Multi-factor thaw collapse coefficient prediction method based on FFT (Fast Fourier Transform), medium and equipment

Abstract

The invention discloses a multi-factor thaw collapse coefficient prediction method based on FFT, a medium and equipment, and relates to the technical field of soil property test.The method comprises the steps that a soil sample of a research area is obtained, the sample is manufactured, and basic parameters of the sample are measured; performing a freeze-thaw test on the soil sample, and measuring a thaw collapse coefficient to obtain a change curve of an actual thaw collapse coefficient; constructing a prediction function of the thaw collapse coefficient containing unknown quantity parameters, wherein the prediction function comprises a trend term generated by dominant internal factors and a fluctuation term generated by dominant external factors; and adopting a least square method, fitting a prediction function of the thaw collapse coefficient according to the change curve of the actual thaw collapse coefficient, obtaining unknown quantity parameters of a thaw collapse coefficient function, obtaining a final prediction function of the thaw collapse coefficient, and predicting the thaw collapse coefficient. According to the method, the thaw collapse coefficient can be simply and effectively predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of soil property testing, and particularly to a multi-factor thaw settlement coefficient prediction method, medium, and device based on FFT. Background Art

[0002] In alpine regions, with the change of temperature, frozen soil will inevitably produce frost heave and thaw settlement, causing a series of engineering problems. According to engineering experience, thaw settlement failure is one of the main reasons for frost damage in engineering construction in permafrost regions. Therefore, researchers have carried out a lot of work in this regard. Currently, the main calculation of the actual thaw settlement mainly considers the superposition of two settlements, namely thermal thaw settlement and compression settlement.

[0003] Let the thickness of the frozen soil layer be h i , the thaw settlement coefficient (thaw settlement coefficient) be A0, the pressure consolidation coefficient be m v , the stress of this layer of soil be σ i , n represents the number of frozen soil layers, and the settlement amount S within the total thaw depth is:

[0004]

[0005] The thaw settlement coefficient is an important parameter index for evaluating the settlement amount after the thawing of frozen soil, and has very important engineering significance for engineering construction in permafrost regions. Since the test of the thaw settlement coefficient is complex and time-consuming, it is necessary to establish a functional relationship between the thaw settlement coefficient of frozen soil and multi-factor indexes, which can simply and reasonably predict the thaw settlement coefficient for engineering construction and provide a reference value for the design data required for the project. In the research, the ratio of the thaw settlement amount Δh to the sample height h is mainly used to represent the thaw settlement coefficient A0:

[0006]

[0007] Through literature investigation, it is known that the thaw settlement properties of frozen soil are affected by many factors, which are mainly divided into internal factors and external factors. The internal factors refer to the basic physical and mechanical property parameters related to the soil mass, including soil quality, water content and dry unit weight. Among them, due to different soil qualities, the soil particle composition, structure and texture are also different. Under the condition of the same water content, the thaw settlement coefficient will also be different. For example, the thaw settlement coefficient of sandy soil is less than that of clay soil; for the dry unit weight, under the unsaturated condition, as the dry unit weight increases, the thaw settlement coefficient will also increase accordingly, and vice versa; as one of the important indicators affecting the thaw settlement coefficient, the greater the water content or the greater the ice content in the soil sample during the frost heaving process, the greater the settlement of the soil mass will be caused by the exclusion of pore water brought by the melting in the soil mass with the periodic change of temperature. In addition, temperature is one of the important external factors affecting the thaw settlement properties of frozen soil. The temperature in alpine regions changes periodically over the years. Repeated frost heaving and thaw settlement will cause changes in the particle connection mode and structure of the soil mass. Therefore, the pores of the soil mass change, and finally the physical and mechanical property parameters of the soil mass will be reduced.

[0008] In summary, many researchers have studied the thaw settlement properties of frozen soil to further clarify the importance of the thaw settlement coefficient, and have conducted research in various directions such as the experimental method, influencing factors, empirical formula, theoretical formula, and prediction and forecasting of the thaw settlement coefficient. Among them, many scholars have designed relevant experiments to obtain the thaw settlement coefficient, and summarized the main influencing factors as water content, dry density and pressure load. Therefore, the grey relational analysis method is used to further study the correlation of the influencing factors of the thaw settlement coefficient, and to understand the change of the thaw settlement coefficient of frozen soil under single factor and multiple factors. Finally, based on the above research, the basic properties of the thaw settlement coefficient are preliminarily understood, and the researchers hope to further predict and forecast the complex and changeable thaw settlement coefficient, and propose empirical formulas and theoretical formulas for estimating the thaw settlement coefficient under saturated and unsaturated conditions to achieve a simple and universal prediction effect.

[0009] However, most of the above prediction methods only consider the internal factors of the thaw settlement coefficient for experimental research and prediction and forecasting research. In fact, the freeze-thaw action of frozen soil causes complex changes in the pores in the soil mass, resulting in changes in the mechanical properties and physical and mechanical processes of frozen soil that are different from the common mechanical laws. Summary of the Invention

[0010] The purpose of the present invention is to: in order to solve the problem that the existing prediction methods of the thaw settlement coefficient only consider the internal factors of the thaw settlement coefficient, a multi-factor thaw settlement coefficient prediction method based on FFT is proposed, including the following steps:

[0011] S1. Obtain soil samples in the research area, make samples, and measure the basic parameters of the samples;

[0012] S2. Conduct freeze-thaw tests on the soil samples according to the measured basic parameters of the samples, measure the thaw settlement coefficient, and obtain the change curve of the actual thaw settlement coefficient;

[0013] S3. Construct a prediction function for the thaw settlement coefficient with unknown parameters, including a trend term dominated by internal factors and a fluctuation term dominated by external factors;

[0014] S4. Use the least squares method to fit the prediction function of the thaw settlement coefficient according to the change curve of the actual thaw settlement coefficient, obtain the unknown parameters of the thaw settlement coefficient function, and obtain the final prediction function of the thaw settlement coefficient to predict the thaw settlement coefficient.

[0015] Furthermore, the basic sample parameters include: dry density, initial water content, liquid limit water content, and void ratio.

[0016] Furthermore, the function of the trend term is:

[0017]

[0018] Where:

[0019]

[0020] Among them, A0 represents the trend term, C r represents the contact rate, γ d represents the dry unit weight, ω represents the water content, ω0 represents the initial water content, ω L represents the liquid limit water content, ρ w represents the water density, γ s represents the unit weight of soil.

[0021] Furthermore, the external factor that generates the fluctuation term is temperature.

[0022] Furthermore, the function of the fluctuation term is:

[0023]

[0024] Among them, δ, α i , β i both represent the unknown parameters of the fluctuation term, n represents the number of temperature signal sequences, f i represents the main amplitude frequency of the i-th signal, and t represents time;

[0025] Use the least squares method to fit the function f T0 (t) of the fluctuation term with the actual temperature data curve to obtain the specific values of the unknown parameters δ, α i , β i and obtain the temperature Fourier function f T (t).

[0026] Furthermore, the final prediction function of the thaw settlement coefficient is expressed as:

[0027] A = A0 + A1

[0028] Among them, A0 represents the trend term, and A1 represents the fluctuation term.

[0029] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the above-mentioned multi-factor thaw settlement coefficient prediction method based on FFT is implemented.

[0030] The present invention also provides an electronic device, including a processor and a memory, the processor is interconnected with the memory, wherein the memory is used to store a computer program, the computer program includes computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the above-mentioned multi-factor thaw settlement coefficient prediction method based on FFT.

[0031] The beneficial effects brought by the technical solution provided by the present invention are:

[0032] The present invention combines the trend term dominated by internal factors and the fluctuation term dominated by external factors, uses actual real data to predict the thaw settlement coefficient under multi-factor conditions, takes temperature data as the dominant factor of external factors, processes the real temperature data using the fast Fourier transform (FFT), adopts the theoretical formula and Fourier function, combines the periodic change characteristics of soil moisture content, dry unit weight and temperature, constructs a new thaw settlement coefficient prediction function, uses the least squares method to fit the Fourier function and the change curve of the actual thaw settlement coefficient, further obtains the specific values of unknown parameters, and finally obtains a prediction function with relatively high accuracy. The present invention considers the thaw settlement coefficient prediction method under multi-factor linkage, takes the internal factors and external factors affecting thaw settlement into the same function, and simply and effectively predicts the thaw settlement coefficient. Description of the Drawings

[0033] Figure 1 is the flowchart of the multi-factor thaw settlement coefficient prediction method based on FFT in the embodiment of the present invention;

[0034] Figure 2 is the actual temperature data curve in the embodiment of the present invention;

[0035] Figure 3 is the amplitude-frequency curve generated after the temperature data in the embodiment of the present invention is subjected to the fast Fourier transform;

[0036] Figure 4 is the comparison between the actual temperature data in the study area and the Fourier series fitting formula in the embodiment of the present invention;

[0037] Figure 5 is the block diagram of an electronic device in an exemplary embodiment of the first embodiment of the present invention. Detailed Embodiments

[0038] To make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0039] The flowchart of the multi-factor thaw settlement coefficient prediction method based on FFT in the embodiments of the present invention is as Figure 1 , and specifically includes the following steps:

[0040] S1. Select soil samples in the research area to be studied. Special soils such as loess, expansive soil, frozen soil, etc. can be selected to conduct comparative studies on the thaw settlement properties of different soils. After sampling, make experimental samples of the soil body and measure the basic parameters of the samples.

[0041] The basic parameters of the samples include: dry density ρ d , initial water content ω0, liquid limit water content ω L , and void ratio e.

[0042] S2. Conduct freeze-thaw tests on the soil samples according to the measured basic parameters of the samples, measure the thaw settlement coefficient, and obtain the change curve of the actual thaw settlement coefficient.

[0043] Assume that the dry density ρ d is fixed, change the water content ω of the soil sample and the temperature T of the test environment, conduct freeze-thaw tests on the soil sample, measure and record the thaw settlement coefficient, and the change curve of the actual thaw settlement coefficient can be obtained.

[0044] S3. Construct a prediction function of the thaw settlement coefficient containing unknown parameters, including a trend term dominated by internal factors and a fluctuation term dominated by external factors.

[0045] The trend term dominated by internal factors adopts the known unsaturated thaw settlement coefficient prediction formula:

[0046]

[0047] Among them, A0 represents the trend term; C r represents the contact rate, which can reflect the proportion of water participating in the frost heaving effect in the unsaturated soil body. The contact rate is 1 in the saturated state (when the water content is the liquid limit value), and the contact rate is 0 at the initial water content; γ d represents the dry unit weight, ω represents the water content, and ρ w represents the water density.

[0048] Calculate the contact rate at different water content states by linear interpolation method:

[0049]

[0050] Among them, ω0 represents the initial water content, and ω L represents the liquid limit water content.

[0051] Since it is in an unsaturated state, the liquid limit can be calculated by the following formula:

[0052]

[0053] where γ s represents the unit weight of soil. The unit weight of soil refers to the mass of soil per unit volume, usually measured in kilograms per cubic meter. The unit weight of soil is affected by various factors, including soil type, water content, stone content, and soil compaction degree, etc. Different types of soil have different ranges of unit weight.

[0054] The external factor that generates the fluctuation term is temperature. Since the essence of freeze-thaw action is the change of temperature, as one of the most important external factors, temperature will inevitably lead to the change of the thaw settlement coefficient. The actual change of temperature data is a periodic cycle on an annual basis. Therefore, the fast Fourier function is selected to process the actual temperature data.

[0055] The Fourier transform is one of the most basic methods in time-domain to frequency-domain transformation analysis, which can convert the target function into trigonometric functions. Therefore, the Fourier transform (FFT) is to convert a segment of signal or known data into the superposition of different sine functions and cosine functions. Among them, the fast Fourier transform can quickly separate and transform the known data to obtain the frequency coefficients required in the fitting function.

[0056] The fast Fourier transform (FFT) is an efficient implementation of the discrete Fourier transform (DFT). The basic principle is to utilize the periodicity, symmetry, and reducibility of the rotation factors of the long-sequence discrete Fourier transform (DFT), and decompose it into several combinations of short-sequence discrete Fourier transforms to reduce the number of operations. Through decomposition and combination, the computational complexity of the DFT is reduced from O(N 2 ) to O(NlogN).

[0057] The principle is as follows. The calculation formula of the discrete Fourier transform (DFT) is:

[0058]

[0059] where X(k) represents the discrete Fourier transform of x(n), n = 0, 1,..., N - 1, x(n) represents the nth discrete signal in the discrete signal sequence, k represents the frequency, and N is the number of discrete signals.

[0060] For each frequency k, it is necessary to perform multiplication operations between each sample x(n) of the signal and the complex exponential and sum them up. This calculation process requires O(N 2 ) multiplication and addition operations for N samples.

[0061] The FFT decomposes the DET problem through the Cooley-Tukey algorithm, and its basic steps include:

[0062] (1) Decomposition: Divide the original signal x(n) into two subsequences:

[0063] ① A subsequence containing even indices: x0(n) = x(0), x(2), x(4),...;

[0064] ② A subsequence containing odd indices: x1(n) = x(1), x(3), x(5),...

[0065] (2) Recursion: Perform Fourier transforms on these two subsequences separately to obtain their frequency-domain representations:

[0066] ① X0(k) is the DFT of the even-index sequence;

[0067] ② X1(k) is the DFT of the odd-index sequence.

[0068] (3) Merging: Utilize the symmetry of complex exponents to merge the results of these two subsequences to obtain the complete frequency-domain representation.

[0069] In summary, assume that the signal x(n) is decomposed into an even-index part x0(n) and an odd-index part x1(n), and their DFTs are X0(k) and X1(k) respectively. According to the periodicity of the complex exponential function, the original DFT can be expressed as the formula:

[0070]

[0071] where, is called the "rotation factor" or "butterfly factor", which is the weighting factor used when merging the frequency-domain information of the odd part and the frequency-domain information of the even part.

[0072] Based on the principle of FFT, the higher the amplitude of a certain frequency in the spectrum after FFT transformation, the more it can represent the main fluctuation period. Assume that the highest frequency obtained through the fast Fourier transform is as follows:

[0073] f i = {f|A i ≥ A0}, i = 1, 2,...

[0074] where, A i is the high-value amplitude frequency greater than any amplitude frequency A0, and i is the high-energy amplitude frequency point in the transformed spectrum, and f i represents the main amplitude frequency of the i-th signal and is the high-energy amplitude frequency.

[0075] Construct a Fourier series fitting function for the periodic time series variable based on the main amplitude-frequency obtained from the fast Fourier transform, as shown in the following formula:

[0076]

[0077] where δ, α i , β i all represent unknown parameter variables, n represents the number of temperature signal sequences, f i represents the main amplitude-frequency of the i-th signal, and t represents time.

[0078] Substitute the Fourier series fitting function into the temperature Fourier function to construct a function whose periodic fluctuation shape basically matches the fluctuation of the actual temperature data. Use the least squares method to fit the Fourier function f T0 (t) with the actual temperature data curve to further obtain the specific values of the unknown parameter variables, and finally obtain a temperature fluctuation term prediction function f T (t) with relatively high accuracy.

[0079] Add the above trend term and fluctuation term to obtain the final thaw settlement coefficient prediction formula:

[0080]

[0081]

[0082] A1 = af T (t)

[0083] where A0 represents the trend term, A1 represents the fluctuation term, and a represents the unknown parameter variable.

[0084] S4. Use the least squares method to fit the prediction function of the thaw settlement coefficient according to the change curve of the actual thaw settlement coefficient, obtain the unknown parameter variable of the thaw settlement coefficient function, and obtain the final prediction function of the thaw settlement coefficient to predict the thaw settlement coefficient.

[0085] According to the formula where the independent variables are time t and water content ω, use the least squares method to fit the prediction function A of the actual thaw settlement coefficient change curve to obtain the parameter a, and finally the thaw settlement coefficient varying with time and water content can be predicted.

[0086] The embodiments of the present invention use a large amount of real temperature data, consider the periodic volatility of temperature, and select the temperature data of each day in the research area for ten years for data processing. For example, Figure 2 and Figure 3 are the actual temperature data curve and the amplitude-frequency curve generated after the temperature data is subjected to the fast Fourier transform in the embodiments of the present invention.

[0087] The constructed temperature Fourier function has a good fitting effect with the actual temperature data curve. Select the top five main amplitude frequencies in the amplitude-frequency curve and substitute them into the formula where n = 1, 2,.... The fitting parameters are shown in Table 1, and the optimal fitting value R 2 = 0.878, with a good effect, as shown in Figure 4 , Figure 4 which is the comparison between the actual temperature data in the research area and the Fourier series fitting formula in the embodiment of the present invention.

[0088] Table 1

[0089]

[0090] In an exemplary embodiment, there is provided a computer-readable storage medium storing a computer program which, when executed by a processor, implements the above-mentioned FFT-based multi-factor thaw settlement coefficient prediction method.

[0091] Please refer to Figure 5 , in an exemplary embodiment, there is also provided an electronic device including at least one processor, at least one memory, and at least one communication bus.

[0092] Among them, the memory stores a computer program which includes computer-readable instructions. The processor calls the computer-readable instructions stored in the memory through the communication bus to execute the above-mentioned FFT-based multi-factor thaw settlement coefficient prediction method.

[0093] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-factor melting-settling coefficient prediction method based on FFT, characterized in that: The following steps are involved: S1. Obtain soil samples from the study area, prepare samples, and determine basic parameters of samples; S2. Perform freeze-thaw tests on soil samples according to the measured basic parameters of the samples, measure the thaw settlement coefficient, and obtain a change curve of the actual thaw settlement coefficient; S3. Construct a prediction function of the melting-settling coefficient containing unknown parameters, including the trend term dominated by internal factors and the fluctuation term dominated by external factors; S4. Using the least square method, the prediction function of the melting-settling coefficient is fitted according to the variation curve of the actual melting-settling coefficient, the unknown parameters of the melting-settling coefficient function are obtained, the prediction function of the final melting-settling coefficient is obtained, and the melting-settling coefficient is predicted.

2. According to the FFT-based multi-factor melting-sinking coefficient prediction method of claim 1, it is characterized in that: The basic parameters of the samples include: dry density, initial moisture content, liquid limit moisture content, and porosity ratio.

3. The method for predicting the multi-factor melting-sinking coefficient based on FFT according to claim 1 is characterized in that: The function of the trend term is: in: Among them, A0 represents the trend term, C r represents the contact rate, γ d represents dry bulk density, ω represents water content, ω0 represents initial water content, ω L represents the liquid limit water content, ρ w represents the water density, γ s Indicates the bulk density of soil.

4. The method for predicting the multi-factor melting-sinking coefficient based on FFT according to claim 1 is characterized in that: The external factor that produces the fluctuation term is temperature.

5. The method for predicting the multi-factor melting-sinking coefficient based on FFT according to claim 4 is characterized in that: The function of the fluctuation term is: A1=off T (hours) Among them, a represents the unknown parameter, f T (t) represents the temperature Fourier function.

6. The method for predicting the multi-factor melting-sinking coefficient based on FFT according to claim 5 is characterized in that: The function of the fluctuation term is: Among them, f T0 (t) represents the function of Fourier wave term, δ, α i , β i All of them represent the unknown parameters of the fluctuation term, n represents the number of temperature signal sequences, and f i represents the main amplitude frequency of the i-th signal, and t represents time; The function f of the Fourier wave term is fitted using the least squares method T0 (t) and the actual temperature data curve to obtain the unknown parameters δ, α i , β i The specific value of the temperature Fourier function f T (t).

7. The method for predicting the multi-factor melting-sinking coefficient based on FFT according to claim 1 is characterized in that: The prediction function of the final melting-settling coefficient is expressed as: A=A0+A1 Among them, A0 represents the trend term and A1 represents the fluctuation term.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the processor and the memory are interconnected, wherein the memory is used to store a computer program, the computer program comprises computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the method according to any one of claims 1 to 7.

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