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ARCTRON: A Rapid Experimental Proving Ground for TPS Experiments and Arcjet Technology Development

Innovation in high-enthalpy facilities is fundamentally limited by the cost and risk of experimentation. New concepts for plasma control, diagnostics, facility components, and plasma-material interaction often require repeated iterations that are impractical to perform in production arcjets. As a result, promising ideas may remain unexplored or reach operational facilities only after significant development effort. ARCTRON is being developed as a rapid experimental proving ground where new ideas in plasma science, arcjet engineering, diagnostics, and material response can be conceived, tested, and quantitatively evaluated before transition to large-scale facilities. The platform combines radio-frequency (RF) and DC arc plasma generation, externally applied magnetic fields, configurable gas composition, reduced-pressure operation, laser heating, electrical biasing, and modular diagnostic access. These capabilities permit the plasma source, applied forcing, test article, and measurement configuration to be modified independently, allowing individual physical mechanisms to be isolated more readily than in a traditional test environment. One class of investigations addresses fundamental plasma-surface interaction physics. Conventional material tests often expose a specimen simultaneously to convective heating, reactive species, pressure, shear, radiation, and surface-current effects. The resulting material response may be measured accurately, while the contribution of each mechanism remains difficult to identify. ARCTRON is designed to vary these effects selectively. Plasma chemistry can be changed independently through configurable gas mixtures; magnetic fields and electrical biasing can modify charged-particle transport; laser heating can provide a non-plasma thermal input; and pressure, flow, and discharge mode can be varied over a broad operating space. This enables controlled tests of hypotheses involving surface catalycity, reactive-species transport, plasma-assisted oxidation, electromagnetic effects, shear, and the relative contributions of thermal and chemical loading. A second class of investigations enabled by this approach concerns the engineering of high-enthalpy facilities themselves. Arc-heated facilities are limited by electrode erosion, unstable arc attachment, localized heating, and damage to nozzles and other plasma-facing components. ARCTRON provides a lower-cost environment for testing concepts intended to mitigate these limitations. Candidate investigations include the use of applied magnetic fields to alter current paths and reduce plasma interaction with nozzle walls, ExB forcing to introduce controlled plasma rotation, magnetic or geometric approaches for distributing arc attachment, and alternative electrode or discharge configurations intended to reduce erosion and improve stability. Because the platform is reconfigurable, these concepts can be evaluated through repeated design--build--test cycles before they are considered for implementation in operational facilities. The platform also supports the development and validation of diagnostics that may be difficult to introduce initially into a large arcjet. Current and planned measurements include spatially resolved optical emission spectroscopy, electrostatic probes, fast imaging, pyrometry, calorimetry, laser-induced fluorescence, and absorption spectroscopy. These diagnostics are intended not merely to document a nominal operating condition, but to constrain the local plasma state and its relationship to component or material response. The modular facility geometry allows diagnostic concepts to be tested, calibrated, and compared under repeatable conditions before deployment in more demanding environments. ARCTRON is also supported by an integrated software suite. Automated control and data acquisition allow discharge parameters, gas composition, magnetic fields, diagnostic timing, and test configuration to be recorded as part of each experiment (STARDAC - Software for Testing, Analysis, Research Data, and Control). The Backend for Experiment Analysis, Storage, and Traceability (BEAST) is a database that provides the infrastructure needed to associate heterogeneous measurements with facility configuration, specimen identity, calibration state, geometry, and analysis provenance. This backend is particularly important for exploratory campaigns, in which many related configurations may be tested, and the value of an individual experiment depends on its connection to earlier and subsequent iterations. Complementary analysis capabilities, including computer-vision-based transient response measurements (arcjetCV), three-dimensional surface reconstruction (STARSCAN), and model-based Bayesian inference (SHIELD), and tomography data analysis (TOMATO, PuMA) can be incorporated when required by a specific hypothesis without becoming the focus of every campaign. The central objective of ARCTRON is therefore not to maximize heat flux or reproduce a complete flight environment. Its purpose is to reduce the cost and time required to ask consequential questions about plasma behavior, plasma-facing materials, diagnostics, and arcjet technology. By providing a controlled environment for rapid reconfiguration, mechanism isolation, quantitative measurement, and iterative engineering, ARCTRON can help mature concepts that would otherwise remain too speculative or too risky for evaluation in production facilities. The resulting knowledge can then guide the design of material models, focus test objectives in larger arcjets, reduce facility-development risk, and improve the physical basis of high-enthalpy ground testing. This work will present the ARCTRON architecture, operating modes, diagnostic suite, and digital experimental workflow. Initial experimental results from the first integrated operation of the facility will be presented, including flow characterization, power limitations, and deployment of the initial diagnostic suite. Ongoing development efforts aimed at catalycity characterization, magnetic plasma control, and advanced optical diagnostics will also be discussed, illustrating how the platform supports rapid iteration from concept to experiment.

experimental diagnostics↗

DOE OSTI2025

Error field measurements with rotating RMP fields for DIII-D H-mode

3D magnetic sensors are employed to identify the amplitude and toroidal phase of error fields (EF) by analyzing the torque balance for magnetic islands entrained by rotating resonant magnetic perturbations (RMPs) in DIII-D H-mode plasmas. This technique of torque balance allows for efficient error field identification, offering a valuable tool for scenario-specific and optimized error field compensation (EFC) and requires only magnetic diagnostics. The torque balance used in this work includes the contribution from electromagnetic torque due to error fields, wall response, RMP fields, and viscous. Results show that viscous torque plays a crucial role, particularly during locked modes and H-mode plasmas, ensuring accurate data fits with lower residuals. The torque balance technique reveals that the L- and H-mode plasmas have distinct EF configurations, and consistent with a model-based EF analysis including MHD response in IPEC and the SURFMN EF simulation. This technique shows great robustness in measuring the intrinsic EF amplitude regardless of its amplitude or toroidal phase. Repeated discharges with EFC disparities exhibit consistent results of intrinsic error field within a reasonable range near the “standard” error field compensation. Additionally, the use of a rotating n = 1 resonant magnetic perturbation offers the advantage of reducing disruption risks by entraining saturated magnetic islands. These findings are instrumental for optimizing EF correction in fusion devices, thereby enhancing tearing mode suppression and overall plasma stability.

3D magnetic sensors↗

NASA NTRS2005

Optimal Sensor Selection for Health Monitoring Systems

Sensor data are the basis for performance and health assessment of most complex systems. Careful selection and implementation of sensors is critical to enable high fidelity system health assessment. A model-based procedure that systematically selects an optimal sensor suite for overall health assessment of a designated host system is described. This procedure, termed the Systematic Sensor Selection Strategy (S4), was developed at NASA John H. Glenn Research Center in order to enhance design phase planning and preparations for in-space propulsion health management systems (HMS). Information and capabilities required to utilize the S4 approach in support of design phase development of robust health diagnostics are outlined. A merit metric that quantifies diagnostic performance and overall risk reduction potential of individual sensor suites is introduced. The conceptual foundation for this merit metric is presented and the algorithmic organization of the S4 optimization process is described. Representative results from S4 analyses of a boost stage rocket engine previously under development as part of NASA's Next Generation Launch Technology (NGLT) program are presented.

Santi, L. Michael↗

NASA NTRS2004

Explanation Constraint Programming for Model-based Diagnosis of Engineered Systems

We can expect to see an increase in the deployment of unmanned air and land vehicles for autonomous exploration of space. In order to maintain autonomous control of such systems, it is essential to track the current state of the system. When the system includes safety-critical components, failures or faults in the system must be diagnosed as quickly as possible, and their effects compensated for so that control and safety are maintained under a variety of fault conditions. The Livingstone fault diagnosis and recovery kernel and its temporal extension L2 are examples of model-based reasoning engines for health management. Livingstone has been shown to be effective, it is in demand, and it is being further developed. It was part of the successful Remote Agent demonstration on Deep Space One in 1999. It has been and is being utilized by several projects involving groups from various NASA centers, including the In Situ Propellant Production (ISPP) simulation at Kennedy Space Center, the X-34 and X-37 experimental reusable launch vehicle missions, Techsat-21, and advanced life support projects. Model-based and consistency-based diagnostic systems like Livingstone work only with discrete and finite domain models. When quantitative and continuous behaviors are involved, these are abstracted to discrete form using some mapping. This mapping from the quantitative domain to the qualitative domain is sometimes very involved and requires the design of highly sophisticated and complex monitors. We propose a diagnostic methodology that deals directly with quantitative models and behaviors, thereby mitigating the need for these sophisticated mappings. Our work brings together ideas from model-based diagnosis systems like Livingstone and concurrent constraint programming concepts. The system uses explanations derived from the propagation of quantitative constraints to generate conflicts. Fast conflict generation algorithms are used to generate and maintain multiple candidates whose consistency can be tracked across multiple time steps.

Narasimhan, Sriram↗

NASA NTRS1988

Diagnosing faults in autonomous robot plan execution

A major requirement for an autonomous robot is the capability to diagnose faults during plan execution in an uncertain environment. Many diagnostic researches concentrate only on hardware failures within an autonomous robot. Taking a different approach, the implementation of a Telerobot Diagnostic System that addresses, in addition to the hardware failures, failures caused by unexpected event changes in the environment or failures due to plan errors, is described. One feature of the system is the utilization of task-plan knowledge and context information to deduce fault symptoms. This forward deduction provides valuable information on past activities and the current expectations of a robotic event, both of which can guide the plan-execution inference process. The inference process adopts a model-based technique to recreate the plan-execution process and to confirm fault-source hypotheses. This technique allows the system to diagnose multiple faults due to either unexpected plan failures or hardware errors. This research initiates a major effort to investigate relationships between hardware faults and plan errors, relationships which were not addressed in the past. The results of this research will provide a clear understanding of how to generate a better task planner for an autonomous robot and how to recover the robot from faults in a critical environment.

Lam, Raymond K.↗

NASA NTRS1989

Diagnosing faults in autonomous robot plan execution

Lam, Raymond K.↗

NASA NTRS1992

Real-time diagnostics for a reusable rocket engine

A hierarchical, decentralized diagnostic system is proposed for the Real-Time Diagnostic System component of the Intelligent Control System (ICS) for reusable rocket engines. The proposed diagnostic system has three layers of information processing: condition monitoring, fault mode detection, and expert system diagnostics. The condition monitoring layer is the first level of signal processing. Here, important features of the sensor data are extracted. These processed data are then used by the higher level fault mode detection layer to do preliminary diagnosis on potential faults at the component level. Because of the closely coupled nature of the rocket engine propulsion system components, it is expected that a given engine condition may trigger more than one fault mode detector. Expert knowledge is needed to resolve the conflicting reports from the various failure mode detectors. This is the function of the diagnostic expert layer. Here, the heuristic nature of this decision process makes it desirable to use an expert system approach. Implementation of the real-time diagnostic system described above requires a wide spectrum of information processing capability. Generally, in the condition monitoring layer, fast data processing is often needed for feature extraction and signal conditioning. This is usually followed by some detection logic to determine the selected faults on the component level. Three different techniques are used to attack different fault detection problems in the NASA LeRC ICS testbed simulation. The first technique employed is the neural network application for real-time sensor validation which includes failure detection, isolation, and accommodation. The second approach demonstrated is the model-based fault diagnosis system using on-line parameter identification. Besides these model based diagnostic schemes, there are still many failure modes which need to be diagnosed by the heuristic expert knowledge. The heuristic expert knowledge is implemented using a real-time expert system tool called G2 by Gensym Corp. Finally, the distributed diagnostic system requires another level of intelligence to oversee the fault mode reports generated by component fault detectors. The decision making at this level can best be done using a rule-based expert system. This level of expert knowledge is also implemented using G2.

Guo, T. H.↗

DOE OSTI2026

Battery Life Prediction Using Reduced-Order Physics Models and Machine Learning (CRADA Final Report)

Phase 1 (Original CRADA, plus no-cost extension modifications #1-3, 6/1/2017 to 3/13/2021): The Australian Department of Defence (AUDoD) is performing accelerated aging tests of Li-ion batteries to benchmark their reliability and degradation characteristics. Using its previously developed battery lifetime predictive model framework, the National Laboratory of the Rockies (NLR) will develop analytical models based the AUDoD data to predict lifetime of the multiple Li-ion battery chemistries under real-world use scenarios of interest to AUDoD. The NLR model is based on physical degradation mechanisms encountered by Li-ion batteries and has been previously validated. Phase 2 (CRADA modification #4, plus no-cost extension modification #5, 2/22/2021 to 3/30/2025): Train and support Australian Department of Defence personnel to use NLR software for model-based estimation of Li-ion battery lifetime using accelerated battery aging data collected by the Australian Department of Defence. Under separate DOE funding from 2019 to 2021, NLR enhanced its battery life-prediction software using machine learning algorithms to automate portions of the model-fitting process, requiring significantly less labor and expert judgment and also adding uncertainty quantification, increasing statistical rigor. Under Phase 2, NLR will customize NLR Software and provide it to AuDoD. NLR will enhance its NLR Model to capture aging modes of AuDoD's multi-cell modules, including cell-balancing effects. NLR will develop example single-cell and multi-cell models based on one AuDoD battery aging dataset. NLR will train AuDoD personnel on NLR Software. By the conclusion of the project, NLR will have provided AuDoD the training materials, a user manual and software needed to perform their own analysis of additional and/or future battery aging datasets.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1988

Diagnosis by integrating model-based reasoning with knowledge-based reasoning

Our research investigates how observations can be categorized by integrating a qualitative physical model with experiential knowledge. Our domain is diagnosis of pathologic gait in humans, in which the observations are the gait motions, muscle activity during gait, and physical exam data, and the diagnostic hypotheses are the potential muscle weaknesses, muscle mistimings, and joint restrictions. Patients with underlying neurological disorders typically have several malfunctions. Among the problems that need to be faced are: the ambiguity of the observations, the ambiguity of the qualitative physical model, correspondence of the observations and hypotheses to the qualitative physical model, the inherent uncertainty of experiential knowledge, and the combinatorics involved in forming composite hypotheses. Our system divides the work so that the knowledge-based reasoning suggests which hypotheses appear more likely than others, the qualitative physical model is used to determine which hypotheses explain which observations, and another process combines these functionalities to construct a composite hypothesis based on explanatory power and plausibility. We speculate that the reasoning architecture of our system is generally applicable to complex domains in which a less-than-perfect physical model and less-than-perfect experiential knowledge need to be combined to perform diagnosis.

Bylander, Tom↗

NASA NTRS1989

Knowledge-based process control and diagnostics for orbital cryogen transfer

AFDex is a rule based system designed to provide intelligent process control, diagnosis, and error recovery for a Shuttle based cryogenic experiment, SHOOT (Superfluid Helium On-Orbit Transfer). This paper describes the AFDex system in the context of traditional associative, model-based, and qualitative systems and discusses the implications of this first expert system in space.

Raymond, Eric A.↗

NASA NTRS1989

CONFIG - Adapting qualitative modeling and discrete event simulation for design of fault management systems

CONFIG is a modeling and simulation tool prototype for analyzing the normal and faulty qualitative behaviors of engineered systems. Qualitative modeling and discrete-event simulation have been adapted and integrated, to support early development, during system design, of software and procedures for management of failures, especially in diagnostic expert systems. Qualitative component models are defined in terms of normal and faulty modes and processes, which are defined by invocation statements and effect statements with time delays. System models are constructed graphically by using instances of components and relations from object-oriented hierarchical model libraries. Extension and reuse of CONFIG models and analysis capabilities in hybrid rule- and model-based expert fault-management support systems are discussed.

Malin, Jane T.↗

NASA NTRS1992

Implementation of an intelligent control system

A laboratory testbed facility which was constructed at NASA LeRC for the development of an Intelligent Control System (ICS) for reusable rocket engines is described. The framework of the ICS consists of a hierarchy of various control and diagnostic functions. The traditional high speed, closed-loop controller resides at the lowest level of the ICS hierarchy. Above this level resides the diagnostic functions which identify engine faults. The ICS top level consists of the coordination function which manages the interaction between an expert system and a traditional control system. The purpose of the testbed is to demonstrate the feasibility of the OCS concept by implementing the ICS as the primary controller in a simulation of the Space Shuttle Main Engine (SSME). The functions of the ICS which are implemented in the testbed are as follows: an SSME dynamic simulation with selected fault mode models, a reconfigurable controller, a neural network for sensor validation, a model-based failure detection algorithm, a rule based failure detection algorithm, a diagnostic expert system, an intelligent coordinator, and a user interface which provides a graphical representation of the event occurring within the testbed. The diverse nature of the ICS has led to the development of a distributed architecture consisting of specialized hardware and software for the implementation of the various functions. This testbed is made up of five different computer systems. These individual computers are discussed along with the schemes used to implement the various ICS components. The communication between computers and the timing and synchronization between components are also addressed.

Simon, D. L.↗

NASA NTRS1993

Model-based reasoning for power system management using KATE and the SSM/PMAD

The overall goal of this research effort has been the development of a software system which automates tasks related to monitoring and controlling electrical power distribution in spacecraft electrical power systems. The resulting software system is called the Intelligent Power Controller (IPC). The specific tasks performed by the IPC include continuous monitoring of the flow of power from a source to a set of loads, fast detection of anomalous behavior indicating a fault to one of the components of the distribution systems, generation of diagnosis (explanation) of anomalous behavior, isolation of faulty object from remainder of system, and maintenance of flow of power to critical loads and systems (e.g. life-support) despite fault conditions being present (recovery). The IPC system has evolved out of KATE (Knowledge-based Autonomous Test Engineer), developed at NASA-KSC. KATE consists of a set of software tools for developing and applying structure and behavior models to monitoring, diagnostic, and control applications.

Morris, Robert A.↗

NASA NTRS1994

Sensor Fault Detection and Diagnosis Simulation of a Helicopter Engine in an Intelligent Control Framework

This paper presents an application of a fault detection and diagnosis scheme for the sensor faults of a helicopter engine. The scheme utilizes a model-based approach with real time identification and hypothesis testing which can provide early detection, isolation, and diagnosis of failures. It is an integral part of a proposed intelligent control system with health monitoring capabilities. The intelligent control system will allow for accommodation of faults, reduce maintenance cost, and increase system availability. The scheme compares the measured outputs of the engine with the expected outputs of an engine whose sensor suite is functioning normally. If the differences between the real and expected outputs exceed threshold values, a fault is detected. The isolation of sensor failures is accomplished through a fault parameter isolation technique where parameters which model the faulty process are calculated on-line with a real-time multivariable parameter estimation algorithm. The fault parameters and their patterns can then be analyzed for diagnostic and accommodation purposes. The scheme is applied to the detection and diagnosis of sensor faults of a T700 turboshaft engine. Sensor failures are induced in a T700 nonlinear performance simulation and data obtained are used with the scheme to detect, isolate, and estimate the magnitude of the faults.

Litt, Jonathan↗

NASA NTRS1993

The effects of AVIRIS atmospheric calibration methodology on identification and quantitative mapping of surface mineralogy, Drum Mountains, Utah

The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) measures reflected light in 224 contiguous spectra bands in the 0.4 to 2.45 micron region of the electromagnetic spectrum. Numerous studies have used these data for mineralogic identification and mapping based on the presence of diagnostic spectral features. Quantitative mapping requires conversion of the AVIRIS data to physical units (usually reflectance) so that analysis results can be compared and validated with field and laboratory measurements. This study evaluated two different AVIRIS calibration techniques to ground reflectance: an empirically-based method and an atmospheric model based method to determine their effects on quantitative scientific analyses. Expert system analysis and linear spectral unmixing were applied to both calibrated data sets to determine the effect of the calibration on the mineral identification and quantitative mapping results. Comparison of the image-map results and image reflectance spectra indicate that the model-based calibrated data can be used with automated mapping techniques to produce accurate maps showing the spatial distribution and abundance of surface mineralogy. This has positive implications for future operational mapping using AVIRIS or similar imaging spectrometer data sets without requiring a priori knowledge.

Kruse, Fred A.↗

NASA NTRS1998

Model-Based Diagnosis in a Power Distribution Test-Bed

The Rodon model-based diagnosis shell was applied to a breadboard test-bed, modeling an automated power distribution system. The constraint-based modeling paradigm and diagnostic algorithm were found to adequately represent the selected set of test scenarios.

Scarl, E.↗

NASA NTRS2007

Hybrid Automated Diagnosis of Discrete/Continuous Systems

A recently conceived method of automated diagnosis of a complex electromechanical system affords a complete set of capabilities for hybrid diagnosis in the case in which the state of the electromechanical system is characterized by both continuous and discrete values (as represented by analog and digital signals, respectively). The method is an integration of two complementary diagnostic systems: (1) beacon-based exception analysis for multi-missions (BEAM), which is primarily useful in the continuous domain and easily performs diagnoses in the presence of transients; and (2) Livingstone, which is primarily useful in the discrete domain and is typically restricted to quasi-steady conditions. BEAM has been described in several prior NASA Tech Briefs articles: "Software for Autonomous Diagnosis of Complex Systems" (NPO-20803), Vol. 26, No. 3 (March 2002), page 33; "Beacon-Based Exception Analysis for Multimissions" (NPO-20827), Vol. 26, No. 9 (September 2002), page 32; "Wavelet-Based Real-Time Diagnosis of Complex Systems" (NPO-20830), Vol. 27, No. 1 (January 2003), page 67; and "Integrated Formulation of Beacon-Based Exception Analysis for Multimissions" (NPO-21126), Vol. 27, No. 3 (March 2003), page 74. Briefly, BEAM is a complete data-analysis method, implemented in software, for real-time or off-line detection and characterization of faults. The basic premise of BEAM is to characterize a system from all available observations and train the characterization with respect to normal phases of operation. The observations are primarily continuous in nature. BEAM isolates anomalies by analyzing the deviations from nominal for each phase of operation. Livingstone is a model-based reasoner that uses a model of a system, controller commands, and sensor observations to track the system s state, and detect and diagnose faults. Livingstone models a system within the discrete domain. Therefore, continuous sensor readings, as well as time, must be discretized. To reason about continuous systems, Livingstone uses monitors that discretize the sensor readings using trending and thresholding techniques. In development of the a hybrid method, BEAM results were sent to Livingstone to serve as an independent source of evidence that is in addition to the evidence gathered by Livingstone standard monitors. The figure depicts the flow of data in an early version of a hybrid system dedicated to diagnosing a simulated electromechanical system. In effect, BEAM served as a "smart" monitor for Livingstone. BEAM read the simulation data, processed the data to form observations, and stored the observations in a file. A monitor stub synchronized the events recorded by BEAM with the output of the Livingstone standard monitors according to time tags. This information was fed to a real-time interface, which buffered and fed the information to Livingstone, and requested diagnoses at the appropriate times. In a test, the hybrid system was found to correctly identify a failed component in an electromechanical system for which neither BEAM nor Livingstone alone yielded the correct diagnosis.

Park, Han↗

DOE OSTI2025

System Engineers and Decisions: It?s All about Knowledge

In order to guarantee that a system meets adequate levels of reliability and availability, system performances are continuously monitored and analyzed thanks to the technological advancements driving the Industry 4.0 revolution. An Industry 4.0 approach is typically based on advanced statistical, big data mining, machine learning, and internet-of-things methods designed to detect anomalies in the behavior of system, detect the most likely failure modes, and provide indications to system engineers on when maintenance activities should be performed before system performance are deemed unacceptable (which can be generated by diagnostic and prognostic methods). However, these analyses, which are designed to automatize and increase the efficacy of the system maintenance program, require large amount of data which can come in various forms: numeric, textual, images, sounds etc. Such data constitutes the historic knowledge benchmark to track system performances and support system engineer decisions. Here we claim that data is not sufficient to support this kind of analyses when applied to systems characterized by complex architectures and behaviors. Robust system engineer decisions require the ability to understand the system operational context that lies behind the observed data elements. In this respect, system models are in fact necessary to “put data in context” and capture relationships between data elements. Industry 4.0 methods require in fact contextual knowledge as a basis upon which hypotheses can be generated and assumptions tested. In our view, for complex systems, model-based system engineering (MBSE) models can afford this contextual knowledge, as they are typically used to describe systems architecture and dynamic behaviors. System knowledge is here intended as the blending of collected data and system architecture which takes the form of a “knowledge graph”. A knowledge graph is a database which consists of a large set of nodes (in our case an entity can be either a data or an MBSE element) which are linked to each other. The types of nodes and links follow a pre-defined topology, sometimes also refers as an ontology, that is designed to fit the actual decisions that needs to be performed. We show here how a knowledge graph can be defined to support system engineer maintenance decisions and how the same graph can be built based on system MBSE models and pre-processed data from numeric (through anomaly detections and diagnostic methods) and textual elements (through technical language processing TLP).

97 - MATHEMATICS AND COMPUTING↗