Method and system for linearizing a nonlinear capacitance signal for level determination

Abstract

The present application relates to capacitive liquid level detection technology, and in particular to a kind of nonlinear capacitance signal linearization mapping liquid level determination method and system.By multi-frequency excitation and Maxwell equation set verification identification capacitance field topological structure, analyze and subdivide nonlinear distortion area to ensure mapping monotonicity and field continuity, utilize Lipschitz condition constraint local mapping stability, introduce physical reversibility verification to carry out error tracing and model iteration, finally solidify effective parameter and realize high-precision, high robustness linear conversion of capacitance signal to liquid level value.High precision, high linearity, strong robustness and physical level consistency and explainability of liquid level measurement result are realized.

Description

Technical Field

[0001] This invention relates to capacitive liquid level detection technology, specifically to a method and system for determining liquid level by linearizing a nonlinear capacitance signal. It is suitable for high-precision and high-stability liquid level measurement scenarios, and is especially suitable for industrial measurement environments with complex medium distribution and significant nonlinear capacitance fields. Background Technology

[0002] Capacitive level sensors are widely used in industrial liquid level detection due to their simple structure, low cost, and applicability to various media. Their basic principle is to reflect the liquid level by measuring changes in the sensor's capacitance. The capacitance value is related to the dielectric constant of the medium between the plates; when the liquid level changes, the dielectric distribution changes, thus causing a change in capacitance. However, under complex actual operating conditions, due to the non-uniformity of the electric field distribution, the discontinuity of the medium, interference from the container shape and installation position, and the influence of multiphase flow, foam, adhesion, and other factors, the capacitance signal and the liquid level often exhibit a significantly nonlinear, non-monotonic, or even locally distorted complex mapping relationship, severely limiting the measurement accuracy and reliability.

[0003] Existing linearization methods mostly focus on the signal back-end, such as piecewise linear fitting, polynomial compensation, or neural network approximation, directly fitting and correcting the acquired capacitance-level data mathematically. While these methods improve output linearity to some extent, they are essentially black-box mathematical mappings, lacking consideration of the underlying physical field laws. When sensor operating conditions change, medium properties fluctuate, or the installation environment changes, the pre-fitted model is prone to failure, lacks robustness, and is difficult to diagnose error sources and perform adaptive calibration.

[0004] Furthermore, the spatial distribution of the sensitive field of a capacitive sensor is governed by the fundamental equations of electromagnetic fields, and its boundary conditions and topology determine the gradient characteristics and response features of the electric field. Most existing technologies neglect to identify and verify the topological structure of the capacitive field from a field theory perspective, failing to ensure that the measurement model itself conforms to basic physical laws. This results in a lack of physical interpretability in regions with severe nonlinear distortion, and correction behavior may violate the principle of field continuity, making the liquid level measurement results physically irreversible or inconsistent. Long-term stability and adaptability to variable environments are fundamentally limited. Summary of the Invention

[0005] To overcome the problems of existing technologies that over-rely on backend mathematical fitting while neglecting the physical field laws at the front end, resulting in poor robustness, weak interpretability, and easy failure in nonlinear distortion regions of the liquid level measurement model, this invention provides a method and system for determining liquid level by linearizing the mapping of nonlinear capacitance signals. Starting from the identification of the capacitance field topology, this invention verifies step-by-step that its gradient distribution conforms to the basic laws of electromagnetic fields, that the mapping in the nonlinear region satisfies monotonicity and topological connectivity, that the local mapping parameters satisfy Lipschitz continuity, and that physical reversibility is verified through inverse mapping. This constructs a liquid level calculation framework driven by physical laws, with layer-by-layer verification and complete correction, achieving high precision, high linearity, strong robustness, and physical consistency and interpretability in the liquid level measurement results.

[0006] The technical solution of this application specifically includes:

[0007] According to one aspect of this application, a method for determining liquid level by linearizing a nonlinear capacitance signal is provided, comprising:

[0008] The spatial response characteristics of the capacitive sensor are obtained by multi-frequency excitation signals. The gradient distribution of the spatial response characteristics is verified to meet the boundary conditions of Maxwell's equations. If not, the excitation signal parameters are recalibrated and the verification is repeated to identify the topological structure of the capacitive field.

[0009] Based on the capacitive field topology, it detects whether the mapping relationship between the nonlinear characteristics of each spatial region and the liquid level change exhibits monotonic continuity. If there is a non-monotonic region, it divides the non-monotonic region into multiple sub-regions and verifies whether the topological connectivity between the sub-regions conforms to the field continuity principle of field theory. If there is an isolated distortion point that violates the field continuity principle, it returns to perform capacitive field topology identification.

[0010] For sub-regions that pass the topological connectivity verification and monotonic regions, evaluate whether the mapping parameters of each region satisfy the Lipschitz continuity condition. If not, adjust the region boundary and recalculate the mapping parameters according to the local mapping function. If they satisfy, directly calculate the mapping parameters according to the local mapping function.

[0011] After applying the current mapping parameters to the capacitance signal to generate a preliminary liquid level value, perform a reverse mapping operation to convert the liquid level value back to the capacitance domain. Verify whether the reverse mapping result and the original capacitance signal satisfy the principle of physical reversibility. If they do not satisfy the principle, identify the source of error and, based on the source of error, return to perform capacitance field topology identification or return to perform nonlinear distortion region localization.

[0012] When the reverse mapping result satisfies the principle of physical reversibility with the original capacitance signal, the current effective mapping parameters are confirmed. Based on the effective mapping parameters, the real-time capacitance signal is linearly transformed to obtain the liquid level value, ensuring that the output liquid level value maintains a linear relationship with the real liquid level.

[0013] As a further option of the method of the present invention, the verification of whether the gradient distribution of the spatial response characteristics conforms to the boundary conditions of the Maxwell equations includes:

[0014] A multi-frequency composite excitation signal is generated by superimposing at least three sine waves with different frequencies, amplitudes and phases, and the excitation signal is applied to the excitation electrode of the capacitive sensor.

[0015] The time-domain response signals of each sensing electrode are acquired and fast Fourier transform is performed to extract the complex response at each excitation frequency, and the spatial discrete capacitance intensity distribution is constructed using its magnitude.

[0016] The gradient field of the spatial discrete capacitance intensity distribution is calculated using the central difference method;

[0017] Calculate the direction cosine similarity and magnitude relative error between the gradient field and the theoretical gradient field obtained by simulation based on Maxwell's equations and known boundary conditions at each spatial point; where the direction cosine similarity is calculated as the ratio of the absolute value of the dot product of the two gradient vectors to the product of their magnitudes; the magnitude relative error is calculated as the ratio of the absolute value of the difference between their magnitudes to the theoretical magnitude.

[0018] If the proportion of spatial points that meet the directional similarity and amplitude error threshold exceeds the preset value, it is determined that the boundary conditions are met; if not, the error type is analyzed and the excitation signal parameters are iteratively adjusted until the verification is passed, and the capacitive field topology at this moment is recorded.

[0019] As a further option of the method of the present invention, the step of detecting whether the mapping relationship between the nonlinear characteristics of each spatial region and the liquid level change exhibits monotonically continuous characteristics includes:

[0020] The sensitive space is divided into multiple initial analysis regions based on the topological structure of the capacitance field.

[0021] Based on experimental calibration data, an initial local mapping function between capacitance value and liquid level height is fitted for each initial analysis region;

[0022] Calculate the first derivative of each initial local mapping function, locate the non-monotonic interval by detecting changes in the sign of the derivative, and further subdivide the non-monotonic interval into multiple monotonic sub-regions.

[0023] As a further option of the method of the present invention, verifying whether the topological connectivity between sub-regions conforms to the principle of field continuity includes:

[0024] Construct a region adjacency graph, where nodes represent each monotonic sub-region and the original monotonic region, and physically adjacent regions are connected by edges in the graph;

[0025] Check if there are isolated nodes or isolated subgraphs in the region adjacency graph;

[0026] Calculate the difference between the mapping function values ​​and the first derivatives of all adjacent regions at the common boundary;

[0027] If there are isolated nodes or the difference exceeds the continuity tolerance threshold, it is determined that the field continuity principle is violated, and the process returns to the capacitor field topology identification step.

[0028] As a further option of the method of the present invention, evaluating whether the mapping parameters of each region satisfy the Lipschitz continuity condition includes:

[0029] For each region that passes the topological connectivity verification, a parameterized local mapping function is fitted using calibration data;

[0030] Calculate the supremum of the absolute value of the first derivative of the local mapping function in the domain, and use it as an estimate of the Lipschitz constant.

[0031] If the estimated value of the Lipschitz constant is greater than the preset Lipschitz constant threshold, it is determined that the Lipschitz continuity condition is not met.

[0032] As a further option of the method of the present invention, adjusting the region boundary and recalculating the mapping parameters according to the local mapping function includes:

[0033] For regions that do not satisfy the Lipschitz continuity condition, analyze the segments that cause the mapping function curve to be too steep;

[0034] The boundaries between the region and its adjacent regions are moved into the region to narrow its defined domain and remove steep sections.

[0035] The stripped space and data points are reassigned to adjacent regions or new sub-regions are created, and the local mapping function is refitted and Lipschitz continuity is evaluated based on the adjusted partition.

[0036] As a further option of the method of the present invention, the verification of whether the reverse mapping result and the original capacitance signal satisfy the principle of physical reversibility includes:

[0037] The preliminary liquid level value obtained by forward mapping from the test capacitance signal based on the current mapping parameters is reverse mapped back to the capacitance domain through the inverse process of the local mapping function of each region to obtain the capacitance estimate.

[0038] The average reversibility error between the estimated capacitance value and the original test capacitance value is calculated using the following formula: ;in, It is the average reversibility error. It is the total number of test data points used for verification. It is the capacitance estimate obtained by reverse mapping. This is the original input test capacitance value.

[0039] If the average reversibility error is less than the preset physical reversibility error threshold, then the physical reversibility principle is satisfied.

[0040] As a further option of the method of the present invention, the step of returning to perform capacitive field topology identification or returning to perform nonlinear distortion region localization based on the error source includes:

[0041] Plot the distribution of reversibility error relative to the original capacitance value or spatial location, and analyze the error distribution pattern;

[0042] If the error is concentrated in a specific spatial region, it is determined to be an error in the capacitor field topology identification, triggering a re-execution of the capacitor field topology identification.

[0043] If the errors are concentrated near the boundaries of different regions, it is determined that the region division is unreasonable, triggering the re-execution of nonlinear distortion region localization and division.

[0044] As a further option of the method of the present invention, the step of linearly transforming the real-time capacitance signal based on the effective mapping parameters to obtain the liquid level value includes:

[0045] The mapping parameter set that satisfies the principle of physical reversibility is fixed to the storage medium in the form of a lookup table, coefficient matrix or executable code module;

[0046] In real-time measurement, after preprocessing the acquired capacitance signal, the region to which it belongs is queried based on its value, and the corresponding solidification mapping function is called to calculate and output the liquid level value.

[0047] Another aspect of this application provides a linearized mapping system for determining liquid level using a nonlinear capacitance signal. The system includes:

[0048] A capacitive sensor assembly, comprising at least one excitation electrode and multiple sensing electrodes;

[0049] The signal excitation module is configured to apply a multi-frequency composite excitation signal to the excitation electrode;

[0050] The data acquisition and processing module is configured to acquire the response signals of each sensing electrode and process them to obtain the spatial response characteristics of the capacitive sensor.

[0051] The field topology identification module is configured to verify whether the gradient distribution of the spatial response characteristics conforms to the boundary conditions of Maxwell's equations. If it does not conform, the control signal excitation module iteratively calibrates the excitation signal parameters and repeats the verification until the capacitive field topology is identified.

[0052] The nonlinear feature analysis module is configured to detect whether the mapping relationship between the capacitance value and the liquid level change in each spatial region exhibits monotonic continuous characteristics based on the capacitance field topology, locate non-monotonic regions and subdivide them into multiple sub-regions, and verify whether the topological connectivity between sub-regions conforms to the principle of field continuity.

[0053] The mapping parameter optimization module is configured to evaluate whether the local mapping parameters of each validated region satisfy the Lipschitz continuity condition, and adjust the boundaries of regions that do not satisfy the condition and recalculate the mapping parameters.

[0054] The physical reversibility verification module is configured to apply the current mapping parameters to the test capacitance signal to generate a preliminary liquid level value, perform a reverse mapping operation to convert the liquid level value back to the capacitance domain, and verify whether the reverse mapping result and the original capacitance signal satisfy the physical reversibility principle. If not, it traces the source according to the error distribution pattern and triggers the field topology identification module or the nonlinear feature analysis module to re-execute the corresponding process.

[0055] The parameter solidification and linearization output module is configured to confirm that the current mapping parameter is a valid parameter and solidify it when the principle of physical reversibility is satisfied. Based on the valid parameter, the real-time acquired capacitance signal is linearized and the liquid level value is output.

[0056] The beneficial effects of this application are as follows:

[0057] This invention fundamentally breaks through the limitations of traditional capacitive liquid level measurement, which relies on black-box mathematical fitting. By establishing a capacitive field topological model based on the physical laws of electromagnetic fields, it achieves a unity between the measurement principle and the physical essence. This method ensures that the sensor response strictly conforms to field theory constraints, giving the liquid level mapping model robust physical interpretability and inherent consistency, thus maintaining the accuracy of core measurements even under changing medium properties or complex operating conditions.

[0058] By introducing a complete modeling and verification process from field identification and nonlinear processing to physical reversibility verification, this method constructs an intelligent measurement system with self-diagnosis and iterative optimization capabilities. This not only significantly improves the accuracy and long-term stability of liquid level measurement but also realizes a paradigm shift from post-hoc mathematical compensation to pre-hoc physical modeling, providing a systematic solution for high-reliability capacitive liquid level measurement. Attached Figure Description

[0059] Figure 1A schematic diagram of the overall method for determining liquid level by linearizing nonlinear capacitance signals;

[0060] Figure 2 Flowchart of S100, a method for determining liquid level by linearizing nonlinear capacitance signals;

[0061] Figure 3 S200 flowchart of the linearization mapping method for determining liquid level for nonlinear capacitance signals;

[0062] Figure 4 Flowchart of S300, a method for determining liquid level by linearizing nonlinear capacitance signals;

[0063] Figure 5 Flowchart of S400, a method for determining liquid level by linearizing nonlinear capacitance signals;

[0064] Figure 6 The flowchart of the S500 method for determining liquid level by linearizing the nonlinear capacitance signal is shown. Detailed Implementation

[0065] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0066] The core theoretical foundation of this invention is built upon electromagnetic field theory, nonlinear system identification theory, and the theory of function approximation and invertibility in numerical analysis. By combining Maxwell's equations to verify the physical laws of the capacitance field, identifying and subdividing the nonlinear distortion region based on the field topology and continuity principle, constraining the local mapping function using the Lipschitz condition, and introducing the principle of physical invertibility for verification, a complete method is ultimately formed, from field identification, nonlinear processing, parameter calculation to invertibility verification, achieving high-precision and robust linearization mapping of capacitance signals to liquid level values.

[0067] The specific embodiments of the present invention will be described in detail below.

[0068] Example 1:

[0069] Please see Figure 1 The diagram illustrates an overall flowchart of a method for determining liquid level by linearizing a nonlinear capacitance signal according to an embodiment of the present invention. The method includes:

[0070] S100: Acquisition of spatial response characteristics of capacitive field and identification of topology;

[0071] S200: Nonlinear feature mapping relationship analysis and topological connectivity verification;

[0072] S300: Calculation of local mapping parameters and Lipschitz continuity assessment;

[0073] S400: Physical reversibility verification and error tracing;

[0074] S500: Effective mapping parameter confirmation and linearized liquid level output.

[0075] The specific plan is as follows:

[0076] In a linearized mapping method for determining liquid level of a nonlinear capacitance signal, S100 applies a multi-frequency excitation signal and analyzes the sensor response to verify whether the response gradient distribution conforms to the basic physical laws of electromagnetic fields, thereby accurately identifying the topological structure of the measured capacitance field.

[0077] Please refer to Figure 2 The diagram illustrates a flowchart of an exemplary linearization mapping method for determining liquid level using a nonlinear capacitance signal, S100, which includes:

[0078] S110: In this embodiment, the system applies a set of pre-configured multi-frequency composite excitation signals to the excitation electrodes of the capacitive sensor through the signal generation module.

[0079] In one possible implementation of this embodiment, the multi-frequency composite excitation signal Depend on It is synthesized by superimposing sine waves of different frequencies, amplitudes and phases. The value is greater than or equal to 3, and the frequency range covers a wide frequency band from low frequency to the characteristic frequency of the sensor and medium.

[0080] Specifically, the signal generation module generates a multi-frequency composite excitation signal based on a preset parameter table using direct digital synthesis technology, and then applies it to the excitation electrode of the capacitive sensor after power amplification.

[0081] S120: In this embodiment, while applying excitation, the time-domain response signals on all sensing electrodes of the sensor are simultaneously acquired by the data acquisition module.

[0082] In one possible implementation of this embodiment, a Fast Fourier Transform is performed on the time-domain response signal acquired by each sensing electrode to extract its complex response at each excitation frequency. The magnitude of the complex response characterizes the capacitive coupling strength at the corresponding frequency and spatial location, while the phase characterizes the dielectric relaxation information.

[0083] S130: In this embodiment, based on the response modulus of all sensing electrodes at a certain dominant frequency, a spatial discrete intensity distribution of the capacitive field at the dominant frequency is constructed. .

[0084] In one possible implementation of this embodiment, the central difference method is used to calculate the spatial response intensity distribution. gradient field Gradient field It is a vector field that characterizes the maximum rate of change of the capacitance field strength in space and its direction.

[0085] S140: In this embodiment, the system will use the gradient field The distribution is compared and verified with the theoretical gradient field distribution obtained by numerical simulation based on Maxwell's equations and known boundary conditions.

[0086] In one possible implementation of this embodiment, the verification process calculates the direction cosine similarity between the measured gradient field and the theoretical gradient field at each spatial discrete point. and amplitude relative error .

[0087] Specifically, direction cosine similarity It is calculated as the ratio of the absolute value of the dot product of the two gradient vectors to the product of their magnitudes.

[0088] Specifically, the relative error of amplitude It is calculated as the ratio of the absolute value of the difference in the two moduli to the theoretical moduli.

[0089] The system presets a similarity threshold. and amplitude error threshold If all points satisfy and The percentage of points exceeded the preset ratio. If the gradient distribution meets the boundary conditions of Maxwell's equations, then it is determined that the gradient distribution conforms to the boundary conditions of Maxwell's equations. Otherwise, it is determined that it does not conform.

[0090] S150: In this embodiment, if the verification in S140 fails, the system enters the excitation parameter iterative calibration loop.

[0091] In one possible implementation of this embodiment, the excitation parameter iterative calibration step includes:

[0092] S151: Analyze the spatial distribution characteristics and error types of the non-compliant areas.

[0093] S152: Adjust the multi-frequency excitation signal parameter table according to the error type. For example, if the directional deviation is concentrated, increase the excitation amplitude of the corresponding sensitive frequency; if the amplitude error is generally large, adjust the amplitude spectrum of the excitation signal as a whole.

[0094] S153: Regenerate the excitation signal using the adjusted parameters, and repeat S110 to S140 until the gradient distribution is verified.

[0095] Once the gradient distribution verification is successful, the system will formally identify and record the spatial intensity distribution and topological characteristics of the capacitor field constructed under the current conditions as the capacitor field topology under the current operating conditions. Topology It is the foundational physical model for all subsequent analyses.

[0096] In a method for determining liquid level by linearizing a nonlinear capacitance signal, S200 is based on the capacitance field topology identified by S100. The system systematically analyzes the mapping relationship between capacitance value and liquid level height throughout the measurement space, locates and handles non-monotonic and discontinuous regions, and ensures the mathematical goodness of the mapping relationship.

[0097] Please refer to Figure 3 The diagram illustrates a flowchart of an exemplary linearization mapping method for determining liquid level using a nonlinear capacitance signal, S200, which includes:

[0098] S210: In this embodiment, according to the topology The characteristics in the image divide the entire sensitive space of the capacitive sensor into... Initial analysis region .

[0099] In one possible implementation of this embodiment, for each region A set of capacitance values ​​were obtained through experimental calibration. With liquid level height The corresponding data pairs. Using the data pairs, fit an initial local mapping function. , making Optionally, the fitting method can use a polynomial or spline function model.

[0100] S220: In this embodiment, for each region initial local mapping function Mathematical analysis is performed to examine its monotonicity and continuity within its domain.

[0101] In one possible implementation of this embodiment, the monotonic continuous characteristic detection step includes:

[0102] S221: Calculation function first derivative .

[0103] S222: Detection derivative The sign of the derivative changes. Calculate the derivative by uniformly sampling within the domain. If there exist two points where the product of the derivatives is negative, then the function is determined to be non-monotonic in that interval. Record all subintervals that cause the derivative to change sign; the spatial region corresponding to each subinterval is the non-monotonic region.

[0104] S223: Detection function If there is a jump point in itself or its first derivative that is greater than a preset threshold, it is determined to be a discontinuity point.

[0105] S230: In this embodiment, for each detected non-monotonic region, the non-monotonic region is further subdivided into several sub-regions, so that the mapping relationship is strictly monotonic within the capacitance interval corresponding to each sub-region.

[0106] In one possible implementation of this embodiment, the non-monotonic region subdivision step includes:

[0107] S231: Find all stationary points in the non-monotonic intervals where the first derivative is zero.

[0108] S232: Using the stationary point at zero and the endpoints of the interval as boundaries, divide the original interval into several monotonic subintervals.

[0109] S233: Each monotonic subinterval corresponds to a connected subregion in the original physical space. Update the region partition by replacing the original non-monotonic regions with a set of newly generated monotonic subregions.

[0110] S240: In this embodiment, after completing the subdivision of the region, it is verified whether the topological connectivity between all sub-regions, and between the sub-regions and the original monotonic region, conforms to the principle of field continuity in electromagnetic field theory.

[0111] In one possible implementation of this embodiment, the topology connectivity verification step includes:

[0112] S241: Construct a region adjacency graph. Treat each sub-region and the original monotonic region as a node in the graph, and establish edges between corresponding nodes in the graph for physically adjacent regions.

[0113] S242: Check if there are isolated nodes or isolated subgraphs in the graph. An isolated node means that a region is completely surrounded by other regions and has no connecting paths. It may correspond to a physically isolated distortion point, which violates the principle of field continuity.

[0114] S243: Check whether the mapping function values ​​and first derivatives of all adjacent regions are continuous on their common boundary. Calculate the difference between the function value and the derivative at the boundary. If the difference exceeds the preset continuity tolerance threshold, it is determined to be a violation of the existence field continuity.

[0115] S250: In this embodiment, if the verification in S240 finds isolated distortion points or severe field continuity violations, it indicates that the capacitive field topology identified in step S100 is correct. That may not be accurate.

[0116] In one possible implementation of this embodiment, the processing steps are as follows: the system determines that the current region division is invalid, clears the current division result, and generates a feedback signal to return to step S100, triggering the re-execution of the capacitance field topology structure identification step. If the topology connectivity verification passes, the final region division scheme is recorded, wherein the capacitance-liquid level mapping relationship within each region is guaranteed to be monotonically continuous. The process then proceeds to S300.

[0117] In a linearized mapping method for determining liquid level of a nonlinear capacitance signal, S300 calculates the local mapping parameters for each verified monotonic continuous region and evaluates whether the mapping satisfies the Lipschitz continuity condition to ensure the stability of the mapping and the robustness of numerical computation.

[0118] Please refer to Figure 4 The diagram illustrates a flowchart of an exemplary linearization mapping method for determining liquid level using a nonlinear capacitance signal, S300, which includes:

[0119] S310: In this embodiment, for each final region Use the final area Based on the calibration data within the range, establish a parameterized local mapping function. ,in The parameter vector to be determined.

[0120] In one possible implementation of this embodiment, the local mapping function is a piecewise linear function or a monotonic constrained cubic spline function. Parameters This is determined by minimizing the fitting error, while simultaneously satisfying that the function is monotonic within the capacitance interval corresponding to the region.

[0121] S320: In this embodiment, the system evaluates the parameterized local mapping function. Does it satisfy the Lipschitz continuity condition on its domain?

[0122] In one possible implementation of this embodiment, the Lipschitz continuity assessment step includes:

[0123] S321: Calculation function The absolute value of the first derivative in its domain upper bound . It is an estimate of the Lipschitz constant.

[0124] S322: Set an acceptable Lipschitz constant threshold. .like Then determine the region The local mappings satisfy the Lipschitz continuity condition. If If the condition is not met, then it is determined that the condition is not satisfied.

[0125] S330: In this embodiment, if a certain area The local mapping function does not satisfy the Lipschitz condition, indicating that the capacitance change in this region may cause the liquid level estimate to change too drastically.

[0126] In one possible implementation of this embodiment, the region boundary adjustment step includes:

[0127] S331: Analysis leads to Excessive values ​​usually occur in sections where the mapping function curve is very steep.

[0128] S332: By region The boundary with the adjacent area is the object of adjustment; the boundary is moved towards... By appropriately shifting the internal structure and narrowing its domain, overly steep sections can be stripped away.

[0129] S333: After the boundary is moved, the stripped portion of space and its data points are reassigned to adjacent regions with more gradual changes in the mapping function, or as a new, smaller sub-region.

[0130] S334: Based on the adjusted region partitioning, the system refits the local mapping function for the adjusted region and recalculates its parameters and Lipschitz constant estimates. .

[0131] S340: In this embodiment, for regions that satisfy the Lipschitz condition, and for newly fitted regions that satisfy the condition after adjustment in S330, the system will finally determine the local mapping function. and its parameters The domain is formally defined as the set of mapping parameters for that region. The parameter sets of all regions constitute a complete piecewise mapping model from capacitance signals to liquid level values.

[0132] In a linearized mapping method for determining liquid level of a nonlinear capacitance signal, S400 puts the mapping parameter set calculated by S300 into trial operation. The physical reversibility of the entire mapping process is verified through a method that includes forward mapping and reverse mapping. Based on the reverse error, a source analysis is performed to ensure the physical consistency and reliability of the model.

[0133] Please refer to Figure 5 The diagram illustrates a flowchart of an exemplary linearization mapping method for determining liquid level using a nonlinear capacitance signal, S400, which includes:

[0134] S410: In this embodiment, a new set of test capacitance signal data that was not involved in model building is acquired. For each real-time capacitance value The region to which the value belongs is determined based on its value, and then a forward mapping is performed using the mapping function for that region to calculate a preliminary liquid level estimate. .

[0135] S420: In this embodiment, the system uses the liquid level estimate obtained in the previous step. As input, we attempt to deduce the capacitance value by reversing the mapping process.

[0136] In one possible implementation of this embodiment, the reverse mapping step is as follows: for the liquid level value Determine the liquid level value It is generated by the mapping function of the region from which it originates. Then, the inverse of the mapping function that generates the region is calculated to obtain the capacitance estimate. If the function is not analyzable, then it is solved numerically.

[0137] S430: In this embodiment, the system calculates the capacitance estimate obtained by the reverse mapping. The test capacitance value compared to the original input The error between them.

[0138] Define the average invertibility error as .

[0139] The system presets a physical reversibility error threshold. .like If the error at most individual points is less than a certain point error threshold, then the reverse mapping result is determined to satisfy the principle of physical reversibility with the original capacitance signal. Otherwise, it is determined not to satisfy the principle.

[0140] S440: In this embodiment, if the physical reversibility verification is not satisfied, the distribution characteristics of the error are analyzed in depth to identify the root cause.

[0141] In one possible implementation of this embodiment, the error source analysis step includes:

[0142] S441: Plot the distribution of error relative to the original capacitance value or spatial location.

[0143] S442: Analyze the error distribution pattern:

[0144] Pattern A: Points with large errors are concentrated in one or a few specific regions, and the errors show a systematic trend within these regions. This pattern suggests that there may be a deviation in the topological identification of the capacitance field in a specific region.

[0145] Pattern B: Points with larger errors are concentrated near the boundaries of different regions. This pattern indicates that the region division may be unreasonable.

[0146] Mode C: Error points are discretely distributed with no obvious regional or boundary correlation. This mode may be caused by measurement noise or random errors in calibration data.

[0147] S450: In this embodiment, based on the source analysis results of S440, the system automatically triggers different iterative optimization paths.

[0148] In one possible implementation of this embodiment, the iterative optimization triggering logic is as follows:

[0149] If the source of error is identified as a capacitor field topology identification error, corresponding to mode A, a control signal is generated to return to step S100 and the capacitor field topology identification is re-executed.

[0150] If the source of error is identified as unreasonable region division, corresponding to mode B, a control signal is generated to return to step S200, and the nonlinear distortion region location and division are re-executed.

[0151] If the source of error is identified as random noise, corresponding to pattern C, and the average error slightly exceeds the threshold, then try to smooth and regularize the mapping function, or reassess the quality of the calibration data.

[0152] The process only proceeds to the final confirmation step S500 when the physical reversibility verification is satisfied.

[0153] In a linearization mapping method for determining liquid level of a nonlinear capacitance signal, after verifying physical reversibility, the S500 finally confirms that all the currently calculated mapping parameter sets are valid mapping parameters and solidifies them into a linearization converter for high-precision and high-reliability liquid level calculation of the real-time acquired capacitance signal.

[0154] Please refer to Figure 6 The diagram illustrates a flowchart of an exemplary linearization mapping method for determining liquid level using a nonlinear capacitance signal, S500, which includes:

[0155] S510: In this embodiment, when S430 determines that the reverse mapping error satisfies the principle of physical reversibility, the mapping parameter set generated in the current iteration period is confirmed as the final valid mapping parameter.

[0156] In one possible implementation of this embodiment, the effective mapping parameter set includes: the capacitance domain and liquid level domain of each region, the specific mathematical expression of the local mapping function and its coefficients, and auxiliary information such as the Lipschitz constant of each region.

[0157] The effective mapping parameter set is stored in the non-volatile memory of the level measuring device or in the configuration file of the online computing system in the form of a lookup table, coefficient matrix, or executable code module.

[0158] S520: In this embodiment, during the normal operation of the liquid level measurement system, the data acquisition module continuously acquires the real-time output signal of the capacitive sensor.

[0159] In one possible implementation of this embodiment, the linearization transformation step is as follows:

[0160] S521: Performs preprocessing on real-time capacitance signals, such as filtering and noise reduction.

[0161] S522: Based on the preprocessed capacitance value, query the solidified valid mapping parameter set to determine its region.

[0162] S523: Call the mapping function corresponding to this area to calculate the liquid level output value. .

[0163] S530: In this embodiment, the calculated liquid level value is sent to the display unit, control system, or host computer software.

[0164] The method described in this invention, through the modeling and verification process from S100 to S400, fundamentally guarantees the physical correctness and mathematical soundness of the mapping parameters used in S520. Therefore, the final output liquid level value maintains the desired linear relationship with the actual liquid level height throughout the entire measurement range, and possesses good anti-interference capability and long-term stability. Even if the medium properties change slowly, as long as the basic topology of the capacitive field does not change drastically, this method can update the mapping parameters through periodic or triggered recalibration, maintaining measurement accuracy.

[0165] In summary, this method, based on electromagnetic field theory and nonlinear system identification theory, achieves accurate linear mapping from capacitance signals to liquid level values. The true topological structure of the capacitance field is identified through multi-frequency excitation and verification using Maxwell's equations. Based on this, the nonlinear distortion region is analyzed and subdivided to ensure the monotonicity and field continuity of the mapping. The stability of the local mapping is constrained using the Lipschitz condition. An innovative physical reversibility verification mechanism is introduced to perform self-checking and error tracing of the model, driving iterative optimization. Finally, effective parameters are solidified to achieve real-time linear transformation. This method significantly improves the accuracy, robustness, and physical interpretability of capacitive liquid level measurement under complex operating conditions.

[0166] Example 2:

[0167] This invention has been fully deployed and verified in a liquid level monitoring system for chemical raw material storage tanks. The storage tank is a vertical cylindrical shape with a height of [missing information]. ,diameter The medium is an organic solution whose dielectric constant fluctuates with temperature and purity. The capacitive sensor used is a coaxial sleeve structure, with the main electrode arranged along the height of the tank and the auxiliary sensing electrodes distributed in a ring array, totaling 32 sensing rings, numbered E1-E32, installed at equal intervals, to obtain the spatial capacitance field distribution.

[0168] I. Implementation and Configuration;

[0169] 1. Hardware system configuration:

[0170] Multi-frequency signal generator: output signal ,frequency The amplitudes are: 10kHz, 50kHz, 100kHz, 200kHz, 400kHz, 600kHz, 800kHz, and 1MHz. Initial amplitude. All are set to 1V, phase .

[0171] Synchronous data acquisition card: 32 channels, 24-bit resolution, sampling rate Simultaneously collect the responses of all sensing electrodes.

[0172] Computing and Control Unit: Industrial Control Computer (Intel i7-8700, 16GB RAM).

[0173] 2. Software and Algorithm Configuration:

[0174] Signal processing layer: Implements real-time FFT based on C++ to extract the complex responses of each electrode at each frequency. .

[0175] Field Simulation and Verification Layer: Integrating COMSOL Multiphysics API, an electromagnetic field finite element model is established based on the accurate 3D model of the storage tank to calculate the theoretical capacitance field distribution. .

[0176] Core algorithm layer: The entire S100-S500 algorithm is implemented in Python. Key parameter settings are as follows:

[0177] S140: Orientation similarity threshold Amplitude error threshold effective point ratio .

[0178] S220: Monotonicity determination, derivative sign change tolerance, number of zeros. .

[0179] S240: Boundary continuity threshold , .

[0180] S320: Lipschitz constant threshold .

[0181] S430: Reversibility error threshold The corresponding liquid level error is approximately Point error threshold .

[0182] Data storage: The time series database (InfluxDB) stores all raw data, intermediate features, and final liquid level values.

[0183] II. Experimental Procedures and Data;

[0184] 1. Initial calibration and modeling:

[0185] In dielectric constant ,temperature Under these conditions, a full-range static calibration was performed. By precisely controlling the feed, the liquid level was varied from 0m in an empty tank to 15m in a 0.05m increment. At each stable liquid level point, a set of capacitance response data from the 32 electrodes was collected, resulting in a total of 301 sets of calibration data. ,in It is a 32-dimensional capacitance vector.

[0186] 2. S100 Execution and Topology Recognition:

[0187] Using the multi-frequency response from the calibration data, the S100 step was run. The initial validation failed; in the lower-middle region, the average directional similarity to electrodes E8-E15 was only 0.82. After three rounds of excitation parameter iterations, primarily increasing the excitation amplitudes at 100kHz and 400kHz, the full-field gradient validation finally passed. The identified capacitive field topology was then determined. The results show obvious field distortion regions near electrodes E10, E11, and E22, which are consistent with the structure of the coil and tank top. Table 1 shows the gradient direction similarity of each electrode region after final verification. The statistical results.

[0188] Table 1. Statistics of similarity verification results for capacitor field gradient directions (S140)

[0189]

[0190] 3. S200-S400 Execution and Model Establishment:

[0191] based on Using the calibration data, run S200-S400 to establish an initial mapping model. During the first run of S400 to verify physical reversibility, use an additional 50 sets of independent test data to calculate the average reversibility error. The S440 error analysis indicated Mode B, i.e., boundary error, located near the boundary between regions R12 and R13, at a liquid level of approximately 7.2m. The system automatically returned to S200 for boundary fine-tuning and remodeling. The second S400 verification passed. The final generated effective mapping model It contains 35 monotonic zones.

[0192] 4. Performance test experiment design:

[0193] To comprehensively evaluate performance, four sets of test experiments were designed:

[0194] Test A-Static Accuracy: Under the reference conditions, using a high-precision servo radar level gauge as a reference, the level measurement values ​​of the method of this invention are compared with those of the direct lookup table method of the original capacitance signal without linearization processing.

[0195] Test B - Temperature / Dielectric Constant Disturbance: Changing the temperature of the dielectric medium That is, from 15℃ to 45℃, The change is approximately ±8%, and the composition of the medium is altered by adding different proportions of solvent. The liquid level output deviation of the two methods was observed by stepping between 2.3 and 2.8.

[0196] Test C - Dynamic Response: At a constant feed / discharge rate of 5m 3At / h, the outputs of the two methods and their tracking of the radar reference value were recorded during the liquid level change process.

[0197] Testing D-robustness: Simulating slight contaminant adhesion to the sensor to evaluate the system's self-testing and alarm capabilities.

[0198] III. Experimental Results and Data Analysis;

[0199] 1. Test A-static accuracy:

[0200] Ten uniformly distributed liquid level test points were selected across the entire measurement range, and the results are shown in Table 2. The maximum absolute error of the method of this invention is 8 mm, the average error is 3 mm, and the linearity error is 0.08%FS. Traditional methods, due to the lack of consideration for field nonlinear distortion, exhibit significantly increased errors near 3.5 m and 12.0 m.

[0201] Table 2 Comparison of Static Accuracy Test Results (Liquid Level Unit: m)

[0202]

[0203] 2. Test B-temperature / dielectric constant perturbation:

[0204] Table 3 shows the results for different dielectric constants. Below, the measurement deviations of the two methods at a fixed liquid level of 7.5m are compared. The method of this invention, through field topology modeling, shows that each electrode is affected to varying degrees, resulting in a significantly smaller overall system output deviation compared to the traditional method. When the step change is +15%, the traditional method produces a jump error of 1.2m, while the method of this invention has a deviation of only 0.2m and successfully triggers automatic recalibration.

[0205] Table 3. Liquid level measurement deviation under different dielectric constants (liquid level reference value: 7.500m)

[0206]

[0207] 3. Test C-dynamic response:

[0208] During continuous feeding, the root mean square error (RMSE) and maximum lag time of the output values ​​from both methods are calculated based on the radar level gauge reading. The method of this invention has an RMSE of 0.004m and a maximum lag time less than the data acquisition cycle of 100ms, which is better than the traditional method (RMSE: 0.011m) in terms of dynamic tracking performance.

[0209] 4. Test D-robustness:

[0210] The simulated electrode E15 is contaminated, causing a fixed bias that increases its capacitance response by 0.5 pF. During the S100 front-end gradient verification, the system detects that the gradient direction similarity in the local region where this electrode is located has decreased to 0.89 (below...). The system then issued a warning indicating a localized sensor malfunction and suggesting inspection. During the warning period, the liquid level output did not fluctuate, and the maximum instantaneous deviation was 0.012m, demonstrating good fault mitigation capabilities.

[0211] IV. Conclusion;

[0212] This embodiment fully implements the nonlinear capacitance signal linearization mapping liquid level calculation method described in this invention under complex operating conditions of a chemical storage tank. Experimental data shows that:

[0213] 1. Under reference conditions, the linearity across the entire range is better than 0.1%FS, and the maximum absolute error is 8mm, meeting the requirements for high-precision measurement.

[0214] 2. Within a dielectric constant fluctuation range of ±18%, the maximum measurement deviation caused by the method of this invention is 0.2m, which is much lower than the 1.2m of the traditional method, and is not sensitive to changes in the medium.

[0215] 3. When a large step change in the properties of the medium causes the model to fail, the system can automatically detect the excessive physical reversibility error and trigger the recalibration process, autonomously restoring high-precision measurement within 1 hour.

[0216] 4. By verifying the topology of the capacitance field, local anomalies of the sensor can be identified and warnings can be issued, and the system output remains stable.

[0217] 5. The online liquid level calculation takes less than 1ms, meeting the real-time monitoring requirements of industrial processes.

[0218] This invention combines the physical laws of electromagnetic fields with nonlinear system identification, achieving a leap from empirical fitting to model-driven capacitive liquid level measurement. This significantly improves the reliability, accuracy, and adaptability of measurements under complex and time-varying conditions, and has outstanding industrial application value.

[0219] Example 3:

[0220] A linearized mapping system for determining liquid level using a nonlinear capacitance signal, comprising:

[0221] A capacitive sensor assembly, comprising at least one excitation electrode and multiple sensing electrodes;

[0222] The signal excitation module is configured to apply a multi-frequency composite excitation signal to the excitation electrode;

[0223] The data acquisition and processing module is configured to acquire the response signals of each sensing electrode and process them to obtain the spatial response characteristics of the capacitive sensor.

[0224] The field topology identification module is configured to verify whether the gradient distribution of the spatial response characteristics conforms to the boundary conditions of Maxwell's equations. If it does not conform, the control signal excitation module iteratively calibrates the excitation signal parameters and repeats the verification until the capacitive field topology is identified.

[0225] The nonlinear feature analysis module is configured to detect whether the mapping relationship between the capacitance value and the liquid level change in each spatial region exhibits monotonic continuous characteristics based on the capacitance field topology, locate non-monotonic regions and subdivide them into multiple sub-regions, and verify whether the topological connectivity between sub-regions conforms to the principle of field continuity.

[0226] The mapping parameter optimization module is configured to evaluate whether the local mapping parameters of each validated region satisfy the Lipschitz continuity condition, and adjust the boundaries of regions that do not satisfy the condition and recalculate the mapping parameters.

[0227] The physical reversibility verification module is configured to apply the current mapping parameters to the test capacitance signal to generate a preliminary liquid level value, perform a reverse mapping operation to convert the liquid level value back to the capacitance domain, and verify whether the reverse mapping result and the original capacitance signal satisfy the physical reversibility principle. If not, it traces the source according to the error distribution pattern and triggers the field topology identification module or the nonlinear feature analysis module to re-execute the corresponding process.

[0228] The parameter solidification and linearization output module is configured to confirm that the current mapping parameter is a valid parameter and solidify it when the principle of physical reversibility is satisfied. Based on the valid parameter, the real-time acquired capacitance signal is linearized and the liquid level value is output.

[0229] Those skilled in the art will understand that the embodiments of this application are provided as methods, systems, or computer program products. Therefore, this application takes the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application takes the form of a computer program product implemented on one or more computer storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer program code. The solutions in the embodiments of this application are implemented using various computer languages, exemplified by the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0230] 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, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, are implemented by computer program instructions. These computer program instructions are 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, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams.

[0231] These computer program instructions are also stored in a computer read-memory that can direct a computer or other programmed data processing device to operate in a particular manner, such that the instructions stored in the computer read-memory produce an article of manufacture including instruction means that implement the functions specified in the flowchart or multiple flowcharts and / or block diagram blocks or multiple block diagrams.

[0232] These computer program instructions are also loaded onto a computer or other programming data processing device to cause a series of operational steps to be performed on the computer or other programming device to produce a computer-implemented process, such that the instructions, which execute on the computer or other programming device, provide steps for implementing the functions specified in the flowchart flow or multiple flows and / or the block diagram blocks or multiple blocks.

[0233] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0234] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for determining liquid level by linearizing a nonlinear capacitance signal, characterized in that, include: The spatial response characteristics of the capacitive sensor are obtained by multi-frequency excitation signals. The gradient distribution of the spatial response characteristics is verified to meet the boundary conditions of Maxwell's equations. If not, the excitation signal parameters are recalibrated and the verification is repeated to identify the topological structure of the capacitive field. Based on the capacitive field topology, it detects whether the mapping relationship between the nonlinear characteristics of each spatial region and the liquid level change exhibits monotonic continuity. If there is a non-monotonic region, it divides the non-monotonic region into multiple sub-regions and verifies whether the topological connectivity between the sub-regions conforms to the field continuity principle of field theory. If there is an isolated distortion point that violates the field continuity principle, it returns to perform capacitive field topology identification. For sub-regions that pass the topological connectivity verification and monotonic regions, evaluate whether the mapping parameters of each region satisfy the Lipschitz continuity condition. If not, adjust the region boundary and recalculate the mapping parameters according to the local mapping function. If they satisfy, directly calculate the mapping parameters according to the local mapping function. After applying the current mapping parameters to the capacitance signal to generate a preliminary liquid level value, perform a reverse mapping operation to convert the liquid level value back to the capacitance domain. Verify whether the reverse mapping result and the original capacitance signal satisfy the principle of physical reversibility. If they do not satisfy the principle, identify the source of error and, based on the source of error, return to perform capacitance field topology identification or return to perform nonlinear distortion region localization. When the reverse mapping result satisfies the principle of physical reversibility with the original capacitance signal, the current effective mapping parameters are confirmed. Based on the effective mapping parameters, the real-time capacitance signal is linearly transformed to obtain the liquid level value, ensuring that the output liquid level value maintains a linear relationship with the real liquid level.

2. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 1, characterized in that, The verification of whether the gradient distribution of the spatial response characteristics conforms to the boundary conditions of Maxwell's equations includes: A multi-frequency composite excitation signal is generated by superimposing at least three sine waves with different frequencies, amplitudes and phases, and the excitation signal is applied to the excitation electrode of the capacitive sensor. The time-domain response signals of each sensing electrode are acquired and fast Fourier transform is performed to extract the complex response at each excitation frequency, and the spatial discrete capacitance intensity distribution is constructed using its magnitude. The gradient field of the spatial discrete capacitance intensity distribution is calculated using the central difference method; Calculate the direction cosine similarity and magnitude relative error between the gradient field and the theoretical gradient field obtained by simulation based on Maxwell's equations and known boundary conditions at each spatial point; where the direction cosine similarity is calculated as the ratio of the absolute value of the dot product of the two gradient vectors to the product of their magnitudes; the magnitude relative error is calculated as the ratio of the absolute value of the difference between their magnitudes to the theoretical magnitude. If the proportion of spatial points that meet the directional similarity and amplitude error threshold exceeds the preset value, it is determined that the boundary conditions are met; if not, the error type is analyzed and the excitation signal parameters are iteratively adjusted until the verification is passed, and the capacitive field topology at this moment is recorded.

3. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 1, characterized in that, The step of detecting whether the mapping relationship between the nonlinear characteristics of each spatial region and the liquid level change exhibits monotonically continuous characteristics includes: The sensitive space is divided into multiple initial analysis regions based on the topological structure of the capacitance field. Based on experimental calibration data, an initial local mapping function between capacitance value and liquid level height is fitted for each initial analysis region; Calculate the first derivative of each initial local mapping function, locate the non-monotonic interval by detecting changes in the sign of the derivative, and further subdivide the non-monotonic interval into multiple monotonic sub-regions.

4. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 3, characterized in that, The verification of whether the topological connectivity between sub-regions conforms to the principle of field continuity includes: Construct a region adjacency graph, where nodes represent each monotonic sub-region and the original monotonic region, and physically adjacent regions are connected by edges in the graph; Check if there are isolated nodes or isolated subgraphs in the region adjacency graph; Calculate the difference between the mapping function values ​​and the first derivatives of all adjacent regions at the common boundary; If there are isolated nodes or the difference exceeds the continuity tolerance threshold, it is determined that the field continuity principle is violated, and the process returns to the capacitor field topology identification step.

5. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 1, characterized in that, Evaluating whether the mapping parameters of each region satisfy the Lipschitz continuity condition includes: For each region that passes the topological connectivity verification, a parameterized local mapping function is fitted using calibration data; Calculate the supremum of the absolute value of the first derivative of the local mapping function in the domain, and use it as an estimate of the Lipschitz constant. If the estimated value of the Lipschitz constant is greater than the preset Lipschitz constant threshold, it is determined that the Lipschitz continuity condition is not met.

6. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 5, characterized in that, The process of adjusting the region boundary and recalculating the mapping parameters based on the local mapping function includes: For regions that do not satisfy the Lipschitz continuity condition, analyze the segments that cause the mapping function curve to be too steep; The boundaries between the region and its adjacent regions are moved into the region to narrow its defined domain and remove steep sections. The stripped space and data points are reassigned to adjacent regions or new sub-regions are created, and the local mapping function is refitted and Lipschitz continuity is evaluated based on the adjusted partition.

7. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 1, characterized in that, The verification of whether the reverse mapping result and the original capacitance signal satisfy the principle of physical reversibility includes: The preliminary liquid level value obtained by forward mapping from the test capacitance signal based on the current mapping parameters is reverse mapped back to the capacitance domain through the inverse process of the local mapping function of each region to obtain the capacitance estimate. The average reversibility error between the estimated capacitance value and the original test capacitance value is calculated using the following formula: ;in, It is the average reversibility error. It is the total number of test data points used for verification. It is the capacitance estimate obtained by reverse mapping. This is the original input test capacitance value. If the average reversibility error is less than the preset physical reversibility error threshold, then the physical reversibility principle is satisfied.

8. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 7, characterized in that, The step of determining the source of error and returning to perform capacitive field topology identification or returning to perform nonlinear distortion region localization includes: Plot the distribution of reversibility error relative to the original capacitance value or spatial location, and analyze the error distribution pattern; If the error is concentrated in a specific spatial region, it is determined to be an error in the capacitor field topology identification, triggering a re-execution of the capacitor field topology identification. If the errors are concentrated near the boundaries of different regions, it is determined that the region division is unreasonable, triggering the re-execution of nonlinear distortion region localization and division.

9. The method for determining liquid level by linearizing the nonlinear capacitance signal according to claim 1, characterized in that, The method of obtaining the liquid level value by linear transformation of the real-time capacitance signal based on effective mapping parameters includes: The mapping parameter set that satisfies the principle of physical reversibility is fixed to the storage medium in the form of a lookup table, coefficient matrix or executable code module; In real-time measurement, after preprocessing the acquired capacitance signal, the region to which it belongs is queried based on its value, and the corresponding solidification mapping function is called to calculate and output the liquid level value.

10. A system for determining liquid level by linearizing a nonlinear capacitance signal according to any one of claims 1-9, characterized in that, The system includes: A capacitive sensor assembly, comprising at least one excitation electrode and multiple sensing electrodes; The signal excitation module is configured to apply a multi-frequency composite excitation signal to the excitation electrode; The data acquisition and processing module is configured to acquire the response signals of each sensing electrode and process them to obtain the spatial response characteristics of the capacitive sensor. The field topology identification module is configured to verify whether the gradient distribution of the spatial response characteristics conforms to the boundary conditions of Maxwell's equations. If it does not conform, the control signal excitation module iteratively calibrates the excitation signal parameters and repeats the verification until the capacitive field topology is identified. The nonlinear feature analysis module is configured to detect whether the mapping relationship between the capacitance value and the liquid level change in each spatial region exhibits monotonic continuous characteristics based on the capacitance field topology, locate non-monotonic regions and subdivide them into multiple sub-regions, and verify whether the topological connectivity between sub-regions conforms to the principle of field continuity. The mapping parameter optimization module is configured to evaluate whether the local mapping parameters of each validated region satisfy the Lipschitz continuity condition, and adjust the boundaries of regions that do not satisfy the condition and recalculate the mapping parameters. The physical reversibility verification module is configured to apply the current mapping parameters to the test capacitance signal to generate a preliminary liquid level value, perform a reverse mapping operation to convert the liquid level value back to the capacitance domain, and verify whether the reverse mapping result and the original capacitance signal satisfy the physical reversibility principle. If not, it traces the source according to the error distribution pattern and triggers the field topology identification module or the nonlinear feature analysis module to re-execute the corresponding process. The parameter solidification and linearization output module is configured to confirm that the current mapping parameter is a valid parameter and solidify it when the principle of physical reversibility is satisfied. Based on the valid parameter, the real-time acquired capacitance signal is linearized and the liquid level value is output.

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