normalized data set of the dynamic response of the marine dynamic cable in S2 Refactoring Input and output Then, the four groups of new normalized data sets are divided into training sets and test sets in chronological order, of which the first 70% is the new normalized training set, which is used for the training and hyperparameter optimization of the deterministic prediction model; the last 30% is the new normalized test set, which is used to evaluate the deterministic prediction performance.

[0031] S3.2. Construct a deterministic prediction model for the dynamic response of marine dynamic cables;

[0032] A bidirectional long short-term memory neural network BiLSTM is used to construct a deterministic prediction model for the dynamic response of marine dynamic cables. Among them, the LSTM unit in BiLSTM includes a forget gate, an input gate, and an output gate. Its gating mechanism can effectively control the retention and discarding of information, thereby dealing with long-term dependency problems and avoiding gradient vanishing or explosion phenomena. In BiLSTM, there are two LSTM layers. The forward LSTM layer processes time series data from front to back, and the backward LSTM layer processes time series data from back to front. This enables BiLSTM to simultaneously utilize the front and back information of time series data and fully explore the contextual dependencies of time series data. When processing time series data, each input time step will be passed to the two LSTM layers separately, and then their outputs will be merged, so as to comprehensively consider the front and back information of the time series data to improve the accuracy of the prediction.

[0033] The expression of the forward LSTM layer is:

[0034] f t =σ(W f x t +U f h t-1 +b f ) (9)

[0035] i t =σ(W i x t +U i h t-1 +b i ) (10)

[0036]

[0037] o t =σ(W o x t +U o h t-1 +b o ) (13)

[0038] h t =o t ⊙tanh(C t ) (14)

[0039] Among them, f t 、i t and t Represent the outputs of the forget gate, input gate, and output gate of the forward LSTM layer, respectively. C t and h t They represent the candidate cell state, cell state and hidden state of the forward LSTM layer, respectively, and x tThe vector representing the tth time step of the time series data, h t-1 represents the hidden state of the previous time step of the forward LSTM layer, C t-1 represents the cell state of the previous time step of the forward LSTM layer, W f and U f is the weight coefficient in the forget gate of the forward LSTM layer, W i and U i is the weight coefficient in the input gate of the forward LSTM layer, W o and U o is the weight coefficient in the output gate of the forward LSTM layer, W c and U c represents the weight coefficient of the candidate cell state of the forward LSTM layer, b f , b i , b o and b c They represent the forget gate, input gate, output gate and bias coefficient in the candidate cell state of the forward LSTM layer, σ(·) represents the sigmoid activation function, and ⊙ represents the Hadamard product.

[0040] The expression of the backward LSTM layer is:

[0041] f′ t =σ(W′ f x t +U′ f h′ t+1 +b′ f ) (15)

[0042] i′ t =σ(W′ i x t +U′ i h′ t+1 +b i ) (16)

[0043]

[0044] o′ t =σ(W′ o x t +U′ o h′ t+1 +b′ o ) (19)

[0045] h′ t =o′ t ⊙tanh(C′ t ) (20)

[0046] Among them, f′ t , i′t and o′ t Represent the outputs of the forget gate, input gate, and output gate of the backward LSTM layer, respectively. C′ t and h′ t They represent the candidate cell state, cell state and hidden state of the backward LSTM layer, respectively, and h′ t+1 represents the hidden state of the next time step of the backward LSTM layer, C′ t+1 represents the cell state of the next time step of the backward LSTM layer, W′ f and U′ f is the weight coefficient in the forget gate of the backward LSTM layer, W′ i and U′ i is the weight coefficient in the input gate of the backward LSTM layer, W′ o and U′ o is the weight coefficient in the output gate of the backward LSTM layer, W′ c and U′ c Represents the weight coefficient of the candidate cell state of the backward LSTM layer, b′ f , b i , b′ o and b′ c They represent the forget gate, input gate, output gate and bias coefficients in the candidate cell state of the backward LSTM layer respectively.

[0047] BiLSTM is used to build a deterministic prediction model for the dynamic response of marine dynamic cables, and the model is trained using the new normalized training set divided in S3.1. During the training process, BiLSTM includes several hyperparameters, including the number of hidden units, learning rate, and batch size. These hyperparameters have an important impact on the prediction performance of the model. Therefore, determining the optimal hyperparameters is the key to improving the prediction performance of the deterministic prediction model. The Bayesian optimization algorithm is used to automatically search for the optimal hyperparameters of BiLSTM, thereby ensuring that the deterministic prediction model reaches the best state during the training process, and finally obtaining the optimal deterministic prediction model after training.

[0048] S3.3, Deterministic prediction of dynamic response of marine dynamic cables;

[0049] Based on the trained optimal deterministic prediction model, the samples in the new normalized test set are predicted to obtain the normalized prediction values ​​of the dynamic response. These normalized prediction values ​​can reflect the prediction results of the model on the dynamic response of the marine dynamic cable, but because the data is trained after normalization, it needs to be denormalized to restore it to the original physical scale. Through denormalization, the normalized prediction value can be converted into a deterministic prediction result of the dynamic response. The denormalized expression is:

[0050]

[0051] in, represents the i-th group of sample values ​​of the normalized prediction value of the dynamic response, Represents the i-th group of values ​​of the dynamic response deterministic prediction results.

[0052] S4. Based on the deterministic prediction results of the dynamic response of the dynamic cable in S3, the deterministic prediction error of the dynamic response is calculated, and the probabilistic prediction method of the dynamic response is established using the adaptive bandwidth kernel density estimation ABKDE, as follows:

[0053] S4.1, calculating the deterministic prediction error sequence of the dynamic response;

[0054] Based on the deterministic prediction results of the dynamic response in S3.3, the absolute error of the deterministic prediction results of the dynamic response at each time point is calculated and combined into a dynamic response deterministic prediction error sequence, which is expressed as:

[0055] er=[er1,er2,…,er N ] (twenty two)

[0056] Where er represents the dynamic response deterministic prediction error sequence and N represents the number of samples.

[0057] S4.2, fitting the probability density function of the dynamic response deterministic prediction error sequence;

[0058] Based on the dynamic response deterministic prediction error sequence er of S4.1, the probability density function of er is fitted by adaptive bandwidth kernel density estimation ABKDE, and its expression is:

[0059]

[0060] Among them, h i (er) represents the adaptive bandwidth at the estimated point er, which is related to the i-th sample point er i The selection of this bandwidth depends on the local density information of the sample points, aiming to use a smaller bandwidth in high-density areas and a larger bandwidth in low-density areas, thereby improving the accuracy of the estimation. In order to calculate the adaptive bandwidth at each estimation point, a local error function C needs to be defined i (er k ), and by minimizing the local error function, we can calculate each target estimation point er k Adaptive bandwidth h at i The local error function can consider the dynamic balance between the deviation and variance in the probability density function fitting process. The expression of the local error function is:

[0061]

[0062] Among them, er k represents the target estimated point, h i Indicates that at the target estimated point er k The adaptive bandwidth at the i-th sample point er i Related, f(er k ) represents the true probability density value at the target estimation point, Indicates that at the target estimated point er k Adaptive bandwidth h is used i The probability density estimate of . and Two of the terms measure the accuracy of the probability density estimate, and the third The smoothness of the probability density estimation is measured. The golden section method is used to minimize the formula (24) to obtain the optimized adaptive bandwidth, which is substituted into the formula (23) to obtain the probability density function of the dynamic response deterministic prediction error sequence.

[0063] S4.3, calculate the probabilistic prediction results of dynamic response based on the quantile solution method;

[0064] Based on the probability density function of the dynamic response deterministic prediction error sequence of S4.2, the cumulative distribution function of the dynamic response deterministic prediction error sequence is obtained by numerical integration According to the specified quantile, calculate the corresponding quantile solution:

[0065]

[0066] Among them, z represents the specified quantile, q(z) represents the quantile solution corresponding to z, Represents the inverse of the cumulative distribution function of the series of deterministic forecast errors of the dynamic response.

[0067] The dynamic response probabilistic prediction results are obtained by using the quantile solution. The upper and lower bounds of the sample prediction interval are used to quantitatively describe the probabilistic prediction results. The calculation expression is:

[0068]

[0069] Among them, Lb i and Ub i They represent the lower and upper bounds of the prediction interval of the i-th sample, respectively. represents the i-th deterministic prediction result of the dynamic response of the dynamic cable, q(1-z) and q(z) represent the quantile solutions corresponding to 1-z and z, respectively.

[0070] S5. According to the deterministic prediction results and the probabilistic prediction results of the dynamic response of the dynamic cable, respectively calculate and determine the prediction evaluation index and the probabilistic prediction evaluation index, and save the evaluation index results. The details are as follows:

[0071] S5.1. Determine the prediction evaluation indicators;

[0072] The prediction evaluation index includes: 2 , mean absolute error MAE, mean absolute percentage error MAPE, and root mean square error RMSE. Its expression is:

[0073]

[0074]

[0075] Where N represents the number of samples, y i represents the ith original value of the dynamic response of the dynamic cable, represents the i-th deterministic prediction result of the dynamic response of the dynamic cable.

[0076] S5.2, Probabilistic prediction evaluation indicators;

[0077] The probability prediction evaluation indicators include: prediction interval coverage rate PICP, prediction interval average width PINAW, coverage width standard CWC and continuous sorting probability score CRPS. The mathematical expression is:

[0078]

[0079] Among them, K i Represents a Boolean variable, Lb i and Ub i They represent the lower and upper bounds of the prediction interval of the i-th sample, respectively. Represents the deterministic prediction result of the dynamic response of the dynamic cable. The larger the PICP, the better the probabilistic prediction performance.

[0080]

[0081] Among them, Z represents the variation range of the original value of the dynamic response of the dynamic cable in the test set. When the PICP results are the same, the smaller the PINAW, the better the probability prediction performance.

[0082]

[0083] β=1-2(1-z) (36)where γ represents the indicator function, z represents the specified quantile, and β represents the confidence level corresponding to z. The smaller the CWC, the better the probability prediction performance.

[0084]

[0085] Where y represents the original value of the dynamic response of the dynamic cable in the test set, represents the deterministic prediction result of the dynamic response of the dynamic cable in the test set, represents the cumulative distribution function of the deterministic response prediction results, express The Heaviside function.

[0086] The beneficial effects of the present invention are:

[0087] The present invention constructs a fully coupled time-domain hydrodynamic analysis model of marine dynamic cables, constructs a dynamic response deterministic prediction model based on a Bayesian optimized bidirectional long short-term memory neural network, and carries out deterministic prediction of dynamic response. Then, the probability prediction of dynamic response is carried out by an adaptive bandwidth kernel density estimation method, thereby realizing a quantitative evaluation of prediction uncertainty. The present invention can realize accurate, fast and reliable prediction of the dynamic response of marine dynamic cables, and provide efficient and reliable technical support for the monitoring and operation and maintenance system of dynamic cables in marine energy development. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 The framework diagram of the deterministic and probabilistic hybrid prediction method for the dynamic response of marine dynamic cables;

[0089] Figure 2 This is the model diagram of dynamic cable fully coupled time-domain hydrodynamic analysis;

[0090] Figure 3 Schematic diagram of the gating mechanism of the LSTM unit;

[0091] Figure 4 This is a schematic diagram of the basic architecture of the bidirectional long short-term memory network BiLSTM;

[0092] Figure 5 It is a deterministic prediction sequence diagram of effective tension response when considering different central moment characteristics;

[0093] Figure 6 It is a deterministic prediction sequence diagram of curvature response when considering different central moment characteristics;

[0094] Figure 7 is the deterministic prediction error sequence diagram of the effective tension response;

[0095] Figure 8 is the deterministic prediction error series diagram of the curvature response;

[0096] Fig. 9 is the probability density fitting curve of the deterministic prediction error of the effective tension response;

[0097] Fig.10The probability density fitting curve of the deterministic prediction error of the curvature response;

[0098] Fig.11 It is the probability prediction interval diagram of effective tension response at different confidence levels;

[0099] Fig.12 The probabilistic prediction interval plot of the curvature response at different confidence levels. DETAILED DESCRIPTION

[0100] The technical solutions in the embodiments of the present invention will be clearly and completely described below in combination with the content of the invention and the drawings and formulas of the specification. The described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0101] Reference Figure 1 The present invention is a deterministic and probabilistic hybrid prediction method for the dynamic response of marine dynamic cables. Taking the dynamic cable system of a 305-meter-deep oil field development system as an example, the specific implementation steps are as follows:

[0102] S1. Construct a fully coupled time-domain hydrodynamic analysis model for marine dynamic cables and generate data to generate the original data set of dynamic response. The specific steps are as follows:

[0103] S1.1. OrcaFlex software is used to build a fully coupled time-domain hydrodynamic analysis model of the marine dynamic cable. The model is composed of an upper floating platform and a dynamic cable system. The time-domain simulation duration of the model is set to 3 hours, and the total length of the dynamic cable is 530 meters. The structural parameters and service sea condition parameters used in this example are shown in Table 1.

[0104] Table 1 Dynamic cable structure parameters and service sea condition parameters

[0105]

[0106]

[0107] S1.2. Extracting dynamic response raw data sets

[0108] After the construction of the fully coupled time-domain hydrodynamic analysis model is completed, a 3-hour dynamic response time-domain simulation calculation is performed. By writing the secondary development interface code of the OrcaFlex software, batch extraction of the original data set of dynamic response of the marine dynamic cable is realized. The original dynamic response data set is divided into two parts: input and output. The input of the original dynamic response data set specifically includes the time series data of the wave height and the six-degree-of-freedom motion response of the upper floating platform. The output of the original dynamic response data set includes the effective tension at the location where the maximum effective tension occurs and the curvature time series data at the location where the maximum curvature occurs:

[0109] p i ={H i ,X i ,Y i ,Z i ,α i ,β i ,γ i} (1)

[0110] y i ={T i eff ,C i} (2)

[0111] Among them, p i and i represents the i-th group of samples of the input and output of the original data set of the dynamic response of the marine dynamic cable, respectively. i represents the ith sample of the wave height time series data, X i , Y i and Z i represents the ith sample of the time series data of the surge, sway and heave motion response of the upper floating platform, α i , β i and γ i represents the i-th sample of the roll, pitch and bow motion response of the upper floating platform, T i eff represents the i-th sample of the effective tension time series data at the location where the maximum effective tension of the marine dynamic cable occurs, C i Represents the i-th sample of the curvature time series data at the location where the maximum curvature of the marine dynamic cable occurs.

[0112] S2. Data processing is performed on the original data set of the dynamic response of the marine dynamic cable, including normalization, central moment feature extraction, and dimensional reconstruction. The specific steps are as follows:

[0113] S2.1. Normalization of the original data set

[0114] Based on the minimum-maximum scale normalization method, the input and output of the original data set of the dynamic cable dynamic response of S1.2 are normalized respectively, and the expression is:

[0115]

[0116] in, and Respectively represent the maximum and minimum values ​​of the i-th group of samples input in the original data set, and Respectively represent the maximum and minimum values ​​of the i-th group of samples output in the original data set, and They represent the i-th group of input and output samples in the dynamic response normalization dataset respectively.

[0117] S2.2. Extracting the central moment features of the input of the normalized data set

[0118] The central moment feature can characterize the statistical characteristics of the data and provide supplementary information for the prediction of dynamic response. The mathematical expression of the central moment feature of the i-th group of samples of the input of the normalized data set is:

[0119]

[0120] Where k represents the order of the central moment, represents the k-th central moment feature of the i-th group of samples input into the normalized data set, express The mean of express The variance of M is , and M represents the data length used to extract the central moment feature. In this example, 10 data lengths are used.

[0121] S2.3. Dimensional reconstruction of normalized dataset input

[0122] Will Combined with the first k-order central moment features of the i-th group of samples of the input of the normalized data set, the normalized data set input is reconstructed by increasing the dimension. In this example, three groups of k values ​​are set, namely 2, 3 and 4, to generate three groups of reconstructed inputs of the normalized data set, and the expressions are:

[0123]

[0124] in, They represent the reconstructed input of the normalized data set considering the first 2-order central moments, the first 3-order central moments, and the first 4-order central moments, respectively.

[0125] S3. Based on the bidirectional long short-term memory neural network BiLSTM and the Bayesian optimization algorithm, a deterministic prediction model of the dynamic response of the marine dynamic cable is constructed, and based on the reconstructed input and output of the normalized data set, the deterministic prediction of the dynamic response of the marine dynamic cable is realized. The specific steps are as follows:

[0126] S3.1. Dividing the training set and test set of the deterministic prediction model

[0127] Input the normalized data set of the dynamic response of the marine dynamic cable in S2.1 With the reconstructed input in S2.3 and output Then, the four groups of new normalized data sets are divided into training sets and test sets in chronological order, of which the first 70% is the new normalized training set, which is used for the training and hyperparameter optimization of the deterministic prediction model; the last 30% is the new normalized test set, which is used to evaluate the deterministic prediction performance.

[0128] S3.2. Constructing a deterministic prediction model for the dynamic response of marine dynamic cables

[0129] A bidirectional long short-term memory neural network BiLSTM is used to build a deterministic prediction model for the dynamic response of marine dynamic cables. The LSTM unit in BiLSTM includes a forget gate, an input gate, and an output gate. Its gating mechanism can effectively control the retention and discarding of information, thereby dealing with long-term dependency problems and avoiding gradient disappearance or explosion. Figure 3 The schematic diagram of the gating mechanism of the LSTM unit is shown. In BiLSTM, there are two LSTM layers. The forward LSTM layer processes the time series data from front to back, and the backward LSTM layer processes the time series data from back to front. This enables BiLSTM to simultaneously utilize the front and back information of the time series data and fully exploit the contextual dependencies of the time series data. When processing time series data, each time step of the input is passed to the two LSTM layers separately, and then their outputs are merged, thereby comprehensively considering the front and back information of the time series data to improve the accuracy of the prediction. Figure 4 A schematic diagram of the basic architecture of the bidirectional long short-term memory network BiLSTM is shown.

[0130] The mathematical expression of the forward LSTM layer is:

[0131] f t =σ(W f x t +U f h t-1 +b f ) (9)

[0132] i t =σ(W i xt +U i h t-1 +b i ) (10)

[0133]

[0134] o t =σ(W o x t +U o h t-1 +b o ) (13)

[0135] h t =o t ⊙tanh(C t ) (14) Where, f t 、i t and t Represent the outputs of the forget gate, input gate, and output gate of the forward LSTM layer, respectively. C t and h t They represent the candidate cell state, cell state and hidden state of the forward LSTM layer, respectively, and x t The vector representing the tth time step of the time series data, h t-1 represents the hidden state of the previous time step of the forward LSTM layer, C t-1 represents the cell state of the previous time step of the forward LSTM layer, W f and U f is the weight coefficient in the forget gate of the forward LSTM layer, W i and U i is the weight coefficient in the input gate of the forward LSTM layer, W o and U o is the weight coefficient in the output gate of the forward LSTM layer, W c and U c represents the weight coefficient of the candidate cell state of the forward LSTM layer, b f , b i , b o and b c They represent the forget gate, input gate, output gate and bias coefficient in the candidate cell state of the forward LSTM layer, σ(·) represents the sigmoid activation function, and ⊙ represents the Hadamard product.

[0136] The mathematical expression of the backward LSTM layer is:

[0137] f′ t =σ(W′ f x t +U′ fh′ t+1 +b′ f ) (15)

[0138] i′ t =σ(W′ i x t +U′ i h′ t+1 +b i ) (16)

[0139]

[0140] o′ t =σ(W′ o x t +U′ o h′ t+1 +b′ o ) (19)

[0141] h′ t =o′ t ⊙tanh(C′ t ) (20)

[0142] Among them, f′ t , i′ t and o′ t Represent the outputs of the forget gate, input gate, and output gate of the backward LSTM layer, respectively. C′ t and h′ t They represent the candidate cell state, cell state and hidden state of the backward LSTM layer, respectively, and h′ t+1 represents the hidden state of the next time step of the backward LSTM layer, C′ t+1 represents the cell state of the next time step of the backward LSTM layer, W′ f and U′ f is the weight coefficient in the forget gate of the backward LSTM layer, W′ i and U′ i is the weight coefficient in the input gate of the backward LSTM layer, W′ o and U′ o is the weight coefficient in the output gate of the backward LSTM layer, W′ c and U′ c Represents the weight coefficient of the candidate cell state of the backward LSTM layer, b′ f , b i , b′ o and b′ c They represent the forget gate, input gate, output gate and bias coefficients in the candidate cell state of the backward LSTM layer respectively.

[0143] BiLSTM is used to construct a deterministic prediction model for the dynamic response of marine dynamic cables, and the four new normalized training sets divided in S3.1 are used to train the model. During the training process, BiLSTM includes several hyperparameters, including the number of hidden units, learning rate and batch size, which have an important impact on the prediction performance of the model. Therefore, determining the optimal hyperparameters is the key to improving the prediction performance of the deterministic prediction model. The Bayesian optimization algorithm is used to automatically search for the optimal hyperparameters of BiLSTM, so as to ensure that the deterministic prediction model reaches the best state during the training process, and finally obtain the optimal deterministic prediction model after training. In this case, a total of 4 groups of optimal deterministic prediction models are obtained, and the results of their optimal hyperparameters are shown in Table 2.

[0144] Table 2 Optimal hyperparameters of the deterministic prediction model

[0145]

[0146] S3.3 Deterministic prediction of dynamic response of marine dynamic cables

[0147] Based on the trained optimal deterministic prediction model, the samples in the new normalized test set are predicted to obtain the normalized prediction values ​​of the dynamic response. These normalized prediction values ​​can reflect the prediction results of the model on the dynamic response of the marine dynamic cable, but because the data is trained after normalization, it needs to be denormalized to restore it to the original physical scale. Through denormalization, the normalized prediction value can be converted into a deterministic prediction result of the dynamic response. The denormalized expression is:

[0148]

[0149] in, represents the i-th group of sample values ​​of the normalized prediction value of the dynamic response, Represents the i-th group of values ​​of the dynamic response deterministic prediction results.

[0150] Based on the four new normalized test sets in S3.1 and the four optimal deterministic prediction models in S3.2, deterministic prediction of dynamic response is performed, and denormalization is performed to obtain the deterministic prediction results of dynamic response. Figure 5 and Figure 6 The deterministic prediction sequence diagrams of the effective tension response and curvature response considering different central moment characteristics are shown respectively.

[0151] S4. Based on the deterministic prediction results of the dynamic response of the dynamic cable, the deterministic prediction error of the dynamic response is calculated, and the probabilistic prediction method of the dynamic response is established by using the adaptive bandwidth kernel density estimation ABKDE. The specific steps are as follows:

[0152] S4.1. Calculation of Deterministic Prediction Error Sequences for Dynamic Response

[0153] Based on the deterministic prediction results of the dynamic response in S3.3, the absolute error of the deterministic prediction results of the dynamic response at each time point is calculated and combined into a dynamic response deterministic prediction error sequence, which can be expressed as:

[0154] er=[er1,er2,…,er N ] (twenty two)

[0155] Where er represents the dynamic response deterministic prediction error sequence and N represents the number of samples. Figure 7 and Figure 8 Deterministic prediction error series plots for the effective tension response and curvature response are shown separately.

[0156] S4.2. Based on the deterministic prediction error sequence of dynamic response, the adaptive bandwidth kernel density estimation ABKDE is used to fit the probability density functions of the effective tension response and curvature response respectively. The mathematical expression is:

[0157]

[0158] Among them, h i (er) represents the adaptive bandwidth at the estimated point er, which is related to the i-th sample point er i The selection of this bandwidth depends on the local density information of the sample points, aiming to use a smaller bandwidth in high-density areas and a larger bandwidth in low-density areas, thereby improving the accuracy of the estimation. In order to calculate the adaptive bandwidth at each estimation point, a local error function C needs to be defined i (er k ), and by minimizing the local error function, we can calculate each target estimation point er k Adaptive bandwidth h at i The local error function can consider the dynamic balance between the deviation and variance in the probability density function fitting process. The expression of the local error function is:

[0159]

[0160] Among them, er k represents the target estimated point, h i Indicates that at the target estimated point er k The adaptive bandwidth at the i-th sample point er i Related, f(er k ) represents the true probability density value at the target estimation point, Indicates that at the target estimated point er k Adaptive bandwidth h is usedi The probability density estimate of . and Two of the terms measure the accuracy of the probability density estimate, and the third The smoothness of the probability density estimation is measured. The golden section method is used to minimize equation (3) to obtain the optimized adaptive bandwidth, which is substituted into equation (2) to obtain the probability density function of the dynamic response deterministic prediction error sequence.

[0161] The deterministic prediction error sequence of the effective tension response and curvature response based on S4.1 is used to fit the probability density function of the error sequence based on ABKDE, and the probability density curve is plotted. Fig. 9 and Fig.10 The probability density fitting curves represent the deterministic prediction errors of the effective tension response and curvature response, respectively.

[0162] S4.3. Probabilistic prediction results of dynamic response based on quantile solution method

[0163] Based on the probability density function of the dynamic response deterministic prediction error sequence, the cumulative distribution function of the dynamic response deterministic prediction error sequence is obtained by numerical integration. According to the specified quantile, the corresponding quantile solution can be calculated:

[0164]

[0165] Among them, z represents the specified quantile, q(z) represents the quantile solution corresponding to z, Represents the inverse of the cumulative distribution function of the series of deterministic forecast errors of the dynamic response.

[0166] Using the quantile solution, the dynamic response probabilistic prediction results can be calculated. The upper and lower bounds of the sample prediction interval are used to quantitatively describe the probabilistic prediction results. The calculation expression is:

[0167]

[0168] Among them, Lb i and Ub i They represent the lower and upper bounds of the prediction interval of the i-th sample, respectively. represents the i-th deterministic prediction result of the dynamic response of the dynamic cable, q(1-z) and q(z) represent the quantile solutions corresponding to 1-z and z, respectively.

[0169] In this example, the specified quantiles z are 0.975, 0.95, and 0.925, which correspond to confidence levels of 95%, 90%, and 85%, respectively. Based on the probability density function of the deterministic prediction error of the effective tension response and curvature response fitted in S4.2, the probabilistic prediction results of the effective tension response and curvature response are obtained based on the above quantile solution method. Fig.11 and Fig.12 The probabilistic prediction interval diagrams of effective tension response and curvature response at different confidence levels are shown respectively.

[0170] S5. According to the deterministic prediction results of the dynamic response of the dynamic cable in S3.3 and the probabilistic prediction results in S4.3, the deterministic prediction evaluation index and the probabilistic prediction evaluation index are calculated respectively, and the evaluation index results are saved. The specific steps are as follows:

[0171] S5.1. Determine the prediction evaluation index

[0172] The prediction evaluation index includes: 2 , mean absolute error MAE, mean absolute percentage error MAPE, and root mean square error RMSE. The mathematical expression is:

[0173]

[0174] Where N represents the number of samples, y i represents the ith original value of the dynamic response of the dynamic cable, represents the i-th deterministic prediction result of the dynamic response of the dynamic cable.

[0175] Substituting the deterministic prediction results of the dynamic response of the dynamic cable in S3.3 into the above formula, the results of the deterministic prediction evaluation index are obtained, as shown in Table 3:

[0176] Table 3 Results of determining prediction evaluation indicators

[0177]

[0178] S5.2. Probabilistic prediction evaluation indicators

[0179] The probability prediction evaluation indicators include: prediction interval coverage rate PICP, prediction interval average width PINAW, coverage width standard CWC and continuous sorting probability score CRPS. The mathematical expression is:

[0180] The probability prediction evaluation indicators include: prediction interval coverage rate PICP, prediction interval average width PINAW, coverage width standard CWC and continuous sorting probability score CRPS. The mathematical expression is:

[0181]

[0182] Among them, K i Represents a Boolean variable, Lb i and Ub i They represent the lower and upper bounds of the prediction interval of the i-th sample, respectively. Represents the deterministic prediction result of the dynamic response of the dynamic cable. The larger the PICP, the better the probabilistic prediction performance.

[0183]

[0184] Among them, Z represents the variation range of the original value of the dynamic response of the dynamic cable in the test set. When the PICP results are the same, the smaller the PINAW, the better the probability prediction performance.

[0185]

[0186] β=1-2(1-z) (36)where γ represents the indicator function, z represents the specified quantile, and β represents the confidence level corresponding to z. The smaller the CWC, the better the probability prediction performance.

[0187]

[0188] Where y represents the original value of the dynamic response of the dynamic cable in the test set, y represents the deterministic prediction result of the dynamic response of the dynamic cable in the test set, represents the cumulative distribution function of the deterministic response prediction results, express The Heaviside function.

[0189] Substituting the probabilistic prediction results of the dynamic response of the dynamic cable in S4.3 into the above formula, the probabilistic prediction evaluation index results are obtained, see Table 4:

[0190] Table 4 Probabilistic prediction evaluation index results

[0191]

[0192] The above-described embodiments merely express the implementation methods of the present invention, but they should not be understood as limiting the scope of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A deterministic and probabilistic hybrid prediction method for dynamic response of marine dynamic cables, characterized in that: The deterministic and probabilistic hybrid prediction method comprises the following steps: S1. Construct a fully coupled time-domain hydrodynamic analysis model for marine dynamic cables and generate the original data set of dynamic response of marine dynamic cables; S2. Data processing is performed on the original data set of the dynamic response of the marine dynamic cable in S1, including normalization, central moment feature extraction, and dimensional reconstruction steps; the details are as follows: S3, based on the bidirectional long short-term memory neural network BiLSTM and the Bayesian optimization algorithm, a deterministic prediction model of the dynamic response of the marine dynamic cable is constructed, and based on the reconstructed input and output of the normalized data set of S2, the deterministic prediction of the dynamic response of the marine dynamic cable is realized; S4, based on the deterministic prediction results of the dynamic response of the dynamic cable in S3, calculate the deterministic prediction error of the dynamic response, and use the adaptive bandwidth kernel density estimation ABKDE to establish a probabilistic prediction method for the dynamic response; S5. According to the deterministic prediction results and the probabilistic prediction results of the dynamic response of the dynamic cable, respectively calculate and determine the prediction evaluation index and the probabilistic prediction evaluation index, and save the evaluation index results.

2. The method for hybrid prediction of dynamic response of marine dynamic cable based on determinism and probability according to claim 1 is characterized in that: The S1 is specifically as follows: S1.

1. Construct a fully coupled time-domain hydrodynamic analysis model; Construct a fully coupled time-domain hydrodynamic analysis model of the marine dynamic cable. The fully coupled time-domain hydrodynamic analysis model is composed of the upper floating platform and the dynamic cable system. It can fully simulate the interaction between the dynamic cable and the ocean waves and the upper floating body movement, and accurately describe the influence of various factors on the dynamic response of the marine dynamic cable. S1.2, extract the dynamic response original data set; After the construction of the fully coupled time-domain hydrodynamic analysis model is completed, a 3-hour dynamic response time-domain simulation calculation is performed; the dynamic response original data set of the marine dynamic cable is extracted in batches; the dynamic response original data set includes two parts, input and output, the input includes the time series data of the wave height and the six-degree-of-freedom motion response of the upper floating platform, and the output includes the effective tension at the location where the maximum effective tension occurs and the curvature time series data at the location where the maximum curvature occurs.

3. The deterministic and probabilistic hybrid prediction method for dynamic response of a marine dynamic cable according to claim 2, characterized in that: In S1.2, the formula for the dynamic response to the original data set is as follows: p i ={H i ,X i ,Y i ,Z i ,a i ,b i ,c i } (1) y i ={T i eff ,C i } (2) Among them, p i and i represents the i-th group of samples of the input and output of the original data set of the dynamic response of the marine dynamic cable, respectively. i represents the ith sample of the wave height time series data, X i , Y i and Z i represents the ith sample of the time series data of the surge, sway and heave motion response of the upper floating platform, α i , β i and γ i represents the i-th sample of the roll, pitch and bow motion response of the upper floating platform, T i eff represents the i-th sample of the effective tension time series data at the location where the maximum effective tension of the marine dynamic cable occurs, C i Represents the i-th sample of the curvature time series data at the location where the maximum curvature of the marine dynamic cable occurs.

4. The method for hybrid prediction of dynamic response of marine dynamic cable based on determinism and probability according to claim 1 is characterized in that: The S2 is specifically as follows: S2.1, dynamically responding to normalization processing of the original data set to obtain a normalized data set; Based on the minimum-maximum scale normalization method, the input and output of the original data set of the dynamic cable dynamic response of S1 are normalized respectively, and the expression is: in, and Respectively represent the maximum and minimum values ​​of the i-th group of samples input in the original data set, and Respectively represent the maximum and minimum values ​​of the i-th group of samples output in the original data set, and They represent the i-th group of samples of input and output in the dynamic response normalization dataset respectively; S2.2, extracting the central moment feature of the input of the normalized data set; The central moment feature characterizes the statistical characteristics of the data and can provide supplementary information for the prediction of dynamic response. The expression of the central moment feature of the i-th group of samples of the input of the normalized data set is: Where k represents the order of the central moment, represents the k-th central moment feature of the i-th group of samples input into the normalized data set, express The mean of express The variance of M represents the data length used to extract the central moment feature; S2.3, dimensionality-increasing reconstruction of normalized dataset input; Will Combined with the first k-order central moment features of the i-th group of samples of the input of the normalized data set, the normalized data set input is reconstructed by increasing the dimension; by setting different k values, the reconstructed input of normalized data sets of different orders is flexibly generated; the present invention considers the following three kinds of reconstructed inputs of normalized data sets, and the expressions are: in, They represent the reconstructed input of the normalized data set considering the first 2-order central moments, the first 3-order central moments, and the first 4-order central moments, respectively.

5. The deterministic and probabilistic hybrid prediction method for dynamic response of a marine dynamic cable according to claim 1, characterized in that: The S3 is as follows: S3.

1. Divide the training set and test set of the deterministic prediction model; First, the input of the normalized data set of the dynamic response of the marine dynamic cable in S2 Refactoring Input and output They are combined into 4 new normalized data sets respectively; then, the 4 new normalized data sets are divided into training sets and test sets in chronological order. The training sets are used for training the deterministic prediction model and optimizing hyperparameters, and the test sets are used for evaluating the deterministic prediction performance. S3.

2. Construct a deterministic prediction model for the dynamic response of marine dynamic cables; A bidirectional long short-term memory neural network BiLSTM is used to build a deterministic prediction model for the dynamic response of marine dynamic cables. In BiLSTM, there are two LSTM layers. The forward LSTM layer processes time series data from front to back, and the backward LSTM layer processes time series data from back to front. When processing time series data, each time step of the input is passed to the two LSTM layers respectively, and the output is merged. BiLSTM is used to build a deterministic prediction model for the dynamic response of marine dynamic cables, and the new normalized training set divided in S3.1 is used for model training. During the training process, BiLSTM includes several hyperparameters, and determining the optimal hyperparameters is the key to improving the prediction performance of the deterministic prediction model. The optimal hyperparameters of BiLSTM are automatically searched to obtain the optimal deterministic prediction model after training. S3.3, Deterministic prediction of dynamic response of marine dynamic cables; Based on the trained optimal deterministic prediction model, the samples in the new normalized test set are predicted to obtain the normalized prediction value of the dynamic response; and the physical scale is restored through denormalization processing; Through the denormalization process, the normalized prediction value is converted into a deterministic prediction result of the dynamic response.

6. The method of hybrid deterministic and probabilistic prediction of dynamic response of marine dynamic cable according to claim 5, characterized in that: In S3.2, the hyperparameters include the number of hidden units, the learning rate and the batch size; the Bayesian optimization algorithm is used to automatically search for the optimal hyperparameters of BiLSTM.

7. The method of hybrid deterministic and probabilistic prediction of dynamic response of marine dynamic cable according to claim 5, characterized in that: In the S3: In S3.1, the first 70% is a new normalized training set, and the last 30% is a new normalized test set, which is used to evaluate the deterministic prediction performance; In S3.2, the LSTM unit in the BiLSTM includes a forget gate, an input gate, and an output gate; The expression of the forward LSTM layer is: f t =σ(W f x t +U f h t-1 +b f ) (9) i t =σ(W i x t +U i h t-1 +b i ) (10) the t =σ(W o x t +U o h t-1 +b o ) (13) h t =o t ⊙tanh(C t ) (14) Where, f t 、i t and t Respectively represent the outputs of the forget gate, input gate, and output gate of the forward LSTM layer, C t and h t Represent the candidate cell state, cell state and hidden state of the forward LSTM layer respectively, x t The vector representing the tth time step of the time series data, h t-1 represents the hidden state of the previous time step of the forward LSTM layer, C t-1 represents the cell state of the previous time step of the forward LSTM layer, W f and U f is the weight coefficient in the forget gate of the forward LSTM layer, W i and U i is the weight coefficient in the input gate of the forward LSTM layer, W o and U o is the weight coefficient in the output gate of the forward LSTM layer, W c and U c represents the weight coefficient of the candidate cell state of the forward LSTM layer, b f , b i , b o and b c denote the forget gate, input gate, output gate and bias coefficient in the candidate cell state of the forward LSTM layer, σ(·) denotes the sigmoid activation function, and ⊙ denotes the Hadamard product; The expression of the backward LSTM layer is: f′ t =σ(W′ f x t +U′ f h′ t+1 +b′ f ) (15) i′ t =σ(W′ i x t +U′ i h′ t+1 +b i ) (16) oh t =σ(W′ o x t +U′ o h′ t+1 +b′ o ) (19) h′ t =o′ t ⊙tanh(C′ t ) (20) Among them, f′ t , i′ t and o′ t Represent the outputs of the forget gate, input gate, and output gate of the backward LSTM layer, respectively. C′ t and h′ t They represent the candidate cell state, cell state and hidden state of the backward LSTM layer, respectively, and h′ t+1 represents the hidden state of the next time step of the backward LSTM layer, C′ t+1 represents the cell state of the next time step of the backward LSTM layer, W′ f and U′ f is the weight coefficient in the forget gate of the backward LSTM layer, W i ′ and U′ i is the weight coefficient in the input gate of the backward LSTM layer, W′ o and U′ o is the weight coefficient in the output gate of the backward LSTM layer, W c ′ and U′ c Represents the weight coefficient of the candidate cell state of the backward LSTM layer, b′ f , b i , b′ o and b′ c They represent the bias coefficients in the forget gate, input gate, output gate, and candidate cell state of the backward LSTM layer respectively; In S3.3, the anti-normalized expression is: in, represents the i-th group of sample values ​​of the normalized prediction value of the dynamic response, Represents the i-th group of values ​​of the dynamic response deterministic prediction results.

8. The method for hybrid prediction of dynamic response of marine dynamic cable based on determinism and probability according to claim 1 is characterized in that: The S4 is specifically as follows: S4.1, calculating the deterministic prediction error sequence of the dynamic response; Based on the deterministic prediction results of the dynamic response in S3.3, the absolute error of the deterministic prediction results of the dynamic response at each time point is calculated and combined into a dynamic response deterministic prediction error sequence, which is expressed as: is=[is1,is2,…,is N ] (22) Among them, er represents the dynamic response deterministic prediction error sequence, and N represents the number of samples; S4.2, fitting the probability density function of the dynamic response deterministic prediction error sequence; Based on the dynamic response deterministic prediction error sequence er of S4.1, the probability density function of er is fitted by adaptive bandwidth kernel density estimation ABKDE, and its expression is: Among them, h i (er) represents the adaptive bandwidth at the estimated point er, which is related to the i-th sample point er i Related, K(·) represents the kernel function; In order to calculate the adaptive bandwidth at each estimation point, a local error function C is defined i (er k ), and by minimizing the local error function, we can calculate each target estimation point er k Adaptive bandwidth h at i ; The local error function considers the dynamic balance between deviation and variance in the probability density function fitting process; The expression of the local error function is: Among them, er k represents the target estimated point, h i Indicates that at the target estimated point er k The adaptive bandwidth at the i-th sample point er i Related, f(er k ) represents the true probability density value at the target estimation point, Indicates that at the target estimated point er k Adaptive bandwidth h is used i The probability density estimate of ; and Two of the terms measure the accuracy of the probability density estimate, and the third The smoothness of the probability density estimation is measured; the golden section method is used to minimize the formula (24) to obtain the optimized adaptive bandwidth, which is substituted into formula (23) to obtain the probability density function of the dynamic response deterministic prediction error sequence; S4.3, calculate the probabilistic prediction results of dynamic response based on the quantile solution method; Based on the probability density function of the dynamic response deterministic prediction error sequence of S4.2, the cumulative distribution function of the dynamic response deterministic prediction error sequence is obtained by numerical integration According to the specified quantile, calculate the corresponding quantile solution: Among them, z represents the specified quantile, q(z) represents the quantile solution corresponding to z, The inverse function of the cumulative distribution function representing the dynamic response deterministic forecast error series; The dynamic response probabilistic prediction results are obtained by using the quantile solution. The upper and lower bounds of the sample prediction interval are used to quantitatively describe the probabilistic prediction results. The calculation expression is: Among them, Lb i and Ub i They represent the lower and upper bounds of the prediction interval of the i-th sample, respectively. represents the i-th deterministic prediction result of the dynamic response of the dynamic cable, q(1-z) and q(z) represent the quantile solutions corresponding to 1-z and z, respectively.

9. The method of hybrid deterministic and probabilistic prediction of dynamic response of marine dynamic cable according to claim 1, characterized in that: The S5 is specifically as follows: S5.

1. Determine the prediction evaluation indicators; The prediction evaluation index includes: 2 , mean absolute error MAE, mean absolute percentage error MAPE, and root mean square error RMSE; S5.2, Probabilistic prediction evaluation indicators; The probability prediction evaluation indicators include: prediction interval coverage rate PICP, prediction interval average width PINAW, coverage width standard CWC and continuous sorting probability score CRPS.

10. The method of hybrid deterministic and probabilistic prediction of dynamic response of marine dynamic cable according to claim 8, characterized in that: The expression of S5.1 is: Where N represents the number of samples, y i represents the ith original value of the dynamic response of the dynamic cable, represents the i-th deterministic prediction result of the dynamic response of the dynamic cable; The expression of S5.2 is: Among them, K i Represents a Boolean variable, Lb i and Ub i They represent the lower and upper bounds of the prediction interval of the i-th sample, respectively. Indicates the deterministic prediction result of the dynamic response of the dynamic cable; the larger the PICP, the better the probabilistic prediction performance; Where Z represents the variation range of the original value of the dynamic response of the dynamic cable in the test set; when the PICP results are the same, the smaller the PINAW, the better the probability prediction performance; β=1-2(1-z) (36)where γ represents the indicator function, z represents the specified quantile, and β represents the confidence level corresponding to z; the smaller the CWC, the better the probability prediction performance; Where y represents the original value of the dynamic response of the dynamic cable in the test set, represents the deterministic prediction result of the dynamic response of the dynamic cable in the test set, represents the cumulative distribution function of the deterministic response prediction results, express The Heaviside function.

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