Prediction of time evolution of process with improved consideration of prior knowledge about the process
By integrating a probabilistic model with a process model that considers prior knowledge and constraints, the method improves prediction accuracy and adherence to known laws, addressing the limitations of existing models.
Patent Information
- Application Number
- JP2024121231
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2023-07-27
- Filing Date
- 2024-07-26
- Publication Date
- 2025-02-06
AI Technical Summary
Existing data-based probabilistic models for predicting time expansions in technical processes often fail to account for known laws and surrounding conditions, leading to inaccurate predictions.
A method that integrates a probabilistic model with a process model that utilizes prior knowledge, including historical data and context information, to generate predictions that adhere to known laws and conditions, using a combination of scores and penalties to filter out unattainable candidates.
This approach enhances prediction accuracy by ensuring that predictions align with process constraints, reducing computational costs and improving the reliability of future time course predictions.
Smart Images
Figure 2025019047000001_ABST
Abstract
Description
[Technical field]
[0001] The present invention relates to the prediction of the time evolution of variables affected by a given process, where any prior knowledge about the process exists and is used. [Background technology]
[0002] Background technology To forecast the time evolution of variables related to technological processes, data-based probabilistic models are often used. Such models infer the future course of a variable from its past course. In particular, they indicate what the probability of a certain future value of the variable is, taking into account its past course.
[0003] The relationship between past and future course is determined by the mechanisms of action of the process being studied: if the model has learned to predict the future evolution of a variable of interest based on a training time series of this variable, then the model has also learned, at least implicitly, these mechanisms of action. Summary of the Invention [Problem to be solved by the invention]
[0004] The behavior of many technological processes follows known laws and / or is limited by strict boundary conditions. Therefore, for practical use, only predictions of time evolutions that are fully compatible with these known laws and / or boundary conditions are useful. Time evolutions that significantly violate this cannot be practically achieved. [Means for solving the problem]
[0005] Disclosure of the Invention The present invention provides a method for predicting the time evolution of a variable x affected by a given process. The method makes use of an already existing probabilistic model, which predicts the prior history V for a time step t. t Starting from x, the value of variable xt+1 The restricted probability distribution p(x t+1 |V t ) to supply.
[0006] Previous History V t In particular, for example, the value x of variable x for time step t t , and / or any previous value x of the variable x for the previous time step tk t-k This means that the probabilistic model does not have to make predictions based on individual previous values, but can also take into account previous time progressions. Thus, for example, the future steering angle of the vehicle can only be predicted based on actual values with a relatively large uncertainty. In contrast, if further past history is considered, it can be identified, for example, that the vehicle is just going around a curve. The prediction of the future value of the variable x can then be, in particular, a continuous continuation of this curve running.
[0007] Alternatively or in combination with this, prior history V t is any other context information C for time step t and / or any preceding time step tk t and / or C. t-k Such context information C t and / or C. t-k may be time-dependent or time-independent. For example, in the case of monitoring an industrial process in an industrial facility, the time-dependent context information C t and / or C. t-k can be related to variables occurring in preceding process steps. This history suggests meaningful future changes in the measurement variable x that characterizes the current process step, thereby improving the accuracy of the prediction. The realization behind this is that the entire industrial process pursues a uniform and overarching goal, and the individual process steps cooperate meaningfully to achieve this goal. Time-independent context information C t and / or C.t-k may relate, for example, to the type of process, the characteristics of the machines and / or equipment, and / or the product currently being manufactured. t and / or C. t-k may also be related to operating conditions such as temperature, air pressure, air humidity, or energy prices at the equipment's location. For example, the age, number of operating hours, and / or degree of wear of the machine or equipment may also be taken into account. For example, the number of hours an operator's current shift has already lasted may also be taken into account. This may affect, for example, personnel response time to a particular event.
[0008] Within this method, the prior history V for time step t t Starting from time step t, the value x of variable x at time step t+1 t+1 k candidates for
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[0009] The candidate wanted
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[0010] candidate
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[0011] In this way, it has been found that prior knowledge about a given process can be taken into account without having to touch the existing, data-based, probabilistic model, and thus the performance of this model is not compromised, as may otherwise occur when optimizing towards a new optimization goal.
[0012] At the same time, as the above examples show, there is maximum flexibility as to which prior knowledge should be considered on an individual basis.
[0013] Probabilistic and process models work synergistically with prior knowledge to dramatically reduce the computational cost of finding future time courses over multiple time steps that are most likely to correspond to the true courses of variables of interest.
[0014] For example, the value x of a variable of interest at time step t t Like, previous history V t Starting from , multiple candidates for the value of variable x at the next time step t+1 are
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[0015] In this situation, a huge amount of cost can be saved if as many candidates as possible are weeded out as early as possible in the tree, and no further investigation is done at later time steps. This roughly equates to the surprisingly large impact on the total number of cases of one person early in an epidemic, where their careful behavior results in three people being infected, instead of one person not being infected (and each of them not infecting three others, etc.).
[0016] This comes at the cost of possibly missing the global optimum: in principle, the first time step of a time evolution may receive only a moderate score from the probabilistic model, but subsequent further time steps may be followed by very good scores: for example, at the end of a forecast horizon consisting of four or five time steps, the moderate score of the first time step may be "forgotten" for a long time, and the overall score of this time evolution may end up exceeding the overall scores of other time evolutions that started out very promising in the first time step, but later disappoint.
[0017] Therefore, to reduce the probability that early discarding of candidates will miss a later transition to a time evolution that is ultimately good, it is advantageous to discard candidates that have more than just a probabilistic score and other valid reasons against further investigation. This is where the process model comes in. The process model is particularly useful for determining the candidate
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[0018] Thus, in a particularly advantageous configuration, the process model includes boundary conditions that the time evolution of the variable x and / or the process behavior resulting therefrom must satisfy. Candidates that can never be realized based on violation of strict boundary conditions are
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[0019] Examples of particularly stringent boundary conditions that may be utilized in this context are: mechanical or electrical constraints, and / or Satisfying the laws of physical conservation, and / or Satisfying the physical continuity equation It is.
[0020] In a particularly favorable configuration, the score
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[0021] Score
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[0022] So, for example, the best score
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[0023] Alternatively or in combination with this, the score
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[0024] In another advantageous configuration, a process model is selected that describes the behavior of the process with at least one differential equation. The differential equation can in particular be used to predict the time behavior of the process, for example under certain simplifying assumptions. Thus, candidates that match the behavior predicted by the differential equation are selected.
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[0025] For example, at least one of the differential equations may be an ordinary differential equation. Here, the score of the process model
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[0026] For example, at least one of the differential equations may be a stochastic differential equation, which provides a probability distribution for the expected future values of a variable x of interest, where the score of the process model
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[0027] In another particularly advantageous configuration, the candidate
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[0028] In another particularly advantageous configuration, the candidate
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[0029] In another particularly advantageous embodiment, the list has a certain capacity, and when this capacity is exceeded, the worst scores are deleted.
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[0030] The limited capacity of the list, on the one hand, makes the heuristic search faster than a complete exploration of the tree of possibilities, and on the other hand, ensures that memory demands do not become unmanageable. As mentioned above, this comes at the cost that the final predicted time evolution of the variable x is not necessarily the best prediction in practice. Candidates discarded early at time step t+1
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[0031] In another particularly advantageous embodiment, a control signal is determined from the determined time evolution of the variable x. A vehicle, a driving assistance system, a robot, an electric tool, an electric household appliance and / or a medical diagnostic device is controlled by this control signal. In this way, the probability that the reaction performed by the respectively controlled system is appropriate for the situation embodied in the time evolution of the variable x is increased.
[0032] In vehicle applications, for example, the time evolution of the speed or trajectory of the vehicle can be predicted. The predicted time evolution of the speed can be used to simulate the exhaust characteristics of the vehicle, for example, in order to determine whether the harmful emissions of this vehicle under real driving conditions meet the legal requirements. In particular, this allows the dependence of the exhaust characteristics on, for example, engine control parameters to be investigated so that a vehicle seeking new type approval passes an exhaust gas test under real conditions, if possible on the first attempt. The predicted trajectories of the own vehicle and of other road users can be used, for example, to make the at least partially automated driving of the vehicle more predictive. For example, if it is predicted that the vehicle will have to be slowed down due to traffic or even stopped, in an electrically operated vehicle the motor can be switched into generator mode in order to store the kinetic energy at least partially in the battery. The predicted trajectory can further be used to determine the load of the entire components and, for example, to trigger a state-dependent maintenance. Similarly, in the case of electric tools or household appliances, the wear state can be predicted as a variable of interest x, and a corresponding state-dependent maintenance can be triggered.
[0033] In a human-controlled vehicle, for example, the driver's behavior can also be predicted as a variable of interest x. For this purpose, multiple data sources can be used, such as, for example, video recordings of eye movements, steering movements, or health data, such as heart rate, determined by the driver's smartwatch. For example, the time evolution of the driver's fatigue or exhaustion state can be predicted so that a corresponding warning can be output more purposefully. If it is predicted that the driver will still reach the destination without any problems, it is not very meaningful to warn the driver on the way. Such a warning may eventually become a self-fulfilling prophecy and further reduce the driver's attention. In contrast, if it is predicted that the destination will not be reached safely, it is meaningful to make the driver aware of this early, so that the driver can focus on alternative solutions.
[0034] In the field of smart homes and industrial buildings, for example, the atmospheric oxygen or carbon dioxide concentration, air humidity, hazardous substance load or temperature can be predicted as variables of interest x. In this way, measures can be introduced preventively to improve the environment of the space. For example, energy-efficient underfloor heating has a high thermal inertia, so that it is desirable to operate it early if necessary so that the room temperature does not drop too much. If the room temperature drops too much, the occupants may likewise be tempted to use electric heating fans, which undermines the energy efficiency of the underfloor heating. For example, if a significant heating of the space is expected, the air conditioning can also be turned on preventively at a time that is particularly favorable for electric energy.
[0035] In all these applications and further applications, the consideration of each relevant prior knowledge in the process model as described herein allows for the identification of likely candidates for the next time step t+1.
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[0036] The method may in particular be fully or partly computer-implemented. The invention therefore also relates to a computer program with machine-readable instructions for instructing one or more computers to carry out the above-mentioned method when the computer program is executed on one or more computers and / or computer instances. In this sense, control devices for vehicles and embedded systems for technical devices, which are capable of executing machine-readable instructions, should also be considered as computers. Computer instances are for example virtual machines, containers or other implementation environments where computing power is provided in the cloud.
[0037] The invention likewise relates to a machine-readable data carrier comprising a computer program and / or a download product, which is a digital product transmittable over a data network, i.e. downloadable by a user of the data network, which may for example be offered for immediate download in an online shop.
[0038] Furthermore, one or more computers and / or computer instances may be equipped with a computer program, a machine-readable data carrier or a downloadable product.
[0039] Further measures for improving the invention are given in more detail below in conjunction with the description of preferred embodiments of the invention based on the drawings. [Brief description of the drawings]
[0040] [Figure 1] FIG. 1 illustrates an embodiment of a method 100 for predicting the time evolution of a variable x. [Diagram 2] Score
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[0041] Working Example 1 is a schematic flow chart of an embodiment of a method 100 for predicting the time evolution of a variable x influenced by a given process. For this prediction, on the one hand, a probabilistic model 1 is used, which is based on a given prior history V at a time step t. t In the above, the value of variable x is t+1 The restricted probability distribution p(x t+1 |V t On the other hand, a process model 2 is also used, which represents prior knowledge about a given process.
[0042] In step 110, the prior history V for time step tk is t Starting from time step t, the value x of variable x at time step t+1 t+1 Candidates for
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[0043] In step 120, in cooperation with the probabilistic model 1 and the process model 2, the candidate
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[0044] In step 130, the score
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[0045] In step 140, the newly selected candidate for time step t+1
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[0046] In this way, the prior history V for time step t t For example, the value x of the measurement variable x at time step t t Starting from , the prediction x for the measured variable x over a range of h time steps t+1 ,…,x x+h can be calculated continuously in the future.
[0047] In the example shown in FIG. 1, the predicted value x t+1 ,…,x x+h In step 160, the vehicle 50, the driving assistance system 51, the robot 60, the electric tool 70, the electric household appliance 80, and / or the medical diagnostic appliance 90 are driven and controlled by the driving control signal 150a.
[0048] According to block 121, the process model 2 may include the time evolution of the variable x and / or the boundary conditions that the behavior of the process resulting from this time evolution must satisfy. These boundary conditions may be determined, in particular, according to block 121a, for example mechanical or electrical constraints, and / or Satisfying the laws of physical conservation, and / or Satisfying the physical continuity equation may include.
[0049] According to block 122, the score
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[0050] In particular, according to block 123, the contribution of the process model may be 1 if the marginal conditions are satisfied and 0 if at least one marginal condition is not satisfied. As described above, this allows candidates that do not satisfy the marginal conditions to be selected.
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[0051] According to block 124, a process model 2 may be selected that describes the behavior of the process with at least one differential equation.
[0052] In this case, for example, according to block 124a, at least one differential equation may be an ordinary differential equation. Then, according to block 124b, the score of the process model 2 is calculated.
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[0053] Alternatively or in combination with this, according to block 124c, at least one differential equation may be a stochastic differential equation. Then, according to block 124d, the score of the process model (2) is calculated.
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[0054] According to Block 131, Best score
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[0055] According to block 132, the candidate
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[0056] In particular, according to block 132a, the candidate
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[0057] Figure 2 shows the candidate over multiple time steps.
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[0058] The prediction is based on the prior history V for time step t.t For example, the value x of variable x at time step t t From this, several candidates are found for the value of the variable x at the first future time step t+1. For ease of viewing, we will show two of these candidates:
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[0059] For the continuation of the prediction at time step t+2, the candidate
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[0060] However, the most promising candidate for time step t+3 is
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[0061] This also means that in the next step,
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[0062] Therefore, the heuristic search strategy in this example does not consider dependencies between time steps and therefore does not consider the candidate
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Claims
1. A method (100) for predicting the time evolution of a variable x influenced by a given process using a given probabilistic model (1), comprising the steps of: The probability model (1) is a prior history V ｔ Given a variable x, the value x ｔ＋１ The restricted probability distribution p(x ｔ＋１ |V ｔ ) and The method (100) comprises: The prior history V for time step t ｔ Starting from time step t, the value x of variable x at time step t+1 ｔ＋１ k candidates for [0010] and determining (110) ·candidate [0025] In cooperation with the probabilistic model (1) and a process model (2) representing prior knowledge about the given process, a score [0030] , the score being calculated for each candidate (120). [0045] is the actual value x of the variable x at time step t+1. ｔ＋１ step, which is a measure of probability equivalent to The candidate [0050] From the set of [006] Based on [0070] Selecting (130) The newly selected candidate for time step t+1 [0080] Starting from time step t, the value x of variable x at time step t+2 ｔ＋２ l candidates for [0090] and determining (140) The method (100),
2. 2. The method (100) of claim 1, wherein the process model (2) comprises (121) the time evolution of variables x and / or boundary conditions that the behavior of the process resulting from the time evolution must satisfy.
3. At least one boundary condition is: Mechanical or electrical constraints, and / or - satisfying the laws of physical conservation, and / or - Satisfying the physical equation of continuity The method of claim 2, further comprising:
4. The score [0010] The method (100) of any one of claims 1 to 3, wherein: comprises a product (122) of a first contribution of the probabilistic model (1) and a second contribution of the process model (2).
5. The method (100) according to any one of claims 2 to 3, additionally to claim 4, wherein the contribution of the process model is 1 if the boundary conditions are satisfied and the contribution of the process model is 0 if at least one boundary condition is not satisfied (123).
6. ・Best score ##EQU00011## The top n candidates with ##EQU00012## and / or ·Score ##EQU00013## Candidates whose ##EQU14## Let us consider the proper subset ##EQU00015## The method (100) of any one of claims 1 to 5, further comprising:
7. The method (100) of any one of claims 1 to 6, further comprising selecting (124) a process model (2) describing the behavior of the process having at least one differential equation.
8. At least one differential equation is an ordinary differential equation (124a); The score of the process model (2) ##EQU00016## The contribution of the candidate ##EQU00017## The method (100) of claim 7, further comprising determining (124b) how much
9. At least one differential equation is a stochastic differential equation (124c); The score of the process model (2) [0018] The contribution to the candidate is calculated by taking into account the probability distribution obtained by the stochastic differential formula. [0019] The method (100) according to claim 7 or 8, further comprising measuring (124d) how likely it is that
10. ·candidate [0020] and the score ##EQU00021## For n ≧ 0, the score [0022] (132) to a list categorized according to the From the list, the best score [0023] Candidate with [0024] Select (133), The candidate [0025] Starting from time step t, the value x of variable x at time step t+n+1 ｔ＋ｎ＋１ New candidates for [0026] The method (100) of any one of claims 1 to 9, further comprising determining (141)
11. ·candidate [0027] Score for [0028] Each time you search for [0029] into a list (132a); From this updated list, the best score is [0030] Candidate with [0031] The method (100) of claim 10, further comprising: selecting (133a)
12. The list has a certain capacity, and when the capacity is exceeded, the worst score is [0032] Candidate with [Equation 33] The method (100) according to claim 10 or 11, further comprising discarding the
13. - determining (150) a drive control signal (150a) from the determined time evolution of the variable x; - The method (100) according to any one of claims 1 to 12, wherein a vehicle (50), a driving assistance system (51), a robot (60), an electric tool (70), an electric household device (80) and / or a medical diagnostic device (90) are driven (160) by the drive control signal (150a).
14. Previous History V ｔ teeth, Value x of variable x for time step t ｔ and / or The previous value x of the variable x for the previous time step t−k, where k>0 ｔ－ｋ and / or Context information C for time step t and / or any preceding time step t−k, where k>0 ｔ and / or C ｔ－ｋ The method (100) of any one of claims 1 to 13, comprising:
15. A computer program comprising machine-readable instructions for instructing one or more computers and / or computer instances to perform a method (100) according to any one of claims 1 to 14, when said computer program is executed on said one or more computers and / or computer instances.
16. A machine-readable data carrier and / or download product comprising a computer program according to claim 15.
17. One or more computers and / or computer instances comprising a computer program according to claim 15 and / or a machine-readable data carrier and / or a download product according to claim 16.