Dam displacement safety monitoring analysis method based on function type regression and related device

Abstract

The invention discloses a dam displacement safety monitoring analysis method based on function regression and a related device, and the method comprises the steps: obtaining original monitoring data of a current monitoring period, the original monitoring data comprising a water level sequence, a temperature sequence, a scalar aging sequence and a displacement sequence; functionalizing the water level sequence, the temperature sequence and the scalar aging sequence to obtain the water level, the temperature and the scalar aging after functionalization, inputting the water level, the temperature and the scalar aging after functionalization into the trained functional regression model, and predicting to obtain displacement information; functionalizing the displacement sequence, and fitting to obtain displacement information; and evaluating the displacement safety of the dam according to the displacement information obtained through prediction and the displacement information obtained through fitting. According to the method and the related device, displacement safety monitoring analysis can be accurately carried out on the dam.

Description

Technical Field

[0001] This invention belongs to the field of monitoring technology and relates to a method and related device for monitoring and analyzing dam displacement safety based on functional regression. Background Technology

[0002] As an important basic water conservancy facility, the safe and stable operation of dams is related to people's property and regional ecological security. Dam displacement is a core monitoring indicator reflecting its structural performance. It is usually affected by three major factors: water pressure (reservoir water level), temperature (air temperature), and time (long-term effects such as concrete creep and foundation consolidation).

[0003] Currently, statistical models (such as multiple linear regression and stepwise regression) or machine learning methods (such as support vector machines and neural networks) widely used in engineering practice mostly treat monitoring data as a scalar sequence at discrete time points. This generally has the following shortcomings: 1. Ignoring data continuity: In the field of dam safety monitoring, displacement, water level, and temperature are essentially continuous changes over time. Traditional methods treat monitoring data as discrete observation points, ignoring the continuity and smoothness of the data in the time dimension, and easily losing the continuous dynamic characteristics of the data.

[0004] 2. Coarse modeling granularity: Modeling daily / hourly data independently makes it difficult to reflect the cumulative or lagged effects of influencing factors in the practical dimension.

[0005] 3. Low prediction accuracy of statistical models / weak interpretability of machine learning: Traditional statistical models have strong interpretability but generally low prediction accuracy and poor robustness; using machine learning algorithms to make predictions can improve prediction accuracy, but their internal black box structure makes it difficult to reveal the specific impact mechanism of water level or temperature on displacement at different time periods.

[0006] The above problems prevent accurate displacement safety monitoring and analysis of the dam. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and related device for monitoring and analyzing dam displacement safety based on functional regression. This method and related device can accurately monitor and analyze the displacement safety of dams.

[0008] To achieve the above objectives, this invention discloses a method for monitoring and analyzing dam displacement safety based on functional regression, comprising: Obtain the raw monitoring data for the current monitoring period, which includes water level sequence, temperature sequence, scalar time-dependent sequence, and displacement sequence; The water level sequence, temperature sequence, and scalar aging sequence are functionalized respectively to obtain the functionalized water level, temperature, and scalar aging. These functionalized water level, temperature, and scalar aging are then input into a trained functional regression model to predict displacement information. ; The displacement sequence is functionalized and fitted to obtain displacement information. ; Based on the predicted displacement information and the displacement information obtained by fitting Assess the displacement safety of the dam.

[0009] Furthermore, the functional regression model is expressed as:

[0010] in, It is the intercept function. and These are two-dimensional regression coefficient functions, describing the effects of water level and temperature at time s on dam deformation at time t. Represents the time-effect function. For random error term, For the standardized time domain.

[0011] Furthermore, , , and The estimated value is:

[0012] ; ;

[0013] in, Represents the regression coefficient vector. Represents the basis function system.

[0014] Furthermore, the displacement information obtained from the fitting... for:

[0015] in,[ ] represents the coefficient vector. Represents the basis function system.

[0016] Furthermore, the process of assessing the displacement safety of the dam based on the predicted displacement information and the fitted displacement information is as follows: Determine the threshold D th; Calculate L between two functions 2 The norm distance D is:

[0017] When D>D th If this occurs, the dam displacement behavior during the current monitoring period will significantly deviate from the normal response pattern.

[0018] Furthermore, take historical L 2 The 95th percentile of the norm distance is used as the threshold D. th .

[0019] This invention discloses a dam displacement safety monitoring and analysis system based on functional regression, comprising: The acquisition module is used to acquire the raw monitoring data of the current monitoring period, which includes water level sequence, temperature sequence, scalar time-dependent sequence and displacement sequence; The prediction module is used to perform functionalization on the water level sequence, temperature sequence, and scalar aging sequence respectively, to obtain the functionalized water level, temperature, and scalar aging. The functionalized water level, temperature, and scalar aging are then input into a trained functional regression model to predict displacement information. ; The fitting module is used to function the displacement sequence and fit it to obtain displacement information. ; The evaluation module is used to evaluate the displacement information obtained from the prediction. and the displacement information obtained by fitting Assess the displacement safety of the dam.

[0020] Furthermore, the functional regression model is expressed as:

[0021] in, It is the intercept function. and These are two-dimensional regression coefficient functions, describing the effects of water level and temperature at time s on dam deformation at time t. Represents the time-effect function. For random error term, For the standardized time domain.

[0022] This invention discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the dam displacement safety monitoring and analysis method based on functional regression.

[0023] This invention discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the dam displacement safety monitoring and analysis method based on functional regression.

[0024] The present invention has the following beneficial effects: In practical operation, the dam displacement safety monitoring and analysis method and related device based on functional regression described in this invention inputs the functionalized water level, temperature, and scalar aging data into the trained functional regression model to predict displacement information. The displacement sequence is functionalized and fitted to obtain displacement information. Based on the predicted displacement information and the displacement information obtained by fitting Assessing the displacement safety of dams involves introducing a regression model based on functional data to establish a "function-function" regression prediction relationship between influencing factors and effect sizes in the field of dam safety monitoring. This approach enables accurate displacement safety monitoring and analysis of dams and is highly practical. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a system structure diagram of the present invention. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0029] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0030] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0031] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0032] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0034] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0035] Example 1 refer to Figure 1 The dam displacement safety monitoring and analysis method based on functional regression described in this invention includes the following steps: 1) Obtain the raw monitoring data for the current monitoring period, including water level sequence, temperature sequence, scalar time-dependent sequence, and displacement sequence; 2) Construct a functional regression model and train the functional regression model to obtain the trained functional regression model; The specific operation of step 2) is as follows: 21) Obtain monitoring data samples of the dam and preprocess the monitoring data samples; Collect vertical or horizontal displacement monitoring data of the dam and the corresponding reservoir water level Temperature and time series k=1,2,...,n, where i represents the i-th monitoring period and n is the number of observation points within the period; missing or abnormal data are interpolated or removed.

[0036] 22) Functionalize discrete data; For discrete observations within each monitoring period, B-spline basis functions are used to fit them to a smooth function. For example, for i monitoring periods, let it contain... The original observations of the day, within this monitoring period, show the following deformation sequence: The corresponding time point is .

[0037] Construct a set of K-order B-spline basis functions The original discrete data is fitted to a smooth function using penalized least squares:

[0038] in, The fitted displacement function; ] represents the coefficient vector.

[0039] Similarly, the exact same basis function system is used for the water pressure and temperature series. By functionalizing, we obtain the coefficient vectors respectively. and To ensure comparability of function sequences across periods, this invention uses the same set of B-spline basis functions to perform function transformation on data within all periods, achieving a dimensionality reduction representation of "function → finite-dimensional vector".

[0040] 23) Construct a functional regression model; Based on the functional data regression framework, the observation sequence of each monitoring period (1 month) is considered as a time domain The smooth function on the surface, according to the displacement function in the i-th monitoring cycle in step 2), is... The water level function is The sum of temperature functions is This invention does not address the time factor. Therefore, we can implement functional representation. Still a scalar (cumulative from the base date), following the form of a functional data regression model, the functional regression model is as follows:

[0041] in, It is the intercept function. and These are two-dimensional regression coefficient functions, describing the effects of water level and temperature at time s on dam deformation at time t. Represents the time-effect function. For random error term, To standardize the time domain, in this embodiment it is [0, 30] days.

[0042] 24) Parameter estimation and optimization of the model; After establishing the regression model and representing the data as functions, the above functional regression problem is transformed into a finite-dimensional multiple linear regression system.

[0043] Suppose there are N monitoring periods, and the displacement, water level, and temperature functions in each period are expanded using K B-spline basis functions. The data from the first N-1 periods are used for parameter estimation, and the data from the last period is used for verification. The coefficient vector after functionalization is denoted as: Deformation coefficient matrix:

[0044] Water level coefficient matrix:

[0045] Temperature coefficient matrix:

[0046] Time-sensitivity vector:

[0047] For each basis function dimension .

[0048] Constructing the response vector ; Constructing a design matrix ,definition ,in, It is an all-1 vector used to estimate the intercept term; Solve the following ridge regression problem:

[0049] in, This is a smoothing parameter used to balance the goodness of fit and complexity of the model.

[0050] The diagonal penalty matrix is This means that L2 regularization is applied only to the correlation coefficients of water level and air temperature, while the intercept and time-dependent terms are not penalized, in order to preserve their physical meaning.

[0051] The ridge regression problem has an analytical solution, namely:

[0052] Using the data from the last period as the validation set, the estimated parameters of the k-th dimension of the basis function are calculated using the dataset from the previous N-1 months. ( ), and calculate the average prediction RMSE, which is used to select the optimal K and .

[0053] Finally, save all dimensions. regression coefficient vector This yields the regression coefficient estimates for the complete model.

[0054] Intercept function:

[0055] Water level influence surface: ; Temperature affects the surface: ; Time-effect function:

[0056] 3) Safety status assessment and anomaly early warning; Based on the trained functional regression model, a real-time safety assessment of the dam displacement behavior in the new monitoring cycle is performed, and an automatic early warning mechanism is triggered when an anomaly is detected.

[0057] The specific operation of step 3) is as follows: 31) Functionalization of new cycle data; When the raw monitoring data of the latest monitoring cycle is obtained, the water level and temperature sequences are functionalized using the same B-spline basis function system (including node positions, order, and number K) as in step 2).

[0058] 32) Prediction of theoretical displacement response curves; The functionalized water level, temperature, and scalar aging are input into the trained functional regression model, and the results are calculated using a unified B-spline basis function system. The measured displacement sequence within the new period is also functionalized to obtain... Calculate the L between the two functions. 2 Norm distance is:

[0059] 33) Anomaly detection; Threshold setting: Take historical L 2 The 95th percentile (or 3 times the standard deviation) of the norm distance is used as the threshold D. th To ensure a low forecast rate; Anomaly detection: When D > D in the current period th If the dam displacement behavior deviates significantly from the normal response pattern, it is determined that there is structural anomaly or external interference.

[0060] It should be noted that the present invention has the following characteristics: This invention preserves the continuity and smoothness of monitoring data. Traditional regression models treat daily observations as independent scalars, ignoring the inherent relationships between adjacent time points. Functional data regression, however, transforms the discrete observation sequence of a monitoring period into a smooth function defined in the continuous time domain. This approach offers several advantages: firstly, it more accurately reflects the physical process; secondly, it avoids information loss and noise interference caused by discretization; and thirdly, it utilizes the smoothness of the function to suppress measurement errors, thus improving the stability of the regression fit.

[0061] This invention characterizes the dynamic response relationship between variables. In dam monitoring, current monitored values ​​(such as displacement) are not only affected by the current water level / temperature, but may also be influenced by the cumulative effects of environmental factors over the past few days. Functional regression uses two-dimensional regression coefficients (such as...) This model depicts the effect of water level at time s on displacement at time t. It explicitly expresses the hysteresis and memory effects, making it more consistent with actual physical mechanisms than static models.

[0062] The model in this invention boasts high accuracy and strong interpretability. The functional regression model, derived from the traditional regression model, offers stronger interpretability than traditional multiple regression. Its regression accuracy, as calculated through engineering practice, demonstrates a high R-value. 2 Indicators such as RMSE and MAE are significantly better than traditional multiple regression or some machine learning models.

[0063] Example 2 refer to Figure 2 The dam displacement safety monitoring and analysis system based on functional regression described in this invention includes: The acquisition module is used to acquire the raw monitoring data of the current monitoring period, which includes water level sequence, temperature sequence, scalar time-dependent sequence and displacement sequence; The prediction module is used to perform functionalization on the water level sequence, temperature sequence, and scalar aging sequence respectively, to obtain the functionalized water level, temperature, and scalar aging. The functionalized water level, temperature, and scalar aging are then input into a trained functional regression model to predict displacement information. ; The fitting module is used to function the displacement sequence and fit it to obtain displacement information. ; The evaluation module is used to evaluate the displacement information obtained from the prediction. and the displacement information obtained by fitting Assess the displacement safety of the dam.

[0064] In this embodiment, the functional regression model is expressed as:

[0065] in, It is the intercept function. and These are two-dimensional regression coefficient functions, describing the effects of water level and temperature at time s on dam deformation at time t. Represents the time-effect function. For random error term, For the standardized time domain.

[0066] The module division in this embodiment is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in each embodiment of this application can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0067] Example 3 A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the dam displacement safety monitoring and analysis method based on functional regression. For example, the steps include: acquiring raw monitoring data for the current monitoring period, the raw monitoring data including a water level sequence, a temperature sequence, a scalar time-dependent sequence, and a displacement sequence; functionalizing the water level sequence, temperature sequence, and scalar time-dependent sequence to obtain functionalized water level, temperature, and scalar time-dependent sequences; and inputting the functionalized water level, temperature, and scalar time-dependent sequences into a trained functional regression model to predict displacement information. The displacement sequence is functionalized and fitted to obtain displacement information. Based on the predicted displacement information and the displacement information obtained by fitting Assess the displacement safety of the dam. The memory may include main memory, such as high-speed random access memory (RAM), or non-volatile memory, such as at least one disk storage device. The processor, network interface, and memory are interconnected via an internal bus, which can be an industry-standard architecture bus, a peripheral component interconnection standard bus, or an extended industry-standard architecture bus. The bus can be categorized as an address bus, data bus, and control bus. The memory stores programs; specifically, the program may include program code, which includes computer operation instructions. The memory may include main memory and non-volatile memory, and provides instructions and data to the processor.

[0068] Example 4 A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the dam displacement safety monitoring and analysis method based on functional regression. For example, the steps include: acquiring raw monitoring data for the current monitoring period, the raw monitoring data including a water level sequence, a temperature sequence, a scalar time-dependent sequence, and a displacement sequence; functionalizing the water level sequence, temperature sequence, and scalar time-dependent sequence to obtain functionalized water level, temperature, and scalar time-dependent sequence; and inputting the functionalized water level, temperature, and scalar time-dependent sequence into a trained functional regression model to predict displacement information. The displacement sequence is functionalized and fitted to obtain displacement information. Based on the predicted displacement information and the displacement information obtained by fitting Assess the displacement safety of the dam. Specifically, the computer-readable storage medium includes, but is not limited to, volatile memory and / or non-volatile memory. The volatile memory may include random access memory (RAM) and / or cache memory, etc. The non-volatile memory may include read-only memory (ROM), hard disk, flash memory, optical disk, magnetic disk, etc.

[0069] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0070] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0071] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0072] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0073] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and disclosure of the invention. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the following claims.

[0074] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

[0075] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for monitoring and analyzing dam displacement safety based on functional regression, characterized in that, include: Obtain the raw monitoring data for the current monitoring period, which includes water level sequence, temperature sequence, scalar time-dependent sequence, and displacement sequence; The water level sequence, temperature sequence, and scalar aging sequence are functionalized respectively to obtain the functionalized water level, temperature, and scalar aging. These functionalized water level, temperature, and scalar aging are then input into a trained functional regression model to predict displacement information. ; The displacement sequence is functionalized and fitted to obtain displacement information. ; Based on the predicted displacement information and the displacement information obtained by fitting Assess the displacement safety of the dam.

2. The dam displacement safety monitoring and analysis method based on functional regression according to claim 1, characterized in that, The functional regression model is expressed as follows: in, It is the intercept function. and These are two-dimensional regression coefficient functions, describing the effects of water level and temperature at time s on dam deformation at time t. Represents the time-effect function. For random error term, For the standardized time domain.

3. The dam displacement safety monitoring and analysis method based on functional regression according to claim 2, characterized in that, , , and The estimated value is: ； ； in, Represents the regression coefficient vector. Represents the basis function system.

4. The dam displacement safety monitoring and analysis method based on functional regression according to claim 1, characterized in that, The displacement information obtained by fitting for: in,[ ] represents the coefficient vector. Represents the basis function system.

5. The dam displacement safety monitoring and analysis method based on functional regression according to claim 1, characterized in that, The process of assessing the displacement safety of the dam based on the predicted displacement information and the fitted displacement information is as follows: Determine the threshold D th ; Calculate L between two functions 2 The norm distance D is: When D>D th If this occurs, the dam displacement behavior during the current monitoring period will significantly deviate from the normal response pattern.

6. The dam displacement safety monitoring and analysis method based on functional regression according to claim 5, characterized in that, Take history L 2 The 95th percentile of the norm distance is used as the threshold D. th .

7. A dam displacement safety monitoring and analysis system based on functional regression, characterized in that, include: The acquisition module is used to acquire the raw monitoring data of the current monitoring period, which includes water level sequence, temperature sequence, scalar time-dependent sequence and displacement sequence; The prediction module is used to perform functionalization on the water level sequence, temperature sequence, and scalar aging sequence respectively, to obtain the functionalized water level, temperature, and scalar aging. The functionalized water level, temperature, and scalar aging are then input into a trained functional regression model to predict displacement information. ; The fitting module is used to function the displacement sequence and fit it to obtain displacement information. ; The evaluation module is used to evaluate the displacement information obtained from the prediction. and the displacement information obtained by fitting Assess the displacement safety of the dam.

8. The dam displacement safety monitoring and analysis system based on functional regression according to claim 7, characterized in that, The functional regression model is expressed as follows: in, It is the intercept function. and These are two-dimensional regression coefficient functions, describing the effects of water level and temperature at time s on dam deformation at time t. Represents the time-effect function. For random error term, For the standardized time domain.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the dam displacement safety monitoring and analysis method based on functional regression as described in any one of claims 1-6.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the dam displacement safety monitoring and analysis method based on functional regression as described in any one of claims 1-6.

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