CN113392583A - Sea surface height simulation method based on quantum migration - Google Patents
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Abstract
The invention discloses a sea surface height simulation method based on quantum migration, which comprises the following steps: (1) generating multi-fluctuation components of sea surface height based on quantum migration; (2) screening sea surface height components; (3) simulating the sea surface height based on the component superposition principle; (4) and (5) experimental verification. The sea surface height change is further analyzed from the angle of multi-scale decomposition, the relation between the sea surface height change and the sea surface fluctuation mode is explored, modeling simulation of the sea surface height change is realized based on the view angle of multi-component superposition coupling, and the method is a great breakthrough in the modeling and simulation direction of the sea surface height.
Description
Technical Field
The invention relates to the technical field of natural geography and marine physics, in particular to a sea surface height simulation method based on quantum migration.
Background
The current sea surface altitude change modeling model can be roughly classified into two types: namely, a traditional model and a machine learning model. In general, the conventional prediction method is based on a parametric model, that is, parameters of the model are solved on the basis of determining a time series prediction model to complete prediction. Such as an autoregressive moving average model (ARIMA), the parameters are simple and the calculation is efficient, but the method can only well predict a stationary sequence with linear characteristics, cannot excavate nonlinear characteristics, generally needs to meet stationarity assumption and is not suitable for sea surface height simulation and prediction. The machine learning model is a strong nonlinear function fitter, namely, data are 'learned' by adopting some algorithms, and hidden information in the data is further mined. Such as Artificial Neural Networks (ANN), Support Vector Machines (SVM), etc. The ANN has strong self-learning capability, can solve some nonlinear mapping problems according to set input and output, is a black box model, is sensitive to training data, and does not consider the physical significance behind sea surface height change; the SVM is a machine learning method based on a statistical learning theory, has specific advantages in the aspects of solving small samples, nonlinear problems and the like, is sensitive to parameters and kernel functions, and is not good enough in performance in massive data samples.
The change of the global sea surface height is closely related to the production life of human beings, and the prevention of natural disasters caused by the change of the sea surface height is an important task of economic and ecological civilized construction. In recent years, there is increasing evidence that classical random walks can predict the non-linear and dynamic characteristics of sea-level altitude changes and give scientific insights. In fact, sea surface altitude changes are not independent, but are the result of multi-factor and multi-process superposition coupling, and in most cases, the independence and randomness assumptions of classical random walk cannot be met, so that the sea surface altitude changes cannot play a role in sea surface altitude change prediction.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a sea surface height simulation method based on quantum migration, further analyze sea surface height change from the angle of multi-scale decomposition, explore the relation between the sea surface height change and the sea surface fluctuation mode, realize the sea surface height change modeling simulation based on the view angle of multi-component superposition coupling, and is a great breakthrough in the sea surface height modeling and simulation direction.
In order to solve the technical problem, the invention provides a sea surface height simulation method based on quantum migration, which comprises the following steps:
(1) generating multi-fluctuation components of sea surface height based on quantum migration;
(2) screening sea surface height components;
(3) simulating the sea surface height based on the component superposition principle;
(4) and (5) experimental verification.
Preferably, in the step (1), the multi-fluctuation component of sea level generated based on quantum migration specifically comprises: when observation is not carried out, the sea surface height of any station appears at any elevation with a certain probability at any time, but at the same time, the sea surface height can only be recorded as | delta at any elevation point>＝{|δ1>,|δ2>,…,|δn>}, wherein:
thus, the quantum-walker state | ε (k) > is defined as the linear superposition of all the ground states:
wherein | αi(k)|∈[0,1]Indicating that the sea surface altitude is at state | δ at a given timen>Based on the unitary transformation, the state vector | epsilon (k)>The evolution over time is represented as follows:
as shown in equation (3), the quantum walking resolution k is continuously adjusted based on a certain rule, that is, all possible fluctuation components of each station are constructed according to the quantum walking.
Preferably, in the step (2), the sea level height component screening specifically comprises: time series of changes in actual sea level altitude
For all possible multi-fluctuation components (| ε (k) |) generated in step (1)1)>,|ε(k2)>,…,|ε(kn)>) Stepwise regression subset screening was performed and is expressed as:
based on the akage pool information content criterion AIC, all possible sea surface height change modes (| epsilon (k) are screened by using the stepwise regression subset screening method in the formula (4)1)>,|ε(k2)>,…,|ε(kn)>) Screening is carried out to obtain a modal screening result which is marked as { | ∈ (k)m)>}。
Preferably, in the step (3), simulating the sea level height based on the component superposition principle specifically comprises: screening the obtained mode { | ∈ (k) based on the step (2)m)>Establishing an aliasing coupling relation between the real sea surface height change time sequence and the sea surface height change component, and expressing the aliasing coupling relation as follows:
wherein M is the component number obtained by screening in the step (2),
for time series of changes in actual sea level altitude, αmIs of the same composition { | ∈ (k)m)>Sea level height variation scale factor of kmThe parameters of the components obtained by screening are important characterization parameters of sea surface height change characteristics, and b is a mapping constant item.
Preferably, in the step (4), the experimental configuration for experimental verification specifically includes: selecting a group of sites with approximately the same latitude and increasing distribution according to longitude, wherein six sites are respectively named as N1,N2,…,N6(ii) a In the multi-modal extraction, 2000 times of quantum migration are carried out in different tide watching stations in a research area, k is increased from 0.01 to 20, and the interval is 0.01; at the same time, isEvaluating the modeling effect, and selecting the average absolute error MAE, the root mean square error RMSE and the decision coefficient R2The fitting effect of the model is measured, and the specific definition is shown in table 1; wherein, deltaiIs the actual sea surface height;
the average value of the sea surface height;
obtaining the fitted sea surface height; n is the number of fitting samples;
TABLE 1 model modeling Effect evaluation index definition
The invention has the beneficial effects that: the invention introduces a key method of quantum migration, further analyzes sea surface height change from the angle of multi-scale decomposition, explores the relation between the sea surface height change and the sea surface fluctuation mode, realizes the modeling simulation of the sea surface height change based on the view angle of multi-component superposition coupling, and is a great breakthrough in the modeling and simulation direction of the sea surface height.
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FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of experimental area and site selection according to the present invention.
Fig. 3 is a schematic diagram of a sea surface height simulation result based on quantum migration in the invention.
FIG. 4 is a schematic diagram of the accuracy assessment of the modeling results of the present invention.
Detailed Description
As shown in fig. 1, a sea surface height simulation method based on quantum migration includes the following steps:
(1) generating multi-fluctuation components of sea surface height based on quantum migration;
(2) screening sea surface height components;
(3) simulating the sea surface height based on the component superposition principle;
(4) and (5) experimental verification.
In global ocean currents, identical/similar environmental factors are abstracted into quantized driver particles, and sea height changes under the action of such environmental factors can be described as the evolution process of the heights of the driver particles along with time, and are single components of the sea height changes. When observation is not applied, the particles can appear at a plurality of possible vertical positions with a certain probability, and a dynamic evolution process of the particles appearing at each elevation probability with time under the fluctuation component is formed.
However, in a practical situation, the sea surface height variation characteristics and structures of different tide stations are different, and it is not practical to use a uniform component to represent the sea surface height variation. Therefore, quantum migration is considered to be carried out under different step lengths, and a plurality of sea surface height change components with different shapes and structures are generated, so that the superposition coupling relation between the complex structure with the sea surface height and the various components is disclosed, and a foundation is provided for building a high-precision and strong-robustness prediction model.
The sea height dynamic evolution process under a single sea height component can be described as the fluctuation process of the same/similar environmental factors (driving particles) among sites, and can be described by quantum migration. In the process of generating the sea surface height multi-fluctuation component, the key is that under given parameters, the driving particles start from fixed sites, quantum migration is carried out on a basic framework formed by an adjacent matrix (topological structure) of a research area tide checking site, and dynamic evolution of the sea surface height distribution probability of a single fluctuation component along with time is formed.
The multi-fluctuation component for generating sea surface height based on quantum migration specifically comprises: when observation is not carried out, the sea surface height of any station appears at any elevation with a certain probability at any time, but at the same time, the sea surface height can only be recorded as | delta at any elevation point>＝{|δ1>,|δ2>,…,|δn>}, wherein:
thus, the quantum-walker state | ε (k) > is defined as the linear superposition of all the ground states:
wherein | αi(k)|∈[0,1]Indicating that the sea surface altitude is at state | δ at a given time>Based on the unitary transformation, the state vector | epsilon (k)>The evolution over time is represented as follows:
as shown in equation (3), the quantum walking resolution k is continuously adjusted based on a certain rule, that is, all possible fluctuation components of each station are constructed according to the quantum walking.
Although sea level height variations are influenced by multiple factors, are complex in structure and different in modality, objective constraints such as human intervention and influence factors are different, so that part of ideal components cannot exist in the sea level height variations. All possible sea surface height change components generated in the step (1) are only a universal component set, are 'bases' of sea surface height modeling simulation, and can only describe ideal sea surface height change conditions. Therefore, under the constraint of actual sea surface height change, the sea surface height change components of different tide stations are obtained through analysis based on a specific sea surface height fluctuation component screening criterion, and the superposition coupling relation between the sea surface height change and the multiple components is conveniently explored subsequently.
The invention takes a stepwise regression subset screening method as a sea surface altitude change mode screening method, and a time sequence of actual sea surface altitude change
For all possible multi-fluctuation components (| ε (k) |) generated in step (1)1)>,|ε(k2)>,…,|ε(kn)>) Stepwise regression subset screening was performed and is expressed as:
based on the akage pool information content criterion AIC, all possible sea surface height change modes (| epsilon (k) are screened by using the stepwise regression subset screening method in the formula (4)1)>,|ε(k2)>,…,|ε(kn)>) Screening is carried out to obtain a modal screening result which is marked as { | ∈ (k)m)>}。
And (3) constructing a one-to-many aliasing coupling mapping relation between the sea surface height components and the sea surface heights based on the plurality of sea surface height components of the tide gauging stations obtained by screening in the step (2) and based on the idea of superposition combination, and finally achieving the purpose of simulating sea surface height change based on multiple components.
Screening the obtained mode { | ∈ (k) based on the step (2)m)>Establishing an aliasing coupling relation between the real sea surface height change time sequence and the sea surface height change component, and expressing the aliasing coupling relation as follows:
wherein M is the component number obtained by screening in the step (2),
for time series of changes in actual sea level altitude, αmIs of the same composition { | ∈ (k)m)>Sea surface height variation of }, kmThe parameters of the components obtained by screening are important characterization parameters of sea surface height change characteristics, and b is a mapping constant item.
The experimental configuration of the experimental verification of the invention is specifically as follows: selecting a group of sites with approximately the same latitude and increasing distribution according to longitude, wherein six sites are respectively named as N1,N2,…,N6(ii) a In the multi-modal extraction, 2000 times of quantum migration are carried out in different tide watching stations in a research area, k is increased from 0.01 to 20, and the interval is 0.01; meanwhile, in order to evaluate the modeling effect, the average absolute error MAE and average are selectedRoot error RMSE and coefficient of determination R2The fitting effect of the model is measured, and the specific definition is shown in table 1; wherein, deltaiIs the actual sea surface height;
the average value of the sea surface height;
obtaining the fitted sea surface height; and n is the number of fitting samples.
TABLE 1 model modeling Effect evaluation index definition
As shown in FIG. 2, the sea surface of the equatorial-pacific region is taken as a research region, the sea surface height change sequence of a month time window is selected as experimental data, the simulation experiment of the sea surface height is completed, and the simulation result is shown in FIG. 3. The modal number of each station is shown (table 2), and the sea surface fluctuation modal number is between 16(N6) and 85(N2), which shows that the sea surface height change situation of the equatorial region and the pacific region is complex, and complex multi-scale oscillation exists. Statistics as shown in FIG. 4 show the average simulation accuracy (R) for six sites2) The range of the MAE is from 11.14(N2) to 26.52(N6), the range of the RMSE is from 14(N2) to 32.32(N6), and the method has the advantages of high modeling precision and capability of reconstructing and inverting random oscillation of sea surface height change of different frequency components. Of the six stations, the N2 station has the highest simulation precision of 0.97, and in addition, the N6 station has the strongest sea surface height change, the MAE is 26.52, the RMSE is 32.32, and the R is2The simulation error of the quantum migration-based sea surface height simulation method for different sites is generally low, and even if the simulation error for sites with high errors is high, the method provided by the invention is proved to be effective.
TABLE 2 sea surface height variation mode number and evaluation index of each site
The invention considers that sea surface height fluctuation is a complex geographical space-time process formed by overlapping a plurality of fluctuation components with different structures. Selecting any tide observation station in the global scope, generating all possible sea surface height change components of the sea surface height of the tide observation station in continuous time by quantum migration, screening fluctuation component subsets by using a specific rule under the constraint of the fluctuation time sequence of the actual sea surface height, exploring the mapping transformation relation between the multi-fluctuation components and the sea surface height, and realizing the modeling simulation of the sea surface height.
Claims (5)
1. A quantum migration-based sea surface height simulation method is characterized by comprising the following steps:
(1) generating multi-fluctuation components of sea surface height based on quantum migration;
(2) screening sea surface height components;
(3) simulating the sea surface height based on the component superposition principle;
(4) and (5) experimental verification.
2. The quantum walking-based sea surface height simulation method according to claim 1, wherein in the step (1), the quantum walking-based sea surface height multi-fluctuation component generation specifically comprises: when observation is not carried out, the sea surface height of any station appears at any elevation with a certain probability at any time, but at the same time, the sea surface height can only be recorded as | delta at any elevation point>＝{|δ1>,|δ2>,...,|δn>}, wherein:
thus, the quantum-walker state | ε (k) > is defined as the linear superposition of all the ground states:
wherein | αi(k)|∈[0,1]Indicating that the sea surface altitude is at state | δ at a given timen>Based on the unitary transformation, the state vector | epsilon (k)>The evolution over time is represented as follows:
as shown in equation (3), the quantum walking resolution k is continuously adjusted based on a certain rule, that is, all possible fluctuation components of each station are constructed according to the quantum walking.
3. The quantum walking-based sea surface height simulation method of claim 1, wherein in the step (2), the sea surface height component screening specifically comprises: time series of changes in actual sea level altitude
For all possible multi-fluctuation components (| ε (k) |) generated in step (1)1)>,|ε(k2)>,...,|ε(kn)>) Stepwise regression subset screening was performed and is expressed as:
based on the akage pool information content criterion AIC, all possible sea surface height change modes (| epsilon (k) are screened by using the stepwise regression subset screening method in the formula (4)1)>,|ε(k2)>,...,|ε(kn)>) Screening is carried out to obtain a modal screening result which is marked as { | ∈ (k)m)>}。
4. The quantum walking-based sea surface height simulation method of claim 1, wherein in the step (3), the simulation method is based onThe simulation sea surface height based on the component superposition principle specifically comprises the following steps: screening the obtained mode { | ∈ (k) based on the step (2)m)>Establishing an aliasing coupling relation between the real sea surface height change time sequence and the sea surface height change component, and expressing the aliasing coupling relation as follows:
wherein M is the component number obtained by screening in the step (2),
for time series of changes in actual sea level altitude, αmIs of the same composition { | ∈ (k)m)>Sea level height variation scale factor of kmThe parameters of the components obtained by screening are important characterization parameters of sea surface height change characteristics, and b is a mapping constant item.
5. The quantum walking-based sea surface height simulation method of claim 1, wherein in the step (4), the experimental configuration of the experimental verification is specifically as follows: selecting a group of sites with approximately the same latitude and increasing distribution according to longitude, wherein six sites are respectively named as N1,N2,...,N6(ii) a In the multi-modal extraction, 2000 times of quantum migration are carried out in different tide watching stations in a research area, k is increased from 0.01 to 20, and the interval is 0.01; selecting average absolute error MAE, root mean square error RMSE and decision coefficient R2The fitting effect of the model is measured, and the specific definition is shown in table 1; wherein, deltaiIs the actual sea surface height;
the average value of the sea surface height;
obtaining the fitted sea surface height; n is the number of fitting samples;
TABLE 1 model modeling Effect evaluation index definition
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Citations (5)
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| CN105825069A (en) * | 2016-03-31 | 2016-08-03 | 南京信息工程大学 | Wave-current coupling sea surface evolution and simulation method based on fractional technology |
| CN111126611A (en) * | 2019-12-09 | 2020-05-08 | 南京师范大学 | High-speed traffic distribution simulation quantum computing method considering destination selection |
| CN112614336A (en) * | 2020-11-19 | 2021-04-06 | 南京师范大学 | Traffic flow modal fitting method based on quantum random walk |
| CN112632452A (en) * | 2020-11-17 | 2021-04-09 | 南京师范大学 | Method for simulating quantum harmonic oscillator of individual granularity long-range high-speed traffic flow random oscillation |
| CN113393488A (en) * | 2021-06-08 | 2021-09-14 | 南京师范大学 | Behavior track sequence multi-feature simulation method based on quantum migration |
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| US11694103B2 (en) * | 2018-09-19 | 2023-07-04 | Microsoft Technology Licensing, Llc | Quantum-walk-based algorithm for classical optimization problems |
| CN110458338B (en) * | 2019-07-23 | 2023-01-03 | 天津大学 | Sea surface height medium-long term statistical prediction method based on reanalysis data |
| CN112445856B (en) * | 2020-12-01 | 2023-04-21 | 海南长光卫星信息技术有限公司 | Sea surface height influence correlation analysis method and device |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105825069A (en) * | 2016-03-31 | 2016-08-03 | 南京信息工程大学 | Wave-current coupling sea surface evolution and simulation method based on fractional technology |
| CN111126611A (en) * | 2019-12-09 | 2020-05-08 | 南京师范大学 | High-speed traffic distribution simulation quantum computing method considering destination selection |
| CN112632452A (en) * | 2020-11-17 | 2021-04-09 | 南京师范大学 | Method for simulating quantum harmonic oscillator of individual granularity long-range high-speed traffic flow random oscillation |
| CN112614336A (en) * | 2020-11-19 | 2021-04-06 | 南京师范大学 | Traffic flow modal fitting method based on quantum random walk |
| CN113393488A (en) * | 2021-06-08 | 2021-09-14 | 南京师范大学 | Behavior track sequence multi-feature simulation method based on quantum migration |
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