A long-sequence internet of things sensing data compression and reconstruction method based on a mamba architecture

Abstract

The application discloses a long-sequence Internet of Things sensing data compression and reconstruction method based on a Mamba architecture, and relates to the technical field of Internet of Things, and comprises the following steps: step 1: continuously sensing signals are divided into a plurality of sampling observation windows, and are sequentially connected according to window numbers to form an innovation event sequence; step 2: the innovation event sequence is input into a Mamba encoder; event fields are sequentially connected after corresponding window head fields to form a compressed feature code stream which is sent to a cloud side; and step 3: according to a preset observation function group, each event field is converted into a Koopman observation vector with time annotation to form a sparse Koopman observation vector sequence. In the application, sparse event components and slowly changing baseline components are jointly represented in the same data structure, so that the time scale of Mamba state coding is strictly aligned with the rhythm of event occurrence, and the technical problem that the compression rate, reconstruction accuracy and terminal deployment feasibility are difficult to be considered in the prior art is solved.

Description

Technical Field

[0001] This invention relates to the field of Internet of Things (IoT) technology, and in particular to a method for compressing and reconstructing long-sequence IoT sensor data based on the Mamba architecture. Background Technology

[0002] Compression and reconstruction of long-sequence sensor data in the Internet of Things (IoT) are crucial for achieving low-power wide-area network (LPWAN) deployment, edge computing power deployment, and large-scale cloud storage. Sensor data such as temperature, humidity, pressure, liquid level, and vibration envelope generally exhibit structural characteristics of a high proportion of stable time periods, sparse events, but significant instantaneous amplitudes. If all data is uploaded to the cloud at the original sampling frequency of the analog-to-digital converter (ADC), communication bandwidth and storage costs will be occupied by a large number of redundant stable time period samples, and the battery life of the sensing terminal will be drastically shortened.

[0003] Existing processing methods can be broadly categorized into three types. The first type is transform-domain compression methods, represented by wavelet transform and discrete cosine transform. These methods achieve compression by retaining significant coefficients while discarding smaller ones in the transform domain. However, transform-domain methods have limited temporal accuracy for event location, and the quantization of sparse coefficients struggles to simultaneously account for slowly varying baselines and transient events, leading to oscillations at event edges after reconstruction. The second type is event-driven methods starting with Nyquist sampling. These methods retain only event samples after differential or threshold comparison of the original sampled sequence at the terminal. While significantly reducing the amount of uploaded data, differential methods are sensitive to quantization noise, often requiring additional de-jitter logic for stable operation. Furthermore, the discarded stationary segments cannot reconstruct the true contours of slowly varying drifts in the cloud. The third type is deep temporal modeling methods, represented by recurrent neural networks and Transformers. These methods allow the neural network to directly predict and encode the sensor sequence. These methods rely on large amounts of training data, have large model parameter scales, are difficult to deploy at the terminal, and lack interpretable temporal semantics in the inference process. While the state-space model, which has recently received widespread attention, has shown advantages in long sequence modeling, its selective scan step size is usually generated by a learnable projection layer. This not only requires training support but also fails to directly align with the physical characteristic of event sparsity in IoT sensor data, making the model's temporal scale meaning and event response relationship lack interpretability.

[0004] Therefore, in the scenario of long-sequence sensing compression and reconstruction in the Internet of Things (IoT), existing technologies have three unresolved problems: First, the slow-varying baseline and sparse event components in the stationary phase cannot be jointly represented by a unified data structure on the terminal side, leading to the easy loss of baseline drift information during cloud reconstruction; second, the lack of physical alignment between the time-scale parameters of the state-space model and the event interval makes it difficult to achieve stable deployment with low parameters and low dependencies on low-power terminals during the encoding process; and third, the cloud reconstruction process lacks a closed-loop evolution mechanism to extend discrete event features to arbitrary reconstruction time nodes, resulting in insufficient support for continuous-time reconstruction within long spatial event windows. Establishing a unified technical link across the three dimensions of event sparsity, baseline preservation, and continuous-time reconstruction has become an urgent technical problem to be solved in this field. Summary of the Invention

[0005] In view of this, the present invention provides a method for compression and reconstruction of long-sequence IoT sensor data based on the Mamba architecture. It jointly represents sparse event components and slowly varying baseline components in the same data structure, so that the time scale of Mamba state coding is strictly aligned with the rhythm of event occurrence. It also supports continuous time reconstruction of arbitrary reconstruction time nodes through a multi-channel Koopman observation function group and matrix exponential evolution. It achieves high compression ratio, high reconstruction fidelity and low power consumption terminal deployability under various working conditions such as long sequences, strong baseline drift and empty event windows. It solves the technical problem of difficulty in balancing compression ratio, reconstruction accuracy and terminal deployment feasibility in the prior art.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for compressing and reconstructing long-sequence IoT sensor data based on the Mamba architecture includes the following steps:

[0008] Step 1: Divide the continuous sensing signal into several sampling observation windows. For each sampling observation window, extract and confirm the innovative event parameter group and window baseline value, and encapsulate them into a window output record. String these records together according to the window number to form an innovative event sequence.

[0009] Step 2: Input the innovation event sequence into the Mamba encoder; the selective state scan layer uses the difference between two adjacent innovation moments as the current selective scan step size, and uses the current innovation amplitude and the current window baseline value to look up the current content adaptive injection coefficient in the two-dimensional selective modulation lookup table, and recursively obtains the hidden state vector corresponding to each innovation event parameter group; the state projection layer projects the hidden state vector onto the main scalar output value, and binds the main scalar output value with the current innovation moment as an event field. The event field is concatenated with the corresponding window header field to form a compressed feature stream and sent to the cloud side;

[0010] Step 3: Based on the preset observation function group, each event field is converted into a Koopman observation vector with time label to form a sparse Koopman observation vector sequence; on the reconstruction time axis, the reconstruction time nodes are divided according to the preset reconstruction time interval. For each reconstruction time node, a dense Koopman observation vector is obtained by selecting the baseline Koopman observation vector and matrix exponential evolution. Then, the current reconstruction signal value is obtained by the vector inner product operation of the inverse observation mapping vector. The reconstructed long sequence of IoT sensing data is arranged in the order of reconstruction time nodes.

[0011] Furthermore, in step 1, the continuous sensing signal is characterized by a window baseline component and local innovation events whose number is limited by a preset single-window event limit within each sampling observation window. On the IoT sensing terminal side, the continuous sensing signal is divided into several sampling observation windows that are connected end-to-end and have a time length equal to the preset observation window length. The continuous sensing signal within the sampling observation window is convolved with a preset smoothing sampling kernel in the time domain to obtain a kernel response signal. The kernel response signal is uniformly discretized according to a preset basic sampling period to obtain a kernel response discrete sequence. The preset smoothing sampling kernel is an impulse response function with a time support length less than the preset observation window length and a value range greater than or equal to 0. A first-order forward difference sequence is calculated for the kernel response discrete sequence. In the first-order forward difference sequence, the positions where the signs of two adjacent elements change from positive to negative and from negative to positive are jointly marked as sign flip positions. For each sign flip position, the position with the larger absolute value of the element between the sign flip position and the immediately following position in the kernel response discrete sequence is taken as a candidate innovation position.

[0012] Further, in step 1, the arithmetic mean of all elements of the discrete kernel response sequence is recorded as the window baseline value of the sampling observation window; for each candidate innovation position, the timestamp corresponding to the candidate innovation position is recorded as the candidate innovation time, and the difference between the element value of the discrete kernel response sequence at the candidate innovation position and the window baseline value is recorded as the candidate innovation amplitude. The candidate innovation time and the candidate innovation amplitude are paired to form a candidate innovation event parameter group; the candidate innovation event parameter groups whose absolute value of the candidate innovation amplitude is greater than the preset significance threshold are arranged in ascending order of candidate innovation time, and the candidate innovation event parameter groups whose rank in the arrangement is less than or equal to the preset single-window event upper limit are taken as the confirmed innovation event parameter group; when the confirmed innovation event parameter group is within the sampling observation window... When the number of innovative event parameter groups is greater than or equal to 1, the number of confirmed innovative event parameter groups is recorded as the event count. The window number, window start time, window baseline value, event count, and all confirmed innovative event parameter groups of the sampling observation window are encapsulated together as the window output record. When the number of confirmed innovative event parameter groups in the sampling observation window is equal to 0, the midpoint time of the sampling observation window is used as the empty window occupancy innovation time, and the preset empty window occupancy amplitude is used as the empty window occupancy innovation amplitude. The two are paired to form 1 empty window occupancy innovative event parameter group. The event count is recorded as 0, and the window number, window start time, window baseline value, event count, and empty window occupancy innovative event parameter group of the sampling observation window are encapsulated together as the window output record.

[0013] Furthermore, in step 2, the Mamba encoder consists of two components, a selective state scan layer and a state projection layer, connected sequentially. The selective state scan layer is pre-configured with a diagonal state transition matrix, an input mapping vector, an initial hidden state vector, and a two-dimensional selective modulation lookup table. The diagonal state transition matrix is ​​a diagonal square matrix with a dimension equal to the preset state dimension, and the elements at the diagonal positions are a preset set of negative real numbers. The input mapping vector is a column vector with the number of components equal to the preset state dimension. The initial hidden state vector is a column vector with the number of components equal to the preset state dimension and all components having a value of 0. The first dimension of the two-dimensional selective modulation lookup table is the amplitude interval index, which defines the amplitude intervals that are sequentially adjacent and completely cover the preset amplitude domain. The second dimension is the baseline interval index, which defines the baseline intervals that are sequentially adjacent and completely cover the preset baseline domain. The two-dimensional selective modulation lookup table pre-assigns a positive real number as a content adaptive injection coefficient for each combination unit of amplitude interval and baseline interval.

[0014] Furthermore, in step 2, the selective state scanning layer processes the innovation event parameter groups carried within the window output records in the innovation event sequence from front to back. For the current innovation event parameter group being processed, the innovation time, innovation amplitude, and window baseline value in the window output record of the current innovation event parameter group are recorded as the current innovation time, current innovation amplitude, and current window baseline value, respectively. When the current innovation event parameter group is at the beginning of the innovation event sequence, the current innovation time is subtracted from the window start value in the window output record of the current innovation event parameter group. The difference obtained at each time step is used as the current selective scan step size; when the current innovation event parameter group ranks greater than or equal to 2 in the innovation event sequence, the difference obtained by subtracting the innovation time of the previous innovation event parameter group from the current innovation time is used as the current selective scan step size; the combined unit that contains both the absolute value of the current innovation amplitude and the current window baseline value is searched in the two-dimensional selective modulation lookup table, and the content adaptive injection coefficient corresponding to the combined unit is recorded as the current content adaptive injection coefficient; when the current innovation event parameter group is a window occupant innovation event parameter group, the current content adaptive injection coefficient is set to the preset window injection constant.

[0015] Furthermore, in step 2, zero-order preserved discretization is performed on the diagonal structure state transition matrix using the current selective scan step size as the discretization time interval to obtain the current discrete state transition matrix of the diagonal structure; zero-order preserved discrete input integration is performed on the input mapping vector based on the current selective scan step size and the diagonal structure state transition matrix to obtain the current discrete input mapping vector; matrix-vector multiplication is performed on the hidden state vector corresponding to the first innovation event parameter group using the current discrete state transition matrix to obtain the current state recursive vector; for the first current innovation event parameter group, the initial hidden state vector is used in the matrix-vector multiplication to obtain the current state recursive vector; scalar vector multiplication is performed on the current discrete input mapping vector using the current content adaptive injection coefficient as the scalar coefficient to obtain the current input contribution vector; the current state recursive vector and the current input contribution vector are added according to the corresponding component positions to obtain the hidden state vector corresponding to the current innovation event parameter group.

[0016] Furthermore, in step 2, the state projection layer pre-configures an output mapping vector with the number of components equal to the preset state dimension; for each hidden state vector corresponding to an innovation event parameter group, the hidden state vector and the output mapping vector are subjected to a vector inner product operation to obtain a principal scalar output value, which is bound to the current innovation moment to form an event field; according to the arrangement order of window output records in the innovation event sequence, the window number, window start time, window baseline value and event quantity of each window output record are encapsulated into a window header field, and the event fields corresponding to all innovation event parameter groups inside the window output record are concatenated immediately after the window header field to form the compressed segment corresponding to the window output record; all compressed segments are concatenated in ascending order of window number to obtain a compressed feature stream, which is sent from the IoT sensing terminal to the cloud side.

[0017] Furthermore, in step 3, five Koopman observation channels are pre-configured on the cloud side. These five channels correspond sequentially to five deterministic observation functions in a pre-defined observation function group. The pre-defined observation function group consists of five deterministic observation functions: identity observation function, time interval coupled observation function, baseline coupled observation function, front-to-back difference observation function, and baseline pass-through observation function. The output of the identity observation function is equal to the principal scalar output value in the current event field. The output of the time interval coupled observation function is equal to the product of the principal scalar output value in the current event field and the difference between the innovation time in the current event field and the innovation time in the previous event field. The output of the baseline coupled observation function is equal to the product of the principal scalar output value in the current event field and the window baseline value in the window header field to which the current event field belongs. The output of the front-to-back difference observation function is equal to... The difference between the main scalar output value in the current event field and the main scalar output value in the previous event field; the output of the baseline pass-through observation function is equal to the window baseline value in the window header field to which the current event field belongs; the preset Koopman observation dimension is 5; further, the Koopman linear evolution operator matrix and the inverse observation mapping vector are pre-configured on the cloud side. The Koopman linear evolution operator matrix is ​​a square matrix with a dimension equal to the preset Koopman observation dimension; the inverse observation mapping vector is a column vector with a number of components equal to the preset Koopman observation dimension. The components in the inverse observation mapping vector corresponding to the Koopman observation channel position of the identity observation function and the Koopman observation channel position of the baseline pass-through observation function are all equal to 1, and the components of the other 3 Koopman observation channel positions are all equal to 0.

[0018] By adopting the above technical solutions, the present invention achieves the following beneficial effects: First, the terminal side, with the help of a preset smoothing sampling kernel, symbol flip position filtering, and saliency threshold filtering, jointly extracts and confirms the innovative event parameter group and the window baseline value within the same window output record. This allows sparse event components and slowly varying baseline components to be co-represented in the same data structure, avoiding the shortcomings of existing event-driven methods that only retain mutation samples and lose the slowly varying trend, thus providing a complete signal profile basis for continuous-time reconstruction on the cloud side. Second, the selective state scanning layer uses the difference between adjacent innovation moments as the selective scanning step size, and uses the innovation amplitude and the window baseline value to jointly look up the injection coefficient through a two-dimensional selective modulation lookup table. This strictly aligns the time scale of Mamba state encoding with the rhythm of event occurrence, and prevents the ill-conditioned phenomenon caused by the difference in baseline dimensions during numerical injection. The encoding process requires no training and has a very small parameter scale, making it easy to deploy stably on low-power IoT terminals. Furthermore, the cloud-based system constructs multi-channel Koopman observation vectors based on five deterministic observation functions: identity, time interval coupling, baseline coupling, front-to-back difference, and baseline passthrough. Through matrix exponential evolution, sparse observation points are extrapolated to arbitrary reconstruction time points. This avoids the degradation of the observation subspace caused by single-channel enhancement and achieves error self-healing capability through the event-by-event refresh mechanism of the reference observation vector. Finally, the compressed feature stream adopts a layered encapsulation structure of window header and event fields, significantly compressing the amount of communication data. Simultaneously, it maintains stable reconstruction accuracy under various adverse conditions such as long sequences, strong baseline drift, and empty event windows. This comprehensively solves the technical challenge of simultaneously achieving high compression rates, reconstruction fidelity, and terminal deployment feasibility for long-sequence sensor data in the Internet of Things (IoT). Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the joint generation process of innovation event sequence and window baseline based on finite innovation rate sampling in an embodiment of the present invention; wherein, (a) is a schematic diagram of the original sensor signal and reference baseline level within the sampling observation window; (b) is a schematic diagram of the kernel response discrete sequence and significance threshold; (c) is a schematic diagram of the first-order forward difference sequence and sign flip position; (d) is a schematic diagram of the confirmed innovation event parameter group after significance threshold screening;

[0020] Figure 2 This is a schematic diagram of the recursive evolution of the hidden state components corresponding to four different preset negative real values ​​under the diagonal structure state transition matrix in this embodiment of the invention, driven by the same set of innovative event parameters; (a) is Hidden state components of time Evolutionary curve; (b) is Hidden state components of time Evolutionary curve; (c) is Hidden state components of time Evolutionary curve; (d) is Hidden state components of time Evolution curve;

[0021] Figure 3 This is a schematic diagram comparing the results of continuous time evolution reconstruction on the cloud side in an embodiment of the present invention. Detailed Implementation

[0022] A method for compressing and reconstructing long-sequence IoT sensor data based on the Mamba architecture includes the following steps:

[0023] Step 1: Divide the continuous sensing signal into several sampling observation windows. For each sampling observation window, extract and confirm the innovative event parameter group and window baseline value, and encapsulate them into a window output record. String these records together according to the window number to form an innovative event sequence.

[0024] Step 2: Input the innovation event sequence into the Mamba encoder; the selective state scan layer uses the difference between two adjacent innovation moments as the current selective scan step size, and uses the current innovation amplitude and the current window baseline value to look up the current content adaptive injection coefficient in the two-dimensional selective modulation lookup table, and recursively obtains the hidden state vector corresponding to each innovation event parameter group; the state projection layer projects the hidden state vector onto the main scalar output value, and binds the main scalar output value with the current innovation moment as an event field. The event field is concatenated with the corresponding window header field to form a compressed feature stream and sent to the cloud side;

[0025] Step 3: Based on the preset observation function group, each event field is converted into a Koopman observation vector with time label to form a sparse Koopman observation vector sequence; on the reconstruction time axis, the reconstruction time nodes are divided according to the preset reconstruction time interval. For each reconstruction time node, a dense Koopman observation vector is obtained by selecting the baseline Koopman observation vector and matrix exponential evolution. Then, the current reconstruction signal value is obtained by the vector inner product operation of the inverse observation mapping vector. The reconstructed long sequence of IoT sensing data is arranged in the order of reconstruction time nodes.

[0026] In long-sequence sensing scenarios in the Internet of Things (IoT), continuous sensing signals often have... Two typical components exist: one is a slowly varying baseline governed by factors such as environmental temperature drift, power supply bias, and media aging; the other is a local mutation triggered instantaneously by a physical event. Uploading all samples to the cloud at equal intervals would drastically increase bandwidth and storage pressure. However, extracting only the mutation moment while discarding the baseline would result in the loss of low-frequency profiles during reconstruction, making it impossible to recover sensor data such as temperature, pressure, and liquid level, which are primarily characterized by slow trends. Therefore, this step extracts both components simultaneously at the IoT sensing terminal and co-encapsulates them in window units, enabling downstream compression encoding to retain sparse innovative events while carrying sufficient baseline information.

[0027] With a certain Taking a water immersion level sensor as an example, this sensor continuously outputs an analog liquid level voltage, which is then controlled by the terminal. A bit-level analog-to-digital converter at a speed of 1000 bps The original digitization is performed in a rhythmic manner. The terminal sets a preset observation window length equal to [a certain value] in the firmware layer. Seconds, then every time the th... The firmware triggers a window-level processing session for each original sample. Alternatively, for sensing objects with more frequent events such as vibration and current, the preset observation window length can be shortened to [missing value]. seconds or even Seconds; for slowly changing objects such as temperature and humidity, the time can be extended to... seconds or Seconds. Windows are connected end to end without overlapping, which avoids events being truncated due to crossing windows and allows window numbers to be directly used as anchor points on the timeline.

[0028] Every The first step within each sampling observation window is to perform temporal convolution with a preset smoothing sampling kernel. This step is not for noise reduction or enhancement, but rather to provide a stable platform for subsequent sign-flip position detection and saliency screening. Due to quantization noise and high-frequency jitter, the original digitized sequence exhibits numerous pseudo-sign-flip positions generated by noise jitter in its first-order forward difference sequence. If the original sequence were directly differencing, these sign-flip positions would be too numerous to use. At this point, the preset smoothing sampling kernel gathers the neighborhood energy of the signal within the window towards the vicinity of the sign-flip positions, making the truly event-driven main peak prominent at the difference sign level, while the pseudo-peaks driven by quantization noise are naturally flattened due to insufficient energy. This is the core consideration behind convolution before differencing.

[0029] Preset smoothing sampling kernels can be selected in engineering. B-spline kernels, Gaussian kernels, or symmetric triangular kernels. For Second window For example, in the case of water immersion level of the sample, a suitable choice is that the time support length is equal to The symmetrical triangular kernel of milliseconds, after normalization, shows a peak at the midpoint of the time support and decays to the two ends. The reason for choosing a triangular kernel instead of a rectangular kernel is that a rectangular kernel has significant sidelobes in the frequency domain, which would introduce high-frequency noise from outside the window into the response; while a triangular kernel is equivalent to... The self-convolution of a rectangular kernel results in faster attenuation of its frequency domain sidelobes. The value range is greater than or equal to... This constraint is crucial: if the preset smoothing sampling kernel has a negative value, the kernel response signal after convolution may generate additional zero-crossing points in the stationary segment, thus obscuring the physical meaning of the sign-flipping position. After convolution, uniform discretization is performed according to a preset basic sampling period to obtain a discrete sequence of kernel responses. This preset basic sampling period is usually consistent with the sampling period of the original analog-to-digital converter, as in the water immersion level example. Milliseconds. Optionally, if the terminal's computing power is limited, it is also permissible to preset the basic sampling period to be a fraction of the original analog-to-digital converter's sampling period. times or This is to reduce the overhead of subsequent difference and table lookup.

[0030] Discrete sequence of nuclear response of Forward difference sequence Calculate using the following formula: ;in The position number in the discrete sequence of the kernel response, with a value ranging from... This reduces the length of the discrete sequence in the kernel response. The integer that stops. Represents the first discrete sequence of the kernel response. The position and the next one The difference between elements at each position. When Greater than and Less than When, it means that the discrete sequence of the nuclear response is at position The surrounding area experienced a transition from rising to falling; at this point, the position... With position Commonly Belongs to The sign is flipped from positive to negative at the beginning; conversely, when... Less than and Greater than At that time, it belongs to The sign flips at the point where the value changes from negative to positive. It's important to note that the sign flip position describes the local neighborhood of the extreme value, and the actual extreme point may not fall exactly on the same location. On the zero-crossing grid, it is more likely to be located at position and location The enclosed sub-grid interval. To correct this sub-grid offset onto the grid, the position is determined. and location The absolute values ​​of the elements in the discrete sequence of the kernel response are relatively large. One can be used as a candidate innovation position. The advantage of this approach is that it avoids the computational cost of parabolic interpolation or sub-grid refinement, while still controlling the timestamp of the true extremum within a certain range. The error range within one basic sampling period fully meets the time resolution requirements of long sequence applications in the Internet of Things.

[0031] The extraction of the window baseline value is performed using another method. An independent path. The arithmetic mean of all elements in the discrete sequence of the kernel response is used as the window baseline value for the current sampling observation window, i.e. ;in This represents the window baseline value for the current sampling observation window. The total number of elements in the discrete sequence of the kernel response. Second, Millisecond discrete period equal , For the discrete sequence of kernel response, the first... The value of each element. The reason for choosing the arithmetic mean instead of the median or sliding low-pass filter output is that the arithmetic mean has... With linear complexity and extremely low memory overhead, this method can be completed in one step on the accumulation register in a low-power IoT microcontroller without additional caching. Furthermore, the arithmetic mean is asymptotically unbiased for slow-change components; when the number of events within the window is small, the baseline estimation error is mainly carried away by the instantaneous contribution of the events themselves, and this contribution will be removed by subtraction in the subsequent calculation of candidate innovation amplitudes. Alternatively, for scenarios with very dense events where event contributions may contaminate the mean, a different approach can be adopted. percentile to The percentile truncated mean was used as a substitute.

[0032] Next, for each Candidate innovation event parameter sets are generated from candidate innovation locations. The candidate innovation time is directly taken as the timestamp corresponding to the candidate innovation location in the kernel response discrete sequence, that is, the location number multiplied by the preset base sampling period and then added to the window start time. The candidate innovation amplitude is obtained by subtracting the window baseline value from the element value of the kernel response discrete sequence at the candidate innovation location. To obtain, that is ;in For candidate innovation amplitude, These are the candidate innovation position indices retained after sub-grid correction. The significance of using the difference rather than the original value as the candidate innovation amplitude is that the difference itself removes the slowly varying baseline, directly reflecting the relative intensity of the event with respect to the current environmental level; similarly... Each event will yield the same candidate innovation magnitude under different baseline drifts, allowing the downstream significance threshold to be set uniformly across windows without changing with baseline drift. Candidate innovation moments are paired with candidate innovation magnitudes to form... A set of candidate innovation event parameters, denoted as .

[0033] refer to Figure 1 (a) is a schematic diagram showing the original sensor signal and the reference baseline level within the sampling observation window. The horizontal axis represents time. The unit is seconds, covering one complete sampling observation window, with a window length of 1 second. The vertical axis represents the original signal. The unit is volts, reflecting the original digitized sequence obtained by the analog-to-digital converter at a rate of 1000 times per second within the sampling observation window. Figure (a) shows that the signal at a slow-varying baseline near 2.0 volts is superimposed with high-frequency jitter caused by the quantization noise of the analog-to-digital converter, as well as five local abrupt changes triggered by physical events, located near 0.12 seconds, 0.28 seconds, 0.45 seconds, 0.62 seconds, and 0.80 seconds, respectively. Three of these abrupt changes point upwards, corresponding to the event excitation phase, while two downwards correspond to the event suppression phase. The horizontal dashed line indicates the reference baseline level for visual comparison, with a value of 2.0 volts. Figure (a) reveals the typical input pattern addressed by this invention: a slow-varying baseline component superimposed with several sparse local events. Directly performing differential processing on the original digitized sequence cannot effectively identify the event locations; smoothing processing is necessary first.

[0034] (b) is a schematic diagram of the discrete sequence of the kernel response and the significance threshold. The horizontal axis is the same as in Figure (a), and the vertical axis represents the kernel response. The unit is volt. Figure (b) shows the discrete kernel response sequence obtained by performing temporal convolution of continuous sensor signals with a symmetric triangular kernel with a time support length of 50 milliseconds within the sampling observation window, followed by uniform discretization at a preset base sampling period of 1 millisecond. The horizontal dashed line indicates the window baseline value obtained by taking the arithmetic mean of all elements of the kernel response discrete sequence, and the two horizontal dashed lines above and below indicate the preset significance threshold. The resulting double-sided envelope region will be used to exclude candidate innovative event parameter sets that are considered pseudo-events driven by quantization jitter. After convolution, the quantization noise is significantly flattened, and the peak values ​​corresponding to the five events are significantly highlighted, laying the foundation for subsequent sign-flip position selection.

[0035] (c) is a schematic diagram of the first-order forward difference sequence and the sign-flipped position. The horizontal axis is the same as in Figure (a), and the vertical axis represents the difference. The unit is volt, of which , This represents the position number in the discrete sequence of the kernel response. Figure (c) shows the positions of all sign flips marked with dots, i.e., satisfying... and ,or and The sign-flipping position physically corresponds to the neighborhood of the local extremum of the discrete sequence of the kernel response. It can be seen that the sign-flipping position not only appears near the 5 events, but also in the baseline fluctuation segment. This reflects that relying solely on the sign-flipping position is not enough to screen out the parameter group that confirms innovation events, and it is necessary to further combine it with the significance threshold.

[0036] Figure (d) is a schematic diagram of the confirmed innovation event parameter groups after saliency threshold screening. The horizontal axis is consistent with Figure (a), and the vertical axis represents the confirmation results, in volts. In Figure (d), the candidate innovation positions that were screened out by the saliency threshold are marked with cross symbols, and the innovation time and corresponding kernel response discrete sequence element values ​​of the five confirmed innovation event parameter groups are marked with dots and vertical line segments. The starting point of the vertical line segment is located at the horizontal line of the window baseline value, and the ending point is located at the corresponding position of the kernel response discrete sequence. The absolute value of its length is the candidate innovation amplitude. It can be seen that all five real events were retained, and the remaining candidate innovation positions caused by baseline fluctuations were successfully eliminated. The absolute value of the candidate innovation amplitude is greater than the preset saliency threshold. This condition effectively suppresses spurious events. The candidate innovation amplitude is obtained by subtracting the window baseline value from the element value of the discrete kernel response sequence at the candidate innovation location. A preset significance threshold can be uniformly set across the window. This eliminates the need for recalibration as the baseline drifts.

[0037] The saliency screening uses a preset saliency threshold. The retention condition is ,in This represents the absolute value of the candidate innovation amplitude. The purpose of taking the absolute value is to simultaneously preserve both the rising and falling edges of the event: for a rectangular pulse, the candidate innovation amplitudes corresponding to the rising and falling edges have opposite signs, but their physical meaning is the event boundary, and both should be preserved. The value of is usually taken as the standard deviation of the discrete sequence of the kernel response under static conditions. to The example of water immersion level is approximately [number] times ... to This is... Empirical extrapolation of detection rules can eliminate most of the pseudo-candidate innovation event parameter groups generated by quantization jitter while ensuring a low false alarm rate.

[0038] After filtering, the candidate innovation event parameter groups are sorted from smallest to largest according to the candidate innovation time. The parameter groups whose rank is less than or equal to the preset single-window event limit are selected as the confirmed innovation event parameter groups. (Preset single-window event limit) This is to lock the upper bound of the bitstream, so that each The amount of data generated by each window is predictable; for the water immersion level example... Pick This can cover the vast majority of natural events, including vibration examples. Available When the number of parameter groups for candidate innovation events exceeds At that time, since the candidates for innovation were already sorted in ascending order of their innovation time, their ranking was greater than [missing information]. The candidate innovation event parameter group will be naturally truncated within the current window and will not participate in subsequent coding; in fact, if the significance threshold is set reasonably, over-limit truncation will almost never occur, and it plays more of a safety role.

[0039] Once the set of innovation event parameter groups is confirmed to be generated, it must be encapsulated together with window metadata into a window output record. This exists... This is the case where the number of confirmed innovation event parameter groups within the sampling observation window is greater than or equal to [a certain number]. At that time, the number of confirmed innovation event parameter groups is recorded as the event count, and the window number, window start time, window baseline value, event count, and all confirmed innovation event parameter groups are encapsulated together. The window number is derived from... The incrementing integer is the window's position index on the timeline; the window's starting time uses a millisecond offset from a certain reference time (such as the power-on time or a certain second boundary of Coordinated Universal Time) for subsequent time alignment on the cloud side and calculation of the first and second event step size.

[0040] When the number of confirmed innovation event parameter groups within the sampling observation window equals This means the window is in a long, stable phase. In this case, if no data is encapsulated, the cloud side will encounter a content-free phase during decoding and reconstruction. The Koopman linear evolution will be unable to update the reference vector within this window, causing the reconstructed signal value to continue using the previous value. The evolution trajectory of each event leads to accumulated biases during long, stable periods. To address this, a parameter set for the "empty window" innovation event is introduced: the midpoint of the sampling observation window is taken as the empty window innovation time, and a preset empty window amplitude is taken as the empty window innovation amplitude (the preset empty window amplitude is taken in engineering). Or a constant with the same sign as the window baseline value and a very small value, for example... (V), and pair the moment of innovation in the void space with the amplitude of innovation in the void space to form a parameter group for innovation in the void space; at the same time, the number of events is recorded as This is encapsulated together with the window number, window start time, window baseline value, and empty window placeholder innovation event parameter group. The reason for choosing the midpoint of the window as the empty window placeholder innovation time instead of the window start or end time is that the midpoint time will affect the time before and after the window. The symmetrical distribution of the Koopman evolution influence of adjacent events ensures that a baseline through-observation function is obtained on the cloud side during long stationary periods. Secondary resampling prevents reconstruction errors from accumulating in one direction. The number of events is... This field semantically informs the cloud side that the current window's main scalar output value comes from the empty window placeholder innovation event parameter group, and that the baseline direct channel should be the primary driver during reconstruction, rather than completely trusting the identity channel.

[0041] All window output records are concatenated in ascending order of the sampling observation window number, forming an innovative event sequence that runs through the entire long sequence of IoT sensor data. This innovative event sequence physically has a two-layer structure: the outer layer, organized by window, carries slowly varying metadata such as the window number and window baseline value; the inner layer carries data within each window... to A confirmed innovation event parameter group or A set of innovative event parameters is placed in a single window. This two-layer structure preserves both the temporal precision of sparse events and the global profile of the baseline, providing the data foundation for subsequent Mamba state encoding and Koopman continuous-time reconstruction to simultaneously drive event-driven discrete recursion and baseline-driven linear evolution.

[0042] When the innovative event sequence reaches the Mamba encoder, its outer structure is already a sequence of window output records arranged in ascending order of window number, and the inner layer is... The records carried in each window output One or more confirmed innovation event parameter groups, or in the absence of a window of opportunity. Each window holds a placeholder for the innovative event parameter set. The Mamba encoder does not directly consume data on a window-by-window basis; instead, within the selective state scan layer, it flattens the window-level encapsulation structure into an event-by-event recursive flow: the scan layer sequentially traverses each window's output record and then processes all the innovative event parameter sets carried within each record, ensuring the state recursion chain remains intact at the event level and is not interrupted by cross-window operations. The direct benefit of this flattened traversal is that when… The events are exactly adjacent When at the intersection of the windows, its front Bit event and after Bit events may come from different windows, but the hidden state vector can still flow naturally along the time sequence, avoiding the loss of long-range dependencies caused by window truncation.

[0043] For the current innovation event parameter group being processed, the scanning layer first reads the innovation time and innovation magnitude from it, and then reads the window baseline value from the window output record where the current innovation event parameter group is located. Each of these is bound to an internal cache variable, which is recorded as the current innovation moment. Current innovation amplitude and the current window baseline value .this Each scalar constitutes the source of all content for the scanning layer in this step. In actual engineering implementation, the current moment of innovation... use Represented as a bit-integrity or double-precision floating-point number, in milliseconds, to accommodate continuous time spans of hours to days in long-sequence IoT scenarios; current innovation amplitude Compared with the current window baseline value This is consistent with the dimensions of the sensor output; for example, in the case of water immersion level, both are measured in volts.

[0044] The logic for calculating the current selective scan step size depends on the position of the current innovation event parameter group within the innovation event sequence. For the current innovation event parameter group that is at the beginning of the innovation event sequence, the terminal has no preceding... The innovation event parameter group can be used as a reference. At this point, the difference between the current innovation time and the window start time in the output record of the window containing the current innovation event parameter group is selected as the current selective scan step size. ;in This is the current selective scan step size. For the current moment of innovation, This represents the window start time in the output record of the window containing the current innovation event parameter group. The window start time is used as the starting point for the first event because it is itself the left-hand anchor point of the entire sampling observation window on the time axis. Choosing it as the starting point ensures that the selective scan step size of the first event has a clear physical meaning—it is equal to the relative occurrence time of the first event within its window. If the window end time or the window midpoint time were used instead, the selective scan step size would become negative or have inconsistent meanings, violating the monotonically forward assumption of zero-order discretization. For events ranking greater than or equal to... The current innovation event parameter group has a previous For the innovation event parameter group, directly take the current innovation moment minus the previous one. The difference obtained from the innovation moment in the innovation event parameter group is used as the current selective scan step size, i.e. ;in For the front The innovation moment in the parameter set of the innovation events. This event-by-event differencing yields the current selective scan step size, which directly reflects the rhythm of physical events: the denser the events, the more frequent the occurrence. The smaller the value, the more rapidly the hidden state vector is recursively calculated; the sparser the events, the more efficient the recursion. The larger the value, the longer the hidden state vector decays on the time axis.

[0045] Will The core consideration that distinguishes this approach from existing Mamba implementations is that it directly binds to physical event intervals, rather than allowing them to become a quantity generated by a learnable linear layer. Conventional Mamba... Each input token is computed through a projection layer. This process relies on a large amount of training data; however, in the context of long-sequence sensing compression in the Internet of Things, the event interval itself is the most natural time scale, and using the event interval as... It removes the dependence on training data and also makes It has an interpretable physical meaning and does not require additional parameters when deployed to the terminal side, greatly reducing storage overhead.

[0046] The acquisition of the current content adaptive injection coefficients relies on a two-dimensional selective modulation lookup table. The lookup table is located in the [missing information - likely a specific location or section]. Indexed by amplitude range on the dimension, at the 1st... The amplitude interval is indexed by the baseline interval. The amplitude interval is defined by taking values ​​within a predefined amplitude universe. Interval boundary points Arranged in ascending order, forming A series of consecutive, adjacent amplitude intervals that completely cover the preset amplitude domain. For the water immersion level example, the preset amplitude domain can be taken from... to Fu, Desirable The dividing point can be taken This involves using a geometrically proportional grid to allow for finer differentiation of small-amplitude events, while large-amplitude events are merged into a coarser grid. The baseline interval is defined similarly, taking values ​​on a predefined baseline universe. The interval boundary points constitute A series of consecutive, adjacent baseline intervals that completely cover the preset baseline domain, in engineering... Commonly used to Each of the two-dimensional selective modulation lookup tables The combination unit of amplitude range and baseline range is pre-specified. A positive real number is used as the content adaptive injection coefficient, and in engineering, its value range is usually set to [value range]. to Between these parameters, the terminal and the cloud distribute the data once according to the factory default values ​​before deployment, and the terminal accesses it directly using a hard lookup table after deployment.

[0047] The table lookup process is as follows: Take the absolute value of the current innovation amplitude to obtain... , in the Binary search is used to determine the dimension. The index of the amplitude range it falls into; the baseline value of the current window. In the The index of the baseline interval into which it falls is determined in the same way on the dimension; The index combination is used as the key to read the positive real number stored in the combination unit in the two-dimensional selective modulation lookup table, which serves as the adaptive injection coefficient for the current content. Compared to directly letting and Multiplication is a simple way to use injection coefficients, and table lookup solves the problem. One key engineering problem: First, when Approaching At that time, direct multiplication will compress the injected terms into a minimum value, so that even if Significant events can hardly drive hidden state vector updates, and event information is unnecessarily obscured; secondly, different physical quantities of sensors... and Due to differences in units and numerical ranges, direct multiplication is difficult to reuse across sensor types. However, a lookup table method discretizes the numerical relationship into intervals, making it easier to perform the same multiplication. The lookup table can be adapted to different sensors by adjusting the interval boundary points, significantly enhancing portability. In cases where the current innovation event parameter group is a placeholder innovation event parameter group, the current content adaptive injection coefficient is directly set to the preset placeholder injection constant. In engineering Usually taken Or a very small positive real number (such as The purpose of setting the default empty window injection constant is to prevent the amplification of the fake amplitude of the innovative event parameter group occupied by the empty window during the long-term stable period, so that the hidden state vector has a natural decay trend during the stable period, thereby dominating the reconstruction output in the cloud-side baseline direct channel.

[0048] Pre-configured diagonal structure state transition matrix for selective state scan layer yes The number of elements is a diagonal matrix whose dimensions are equal to the preset state dimensions, and the elements at the diagonal positions are preset. Group of negative real numbers ,in For the preset state dimension, in engineering Commonly used , or Taking negative real numbers is to ensure that each Each state component decays naturally without the injection of new events, which is consistent with the objective fact that physical events are gradually forgotten over time; to Arranged in ascending order: This geometric progression allows the state vector to correspond to memories at different time scales at different components. Corresponding to slow-changing memories ranging from seconds to minutes, components Corresponding to millisecond-level instantaneous response, with overall coverage of nearly The time scale is orders of magnitude larger. The biggest advantage of a diagonal structure compared to a full matrix is ​​that the zeroth order matrix retains its diagonal shape after discretization, and subsequent matrix-vector multiplication operations can degenerate into component-wise multiplication. The computation of each component can be fully parallelized, making it particularly suitable for fixed-point computation on low-power IoT terminals.

[0049] The zero-order preserved discretization operation transforms the continuous-time state-space equation into a discrete recursion between event moments. This is due to the current selective scan step size. Depending on the event, discretization must be performed again for each event. For a diagonal structure state transition matrix, the zeroth-order preserved state transition matrix is ​​the current discrete state transition matrix of the diagonal structure obtained after discretization. can be ; given, among which The current discrete state transition matrix is ​​represented in the th order. Elements at diagonal positions, The state transition matrix of the diagonal structure is in the th... Preset negative real numbers at diagonal positions, This represents the natural exponential function. Because... For negative real numbers, Always in to Within the open interval, the recursive process of the hidden state vector is guaranteed to be stable.

[0050] Perform a zeroth-order discrete-input-preserving integral operation on the input mapping vector to obtain the current discrete input mapping vector. Its first Each component Depend on ; given, among which For the input mapping vector at the th Preset components at each position. This discrete input mapping relationship comes from a continuous-time system. ; in the interval Internal input The closed-form solution that keeps the expression constant, where The hidden state vector represents the first... Each component in continuous time The value at that location, Indicates the injection intensity over continuous time The value at that point. Compared to the simplified approach of only discretizing the state transition matrix while retaining the continuous-time input terms, the above zero-order discrete-input-preserving integral more rigorously reflects the cumulative effect of events within the interval, making the recursion error of the hidden state vector vary with... It increases but is bounded by an upper bound, and will not deviate from the true value due to long time intervals.

[0051] Next, we perform state recursion. Using the current discrete state transition matrix, we iterate through the previous... Hidden state vector corresponding to the parameter set of the innovation event The current state recursive vector is obtained by performing matrix-vector multiplication. For diagonal structures, The Each component is composed of Given, among which For the front The hidden state vector corresponding to the parameter set of the innovation event is the first... Each component. For the parameter group of the current innovation event that ranks first, the initial hidden state vector participates in this matrix-vector multiplication operation, and all components of the initial hidden state vector take the value of... Therefore, at this time All components are also The hidden state vector evolves forward from zero. Then, coefficients are adaptively injected based on the current content. The current input contribution vector is obtained by performing a scalar vector product operation on the current discrete input mapping vector for the scalar coefficients. ,Right now Finally, and The hidden state vector corresponding to the parameter set of the current innovation event is obtained by adding the components according to their positions. ,Right now Hidden state vector It was then saved to the internal cache as a next... During the next iteration .

[0052] The state projection layer is responsible for compressing the hidden state vector into a scalar output value, enabling it to enter the compressed feature stream. The state projection layer is pre-configured. The output mapping vector has a number of components equal to the preset state dimension. All components are distributed to the terminal and cloud at once according to factory preset values ​​before deployment. The components of the output mapping vector can be taken as follows in engineering: This isotropic uniform weight can also be taken as decreasing with the preset state dimension index. This emphasizes the geometric decay weights of slowly varying memory channels. (Main scalar output value) It is obtained by performing a vector dot product operation between the hidden state vector and the output mapping vector, i.e. ;in Main scalar output value, For the output mapping vector at the th Preset components at each position, The hidden state vector corresponding to the current innovation event parameter set is in the th... The value at each component position. Main scalar output value. It integrates state components across multiple time scales, preserving both the ability to describe the instantaneous intensity of events and the decaying residue of historical events at the current moment.

[0053] The compressed feature stream employs a hierarchical encapsulation structure of window header fields and event fields. Each event is encapsulated according to the order of window output records in the innovation event sequence. The window number, window start time, window baseline value, and number of events for each window's output record are encapsulated as follows: Each window header field. In binary packing format, the window number uses... Bit unsigned integer occupies Bytes, window start time uses Double-precision floating-point number accounts for Bytes, window baseline value adopted Single-precision floating-point numbers account for Bytes, number of events Bit unsigned integer occupies bytes, total Byte. For each The event fields corresponding to each innovation event parameter group bind the main scalar output value to the current innovation moment; the main scalar output value adopts... Single-precision floating-point numbers account for The current innovation moment is expressed in milliseconds offset relative to the start time of the window. Bit unsigned integer occupies bytes, total Bytes. The event fields corresponding to all innovative event parameter groups within a window's output record are concatenated after its window header field to form the compressed segment corresponding to that window's output record. Concatenating all compressed segments in ascending order of window number yields the compressed feature stream. The advantage of this layered encapsulation structure of window header and event fields is that slowly changing metadata at the window level only appears in the window header field. Even if Even if multiple events exist within a single window, they will not be transmitted repeatedly, compared to each A flat encapsulation method that carries all metadata for each event can reduce the bitstream size. percentage to Percentage. This compressed feature stream is transmitted from the IoT sensor terminal to the cloud via channels such as Narrowband IoT, Low Power Wide Area Network, or Bluetooth Low Energy.

[0054] refer to Figure 2There are seven innovative event parameter groups that occur sequentially at 0.10 seconds, 0.22 seconds, 0.37 seconds, 0.52 seconds, 0.68 seconds, 0.80 seconds, and 0.92 seconds. The event symbols are numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 1 ... , , , , , Alternating arrangement, with corresponding content adaptively injected coefficients The values ​​are 1.2, 0.9, 1.4, 0.7, 1.0, 0.8, and 1.1, respectively. The four sub-graphs correspond to the diagonal structure state transition matrix at the [missing value]. Preset negative real numbers at each diagonal position Pick , , and The situation is as follows. (a) is... Hidden state components of time Evolution curve. The horizontal axis represents time. The unit is seconds. The vertical axis represents the hidden state components. .exist Below, the continuous-time decay rate is extremely fast, and the diagonal elements of the discrete state transition matrix obtained after zero-order discrete preservation are... For common event intervals The minimum value is taken so that the latent state component brought in by the previous innovation event parameter set decays to near zero almost before the next innovation event parameter set arrives. As can be observed in Figure (a), each event injection generates a sharp, pulse-like spike, which rapidly returns to zero within tens of milliseconds. This channel therefore primarily handles the direct response to the instantaneous intensity of events, corresponding to a millisecond-level memory timescale, and there is no long-range coupling between events. (b) is... Hidden state components of time Evolution curves. Compared to Figure (a), the time decay rate slows down significantly. The peak width brought by each event injection expands to the order of one event interval, and the hidden state components between two adjacent events still retain considerable tail amplitudes, thus superimposing with the next event injection. Figure (b) depicts the memory channel at the hundred-millisecond level, providing an information carrier for medium-timescale coupling between events. (c) is... Hidden state components of time Evolution curve. The decay rate slows further, the decay between adjacent events is very limited, and the hidden state components show a clear cumulative trend. The injection contributions of multiple events gradually superimpose along the time axis, forming a directional fluctuation envelope. Figure (c) corresponds to a second-level memory channel, mainly responsible for encoding the cumulative effect of events. (d) is... Hidden state components of time Evolution curve. At this value, the decay rate is extremely slow; almost no visible decay occurs within a 1-second sampling observation window, and the latent state component is approximately equal to the sum of all events according to the corresponding injection coefficient signs. Figure (d) corresponds to a long-term memory channel on the order of tens of seconds or even minutes, which undertakes the function of preserving slow-changing trends.

[0055] The decoding process on the cloud side is performed in reverse order. The cloud side first parses the compressed feature stream in the order it is received, identifies the fixed-length block of the window header field, and then reads the corresponding number of event fields immediately following the number of events in the window header field. This restores the compressed feature stream to several window header fields and the corresponding number of event fields following each event. The memory data structure of the event fields is arranged after the window header fields. Next, we proceed to continuous-time evolution reconstruction.

[0056] Based on the preset observation function set, the cloud side performs observations on each... Calculate each event field Each observation component is stacked in the order corresponding to the Koopman observation channels. Koopman observation vectors The preset observation function set consists of identity observation functions, time interval coupled observation functions, baseline coupled observation functions, front-to-back difference observation functions, and baseline through observation functions. Composed of deterministic observation functions, The Koopman observation channels are sequentially connected to... Each deterministic observation function corresponds one-to-one. The identity observation function is in the th... The primary scalar output value in the current event field is output on each Koopman observation channel, denoted as... ;Time interval coupled observation function in the first Output the principal scalar output value in the current event field on each Koopman observation channel. With the innovation moment in the current event field Subtract before Innovation Moment in Bit Event Field The product of the differences obtained, i.e. Baseline coupled observation function at the 1st Output the principal scalar output value in the current event field on each Koopman observation channel. The window baseline value in the window header field to which the current event field belongs. The product of, i.e. The difference observation function before and after the first observation is in the first... Output the principal scalar output value in the current event field on each Koopman observation channel. Subtract before Main scalar output value in the bit event field The resulting difference, i.e. The baseline through-observation function is at the 1st The window baseline value in the header field of the window containing the current event field is directly output on each Koopman observation channel. ,Right now . The preset Koopman observation dimension for each Koopman observation channel is equal to... Choose from identity, time interval coupling, baseline coupling, front-to-back difference, and baseline pass-through. The observation channels constitute the Koopman observation function set, which is to make the observation vector It also covers the instantaneous intensity of the event, the temporal density of the event, baseline drift, the trend of event changes, and the baseline itself. A complementary dynamic dimension, avoiding a single The observation subspace degradation problem caused by fixed vector lifting of the channel.

[0057] For the event field that ranks first in the compressed feature bitstream, since there is no preceding... Bit event field, time interval coupled observation function Replace it with the window start time in the window header field to which the current event field belongs, and directly set the output of the before and after difference observation functions to 0. . All boundary treatments are to avoid the lack of a preceding boundary. This undefined behavior, stemming from the bit event field, allows the Koopman observation vector of the first event to legally enter the subsequent matrix exponential evolution process. Each Koopman observation vectors With the innovation moment in the corresponding current event field Binding formation A set of time-labeled Koopman observation vectors are arranged in ascending order of innovation time to form a sparse Koopman observation vector sequence.

[0058] Pre-configured Koopman linear evolution operator matrix on the cloud side It is a square matrix whose dimension is equal to the preset Koopman observation dimension, and whose dimension is... The specific values ​​are sent out by the terminal and the cloud according to the factory preset values ​​before deployment. In engineering practice, values ​​such as... This sparse, diagonally dominant form, where the main diagonal elements to Corresponding to the independent attenuation rate of each Koopman observation channel, off-diagonal elements Provides weak coupling between channels. The reason why the main diagonal element is chosen to be cross Negative values ​​of several orders of magnitude are intended to make Each observation channel corresponds to a different time scale during reconstruction: the baseline through channel... The attenuation is extremely slow, corresponding to a long-term baseline drift; the differential channels before and after... The fastest decay corresponds to the instantaneous response to a sudden event. Inverse observation mapping vector. It is a column vector with the number of components equal to the preset Koopman observation dimension, and the dimension is... The component corresponding to the Koopman observation channel position of the identity observation function takes the value equal to The component value corresponding to the Koopman observation channel position of the baseline through observation function is equal to... ,the remaining The component values ​​at each Koopman observation channel position are all equal to The design of this inverse observation mapping vector aims to ensure that the final reconstructed signal value is a linear superposition of the identity channel and the baseline through channel, meaning that the event-driven component and the baseline-driven component each account for a portion of the signal. This provides a degree of freedom that avoids both the loss of event information and the loss of baseline profile during long, stable segments.

[0059] Reconstruction timeline with preset reconstruction intervals Divide the reconstruction time nodes evenly. The value is usually consistent with the sampling period of the original analog-to-digital converter at the terminal, for example, in the water immersion level example. Milliseconds, so that the reconstructed sequence can be directly aligned with the original sampling raster; for storage-constrained scenarios, It can be relaxed to milliseconds or Milliseconds, forming downsampling reconstruction. For each Reconstruction time nodes First, determine the current baseline Koopman observation vector. If the innovation time is later than or equal to the first innovation time in the sparse Koopman observation vector sequence, then search for innovation times earlier than or equal to the first innovation time in the sparse Koopman observation vector sequence. Furthermore, the Koopman observation vector with the largest innovation time and time label is used as the current baseline Koopman observation vector. The direct advantage of choosing the Koopman observation vector with the largest innovation moment as the baseline is that it minimizes the current evolution time between the baseline and the reconstructed time point, minimizes the power of the matrix exponential evolution term, minimizes numerical error, and ensures that the physically most recent event has the strongest influence on the current moment. Earlier than the first innovation moment in the sparse Koopman observation vector sequence, no events have occurred in the initial segment of the long sequence of IoT sensor data. At this time, a baseline cannot be obtained from the sparse Koopman observation vector sequence. Instead, an initial Koopman observation vector is constructed: the components in the initial Koopman observation vector corresponding to the Koopman observation channel position of the identity observation function and the Koopman observation channel position of the baseline through observation function are all equal to the window baseline value in the first window header field, and the remaining... The component values ​​at each Koopman observation channel position are all equal to The initial Koopman observation vector is bound to the window start time in the first window header field and used as the current baseline Koopman observation vector. Injecting both the identity channel and the baseline through channel into the window baseline value simultaneously is to ensure that the reconstructed signal value in the initial segment immediately approaches the slowly varying baseline rather than the zero line, thus avoiding a step-like baseline jump at the beginning of long sequences of IoT sensor data.

[0060] Based on the current reconstruction timeline Subtract the time of the current benchmark Koopman observation vector binding The resulting difference is used as the current evolution duration. .by Perform scalar matrix multiplication on the Koopman linear evolution operator matrix to obtain the current exponential base matrix. ,right Performing matrix exponentiation yields the current linear evolution matrix. ,in This refers to the matrix exponential function. Matrix exponentiation can be achieved using the Pad approximation combined with the scaling method. 3D matrix adopts The Padre approximation can achieve double-precision machine error, with the number of floating-point operations in a single matrix exponentiation operation on the order of hundreds, easily achieving sub-millisecond processing time on conventional cloud servers. It performs matrix-vector multiplication on the current baseline Koopman observation vector using the current linear evolution matrix. This yields the dense Koopman observation vector corresponding to the current reconstruction time point. .

[0061] Ultimately, for each The current reconstructed signal value is obtained by performing a vector dot product operation on a dense Koopman observation vector and an anti-observation mapping vector. ;in To rebuild time nodes The current reconstructed signal value on, For the inverse observation mapping vector at the th Preset components at each position, For dense Koopman observation vectors in the first... The values ​​of each component position are determined. Arranging all the currently reconstructed signal values ​​in ascending order of reconstruction time points forms the long sequence of reconstructed IoT sensor data.

[0062] The entire cloud-side evolution and reconstruction process has An additional engineering advantage: First, matrix exponential evolution extrapolates from the benchmark Koopman observation vector of the most recent events, rather than performing a global integration starting from zero. This local extrapolation method has error self-healing properties—every... The arrival of each new event refreshes the baseline Koopman observation vector. The accumulated error from segment evolution will be recalibrated; secondly, the inverse observation mapping vector is only a linear combination. With a single Koopman observation channel, the computational overhead is extremely low. For long-sequence IoT sensor data of arbitrary length, the time required for single-point reconstruction on the cloud side is independent of the length, and depends only on the event density and reconstruction time node density in the sparse Koopman observation vector sequence. This has direct value for large-scale IoT deployment.

[0063] As an optional implementation, when the cloud side needs to quantify the uncertainty of the reconstruction results, it can be done in each of the sparse Koopman observation vector sequences. At the secondary reference switching point, a conformal prediction error band is added, and the reconstruction residuals under each event reference are used as an inconsistency fraction sequence. The reconstruction signal value intervals with upper and lower bounds of the reconstruction signal value band are output along the reconstruction time nodes. When the computing power on the terminal side is further limited, the preset state dimension of the diagonal structure state transition matrix can also be used. Depend on Compress to Only retain the corresponding millisecond, second, minute, and hourly values. Each timescale component sacrifices timescale coverage in exchange for a reduction in memory footprint. Percentage; when processing multi-channel synchronous sensor data (such as triaxial accelerometers), it can be per Each physical channel executes this method independently, and then the channels are combined into a multi-channel reconstructed signal value sequence on the cloud side. The preset observation window length, preset saliency threshold, and preset single-window event limit of each physical channel can be configured independently according to its event rhythm, so as to realize the unified compression and reconstruction of heterogeneous sensor clusters.

[0064] Accordingly, in step 3, the cloud side parses the compressed feature stream in the order of reception, restoring the compressed feature stream into several window header fields and event fields arranged immediately after the window header fields; for each event field, five observation components are obtained according to the calculation rules of the five preset observation functions, and the five observation components are stacked into a Koopman observation vector in the order corresponding to the Koopman observation channels. The Koopman observation vector is bound to the innovation time in the current event field to form a Koopman observation vector with time annotation; for the event field at the beginning of the compressed feature stream, the innovation time of the first event field in the time interval coupling observation function is replaced with the window start time in the window header field to which the current event field belongs, and the output of the preceding and following difference observation functions is set to 0; all Koopman observation vectors with time annotation are arranged in ascending order of innovation time to form a sparse Koopman observation vector sequence.

[0065] In step 3, the reconstruction timeline is evenly divided into reconstruction time nodes at a preset reconstruction time interval. For each reconstruction time node, if the reconstruction time node is later than or equal to the first innovation moment in the sparse Koopman observation vector sequence, the Koopman observation vector with the largest innovation moment and time label in the sparse Koopman observation vector sequence, whose innovation moment is earlier than or equal to the current reconstruction time node, is used as the current baseline Koopman observation vector. If the reconstruction time node is earlier than the first innovation moment in the sparse Koopman observation vector sequence, an initial Koopman observation vector is constructed. The component values ​​of the Koopman observation channel position corresponding to the identity observation function and the Koopman observation channel position corresponding to the baseline through observation function in the initial Koopman observation vector are all equal to the window baseline value in the first window header field, and the component values ​​of the other three Koopman observation channel positions are all equal to 0. The Koopman observation vector is bound to the window start time in the first window header field and used as the current baseline Koopman observation vector. The difference between the current reconstruction time node and the time bound to the current baseline Koopman observation vector is used as the current evolution duration. The current evolution duration is used as the scalar coefficient to perform a scalar matrix product operation on the Koopman linear evolution operator matrix to obtain the current exponential base matrix. The current exponential base matrix is ​​then subjected to a matrix exponent operation to obtain the current linear evolution matrix. The current linear evolution matrix is ​​then subjected to a matrix-vector product operation on the current baseline Koopman observation vector to obtain the dense Koopman observation vector corresponding to the current reconstruction time node. For each dense Koopman observation vector, the dense Koopman observation vector and the anti-observation mapping vector are subjected to a vector inner product operation to obtain the current reconstructed signal value. All reconstructed signal values ​​are arranged in ascending order of reconstruction time nodes to form the reconstructed long sequence of IoT sensing data.

[0066] The horizontal axis represents time. The unit is seconds, covering a 2-second long sequence of IoT sensor data from 0 seconds to 2 seconds. The vertical axis represents signal amplitude, in volts. Three key data trajectories are plotted in the figure: the first is the solid line of the original long sequence of IoT sensor data; the second is the dashed line of the Koopman evolution reconstruction data; and the third is the six baseline Koopman observation points marked with dots. The original long sequence of IoT sensor data consists of a baseline component near 2.0 volts superimposed with six local events located at 0.18 seconds, 0.55 seconds, 0.95 seconds, 1.30 seconds, 1.62 seconds, and 1.85 seconds, respectively. Three events point upwards and three downwards, representing a real IoT sensing process excited by discrete events occurring on a slowly varying baseline.

[0067] refer to Figure 3 The baseline Koopman observation point is the reconstruction anchor point corresponding to the superposition of the identity observation function and the baseline through observation function for each time-annotated Koopman observation vector in the sparse Koopman observation vector sequence on the cloud side. Its position is strictly aligned with the innovation time of the six events. The Koopman evolution reconstruction data is generated by the cloud side dividing the reconstruction time axis into reconstruction time nodes at a preset reconstruction time interval. For each reconstruction time node, the time-annotated Koopman observation vector with an innovation time earlier than or equal to that reconstruction time node and the largest innovation time is found as the current baseline Koopman observation vector. The current evolution duration is then used as the reference. Perform scalar matrix multiplication on the Koopman linear evolution operator matrix to obtain the current exponential base matrix, and then perform matrix exponentiation on the current exponential base matrix to obtain the current linear evolution matrix. ,in The Koopman linear evolution operator matrix is ​​used to perform a matrix-vector product operation on the current baseline Koopman observation vector to obtain the dense Koopman observation vector. Finally, a vector dot product operation is performed with the inverse observation mapping vector to obtain the current reconstructed signal value. The curve is formed by arranging the reconstruction time nodes in ascending order.

[0068] Figure 3 The evolutionary segment between two adjacent baseline Koopman observation points is further marked with arrows and text annotations. The reconstruction of this segment is entirely based on matrix exponential evolution. Complete, without transmitting any additional sampling points. It can be observed that the Koopman evolution reconstruction data and the original long-sequence IoT sensing data maintain a high degree of fit throughout the entire 2-second segment. The slowly varying baseline profile is completely restored, and the positions and amplitudes of the event's main peak and valley are accurately reproduced, with only minor detail deviations near the event peak. This fit directly verifies the strategy of linearly combining the identity observation channel and the baseline direct-through observation channel under the inverse observation mapping vector adopted in this invention. This strategy can simultaneously maintain the reconstruction capability of both the event-driven component and the baseline-driven component in long-sequence IoT sensing scenarios with sparse events, avoiding baseline loss or event annihilation phenomena that occur during single-channel reconstruction. Therefore, it provides a reasonable and quantifiable reconstruction path for the compression and reconstruction of long-sequence IoT sensing data.

[0069] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A method for compressing and reconstructing long-sequence IoT sensor data based on the Mamba architecture, characterized in that, Includes the following steps: Step 1: Divide the continuous sensing signal into several sampling observation windows. For each sampling observation window, extract and confirm the innovative event parameter group and window baseline value, and encapsulate them into a window output record. Serialize these records according to window number to form an innovative event sequence. Within each sampling observation window, the continuous sensing signal is characterized by one window baseline component and a number of local innovative events limited by a preset single-window event limit. On the IoT sensing terminal side, divide the continuous sensing signal along the time axis into several sampling observation windows with consecutive beginnings and end, and a time length equal to the preset observation window length. Perform time-domain convolution of the continuous sensing signal within each sampling observation window with a preset smoothing sampling kernel to obtain the kernel response signal, and then concatenate it according to a preset... The kernel response signal is uniformly discretized using a basic sampling period to obtain a discrete kernel response sequence. A preset smoothing sampling kernel is an impulse response function with a time support length less than a preset observation window length and a value range greater than or equal to 0. A first-order forward difference sequence is calculated for the kernel response discrete sequence. In the first-order forward difference sequence, the positions where two adjacent elements change sign from positive to negative and vice versa are jointly marked as sign flip positions. For each sign flip position, the position with the larger absolute value between the sign flip position and its immediately following position in the kernel response discrete sequence is selected as a candidate innovation position. The arithmetic mean of all elements in the kernel response discrete sequence is recorded as the sampling observation window value. Window baseline value; for each candidate innovation location, the timestamp corresponding to the candidate innovation location is recorded as the candidate innovation time, and the difference between the element value of the kernel response discrete sequence at the candidate innovation location and the window baseline value is recorded as the candidate innovation amplitude. The candidate innovation time and the candidate innovation amplitude are paired to form a candidate innovation event parameter group; the candidate innovation event parameter groups whose absolute value of the candidate innovation amplitude is greater than the preset significance threshold are arranged in ascending order of candidate innovation time, and the candidate innovation event parameter groups whose rank in the arrangement is less than or equal to the preset single-window event upper limit are taken as the confirmed innovation event parameter groups; when the number of confirmed innovation event parameter groups in the sampling observation window is greater than or equal to 1, The number of confirmed innovation event parameter groups is recorded as the event count. The window number, window start time, window baseline value, event count, and all confirmed innovation event parameter groups of the sampling observation window are encapsulated together as a window output record. When the number of confirmed innovation event parameter groups in the sampling observation window is equal to 0, the midpoint time of the sampling observation window is used as the empty window occupancy innovation time, and the preset empty window occupancy amplitude is used as the empty window occupancy innovation amplitude. The two are paired to form one empty window occupancy innovation event parameter group, the event count is recorded as 0, and the window number, window start time, window baseline value, event count, and empty window occupancy innovation event parameter group of the sampling observation window are encapsulated together as a window output record. Step 2: Input the innovative event sequence into the Mamba encoder; the Mamba encoder consists of two components, a selective state scan layer and a state projection layer, connected in series; the selective state scan layer is pre-configured with a diagonal state transition matrix, an input mapping vector, an initial hidden state vector, and a two-dimensional selective modulation lookup table; the diagonal state transition matrix is ​​a diagonal square matrix with a dimension equal to the preset state dimension, and the elements at the diagonal positions are a preset set of negative real numbers; the input mapping vector is a column vector with the number of components equal to the preset state dimension; the initial hidden state vector is a column vector with the number of components equal to the preset state dimension and all components having a value of 0; the first dimension of the two-dimensional selective modulation lookup table is the amplitude interval index, which defines the amplitude intervals that are sequentially adjacent and completely cover the preset amplitude domain; the second dimension is the baseline interval index, which defines the baseline intervals that are sequentially adjacent and completely cover the preset baseline domain; the two-dimensional selective modulation lookup table pre-defines each combination unit of amplitude interval and baseline interval. A positive real number is assigned as the content adaptive injection coefficient. The selective state scanning layer processes the innovation event parameter groups carried within the window output records in the innovation event sequence from front to back. For the current innovation event parameter group being processed, the innovation time, innovation amplitude, and window baseline value in the window output record of the current innovation event parameter group are respectively recorded as the current innovation time, current innovation amplitude, and current window baseline value. The selective state scanning layer uses the difference between two adjacent innovation times as the current selective scanning step size, and uses the current innovation amplitude and current window baseline value to look up the current content adaptive injection coefficient in the two-dimensional selective modulation lookup table, recursively obtaining the hidden state vector corresponding to each innovation event parameter group. The state projection layer projects the hidden state vector onto the main scalar output value, binds the main scalar output value with the current innovation time as an event field, and concatenates the event field with the corresponding window header field to form a compressed feature stream sent to the cloud side. Step 3: Based on the preset observation function group, each event field is converted into a Koopman observation vector with time label to form a sparse Koopman observation vector sequence; on the reconstruction time axis, the reconstruction time nodes are divided according to the preset reconstruction time interval. For each reconstruction time node, a dense Koopman observation vector is obtained by selecting the baseline Koopman observation vector and matrix exponential evolution. Then, the current reconstruction signal value is obtained by the vector inner product operation of the inverse observation mapping vector. The reconstructed long sequence of IoT sensing data is arranged in the order of reconstruction time nodes.

2. The method according to claim 1, characterized in that... In step 2, when the current innovation event parameter group is ranked first in the innovation event sequence, the difference between the current innovation time and the window start time in the output record of the window where the current innovation event parameter group is located is used as the current selective scan step size; when the current innovation event parameter group ranks second in the innovation event sequence, the difference between the current innovation time and the innovation time in the previous innovation event parameter group is used as the current selective scan step size; the combined unit that contains both the absolute value of the current innovation amplitude and the current window baseline value is searched in the two-dimensional selective modulation lookup table, and the content adaptive injection coefficient corresponding to the combined unit is recorded as the current content adaptive injection coefficient; when the current innovation event parameter group is a blank window occupant innovation event parameter group, the current content adaptive injection coefficient is set to the preset blank window injection constant.

3. The method according to claim 2, characterized in that... In step 2, zero-order preserved discretization is performed on the diagonal structure state transition matrix using the current selective scan step size as the discretization time interval to obtain the current discrete state transition matrix of the diagonal structure; zero-order preserved discrete input integration is performed on the input mapping vector based on the current selective scan step size and the diagonal structure state transition matrix to obtain the current discrete input mapping vector; matrix-vector multiplication is performed on the hidden state vector corresponding to the first innovation event parameter group using the current discrete state transition matrix to obtain the current state recursive vector; for the first current innovation event parameter group, the initial hidden state vector is used in the matrix-vector multiplication to obtain the current state recursive vector; scalar vector multiplication is performed on the current discrete input mapping vector using the current content adaptive injection coefficient as the scalar coefficient to obtain the current input contribution vector; the current state recursive vector and the current input contribution vector are added according to the corresponding component positions to obtain the hidden state vector corresponding to the current innovation event parameter group.

4. The method according to claim 1, characterized in that... In step 2, the state projection layer pre-configures an output mapping vector with the number of components equal to the preset state dimension. For the hidden state vector corresponding to each innovation event parameter group, the hidden state vector and the output mapping vector are subjected to a vector inner product operation to obtain the main scalar output value. The main scalar output value is bound to the current innovation moment to form an event field. According to the arrangement order of the window output records in the innovation event sequence, the window number, window start time, window baseline value and event quantity of each window output record are encapsulated into a window header field. The event fields corresponding to all innovation event parameter groups inside the window output record are concatenated immediately after the window header field to form the compressed segment corresponding to the window output record. All compressed segments are concatenated in ascending order of window number to obtain the compressed feature stream. The compressed feature stream is sent from the IoT sensing terminal to the cloud side.

5. The method according to claim 1, characterized in that... In step 3, five Koopman observation channels are pre-configured on the cloud side. These five channels correspond sequentially to five deterministic observation functions in a pre-defined observation function group. The pre-defined observation function group consists of five deterministic observation functions: identity observation function, time interval coupled observation function, baseline coupled observation function, front-to-back difference observation function, and baseline pass-through observation function. The output of the identity observation function is equal to the principal scalar output value in the current event field. The output of the time interval coupled observation function is equal to the product of the principal scalar output value in the current event field and the difference between the innovation time in the current event field and the innovation time in the previous event field. The output of the baseline coupled observation function is equal to the product of the principal scalar output value in the current event field and the window baseline value in the window header field to which the current event field belongs. The output of the front-to-back difference observation function is equal to the product of the principal scalar output value in the current event field and the window baseline value in the window header field to which the current event field belongs. The difference between the main scalar output value in the previous event field and the main scalar output value in the previous event field; the output of the baseline through observation function is equal to the window baseline value in the window header field to which the current event field belongs; the preset Koopman observation dimension is 5; the Koopman linear evolution operator matrix and the inverse observation mapping vector are further pre-configured on the cloud side. The Koopman linear evolution operator matrix is ​​a square matrix with a dimension equal to the preset Koopman observation dimension; the inverse observation mapping vector is a column vector with a number of components equal to the preset Koopman observation dimension. The components in the inverse observation mapping vector corresponding to the Koopman observation channel position of the identity observation function and the Koopman observation channel position of the baseline through observation function are all equal to 1, and the components of the other 3 Koopman observation channel positions are all equal to 0.

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